Math+is+Cool+Four

“Math is Cool” Masters-2001-02 Sponsored by: IEEE - Wenatchee Section 4th Grade - May 11, 2002 Individual Contest

Leave answers in terms of π where applicable. Do not round any answers unless stated otherwise. Record all answers on the colored cover sheet. 1

Evaluate: 100010 - 90090

2

What is the product of 123,870,000 and 0?

3

How many total legs would 3 cats and 4 chickens have?

4

At the “Academics are Cool” Survivor Camp, Eric found 14 equations in the woods while on his intellectual expedition. He decided to divide his equations evenly among his 7 tribe members. How many equations did each tribe member get?

5

One of the “Immunity Challenges” at Survivor Camp was to wrangle an “udderly amazing cow pi” and see how much milk they could extract in 5 minutes. The Trimathlete tribe got 5 gallons of milk, while the Mathletes got 3½ gallons. How many more quarts did the Mathletes need to get in order to tie the Trimathletes?

6

John has 3 social studies books. If the first has 125 pages, the second has 75 pages, and the total number of pages is 325, how many pages does the third book have?

7

If there are 50 school buses and each can hold 24 children, how many children will it take to fill all of the buses?

8

Brittany wants the pony that costs $500.00, but her mother is only willing to contribute $200.00 to help pay for the pony. If Brittany earns $25.00 a week, how many weeks will it take before she has enough money to pay the remaining cost of the pony?

9

What is the sum of all the odd numbers between 4 and 18?

10

If Silas and Powei played ultimate frisbee for 18 years, how many months did they play?

11

Sarah has been a crime detective for 3 times as long as Carl. If Carl has been a crime detective for 6 years, how many has Sarah been a crime detective?

12

How many sides does a nonagon have?

13

Tealah bought 10 pineapples for $2.75 each and 5 tangerines for $0.35 each. How much money, in dollars, did she pay?

14

True or False: 5 + 398 - 17 + 4 = 382

15

Bob’s family of 4 can eat 3 cans of tuna in a week. How many weeks would it take Bob’s family to eat 21 cans of tuna?

16

If Marlee uses 7 pieces of paper for each assignment, how many pieces of paper does she use for 25 assignments?

17

If Trip is half of Chase’s age and Chase is 10, how many years old will Trip be in 13 years?

18

If a roll of yarn can make half a sweater, how many rolls are required to make 22 sweaters?

19

What is the area of a square with a side length of 15?

20

Kent, Tyler, Brandt, and David line up to play four square at school. How many ways can they line up?

21

A lithium ion battery can operate a CD player for 12 hours. How many seconds can a lithium ion battery operate a CD player?

22

What is the product of 356 and 366?

23

What is the remainder when 4100 is divided by 8?

24

The Jazz Band is going to a Jazz Festival 837 miles away. After traveling 123 miles, they realize that Mark forgot his saxophone and must go back to get it. How many total miles was their trip to the Jazz Festival?

25

How many 45E angles are on the interior of a square with both diagonals drawn?

26

What is the product of the first six non-negative even numbers?

27

Kyle has $900.00. Brasswind is having a sale for all trumpets. 4 trumpets cost $500.00. 3 trumpets cost $450.00. 2 trumpets cost $350.00. 1 trumpet costs $200.00. What is the maximum number of trumpets Kyle can buy?

28

Sarah has 4 identical pairs of white shoes, 5 identical pairs of red shoes, and 7 identical pairs of flip-flops. How many shoes should she pick to be sure of getting a matching pair? Right and left shoes are important.

29

Si-rex, Powei, Sister Mampson, Ohring, and Junior Bird Man are standing in a line. Si-rex is not in the front. There are exactly two people in front of Sister Mampson. Powei is directly behind Si-rex. Who is 4th in line?

Challenge Questions 30

Each trumpet needs 3 valves, 1 bell, 3 valve slides, and 1 lead pipe. Wayne has 12 lead pipes, 11 bells, 39 valve slides, and 28 valves. How many trumpets can he build?

31

A beetle sits on each square of a 9x9 checkerboard. Each beetle can crawl diagonally to a neighboring square, leaving some squares empty and others with multiple beetles. What is the smallest possible number of empty squares after each beetle has moved exactly once?

32

Max weighs 156 lbs and carries 40 lbs in his backpack. Sarah weighs 105 lbs and carries 30 lbs in her backpack. Who carries the greater load in their backpack by percent of their body weight?

33

Caitlin drove from the Miss Moses Lake Pageant to home and returned along the same path. Her average speed going was 20 mph. Her average speed returning was 30 mph. What was her average speed, in mph, for the entire trip?

34

Tom Hanks is stranded on an island. He eats one fourth of his food supply on the first day. On the second day, he eats one fourth of the remaining food. On the third day, he eats one fourth of the remaining food. If he had 3/4 of a pound left after the third day, how many pounds of food did he start with?

35

A ball is dropped 243 feet. Each time the ball hits the ground it bounces back up 2/3 the height it has fallen. Find the total distance, in feet, traveled when the ball hits the ground the 5th time.

36

The sum of the perimeters of three squares is 48 units. What is the smallest possible sum of their areas?

37

A group of people is standing in a circle spaced evenly apart. Each person is assigned a number starting with 1 and increasing in order as they go around the circle by 1. Each person is assigned only one number. It is noted that the person assigned the number 53 is standing directly across from the person assigned the number 123. What is the number assigned to the person standing directly across from the person assigned the number 80?

38

Two regular 6-sided dice were rolled and it was determined that the probability of rolling a sum of x was 1/12. What is the sum of all possible values of x?

39

At the Annual Math Open held at Cow Pi Beach, the Mathletes outnumbered the Trimathletes 7:x. If a competitor was chosen at random, the probability that it was a Trimathlete was y/12. What is the product of x and y?

40

Abe pushed a boulder up a 40 foot hill. He pushes it 12 feet each day, and each night it rolls down x feet, where x is an integral value . Abe reached the top of the hill with the boulder on the 7th day. What is the sum of all the possible values of x?

“Math is Cool” Masters-2001-02 Sponsored by: IEEE - Wenatchee Section 4th Grade, May 11, 2002 Team Multiple Choice Contest Julie’s Farm Fresh Eggs Julie owns a small fresh egg business. She has 50 laying hens, of which 96% produce one egg per day. The rest do not produce. Of the eggs collected each day, 1 egg is not fit for selling. These eggs will be considered defective. Julie sells her eggs for $1.50 per dozen and only sells a full dozen at a time. For simplicity, assume months are 30 days long (one year is 360 days). Costs Food

Miscellaneous

Layena Crumbles

$9.00 per 50 lb bag

Electricity

$2.00 per month

Chicken Scratch

$7.00 per 70 lb bag

$0.25 each

Oyster Shell

$14.00 per 40 lb bag

Egg cartons (holds 1 dozen eggs)

Daily Food Rations for all 50 chickens Each day Julie feeds her chickens: 2 lbs of Layena Crumbles 3 lbs of Chicken Scratch ½ lb of Oyster Shell

Using the given information, solve the following questions:

1

How many pounds of Layena Crumbles does Julie feed her chickens each day? A) 4 B) 3 C) 2 D) 1 E) Answer not given

2

How many dollars would Julie spend a year on electricity? A) 21 B) 22 C) 23 D) 24 E) Answer not given

3

How many dollars would 210 pounds of chicken scratch cost? A) 21 B) 22 C) 23 D) 24 E) Answer not given

4

How many total eggs does Julie collect each day? A) 47 B) 48 C) 49 D) 50 E) Answer not given

5

How many pounds of food does Julie feed her chickens each month? A) 5.5 B) 60 C) 90 D) 15 E) Answer not given

6

Assuming the chickens eat equal amounts of food, how many pounds, does each chicken eat a day? A) .5 B) .11 C) .7 D) .9 E) Answer not given

7

If Julie were to sell one egg, how much would it cost to purchase? A )$1.25 B) $12.50 C) 1.25¢ D) 12.5¢ E) Answer not given

8

If Julie sells all of her non-defective eggs, how many cartons of eggs would Julie sell each month? A) 110 B) 117 C) 120 D) 127 E) Answer not given

9

How much does Julie spend each day to feed her chickens? A) $30 B) 83.5¢ C) 30¢

D) $83.5 E) Answer not given

“Math is Cool” Masters-2001-02 Sponsored by: IEEE - Wenatchee Section 4th Grade - May 11, 2002 Team Contest

Leave answers in terms of π where applicable. Do not round any answers unless stated otherwise. Record all answers on colored cover sheet. 1

Is 0 positive, negative, or neither?

2

Eho is thinking of a number. Biff asked the following yes/no questions and got the following answers: Is the number smaller than 50? Eho’s answer: No Is the number larger than 50? Eho’s answer: No What is the number?

3

What is the hundred thousands’ digit of 9,876,543?

4

Biff and Eho were working on a math problem. Biff wrote

miscopied the 0. Eho wrote

+

7 8 + 9 0

but

1 8 but miscopied the 1. What should 9 3

the sum be? 5

A group of 35 Mathletes are planning a summer of intellectual fun. They decided to find the answers to 6300 math problems during the 45 days of summer. How many problems will each Mathlete need to solve each day if they wanted the number of problems evenly distributed among them?

6

Colin is flying to England on a Boeing 747 that travels at 250 geckles per hour. If the distance to England is 5,040 geckles, and a crosswind is slowing the plane by 10 geckles per hour, how many hours will it take him to get to England?

7

I am thinking of a number. If I add 3 to the number, then multiply the result by 3, then subtract 5 from the result, and at last, take the square root of the result the answer is 5. What is the number I am thinking of?

8

There are six “Math is Cool” teams in a championship. Each team will compete twice against each of the other teams. What is the total number of match-ups?

9

Mr. Sampson made a tile patio that was 15 tiles long and 12 tiles wide. When he finished, there was a sudden earthquake and a crack passed directly from the upper left corner directly to the bottom right corner. How many tiles did the crack pass through?

10

Out of 150 students, 54 are taking wood shop, 48 are taking arts and crafts, 12 are taking both wood shop and arts and crafts, 9 are taking both home economics and wood shop, 8 are taking both home economics and arts and crafts, 2 are taking all 3 classes, and 5 are not taking any. How many students are taking only home economics?

“Math is Cool” Masters-2001-02 Sponsored by: IEEE - Wenatchee Section 4th Grade - May 11, 2002 Mental Math

Express all answers as fractions and in terms of radicals and π, where applicable, unless otherwise instructed. Person 1 1


12

2

What is the perimeter of a triangle with sides of length 5, 6 and 7?

18

3

How many seconds are in 1 minute?

60 [seconds]

4

If one clown can hold 3 balloons, how many balloons can 11 clowns hold?

33 [balloons]

Person 2 1

What is the quotient of 18 and 2?

9

2

What is the perimeter of a rectangle with sides of length 4 and 5?

18

3

How many minutes are in three hours?

180[minutes]

4

If the wool from 1 sheep can make 4 coats, then wool from how many sheep are needed to make 20 coats?

5[sheep]

Person 3 1

What is sum of 37 and 4?

41

2

If the Beef family eats 15 hamburgers a day, how many hamburgers will they eat in one week?

105 [hamburgers]

3

How many days are in the longest month of the year?

31[days]

4

If it takes four people to make a team, how many people are needed to make 12 teams?

48 [people]

Person 4 1

What is the difference of 45 and 34?

11

2

What is the perimeter of a regular pentagon with sides of length 4?

20

3

How many days are in a non-leap year?

365[days]

4

There are 16 cups of water in one gallon of water. How many cups of water are in four gallons of water?

64[cups]

“Math is Cool” Masters-2001-02 Sponsored by: IEEE - Wenatchee Section

4th

Grade - May 11, 2002

College Knowledge Bowl Questions #1 1

What is 3,993 rounded to the nearest hundreds place?

4000

2

Biff is 5 feet 3 inches tall. How many inches tall is Biff?

63[inches]

3

Amanda, Caleb, David and Grace were all born 2 years apart. The sum of their ages is 40. A year ago, Grace was half as old as Amanda was then. Caleb, who is 9, is younger than Amanda. How many years old is David?

11[years]

4

What is the greatest common factor of 12, 36 and 20?

4

5

A barrel contains 57,643 sardines. Some are gray and some are yellow. 10,472 are gray. How many sardines are yellow?

47,171 [sardines]

6

What is the product of all of the even numbers between 1 and 5?

8

7

Keisha wants to buy some roller skates that cost $244.00. If her allowance is $11.00 a week, how many weeks will it take before she has enough money to buy the roller skates?

23 [weeks]

Extra Question: Only use it if needed 8

What is the difference between 79,003 and 9,714?

th

4 Grade

69,289


4th



Find the remainder when 7,821 is divided by 200.

21

2

A mouse ran on his wheel for 2 minutes and 10 seconds. How many total seconds did he run on his wheel?

130 [seconds]

3

Flip flops cost $0.50 a pair to make. Shopko sells them for $1.10 a pair. If 20 pairs of flip flops are sold, what is the profit in dollars?

[$]12.00

4

Eho is the battery carrier for his math team. Each time a competitor’s calculator has a battery failure, Eho must replace 4 batteries. If he started with 200 batteries at the beginning of a math competition and 32 competitors on his math team had battery failures, how many batteries did he have left at the end of the competition?

72 [batteries]

5

What is the sum of the ten thousands’ digit and the hundreds’ digit of 23,765? Read number as: 23 thousand 7 hundred sixty-five

9

6

Joe had 5 dozen eggs but broke two eggs trying get them all in the refrigerator. How many single unbroken eggs does he have now?

58 [eggs]

7

What is the sum of the next two numbers in the sequence? 17, 22, 27, 32.

79


If six people all shake hands with each other once, how many handshakes occur?

th

4 Grade

15


4th



What is the value in dollars of 7 quarters, 2 dimes, 11 nickels, and 9 pennies?

[$]2.59

2

The sum of two consecutive odd numbers is 64. What is the biggest number?

33

3

What is the probability of drawing a red king or a club from a standard deck of cards?

15/52

4

What time is it 110 minutes before 3:10 p.m.?

1:20 p.m.

5

41 is 22 more than what number?

19

6

What is the sum of all the prime numbers greater than 30 and less than 39?

68

7

What is 92 + 92 + 92 + 108 + 108 + 108?

600


What is the area of a square with a perimeter of 28?

th

4 Grade

49

“Math is Cool” Masters - 2001-02

Final Score:

th

4 Grade - May 11, 2002 School Name_____________________________Team #________ Proctor Name____________________________Room #_______

Full Name:____________________________________

1st Score

Individual Contest - Score Sheet

DO NOT WRITE IN SHADED REGIONS

Answer

1 or 0

1 or 0

Answer

1

21

2

22

3

23

4

24

5

25

6

26

7

27

8

28

9

29

10

30

11

31

12

32

13

33

14

34

15

35

16

36

17

37

18

38

19

39

20

40

Out of 40 1 or 0

1 or 0


Final Score:

th


Team Multiple Choice Contest-Score Sheet Correct responses are worth 2 points, incorrect responses are worth -1 point and no response is 0 points. DO NOT WRITE IN SHADED REGIONS Answer

1 2 3 4 5 6 7 8 9

1st Score

Out of 18


Final Score:

th


Team Contest-Score Sheet

1st Score

DO NOT WRITE IN SHADED REGIONS Answer

1 2 3 4 5 6 7 8 9 10

1 or 0

1 or 0

Out of 10

“Math is Cool” Masters - 2001-02 th


Final Score:

“Math is Cool” Masters -- 2001-02

4th grade - May 11, 2002 School Name_____________________________Team #________ Proctor Name____________________________Room #_______

Full Name:____________________________________

Key 1st Score



Answer

1 or 0

1 or 0

Out of 40

Answer

1

9920

21

43,200 [seconds]

2

0

22

130,296

3

20[legs]

23

4

4

2 [equations]

24

1083 (miles)

5

6 [quarts]

25

8 [angles]

6

125 [pages]

26

0

7

1,200 [children]

27

6 [trumpets]

8

12 [weeks]

28

17 [shoes]

9

77

29

Si-rex

10

216 [months]

30

9 [trumpets]

11

18 [years]

31

9 [squares]

12

9 [sides]

32

Sarah

13

[$]29.25

33

24 [mph]

14

False

34

16/9 or 1 7/9 [lbs]

15

7 [weeks]

35

1023 [ft]

16

175 [pieces]

36

48 [units2]

17

18 [years old]

37

10

18

44 [rolls]

38

14

19

225 [units2]

39

25

20

24 [ways]

40

7

1 or 0

1 or 0



Team Multiple Choice Contest-Score Sheet

1st Score

Correct responses are worth 2 points, incorrect responses are worth -1 point and no response is 0 points. DO NOT WRITE IN SHADED REGIONS Answer

1

C

2

D

3

A

4

B

5

E

6

B

7

D

8

B

9

B

-1, 0 or 2

Key

-1, 0 or 2

Out of 18



1st Score

Team Contest-Score Sheet DO NOT WRITE IN SHADED REGIONS Answer

1

neither

2

50

3

8

4

171

5

4 [problems]

6

21 [hours]

7

7

8

30 [match-ups]

9

24[tiles]

10

55 [students]

1 or 0

Key

1 or 0

Out of 10



Relay Contest - Score Sheet Answer for relay #1 42 30 60 10 Answer for relay #2 16 36 4 39

Key

“Math is Cool” Masters - 2001-02 4th Grade - May 11, 2002

Relay #1 Contest

Answer for person #1




42

30

60

10

1 or 0

1 or 0

1 or 0

2 or 0

Relay #2 Contest Answer for person #1




16

36

4

39

1 or 0

1 or 0

1 or 0

2 or 0

“Math is Cool” Masters – 2007-08 Sponsored by:

4th Grade – May 17, 2008 Individual Contest GENERAL INSTRUCTIONS applying to all tests:

Good sportsmanship is expected throughout the competition by all involved.

Bad sportsmanship may result in disqualification. Calculators or any other aids may not be used on any portion of this contest. Unless stated otherwise: o For problems dealing with money, a decimal answer should be given. o Express all rational, non-integer answers as reduced common fractions. For fifth and sixth grade, all fractions and ratios must be reduced. Units are not necessary unless it is a problem that deals with time and, in that case, am or pm is needed. However, if you choose to use units, they must be correct. Leave all answers in terms of π where applicable. Do not round any answers unless stated otherwise. Record all answers on the colored cover sheets in the answer column only. Make sure all answer sheets have all the information filled out at the top of the sheet. Tests will be scored as a 0 if answers are not recorded correctly on the answer sheets. Blank answer sheets and answer sheets with no name will also be scored as a 0.

INDIVIDUAL TEST - 35 minutes

When you are prompted to begin, tear off the colored sheet and begin testing. Make sure your name and school are recorded on the answer sheet. Each problem is scored as a 1 or 0. Record your answers on the score sheet. No talking during the test. You will be given a 5 minute warning.


4th Grade – May 17, 2008 Individual Contest Record all answers on the colored cover sheet. Find the area in square units of a rectangle with sides of length 5 and 7.

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18

Find the missing number: 5 + 3 – 2 + 8 + ? = 30 Find the sum of the thousands digit and the tens digit of 7,832,154. Joe has $72 in his savings account. He is saving money to buy a calculator for $110. He saves $2 a week. How many weeks will it take before he has $110? What is the probability of spinning an even number in one spin of a spinner with equal sections numbered 1 through 7? Find the positive difference between 5.32 and 10.09, and give your answer as a decimal. Colin is buying bananas. Bananas cost 50 cents each, or 2 for 75 cents, or 3 for 90 cents. (You must buy groups of 2 or 3 to get the lower prices.) He has $7.83. What is the largest number of bananas he can buy? Two angles in a triangle are 37 degrees and 55 degrees. What is the degree measure of the other angle? If all piano players are poor, and Biff is poor, does it follow logically (necessarily) that Biff is a piano player? Answer “yes” or “no”. Fred went 210 miles in 5 hours. What was his average speed in miles per hour? How many yards are in 180 inches? What is the number of units in the perimeter of a pentagon with 3 sides of length 8 units each, and 2 sides whose lengths average to 6 units? What is the 73rd letter in the pattern MATHISCOOLMATHISCOOLMA… How many sets of parallel lines does a parallelogram have? What is the seventh term in the following sequence: 3, 4, 6, 9, 13, and so on? Find the average of the following values: 3, 5, 7, 8, and 2. Dan Marino threw for 2,290 yards over 11 games. What was his average passing yards per game, to the nearest yard? Eho’s school has 15 steps between each floor, but no steps are required to enter the building on the first floor. Eho’s 1st period class is on the first floor, his 2nd

19 20 21 22 23 24 25 26 27 28 29 30

period class is on the 4th floor, and his 3rd period class is on the 2nd floor. After 3rd period Monday, he left for a dentist appointment and stayed home the rest of the day. How many steps at school did Eho go up or down on Monday? Shane is headed to Seattle from Spokane, which is 280 miles away. He was scheduled to stop at Moses Lake in order to pick up supplies. However, he didn’t remember until he was 35 miles past Moses Lake. He traveled back and got his supplies. What is the total number of miles he drove before he arrived in Seattle? What is the hundreds digit of the quotient of 76,842 divided by 3? Tom has 7 green socks, 3 purple socks, and 5 red socks in a drawer. What is the minimum number of socks he would need to take out of the drawer without looking to guarantee a matching pair of purple socks? This year at state track Kai finished 4th place in the mile race. He was also 4th place from last. If there were no ties, how many runners were in the race? A square number is the product of a counting number times itself. What is the difference between the smallest 3-digit square number and the largest 2-digit square number? From a list of the first ten counting numbers, Lynn selects 3 different numbers and adds them. If the sum she gets is the largest even sum possible, what is it? What is the smallest counting number I could add to forty-five to get a number that can be divided by eight with no remainder? A large group of mathletes stood equally spaced in a circle. They counted off and Biff said the number seven. He noticed Eho, number nineteen, was directly across from him. How many mathletes are in the circle? A telephone call has a charge of 30 cents for the first five minutes and 4 cents for each minute after five minutes. Colin spent 62 cents on this phone call. How many minutes long was the phone call? Find the largest possible odd remainder when a counting number is divided by 23. If it takes one-fourth ounce of peanut butter to cover one cracker, how many crackers could I cover with half a pound of peanut butter? Linda opened a book and noticed that the product of the two page numbers where she had the book open was 5256. What is the smaller of the two page numbers?

Challenge Questions 31 32 33 34 35

36 37 38

39 40

A line is drawn down the middle of a square, from the midpoint of one side to the midpoint of the opposite side, creating two equal rectangles. If the perimeter of the original square was 48 centimeters, what is the number of centimeters in the perimeter of one of these two equal rectangles? A dog has three different toys, but plays with its favorite toy exactly twice as often as either of the other two. If the dog is currently playing with a toy, what is the likelihood that it is playing with its favorite toy? Give your answer as a fraction. What are the odds in favor of an event occurring if the probability that the event will occur is 5/7? Write .2222… as a reduced fraction. I left my calculator out in the rain, and now it gives me weird answers to division problems. When I enter “175 ÷ 4”, it shows the answer 433. When I enter “88 ÷ 3”, it shows the answer 291. When I enter “315 ÷ 2”, it shows the answer 1571. When I try to divide a certain number n by 5, it shows the answer 933. What is n? After four boys moved away, exactly half of the students on the math team were boys. Before they moved, the proportion of boys was 21 boys out of every 40 math team members. How many girls are on the math team? A snail tries to get out of a well. Each day it climbs up the side of the well 4 feet and each night it slides down the well 2 feet and 6 inches. If the snail starts 40 feet down inside in the morning, how many days will the snail take to get out of the well? ABCD is a rectangle with area 36 units2. Tony makes the following 5 statements about this rectangle: (1) AB = DA; (2) AB = AC; (3) CD = BC > AB; (4) AD < DC < BD; (5) DB = CA. Let x = the number of Tony’s statements that cannot ever be true; y = the number of Tony’s statements that might be true or might not be true; and z = the number of Tony’s statements that must always be true. Give the ratio x : y : z. The ratio of the side lengths of two similar triangles is 2:3. What is the ratio of their areas? Colin, Kai, and Sampson are playing a dice game. Colin goes first, Kai second, and Sampson third. The first person to roll a three wins and the game is over. The dice are continuously passed in the above order until someone wins. What is the probability that Sampson wins?


4th Grade – May 17, 2008 Team Multiple Choice Contest When the Jay family went on safari in East Africa, they kept track of the numbers of big animals they saw per day. Below is their record for one day, in addition to some facts about these animals. All questions about the numbers of animals seen refer to the day for which the record is shown, unless you are told otherwise. Lions and cheetahs are predators, and have paws. Gazelles and zebras are prey, and have hooves. Notes: The abbreviation “mph” stands for miles per hour. One ton is 2000 pounds. Animal Cheetah Lion Gazelle Zebra

Top speed 70 mph 50 mph 35 mph 40 mph

Average adult weight 125 pounds 500 pounds 25 pounds 600 pounds

Number of animals seen 10 15 40 30

1

All the cheetahs seen were young adult males (brothers) living together in family groups. If there are always 3 to 5 males per family group, what is the largest number of cheetah family groups the Jay family could have seen? A) 10 B) 5 C) 4 D) 3 E) 2

2

How many animals of these four types did the Jay family see in all? A) 95 B) 85 C) 80 D) 75 E) answer not given

3

How many more hooves than paws did the Jay family see? A) 15 B) 45 C) 90 D) 35 E) answer not given

4

Assume each animal seen is of average adult weight. What is the total weight in pounds of all the animals seen by the Jay family? A) 6,150 B) 1,250 C) 2,775 D) 11,550 E) 27,750

5

A newborn lion cub weighs 40 ounces. By what factor will its weight increase if it reaches the average weight for an adult lion? A) 560 B) 12.5 C) 200 D) 15 E) 20

6

If a lion’s average speed when chasing prey is 10 miles per hour slower than its top speed, how fast does a lion run, on average, when chasing prey? A) 70 mph B) 60 mph C) 50 mph D) 40 mph E) 30 mph

RESTATED: When the Jay family went on safari in East Africa, they kept track of the numbers of big animals they saw per day. Below is their record for one day, in addition to some facts about these animals. All questions about the numbers of animals seen refer to the day for which the record is shown, unless you are told otherwise. Lions and cheetahs are predators, and have paws. Gazelles and zebras are prey, and have hooves. Notes: The abbreviation “mph” stands for miles per hour. One ton is 2000 pounds. Animal Cheetah Lion Gazelle Zebra

Top speed 70 mph 50 mph 35 mph 40 mph

Average adult weight 125 pounds 500 pounds 25 pounds 600 pounds

Number of animals seen 10 15 40 30

7

A gazelle and a zebra are five miles apart and are running toward each other at their top speeds. How many minutes does it take them to meet? A) 15 B) 24 C) 4 D) 3 E) 7.5

8

On a different day, the only animals the Jay family saw were five cheetahs and two gazelles. What was the average speed in mph of the animals they saw on this day? A) 50 B) 60 C) 70 D) 52.5 E) 48.75

9

Park rangers need to move some of the animals to another part of the park due to overcrowding. They have a truck that will carry as much weight as two elephants averaging 5 tons each. If the rangers put the largest possible number of zebras of average weight in the truck, then fill up the truck with gazelles of average weight, how many animals will be in the truck? A) 41 B) 32 C) 16 D) 33 E) 49


4th Grade – May 17, 2008 Team Contest 1

Vowels are a, e, i, o, and u. Consider all the other letters to be consonants. What fraction of the letters in this problem are vowels?

2

In the stack of identical cubes at right, each cube that is not resting on the table must be resting on another cube. What is the smallest number of cubes there could be in the stack?

3

Put the following five values in order from smallest to largest. Your answer should consist of 5 letters in the correct order.

A= 8×8

B = 88

C = 8−8

D =8+8

E =8÷8

4

An experimental robotic vehicle moves at constant speed in half-hour time blocks. At the end of any half-hour block it may change its speed (which then remains the same for the next half-hour). In one test, the vehicle moved 220 kilometers in 4 hours. If its fastest speed is 60 kilometers per hour, what is the least possible distance in kilometers the vehicle could have moved during any halfhour block of this test trip?

5

Sarah and Millie are collecting shells at the beach. Sarah has 47 shells and Millie has 40 shells. After Sarah gives some of her shells to Millie, Sarah is left with 34 shells. How many shells does Millie now have?

6

Toad has a number line painted on the floor of the exercise room of Toad Hall. One day, Toad starts on the number 14, jumps x units forward, then 5 units backward, then 7 units forward. He ends on the number 37. What is x ?

7

Find the value of (6 x 5) + (2 x 2 x 2) – (4 x 3) + (15 ÷ 3).

8

Harriet spent a total of 85¢ on a mixture of gumballs and jawbreakers, each costing a whole number of cents. A gumball costs 25¢, and a jawbreaker is more expensive than a gumball. If Harriet got an even number of jawbreakers, what is the price in cents of each jawbreaker?

9

Marty takes 5 steps for every 6 steps that Jon takes. Each of Jon’s steps is 3 feet, and each of Marty’s steps is 2 feet. In the time it takes Jon to walk 630 feet, how many feet does Marty walk?

10

My favorite number is a 2-digit counting number. One of its digits is in 12,450 and one of its digits is in 2,793. The sum of its digits is odd, and the difference between its digits is 3. Find the sum of all possible numbers that could be my favorite number.


4th Grade – May 17, 2008 Relay Contest RELAYS - 5 minutes per relay There is no talking during this event and you must always be facing forward. Person #1 will be given an answer sheet(s) and will need to fill out the top. The proctor will hand out a strip of paper to each person. These need to be face down on your desk until it is time for the relay to start. Once the relay begins, everyone may turn over their strip of paper and begin working. You may write on the strip of paper to come up with your answer. However, when person #1 figures out his/her problem, he/she will record just his/her final answer on the answer sheet and pass only the answer sheet back to the person behind. This continues until person #4 puts an answer on the answer sheet and gives it to the proctor. A correct answer from person #1, #2 and #3 is worth 1 point each. A correct answer from person #4 is worth 2 points making each relay worth 5 points. You will see the expression TNYWG [Proctor: write this on the board] which means: “the number you will get”. This is where you put your teammate’s answer that they pass back to you, and then you should be able to solve your question. Once the relay begins, turn over your strip of paper and make sure you have the right person number. Remember, no talking and remain facing forward to avoid being disqualified!

Person 1

Relay #1

Answer

What is the product of the number of sides a triangle has and the number of sides a square has? Evaluate: TNYWG – (47-39)

12 4

Person 2 Person 3 To square a number means to multiply the number by itself.

484

Person 4

490

Square 11, and then multiply that product by TNYWG. Add TNYWG to the number of different 3-digit counting numbers that can be formed from the digits 2, 4, and 7, if each digit is used exactly once in each 3-digit number. Relay #2

Answer

Person 1 Evaluate: 2 × 7 + 8 – 6 Person 2 A spider has 8 legs and a cricket has 6 legs. If I keep my

16

Person 3

280 [miles]

Person 4

(TNYWG – 12) vegetarian spiders and my 8 crickets in a cage together, how many legs in all are there in the cage? Colin drove 60 miles per hour for 4 hours, and then drove TNYWG miles per hour for 0.5 hours. How many miles did Colin drive in all? What is the remainder when TNYWG is divided by the sum of (3 + 0) plus (3 + 1) plus (3 + 2)?

80 [legs]

4


4th Grade – May 17, 2008

Final Score:

KEY

Mental Math Contest PERSON 1 NAME: 1.1 Find the value of fifty-one plus eleven.

1.2

1 or 0 62

What is the side length in centimeters of a square with area eighty-one square centimeters? 1.3 Joel falls into the lake. He sinks at a rate of three feet per second. The lake is twenty-four feet deep. How many seconds does it take Joel to reach the bottom? 1.4 What is the next number in this sequence: seventeen, fourteen, eleven, eight, and so on? PERSON 2 NAME: 2.1 What is one-half of twenty-one? Express your answer as a decimal.

9 [cm]

2.2 2.3 2.4

What is the remainder when the product of 18 and 7 is divided by 2?

0

Three days ago it was Monday. What day of the week will it be tomorrow?

Friday

8 [seconds] 5

10.5

I gave my bunny six carrots, but one-third of the carrots were moldy. How many carrots can the bunny eat if he cannot eat moldy ones? PERSON 3 NAME: 3.1 Evaluate: three times six plus seven.

4 [carrots]

3.2

3/52

3.3

When I draw one card from a standard deck, what is the probability that the card will be a queen, but not the queen of hearts? Give your answer as a fraction. When the following three measurements are listed in order of size, which one will be in the middle? one meter, one inch, one foot

3.4

If three cogs equal one dog, and one dog equals one slog, then one slog is equal to how many cogs? PERSON 4 NAME: 4.1 If three plus my number is equal to five plus two, what is my number?

4.2 4.3 4.4

What is the digit in the ones place of the product that you get when you multiply 17 by itself? If the area of a square is sixteen square yards, what is the number of yards in the perimeter of the square? How many whole flowers can you buy with eighty-five cents, if each flower costs ten cents?

25

1 foot [or just “foot”] 3 [cogs]

4 9 16 [yards] 8 [flowers]


May 17, 2008

4th Grade - Division 1 & 2 COLLEGE KNOWLEDGE BOWL ROUND #1 #

Problem

1

Cathy had 19 balloons, and Dan had twice as many balloons as Cathy. How many balloons did they have altogether? How many positive even counting numbers are less than 44? Arnold is watching a Spongebob Squarepants video, which started at 8:15 PM and will last for 55 minutes. If he watches it all, what is the largest number of minutes he can read after the video and still get to bed by 9:30 PM, given that he does not read in bed? If three dozen cookies are put into 4 boxes with an equal number of cookies in each box, how many cookies will be in each box? What is the difference between one-half of 200 and one-fourth of 100? If the letter A is worth one dollar, B is worth two dollars, C is worth three dollars, and so on, then what is the value in dollars of the phrase “BAD CAT”, spelled BA-D C-A-T? What is the product of the digits of two thousand eight?

2 3

4 5 6

7 7 8

Answer 57 [balloons]

21 [numbers] 20 [min]

9 [cookies]

75 31 [dollars]

0

Extra Problem – Only if Needed The radius of a circle is two-thirds of an inch. What is the diameter of the circle, as a mixed number of inches?

1

1 [inches] 3


May 17, 2008

4th Grade - Division 1 & 2

COLLEGE KNOWLEDGE BOWL ROUND #2 #

Problem

1

When Karen rolls three dice, the numbers showing on the top faces are all different. What is the largest possible sum of the numbers on the top faces? What is the probability of drawing either a black card or a diamond in a single random draw from a standard deck of cards? When you reverse the digits of my friend’s 7-digit telephone number, you get the number three million forty-two thousand eight hundred ninety-seven. In the correct order, what digits should I dial to telephone my friend? How many days total are in the years 2007 and 2008, given that 2008 is a Leap Year? What is the name of the flat, straight-sided geometric shape that has twice as many sides as a rectangle? If the average of my number and 17 is 23, what is my number? In a Quidditch match, Gryffindor has seventy points, while Slytherin has eighty-three points. If Slytherin does not score again, how many more points does Gryffindor need to score in order to win?

2

3

4 5

6 7

7.1 8

Answer 15

39 52

or

4

7982403

731 [days] octagon

29 14 [points]

Extra Problem – Only if Needed Multiply ninety-eight times fifty-five.

3

5390


May 17, 2008



Problem

1

Find the mode of the following set of data: 5, 3, 7, 3, 8, 7, 5, 3, and 4. April Fool’s Day is the first day of April, and May Day is the first day of May. If April Fool’s Day is on a Thursday in a certain year, on what day of the week will May Day fall that year? A string is eighty-nine inches long. How many pieces of length one foot can be cut from this string? How many dimes will it take to equal the same amount of money as 100 quarters? What time would it be 80 minutes before 12:18 PM?

2

3 4 5

6

7 7.1 8

I have 97 candy bars. What is the largest whole number of candy bars I can eat and still leave at least 20 candy bars for each of my two sisters? Find the value of A plus B plus A plus B minus A, if A equals seven and B equals eleven.

Answer 3

Saturday

7 [pieces] 250 [dimes] 10:58 AM [or 2 minutes before 11:00 A.M.] 57 [candy bars] 29

Extra Problem – Only if Needed Subtract nineteen from fifty, and then multiply that result by two.

62

“Math is Cool” Masters – 2007-08

Final Score:

KEY


School Name__________________________________Team #________

First Score

Proctor Name__________________________________Room #_______

STUDENT NAME________________________________Division: Individual Contest – Score Sheet DO NOT WRITE IN SHADED REGIONS Answer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

35 [sq units] 16 7 19 [weeks] 3/7 4.77 25 [bananas] 88 [degrees] no 42 [mph] 5 [yards] 36 [units] T 2 [sets] 24 5 208 [yards] 90 [steps] 350 [miles] 6

1 or 0 1 or 0

Answer 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

14 [socks] 7 [runners] 19 26 3 24 [mathletes] 13 [minutes] 21 32 [crackers] [page] 72 36 [cm] 1/2 5:2 or 5/2 or 5 to 2 2/9 [n =] 468 38 [girls] 25 [days] 2: 2: 1 4:9 or 4/9 25/91

1 or 0

1 or 0

“Math is Cool” Masters – 2007-08 4th Grade – May 17, 2008

Final Score:

KEY

School Name__________________________________Team #________ Proctor Name____________________Room #_______Division:

First Score

(out of 18)

Team Multiple Choice Contest – Score Sheet TEAM MULTIPLE CHOICE - 15 minutes

This test is the only test where you will be penalized for incorrect responses. You will receive 2 points for a correct letter response, 0 points for leaving it blank and -1 point for an incorrect response. When you are prompted to begin, tear off the colored sheet, pass out a copy of the test to each team member, and begin testing. Since this is a multiple choice test, ONLY a letter response should be listed as an answer on the answer sheet.

Correct responses are worth 2 points, incorrect responses are worth -1 point and no response is 0 points. DO NOT WRITE IN SHADED REGIONS

Answer

1 2 3 4 5 6 7 8 9 10

D A E [180] E C D C B A

-1, 0 or 2

-1, 0 or 2


Final Score:

KEY

School Name__________________________________Team #________ Proctor Name_________________________Room #_______Div:

First Score

(out of 20)

Team Contest – Score Sheet TEAM TEST - 15 minutes

When you are prompted to begin, tear off the colored sheet and give a copy of the test to each of your team members and begin testing. Each problem is scored as a 2 or 0.


Answer

1 2 3 4 5 6 7 8 9 10 10

40 103

17 [cubes] CEDAB

[in order]

10 [km] 53 [shells] 21 [units] 31 30 [cents] 350 [ft] 228

2 or 0

2 or 0

“Math is Cool” Masters -- 2007-08 4th Grade – May 17, 2008

KEY

School:_______________________________Team #________ Proctor: ______________________________ Room #_______Div RELAY # 1 Answer for person

Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

12

4

484

490

1 or 0

1 or 0

1 or 0

2 or 0

RELAY # 2 Answer for person #1

16 1 or 0


80 [legs] 1 or 0


280 [miles] 1 or 0


4 2 or 0

“Math is Cool” Championships – 2008-09 Sponsored by:

4th Grade – March 19, 2009 Individual Contest GENERAL INSTRUCTIONS applying to all tests:






4th Grade – March 19, 2009 Individual Contest Record all answers on the colored cover sheet.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

What is 1 times 0? If Andrew uses up 5 hours of his 12 hour battery on his laptop, then how many hours are left in the battery? What is the area, in square feet, of a square with side length of 5 feet? What is the perimeter, in inches, of an equilateral triangle with sides of length of 12 inches? What is the quotient when 492 is divided by 3? Tim has just inherited 17 acres of land and wants to build greenhouses on his new land. If each greenhouse has an area of 3 acres, how many complete greenhouses can Tim build? If a wooden pencil costs 5 cents and a mechanical pencil costs 10 cents, then how many cents do 2 wooden pencils and 3 mechanical pencils cost? What is 10 + 11 + 12 + 13? Helen owns 9 elephants and Andrew owns 5 elephants. Elephants can eat 27 bags of peanuts in one day. How many bags of peanuts can Andrew’s elephants eat in one day? If the area of a rectangle is 10 square centimeters and the length of one side is 5 centimeters, then what is the length of the other side, in centimeters? One out of every 4 fish in a particular lake has spots. Out of 24 fish from this lake, how many fish would you expect to have spots? Find the missing number to make this a true statement: (56 x 4) + (56 x 5) + (56 x 6) + (56 x 8) = 56 x . Suppose that Tom buys 10 apples and eats 2 of them right away. Then suddenly a random chipmunk appears and eats half of the remaining apples. How apples does Tom have left? If the number of bacteria on a kitchen sink doubles every 5 minutes, then how many bacteria would there be in 15 minutes, given that there was 1 bacterium initially? What is the area, in square feet, of a triangle with a height of 6 feet and a base of 10 feet? If Hannah rolls a six-sided die and flips two coins, then how many possible ways exist of getting an even number on the die and 1 head and 1 tail from the coins? If I flipped 10 coins and got 7 tails, how many heads did I get? What is the sum of the two missing terms of this sequence: 1, 1, 2, 3, 5, 8,

,

, 34

A certain plant grows 2 flowers every day until 10 flowers are grown, at which point the plant is considered fully grown. How many days are required for 3 plants to be fully grown if the first plant grows its first flower on the first day, the second plant grows its first flower on the second day, etc?

20

21 22 23 24 25 26 27 28 29 30

Put the following numbers A, B, C, D and E in order from greatest to smallest: A = Area of a triangle with a height of 10 and base of 2. B = Area of a square with side of length 4. C = Area of a rectangle with sides of length 7 and 2. D = The mean of A, B and C E = The range of the set of numbers: {A, B, C} What is the difference between the sum of the first 10 counting numbers and the sum of the first 5 counting numbers? In how many ways can you roll a sum of 7 with 2 standard six-sided dice? If (a * b) = 2a + 2b, then what is ((1 * 2) * 3)? My neighbor wants to make a pen for her horses with 100 feet of fencing. What shape should the pen be if she wants to give her horses the most space possible? What is the product of 145 and 63? What number can you add to 67 so that the resulting sum is equal to two times 70? If today is Sunday, then what day is it 69 days after tomorrow? If Amanda runs 2 miles every day, then how many miles has she run by the end of June, if she started running on June 1st? If 20 – x = 15, then what is 3x? What is the ratio of the shaded figure’s area to the shaded figure’s perimeter?

Challenge Questions 31 32 33 34 35 36 37 38

39 40

Bertha has a special number. If you add the digits of Bertha’s number and double it, then you get Bertha’s number again. What is Bertha’s number? What is the sum of the two largest 2-digit distinct counting numbers that are not multiples of 2, 3 or 5? How many possible 7 digit phone numbers are possible if the first three digits must be odd and the last digit must be prime? If Ryan draws a rectangle and draws squares protruding out on each side of the rectangle, then what is the area, in square yards, of the new figure if the original rectangle has sides of length 4 yards and 6 yards? Let (a @ b) = (a + b)(a – b), then what is ((5 @ 4) @ 3)? If 1 + 3 + 5 + ...+ 99 = 2500, then 2 + 4 + 6 + ... + 100 = x. What is the value of x? Assign the numbers 4, 5, 1 and 6 each once for w, x, y and z in the expression (x + y) ÷ (w + z)2 and evaluate to find an answer. What is the largest possible answer you can get? Express your answer as a decimal OR as a fraction. [Note: 32 means 3 x 3] How many triangles are in this figure?

In a soccer tournament with eight teams, how many games will be played if each team is to play every other team twice? Each small square has an area of 4 units squared. If a rectangle is picked at random from all possible rectangles, what is the probability it has a perimeter of 12?


4th Grade – March 19, 2009 Team Multiple Choice Contest Triscia has taken to feeding the birds at her house and has various bird feeders around the yard. Since she started feeding the birds, the bird population has grown and to keep costs down, Triscia only fills the bird feeders or puts seed on the ground so many times per week as shown below: Type of Feeder How # cups needed *Largest Type of Seed # of times many? to fill it number of birds refilled in a per feeder week 1 40 Not Applicable Black Oil 1 Ground (Just place Sunflower Seed spread food on ground) Thistle Seed 2 4 6 Thistle Seed 2 Feeder Octagonal Prism 1 20 12 Wild Bird Seed 1 Feeder Wooden Tray 1 7 15 Black Oil 3 Feeder Sunflower Seed

1 2 3 4 5 6

Triscia’s favorite birds are the gold finch and they love thistle seed! Triscia has one thistle seed feeder outside her dining room window. How much will it cost her to fill this feeder one time with thistle seed? A) $1 B) $2 C) $3 D) $4 E) Answer not given. How many total cups of seed (thistle, wild bird seed & black oil sunflower seeds) does Triscia put out for the birds each week? A) 97 B) 89 C) 57 D) 49 E) Answer not given. What is the largest number of birds that can be fed at one time on the three types of bird feeders (thistle seed feeders, octagonal prism feeder and wooden tray feeder) available in Triscia’s yard? A) 27 B) 29 C) 33 D) 39 E) Answer not given. In the spring when the quail come to eat at Triscia’s house, they eat 50% of the black oil sunflowers per week from both the ground and the wooden tray feeder. How many cups of black oil sunflowers do the quail eat per week when they are visiting? A) 10.5 B) 20 C) 23.5 D) 30.5 E) Answer not given. On average, how many total cups of bird feed do all Triscia’s birds eat each day? [Round to the nearest whole number.] A) 4 B) 5 C) 8 D) 10 E) Answer not given. If at one time there are 162 birds at Triscia’s house eating bird seed and all the bird feeders are full, how many birds are eating on the ground? A) 93 B) 123 C) 129 D) 135 E) Answer not given.

7

8 9

On a lazy afternoon, Triscia’s cat, Isaac Newton, likes to watch the birds from under a bush. As you can imagine, this makes the birds very nervous and they no longer eat the seeds on the ground. If Triscia stops putting sunflower seeds on the ground, what is the least number of times Triscia would have to fill the wooden tray bird feeder in a week to ensure that the birds have at least the same amount of sunflower seeds each week they would normally have if seeds were still put on the ground? A) 6 B) 7 C) 8 D) 9 E) Answer not given. Triscia buys the black oil sunflower seed in 45.75 pound bags. If 3 pounds of black oil sunflower seed is equivalent to one gallon of seed, how many weeks will one 45.75 pound bag last Triscia? Choose the best answer. A) 5 B) 4 C) 3 D) 2 E) 1 Thistle seed costs $0.50 per cup, wild bird seed costs $0.12 per cup and black oil sunflower seed costs $0.25 per cup . “How much does Triscia pay for all the bird feed she uses in a week?” A) $16.15 B) $15.65 C) $21.65 D) $25.65 E) Answer not given.

Problem Restated: Triscia has taken to feeding the birds at her house and has various bird feeders around the yard. Since she started feeding the birds, the bird population has grown and to keep costs down, Triscia only fills the bird feeders or puts seed on the ground so many times per week as shown below: Type of Feeder

Ground (Just spread food on ground) Thistle Seed Feeder Octagonal Prism Feeder Wooden Tray Feeder

How # cups needed many? to fill it 1 place

40

**Largest number of birds per feeder Not Applicable

Type of Seed

2

4

6

Thistle Seed

2

1

20

12

Wild Bird Seed

1

1

7

15

Black Oil Sunflower Seed

3

Black Oil Sunflower Seed

# of times refilled in a week 1


4th Grade – March 19, 2009 Team Contest 1 2 3 4 5

Suzanne has 14 pairs of shoes. How many shoes does Suzanne have? Alex had already read 49 pages of his 314-page book when Randy started reading. Alex finished the rest of his book in the same time it took Randy to read two books, one of 93 pages and one of 89 pages. How many more pages did Alex read during this time than Randy? Matt’s jacket had 6 buttons down the front, two on each sleeve, and one on each of the two pockets. After a day of sledding and snowball-fighting, Matt had lost one-third of the buttons on his jacket. How many buttons did Matt have left on his jacket? Karen gets two dimes, four nickels, and one quarter for each quarter-hour she spends dusting. If she starts dusting at 11:40 AM and finishes dusting at 5 minutes before 2:00 PM, how much money (in dollars) has she earned? [Express your answer as a decimal.] The 5 puzzle pieces fit into the frame shown. Give the letter or letters a (a, b, c, d) of all squares where the single square puzzle piece could go. b c b (Puzzle pieces may be flipped or turned to fit in the frame.) a c d c a b c b a

6

In the phrase “MATH IS COOL”, each letter stands for a different digit and each word stands for a number. If the product of all the digits is 0, what is the largest possible sum of MATH + IS + COOL?

7

The mode of a set of values is the value that occurs most often. Jackie kept a record of how many dog biscuits her dog Zero ate each day for a week. She wrote: Sunday, 4; Monday, 7; Tuesday, 3; and Wednesday, 5. Jackie lost her records for the rest of the week, but she remembers that the average was 4 biscuits per day and that Zero ate at least one dog biscuit each day. What was the mode of all seven of Jackie’s recorded values for the week if there was only one mode? Give all possible answers.

8

The first term of a certain number pattern is 5, the second term is 515, the third term is 51515, and so on. The number of digits increases by two with each new term, and there is always a “1” between each pair of 5s. How many times would you write the digit “5” in writing the first 8 terms of this pattern?

9

Five coins (a penny, a nickel, a dime, a quarter, and a half-dollar) are in a box. Alma, Brenda, Clara, Dora, and Edna reach into the box, and each girl takes one coin, at random. They sit in a circle, in alphabetical order of their names, and Alma passes her coin to Brenda. Brenda keeps the coin of larger value, and passes the other coin to Clara. This continues until Alma has one coin again. What is the probability (as a fraction) that Alma gets the same coin she started with?

10

48 points are marked around a circle, spaced an equal distance apart. They are numbered in order, 1 through 48. What point is opposite number 17?


4th Grade – March 19, 2009 Relay Contest RELAYS - 5 minutes per relay There is no talking during this event and you must always be facing forward. Person #1 will be given an answer sheet(s) and will need to fill out the top. The proctor will hand out a strip of paper to each person. These need to be face down on your desk until it is time for the relay to start. Once the relay begins, everyone may turn over their strip of paper and begin working. You may write on the strip of paper to come up with your answer. However, when person #1 figures out his/her problem, he/she will record just his/her final answer on the answer sheet and pass only the answer sheet back to the person behind. This continues until person #4 puts an answer on the answer sheet and gives it to the proctor. A correct answer from person #1, #2 and #3 is worth 1 point each. A correct answer from person #4 is worth 2 points making each relay worth 5 points. You will see the expression TNYWG [Proctor: write this on the board] which means: “the number you will get”. This is where you put your teammate’s answer that they pass back to you, and then you should be able to solve your question. Once the relay begins, turn over your strip of paper and make sure you have the right person number. Remember, no talking and remain facing forward to avoid being disqualified!

Person 1 Person 2 Person 3 Person 4 Person 1 Person 2 Person 3 Person 4 Person 1 Person 2 Person 3 Person 4

Practice Relay

Answer

How many digits are in the number 74,389?

5

Evaluate: TNYWG + 6

11

Evaluate: TNYWG – 9

2

Evaluate: 6 x TNYWG + 1

13

Relay #1

Answer

What is the average (mean) of 10 and 20?

15

What is the sum of TNYWG and 10 times the TNYWG?

165

What is the TNYWG divided by 5?

33

Find the product of TNYWG and TNYWG/3.

363

Relay #2

Answer

Find the area of a rectangle with sides of length 8 and 4, then subtract 5. Find the area of a triangle with base of (20 ÷ 2) and height of (6 x 2), then add TNYWG. Find the area of a square whose side length is 2 less than the number of sides on a pentagon. Add this result to the remainder of TNYWG divided by 5. A prime number has only two numbers that divide into it with no remainder (1 and the prime number itself). If TNYWG is prime, then find the sum of the area of a square of side length of TNYWG and the area of a square of side length 11. If TNYWG is not prime, find the sum of the area of a rectangle with sides of length 6 and 7, and the area of a triangle whose base is TNYWG and height is 10.

27 87 11 242


4th Grade – March 19, 2009

Final Score:

KEY

School Name__________________________________Team #________ Proctor Name_________________________________Room #_______ Division:

Mental Math Contest MENTAL MATH - 30 seconds per question When it is time to begin, I will read the first question twice. You may not do any writing or talking while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You may not change or cross out answers once you have written an answer down. If there are eraser marks, write-overs, or crossed out answers, they will be marked wrong. Once all students have laid their pencils on the desk, another question will be asked. If a student doesn’t lay his/her pencil down, the maximum wait time is 30 seconds from the second reading of the question before another question is asked. You may continue to work on a problem while the next question is being read. The value of each question is a one or zero. Each student may answer only four questions, and then another member of your team will come up, until each team member has had a turn. If your team has fewer than 4 members, missing team members will receive a zero. PERSON 1 NAME:

1 or 0

1.1 1.2 1.3

Find the sum of eight, nine and ten.

27

How many total cents is one nickel, two dimes and one quarter?

50 [cents]

What is the probability of picking a red card from a standard deck of cards?

1/2 [or equiv

1.4

What is three-fifths of 25?

frac]

15

PERSON 2 NAME:

2.1 2.2 2.3 2.4

Find the product of one, six and eight.

48

Katie has 3 red shirts, 5 blue shirts and 3 orange shirts. If Katie picks one shirt at random, what is the probability that Katie picks an orange shirt? What is the remainder when you divide 113 by 7?

3/11 [or

What is the perimeter of a square, in feet, that has an area of 100 square feet?

40 [ft]

equiv frac]

1

PERSON 3 NAME:

3.1 3.2 3.3 3.4

Find the quotient of 63 and 9.

7

How many total pints is 1 gallon, 3 quarts and 1 pint?

15 [pints]

Find the sum of the next two terms in the sequence whose first three terms are 3,4 and 5. When 14 is subtracted from my number, the answer is 12. What is my number?

13 26

PERSON 4 NAME:

4.1 4.2 4.3 4.4

Multiply eight times the sum of four and seven.

88

What is the eleventh term of the sequence whose first three numbers are 3, 6, 9?

33

How many inches total is 1 yard, 2 feet and 2 inches?

62 [in]

What is the perimeter of a regular octagon with side length of 1 and three-fourths?

14 [un]



Set A


Problem

Answer

1

For Science class, each student needs to have one worm. If there are three classes with 20 students each and two classes each with 14 boys and 13 girls, how many worms are needed? If it takes two and one-half cups of flour to make one batch of chocolate chip cookies, how many cups of flour will it take to make four batches of chocolate chip cookies? What is five squared plus the first even number greater than ten? One-fifth of the animals on Dog Street are cats, one-half of the animals are dogs and the rest are turkeys. If there are 30 animals on Dog Street, how many turkeys are there on Dog Street? Find the sum of the smallest number in the set of numbers and mode of the set of numbers: 9, 6, 16, 4, 9, 2, 3 A leap year occurs when the year is divisible by 4. A century year occurs when the year is divisible by 100. A century year is a leap year if it is divisible by 400. Name the most recent century leap year. An apartment currently rents for seven hundred fifty dollars a month. The monthly rent is expected to increase fifteen dollars every twelve months. What will the monthly rent be at the end of five years, in dollars?

114 [worms]

2 3 4

5 6

7

7 8

10 [cups]

37 9 [turkeys]

11 2000

[$] 810

Extra Problem – Only if Needed How many different ways can you arrange the letters in the word “ANT”?

6 [ways]



Set A


Problem

Answer

1

Each ant hill in Karen’s yard contains 1000 ants. Each ant hill in Annie’s yard contains 750 ants. If Karen has 5 ant hills in her yard and Annie has 4 ant hills in her yard, how many total ants are in the ant hills in Karen’s and Annie’s yard? Find the positive difference of the area of a rectangle of sides of length 8 and 12, and the area of a square with perimeter of 36. What is the smallest four-digit counting number which has exactly two digits that are the same? Evaluate: The smallest prime number multiplied by 8 squared.

8000 [ants]

If Amanda has a rectangular garden with an area of 35 square feet and one side has a length of 7 feet, how much fencing, in feet, will she need to enclose the perimeter of her garden? Mark purchased four pens at 70 cents per pen. The total sales tax on his purchase was fourteen cents. He paid for his purchase with a ten dollar bill. How much money, in dollars, did he get back? Evaluate: Two-thirds times two-thirds.

24 [feet]

2 3 4 5 6

7 7.1 8

15 [un2]

1002 128

[$] 7.06

4/9 [or equiv]

Extra Problem – Only if Needed When will it be 3 hours 46 minutes past 5:45 am?

9:31 AM



Set A


Problem

Answer

1

A committee is made up of three women and four men. What fraction of the committee members are men? Using pennies, nickels, dimes and quarters, what is the least number of coins needed to make 68 cents? How many odd numbers are between 12 and 36?

4/7 [or equiv] 7 [coins]

2 3 4 5 6 7

7.1 8

What is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10?

12 [numbers] 55

What is the largest number of times a triangle and a circle could cross each other? Reduce the fraction 4/12 to lowest terms.

6 [times]

Evaluate: A – B + C Where A = 100 ÷ 2 Where B = the number of red cards in a standard deck of 52 cards Where C = the number of socks in 12 pairs

48

1/3

Extra Problem – Only if Needed Today Amanda is two years older than David. In ten years, how many years older will Amanda be than David?

2 [years]



Set B COLLEGE KNOWLEDGE BOWL ROUND #1 #

Problem

Answer

1

There are three “Math is Cool” regions in Washington State where each region has 35 schools competing and each school brought 3 teams. How many total “Math is Cool” teams are competing in Washington? What is the sum of the number of ounces in a pound, the number of inches in a yard, and the number of days in a week? How many boards of length two feet six inches, can be cut from a board 20 feet long? Grace attends ballet class three days a week for one and one half hours each day. How many total hours does Grace attend ballet class in twenty weeks? Caleb rides his motorcycle after school 55 percent of the time and he chews gum 45 percent of the time. If he rides his motorcycle AND chews gum 20 percent of the time, what percentage of the time does he ride his motorcycle without chewing gum? What is the hundreds digit when you multiply 63 by four hundred fifty two? What is the difference between the number of ways to arrange four people in a line and the number of ways to arrange three people in line?

315 [teams]

2 3 4 5

6 7 7 8

59

8 [boards] 90 [hours]

35 [%]

4 18

Extra Problem – Only if Needed A five-ringed binder has 31 sheets of paper contained in the rings. How many holes were punched in these sheets of paper to put them in the rings?

155 [holes]



Set B


Problem

Answer

1

If one angle of a right triangle is 23 degrees, what is the measure of the other acute angle, in degrees? What is the radius of a circle, in feet, that has a diameter of 4 yards? Two hundred eighty five is five times what number?

67 [º]

What is the sum of all the one-digit prime numbers?

17

Talitha took a multiple choice test portion of an exam. For every wrong answer she gives, one-fourth of a point is subtracted from her exam score. If there are 44 questions on the multiple choice test, what is the lowest score Talitha could make? If Kendall has 6 red marbles, 5 blue marbles, 3 white marbles and 2 yellow marbles in a bag, what is the probability that she will draw one yellow marble out of the bag? Evaluate the product of 24 and 26.

-11 [points]

2 3 4 5

6

7 7.1 8

6 [ft] 57

1/8 [or 2/16 or equiv] 624

Extra Problem – Only if Needed How many eggs would each person have if 2 dozen eggs were divided equally among 6 people?

4



Set B


Problem

Answer

1

Terry is 5 feet 3 inches tall, and Chris is 4 feet 10 inches tall. How many inches taller is Terry than Chris? How many different counting numbers have two digits?

5 [in]

2 3 4 5 6 7 7.1 8

An outfit is made up of 1 hat, 1 shirt, and 1 pair of pants. If Grace has 5 hats, 5 shirts and 3 pants to wear on any given day, how many different outfits can she wear? If “A” equals 9 and “B” equals 21, evaluate the following: A times B Including Caroline, how many total legs are there if Caroline has 3 dogs? How many diagonals can be drawn in a rectangle? What is the smallest counting number into which both 10 and 15 will divide with no remainder?

90 [ctg num] 75 [outfits] 189 14 [legs] 2 [diagonals] 30

Extra Problem – Only if Needed What is the sum of the units digit of forty-three and the tens digit of eighty-seven?

11

“Math is Cool” Championships – 2008-09

Final Score:

KEY


School Name__________________________________Team #________

First Score


STUDENT NAME________________________________Division: Individual Contest – Score Sheet DO NOT WRITE IN SHADED REGIONS Answer 1 2 3 4 5 6 7 8 9 10

0

11 12 13 14 15 16 17 18 19 20

6 [fish]

7 [hours] 25 [ft2] 36 [in] 164 5 [greenhouses] 40 [cents] 46 135 [bags] 2 [cm]

23 4 [apples] 8 [bacteria] 30 [ft2] 6 [ways] 3 [heads] 34 7 [days] BCDAE [in that order]

1 or 0 1 or 0

Answer 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

40 6 [ways] 18 Circle 9135 73 Sunday 60 [miles] 15 12/20 [6/10 or 3/5 or equiv] 18 188 500,000 128 [yd2] 72 2550 11/25 [or .44] 44 [triangles] 56 [games] 12/36 [6/18 or 3/9 or 1/3 or equiv]

1 or 0

1 or 0

“Math is Cool” Championships – 2008-09 4th Grade – March 19, 2009

Final Score:

KEY


First Score

(out of 18)




Answer

1 2 3 4 5 6 7 8 9 10

B A D D E [14 cups] B D B D

-1, 0 or 2

-1, 0 or 2


Final Score:

KEY


First Score

(out of 20)




Answer

1 2 3 4 5 6 7 8 9 10 10

28 [shoes] 83 [pages] 8 [buttons] [$] 5.85 b 18465 3, 4 [biscuits] [either order] 36 [times] 1/5 [or equiv frac] [#] 41

2 or 0

2 or 0

“Math is Cool” Championships -- 2008-09 4th Grade – March 19, 2009

KEY

School:_______________________________Team #________ Proctor: ______________________________ Room #_______Div PRACTICE RELAY Answer for person

Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

5

11

2

13

1 or 0

1 or 0

1 or 0

2 or 0

RELAY # 1 Answer for person

Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

15

165

33

363

1 or 0

1 or 0

1 or 0

2 or 0


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

27

87

11

242

1 or 0

1 or 0

1 or 0

2 or 0

“Math is Cool” Masters – 2008-09 4th Grade – May 16, 2009 Individual Contest

GENERAL INSTRUCTIONS applying to all tests:





“Math is Cool” Masters – 2008-09 4th Grade – May 16, 2009 Individual Contest

Record all answers on the colored cover sheet.

1 2 3 4 5 6 7 8 9 10 11 12 13

Josh ran 12 yards. How many feet did he run?

14 15 16 17 18 19 20 21

Evaluate 1.23 + 0.69 − 0.04 , and give your answer as a decimal.

Write the number that has a 1 in the tens place, an 8 in the thousands place, a zero in the ones place, and a 5 in the hundreds place. How many counting numbers (positive whole numbers, also called natural numbers or positive integers) are bigger than 7 but smaller than 20? What is the value of 1 × 2 × 1 × 2 × 1 ? On a digital clock showing only the hour and the minute, what is the sum of the digits showing at 10 minutes before noon? What value of x makes the following equation true? 12 + 3 + 8 = 1 + 6 + x

Emma has one quarter, three pennies, and two nickels. How many cents does she have? (Note: Answer in cents, not dollars.) What is the largest counting number less than 10000? Barry weighs twice as much as Larry. When Larry stands on the scales holding his 5-kilogram cat Harry, together they weigh 20 kilograms. How many kilograms does Barry weigh? Let A = 14 − 8 and B = 5 ÷ 5 . What is A + B ? Only giraffes and ostriches are feeding on a savanna. If there are 30 legs and 8 heads, how many giraffes are on the savanna? Each of 79 boxes has 50 cookies in it. How many cookies are there in all the boxes? How many of the following six values are odd? 714

8887

100

(7 × 5)

(1 + 1 + 1 + 1)

(7 − 3 + 7 − 3)

Ruthie wanted to add the first 9 counting numbers, but she mistakenly left out one of the numbers. Otherwise, she added correctly, and got a sum of 37. What number did she leave out? What is the median of the following set of 7 values? 18, 77, 43.5, 9, 0.567, 1/2, 25.4 Milly gets paid 25 cents for every newspaper she delivers. How much money, in dollars, will she get paid for delivering 42 newspapers? Find the value of 18 + 18 + 18 + 18 + 18 + 19 + 19 + 19 + 18 + 18 . How many prime numbers are less than 10? (A prime number is a counting number than can be divided without remainder by exactly two numbers, itself and 1.) Anna has four M&Ms (two red, one yellow, and one blue), which are identical except for color. In how many distinct (different) orders can Anna eat her M&Ms if she eats them one by one? When my number is divided by 7, the remainder is 3. When my number is divided by 5, the remainder is 4. Find my number if it is greater than 10 but less than 50.

22 23 24

25 26

A sponge can soak up 5 times its weight in water. A fully soaked sponge weighs 30 ounces. How many ounces does the sponge weigh when dry? Miya bought some apples at the grocery store. She gave 1/2 of her apples to John, who then gave 2/5 of these apples to Henry. Henry got 6 apples from John. How many apples did Miya buy at the store? Two counting numbers, each a multiple of 3, are multiplied together. Give the letters of all of the following statements that must be true of the product. (If none of the statements must be true, answer “none”.) A) The product is even. B) The product is odd. C) The product is a multiple of 3. D) The product is a multiple of 6. E) The product is a multiple of 9. Linda has 36 books that are either math books or cookbooks. She has 6 more math books than cookbooks. How any cookbooks does she have? In an arithmetic sequence or addition pattern, you add the same B amount to each term to get the next term. The first term of a certain arithmetic sequence is 8 and the third term is 19. What is the seventh term of this sequence? A

D

C

27

Find the number of square inches in the area of triangle ABC, given that AD is 5 inches, BD is 6 inches, and CD is 13 inches. BD forms a right angle with AC.

28

Katie is going to sell lemonade at a lemonade stand. Each pitcher of lemonade requires one and a half lemons and 2/3 cups of sugar. If she wants to use a whole number of lemons and full cups of sugar, what is the smallest number of pitchers of lemonade Katie could make? When I add one more than my number to five times my number, the sum is 25. What is my number?

29 30

When a counting number is selected at random from the first 99 counting numbers, what is the probability that it can be divided by 5 with no remainder? Give your answer as a fraction.

Challenge Questions 31 32 33 34 35

Biff is riding his bike from his house to Eho’s house to study math. Biff has ridden 8 miles plus two-thirds of the total distance, and still has 5 miles to go. How many miles is it from Biff’s house to Eho’s house? Alice and Bertie are skipping rocks across a pond. Alice’s rock bounces every 6 inches and Bertie’s rock bounces every 8 inches. The pond is 25 feet wide and both rocks make it across, starting and ending at the same time and place. How many times will the 2 rocks be touching the water at the same time? Helen only likes numbers that are multiples of 13, and Ellen only likes numbers whose units digit (ones place digit) is 1. What is the second smallest positive number that Helen and Ellen both like? Randy and Alex are racing bikes around a circular track 800 meters long. If Randy bikes one and one-fourth times as fast as Alex, but Alex has a 500 meter head start, how many laps will it take for Randy to catch up with Alex? Assume that Randy bikes at a rate of 8 meters per second, and that Randy and Alex start at the same time and bike in the same direction. If your answer is not a whole number, give it as a decimal. A fast clock is set correctly at 12:00 noon, but it gains 4 minutes an hour. What will be the correct time when the fast clock next shows 12:00 midnight?

36 37 38 39 40

If a rectangle has a perimeter of 30 inches and the length is 3 inches more than twice the width, what is the area of the rectangle, in square inches? Originally, Rosa had only red marbles and Billy had only blue marbles. First, Rosa gave half her marbles to Billy. Then Billy gave half his blue marbles to Rosa. Finally, Rosa gave half her blue marbles to Billy. Now Billy has 11 marbles (5 red and 6 blue). How many marbles does Rosa have now? Jamie and Julie are on a roller coaster ride at Silverwood Park. The probability that Julie will let go of the bar is 1/3. When riding alone, Jamie will scream with a probability of 1/4. However, when they ride together, the probability that Jamie screams is doubled if Julie lets go of the bar. As a reduced fraction, what is the probability that Jamie screams when the two ride together? Before it performs calculations, my Enlarging Calculator automatically adds 77 to every even number I enter and triples every odd number I enter. It calculates correctly, using the enlarged numbers, then correctly displays the results of its calculations. I enter a 2-digit counting number, then “+”, then a second 2-digit counting number. The calculator displays the sum “146”. What is the largest possible number I could have entered? A cube three inches on an edge is made from white unit cubes, each one inch on an edge. I want to paint as many of the unit faces blue as possible, but no two blue unit faces can share a side. It's OK for blue unit faces to touch diagonally, however. (See the NOT ALLOWED NOT ALLOWED diagrams for examples.) Find the largest number of unit faces of this cube that I can paint blue. ALLOWED

“Math is Cool” Masters – 2008-09 4th Grade – May 16, 2009 Team Multiple Choice Contest - Scenario

MOSES LAKE BALLOON FESTIVAL

May 17-25, 2009

Welcome to the 38th annual Moses Lake Balloon Festival, an international celebration of hot-air balloons! Since its first year with 13 balloons, the Festival has increased in size every year to over 600 balloons in 2009. During the Dawn Patrol, volunteer pilots test the wind speed and direction at different heights above ground. A Mass Launch is when all balloons launch within a short time. For a Glow Show, balloons are lit from inside to glow in the dark. In Flying Contests, pilots must drop markers on targets to win prizes. The “Shapes” display is for balloons with special shapes. SCHEDULE

Sat 5/17

Sun 5/18

Mon 5/19

Tu 5/20

Wed 5/21

Th 5/22

Fri 5/23

Sat 5/24

5:15-6:30 AM 6:30-8:00 AM 8:00-10:00 AM 5:00-6:00 PM 6:00-8:00 PM 8:00-9:00 PM

Dawn Patrol Mass Launch


Dawn Patrol

Dawn Patrol

Flying Contest

Dawn Patrol ‘Shapes’ Display Flying Contest

Dawn Patrol ‘Shapes’ Display Flying Contest


Flying Contest

Dawn Patrol Mass Launch Flying Contest

GasRace* starts Glow Show

Glow Show

Glow Show

Glow Show

Glow Show

Fireworks

Fireworks

Fireworks

Fireworks

Fireworks

*GasRace: Pilots in helium balloons try to see who can get farthest before touching down. Results of the 2008 race are given below (some results missing). Assume all flight for a balloon is in the same direction. Balloon name Fire-Fly Uplift Joyride Light Show

Time aloft 40 hr 70 hr 68 hr

Distance 1080 km 1295 km

Questions are on next page.

Ave. speed

TICKET PRICES Half-day: $5 Full day: $8 9-day pass: ??

Sun 5/25 Dawn Patrol Mass Launch

N W

E

S

RANK

Date & Time 5/17/09 6:00 AM

Wind speed 5.0 mph

Wind direction SE (140°)

“Math is Cool” Masters – 2008-09 4th Grade – May 16, 2009 Team Multiple Choice Contest - Questions

MOSES LAKE BALLOON FESTIVAL

1 2 3 4 5 6 7 8 9

May 17-25, 2009

In what year was the first annual Moses Lake Balloon Festival? A) 1971 B) 1972 C) 1973 D) 1983 E) Answer not given. Kathy’s family will go to the Festival for 3 days in a row, and Kathy gets to choose the dates. However, it is impossible for Kathy to choose the dates so that she can see her favorite event 3 times. What is Kathy’s favorite event? A) Glow Show B) Dawn Patrol vC) Mass Launch D) Flying Contest E) Fireworks Gordon wants to see at least 3 Mass Launches, 2 Glow Shows, 1 Shapes Display, and 3 Flying Contests. Gordon must attend the Festival for at least how many different days? (The days he attends do not need to be consecutive.) A) 9 B) 4 C) 3 D) 6 E) Answer not given. A half-day ticket gets you into either all AM events or all PM events for one day. If the 9-day pass saves you $10 over the cheapest combination of half-day and full-day tickets that would allow you to attend the entire festival, how much does a 9-day pass cost? A) $50 B) $60 C) $62 D) $40 E) Answer not given. In every year of the Festival, the number of participating balloons has been a multiple of the original number. What is the smallest number of balloons that could be participating in 2009? A) 601 B) 494 C) 611 D) 507 E) Answer not given. In the 2008 GasRace, Uplift averaged 3 kilometers (km) per hour more than Light Show’s average speed, which was 2.5 km per hour more than Joyride’s average speed. How long was Uplift aloft, to the nearest whole hour? A) 51 hr B) 50 hr C) 24 hr D) 45 hr E) Answer not given. Fire-Fly’s average speed in the 2008 GasRace was 4 km/hr less than the highest average speed of any of the four balloons. Fire-Fly’s total distance was how many km less than the first-place winning distance? A) 800 B) 495 C) 628 D) 680 E) Answer not given. If each Dawn Patrol has 12 balloons, five with 2 pilots and the rest with 1 pilot each, what is the total number of pilot-hours spent on Dawn Patrol during the festival? Round to the nearest whole hour. (A pilot-hour is one hour of one pilot’s time.) A) 21 B) 191 C) 135 D) 153 E) Answer not given. There are 200 balloons with special shapes. They launch in groups, each group taking 4 minutes to launch. All groups have the same number of balloons (N), except the last group (which may have fewer balloons.) The first group begins its launch at the start of the Shapes Display (and finishes 4 minutes later). If each group begins to launch as soon as the previous group has finished launching, what is the smallest value of N that would allow all “shapes” balloons to be completely launched and in the air by 7:15 AM? A) 18 B) 9 C) 19 D) 38 E) Answer not given.

“Math is Cool” Masters – 2008-09 4th Grade – May 16, 2009 Team Contest

1

What point on a number line is halfway between 14 and 38?

2

Each face of a 2 × 2 × 2 inch cube has been marked off in four equal unit squares, 2 1 which are numbered 1 through 4, as shown. You can see three faces of the cube in 3 4 1 the figure. For the faces you can’t see, each unit square is numbered the same as 2 1 2 3 the unit square exactly opposite it. (For example, the unit square on the bottom 4 3 4 face that is directly beneath the square labeled “4” on the top face will also be labeled “4”.) At each corner, we can calculate the “corner sum” by adding the numbers of the 3 unit squares that meet at that corner. List all whole number values from 3 through 12 inclusive that cannot be a corner sum for this cube.

3

Josh worked for 4 hours. He spent

1

of his earnings from this job to buy candy, and then put $7 2 in his savings account. He then had $9 of his earnings left. How much (in dollars) did Josh earn per hour for this job?

4

Patricia is adding 7s and 17s together. She gets a sum of exactly 100. How many numbers did Patricia add together to get this sum?

5

A slow clock loses 4 minutes per hour. A fast clock gains 2.5 minutes per hour. Both clocks were set to the correct time at noon. By 2 PM that day, the fast clock will be how many minutes ahead of the slow clock? (If your answer is not a whole number of minutes, give it as a decimal.)

6

For every 2 blueberries Cathy eats, Denise eats 3. When Cathy has eaten 60 blueberries, how many blueberries has Denise eaten?

7

In Gridtown, the streets are all 2-way and run either north-south or east-west, one block apart in each case. From his house, Colin went searching for a coffee shop. He drove along the streets 18 blocks north, then 7 blocks east, then 4 blocks south, then 11 blocks west. There he stopped for a cup of coffee. He then drove back home along the streets by the shortest route. How many blocks long was Colin’s return trip from the coffee shop to his house?

8 9

What is the difference between the largest and the smallest possible value of the following expression, when one of the @ symbols is replaced by an addition symbol, and the other two @ symbols are replaced by multiplication symbols? 1@2@3@4 There is a glitch in the display of my calculator. When I enter a number with three or more digits, it randomly selects two of those digits and adds 2 to each of them before displaying the entry. (For example, if I enter “123”, it will display either 145, 343, or 325.) When I entered the same 3digit counting number twice, the display showed 647 the first time and 629 the second time. What number did I enter?

10

In a particular year, March had 5 Fridays. If this was not a Leap Year, January 1st could only have been on what day or days of the week? Give the names of all possible days of the week.

“Math is Cool” Masters – 2008-09 4th Grade – May 16, 2009 Relay Contest

RELAYS - 5 minutes per relay There is no talking during this event and you must always be facing forward. Person #1 will be given an answer sheet(s) and will need to fill out the top. The proctor will hand out a strip of paper to each person. These need to be face down on your desk until it is time for the relay to start. Once the relay begins, everyone may turn over their strip of paper and begin working. You may write on the strip of paper to come up with your answer. However, when person #1 figures out his/her problem, he/she will record just his/her final answer on the answer sheet and pass only the answer sheet back to the person behind. This continues until person #4 puts an answer on the answer sheet and gives it to the proctor. A correct answer from person #1, #2 and #3 is worth 1 point each. A correct answer from person #4 is worth 2 points making each relay worth 5 points. You will see the expression TNYWG [Proctor: write this on the board] which means: “the number you will get”. This is where you put your teammate’s answer that they pass back to you, and then you should be able to solve your question. Once the relay begins, turn over your strip of paper and make sure you have the right person number. Remember, no talking and remain facing forward to avoid being disqualified!

Person 1

Relay #1

Answer

Find the number of square inches in the area of a rectangle with side lengths 3 inches and 5 inches. Multiply TNYWG by the sum of 4 and 8.

15 [sq in]

Person 2 Person 3 Double TNYWG, then multiply by 5. Person 4 How many days are equal to TNYWG hours? Person 1 Person 2 Person 3 Person 4

180 1800 75 [days]

Relay #2

Answer

A painter can paint a shed in 4 hours. At this rate, how many sheds can 4 painters paint in 10 hours? A baker is carrying TNYWG dozen bagels to his display case, but he trips and drops one-third of them. How many bagels does he have left? There are only cows and chickens in a field. If there are eight cows and TNYWG legs, how many chickens are there in the field? How many positive whole numbers will divide into TNYWG with no remainder?

10 [sheds] 80 [bagels]

24 [chickens] 8 [numbers]


School Name_________________________________Team #________

Final Score:

KEY

Proctor Name_________________________________Room #_______ Division:

Mental Math Contest

MENTAL MATH - 30 seconds per question

PERSON 1 NAME:

1.1 1.2 1.3 1.4

1 or 0

Find the sum of 27 and 18.

45

How many ways can I arrange the letters in the word “May”, spelled M-A-Y, if the capital M must come first? When counting backwards from 100 by 13s, the first number I say is “100”. What is the next even number I will say? What is the area, in square meters, of a square that is just large enough to enclose a circle of radius 10 meters?

2 [ways] 74 400 [sq m]

PERSON 2 NAME:

2.1 2.2 2.3 2.4

What is the sum of 6 plus 3 more than 6?

15

Wendy has 8 boxes with 5 bags in each box. Each of the bags holds the same number of pearls. If Wendy has a total of 120 pearls in all her boxes, how many pearls are in each bag? How many meters are in two point three one kilometers?

3 [pearls]

What is the difference in inches between the perimeter of a regular pentagon with sides of length 10 inches and the perimeter of a regular triangle with sides of length 7 inches?

29 [inches]

2310

PERSON 3 NAME:

3.1 3.2 3.3 3.4

How many seconds are in 3 minutes?

180 [sec]

A shelf in my kitchen has 3 spotted cups, 5 striped cups, and 1 checkered cup. If I select a cup at random, what is the probability that it will be spotted? Give your answer as a reduced fraction. If fifty-three plus X is equal to seventy, then what is seventy plus X?

1/3

My number has two digits. If the sum of these two digits is less than 10, what is the largest my number can be?

90

87

PERSON 4 NAME:

4.1 4.2 4.3 4.4

What is 555 divided by 5?

111

Find the largest whole number that can divide into both 48 and 60 with no remainder in either case. Evaluate: twenty point four plus thirty point five plus ten point two. If your answer is not a whole number, give it as a decimal. The day after tomorrow is a Sunday. What day of the week will it be twelve days after today?

12 61.1 Wednesday

“Math is Cool” Masters – 2008-09 May 16, 2009


1

Problem

Answer Farmer John is baling hay. He makes five bales. Three bales 48 [pounds]

weigh forty pounds each, and two bales weigh sixty pounds each. What is the average weight in pounds of the five bales of hay? 8:40 PM What time is it thirty-five minutes before 9:15 PM?

2 3 The area of a rectangular playground is four thousand eight

80 [feet]

4

2 [mph]

5 6 7 7 8

hundred square feet. The length of one side is sixty feet. In feet, what is the length of the other side? Biff wanted to walk to Grandma’s house thirty miles away in ten hours. For the first five hours Biff walked at 4 miles per hour. What average speed, in miles per hour, does Biff need to travel in the remaining time to make it to Grandma’s house in ten hours from when he started? The measures of two angles in a triangle are 17 degrees and 53 degrees. What is the degree measure of the third angle? The product of three positive counting numbers is four hundred. What is the largest possible value of any of these three numbers? The radius of a circle is 22 inches. What is the number of inches in the diameter of the circle?

110 [degrees] 400

44 [inches]

Extra Problem – Only if Needed The perimeter of a quadrilateral is 47 feet. The lengths of three sides are 15 feet, 10 feet and 20 feet. What is the length of the fourth side, in feet?

2 [feet]




Problem

1

Today Biff is five years older than Eho and the sum of their ages is twenty-three years. In years, what will the sum of their ages be ten years from now? If I ate one apple every six hours, how many apples would I eat in one week? The sum of seven, eight, eleven and another number I am thinking of equals thirty. What is the number I am thinking of? My birthday was Wednesday. What day of the week is nine days before my birthday? How many zeros are need to write the numeral one thousand? The product of two different counting numbers is 11. What is the sum of these two numbers? Sally picked eleven flowers. Six of the flowers had five petals, three of the flowers had four petals, and the rest had three petals. How many petals total were on all the flowers she picked?

2 3

4 5 6 7

7.1 8

Answer 43 [years]

28 [apples] 4

Monday 3 12 48 [petals]

Extra Problem – Only if Needed What is the smallest whole number into which both twenty-one and fourteen will divide with no remainder?

42




Problem

1

When two lines cross each other, they are said to “intersect”. At most, how many times can a triangle and a square intersect? The product of seven and eight is equal to the product of four and what number? Miya has seven US coins worth exactly forty-nine cents. How many nickels does Miya have? The wool from five sheep can make nine coats. At this rate, you would need the wool from how many sheep to make twenty-seven coats? In the sequence of letters M-A-T-H-M-A-T-H-M-A-T and so on, what is the twenty-fifth letter? On a fishing trip in Alaska, Helen caught thirty-six salmon, and now she needs to ship her catch home. Each crate holds four and one-half salmon. How many crates are needed to ship the catch home, if Helen is willing to cut her salmon in half? Each of Matt’s superhero costumes consists of one cape and one mask. If Matt has 7 different capes and can make 63 different superhero costumes, how many different masks does he have?

2 3 4

5 6

7

7.1 8

Answer 6 [times]

14 0 [or “none”] 15 [sheep]

M 8 [crates]

9 [masks]

Extra Problem – Only if Needed The sum of two numbers is twenty-five, while the difference between the two numbers is one. What is the smaller of the two numbers?

12


Final Score:

KEY


School Name__________________________________Team #________

First Score



36 [feet] 8510 12 [numbers] 4 7 16 38 [¢] [NOT $0.38] 9999 30 [kilograms] 7 7 [giraffes] 3950 [cookies] 2 [values] 1.88 8 18 [$] 10.50 183 4 [prime numbers] 12 [orders]

1 or 0 1 or 0

Answer 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

24 5 [ounces] 30 [apples] C, E [either order] 15 [cookbooks] 41 54 [in2] 6 [pitchers] 4 19/99 39 [miles] 12 [times] 221 3.125 [laps] 11:15 PM 44 [in2] 7 [marbles] 1/3 36 22 [faces]

1 or 0

1 or 0


Final Score:

KEY


First Score

(out of 18)




1 2 3 4 5 6 7 8 9 10

Answer B C E [5] A C D C B C

-1, 0 or 2

-1, 0 or 2


Final Score:

KEY


First Score

(out of 20)




Answer

1 2 3 4 5 6 7 8 9 10 10

26 4, 11 [either order] [$] 8.00

or [$] 8

10 [numbers] 13 [minutes] 90 [blueberries] 18 [blocks] 15 427 Sun, Mon, Tues [any order]

2 or 0

2 or 0


KEY


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

15

180

1800

75

[sq in] 1 or 0

[days] 1 or 0

1 or 0

2 or 0


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

10

80

24

8

[sheds]

[bagels]

[chickens]

[numbers]

1 or 0

1 or 0

1 or 0

2 or 0

“Math is Cool” Championships-2003-04 4th Grade - March 12, 2004 Individual Contest

Express all answers as reduced fractions unless stated otherwise. Leave answers in terms of π where applicable. Do not round any answers unless stated otherwise. Record all answers on the colored cover sheet. 1

823 + 782

2

What is the sum of the number of letters in MATH and the number of letters in ADD?

3

Evaluate 3 + 3 - 3 + 3 - 3 + 3 - 3

4

What is the sum of the first five positive integers?

5

If there are nine people standing in three even lines, how many people are in each line?

6

If Kai rides his bike for 5 hours, traveling 100 miles, what is his average speed in miles per hour?

7

What is 7 x 6 x 2 ÷ 12?

8

Round to the nearest tenth: 31.259

9

Evaluate 4 × 5 × 3

10

How many inches are in 5 feet?

11

What is the perimeter of a square with side length 15 feet?

12

If today is Friday, what day is it 78 days from now?

13

What is 75% of 16?

14

If Kai runs a 6-minute mile, and Teddy runs a 8-minute mile, how many more miles will Kai run in 48 minutes?

15

Which is larger, eight-fifths or five-eighths?

16

The ratio of cows to sheep on a ranch is 3 to 5. If there are 120 cows on the ranch, how many sheep are there?

17

My number has a remainder of 1 when divided by 2. My number is less than 90 but greater than 65. My number is a multiple of 7. Find my number.

18

If Kai says “Math” every 4 minutes, Teddy says “Is” every 5 minutes, and Peter says “Cool” every 8 minutes, in how many minutes will they say “Math Is Cool” together after they start together?

19

A white car has no muffler. It annoys people who hear it 3/4 of the time. The probability Mikey will hear the car on any given day is 1/2. What is the probability that Mikey will be annoyed by the white car tomorrow?

20

What is 3 hours, 47 minutes after 9:35 am?

21

Find the smallest whole number that when added to 830 makes a sum greater than 1000.

22

Find the largest 5-digit even palindrome.

23

Person A says the number 122. Person B says 11,222. Person C says 1,112,222. Following this pattern, what would Person D say?

24

A is a circle with a radius of 7 inches, and B is a circle with a diameter of 10 inches. Which is larger in area, A or B, or are the areas the same?

25

If a robot makes 2 cars in 3 days, how many days does it take 3 robots to make 12 cars?

26

Take the smallest 3-digit number which has all its digits different. Then rearrange these three digits to form the largest possible 3-digit number.

27

If 51 more than my number is 50, what is my number?

28

What is the area of a square with perimeter 24?

29

Find the number of centimeters difference between the perimeter of a regular octagon of side length 9 centimeters and the perimeter of a regular hexagon of side length 7 centimeters.

30

Colin has math, science, and English textbooks. Colin has three times as many math textbooks as science text books and seven more science textbooks than English textbooks. Assuming he has at least one of each textbook, what is the least number of math textbooks he could have?


Find the volume, in cubic centimeters, of a rectangular prism with a base area of 12 square centimeters and a height of 4.5 centimeters.

32

Lee rolls two standard dice. Find the probability that the product of the showing numbers is greater than 1.

33

Libber takes a rectangle and divides it in half. If the two resulting figures are squares with area 36, what is the perimeter of the rectangle?

34

One third of Lakeisha’s shirts are red, one fourth of her shirts are white, and one sixth of her shirts are purple. If Lakeisha has only red, white, purple and green shirts, and Lakeisha has 36 shirts total, how many green shirts does she have?

35

The number of restaurants in Mathington doubles every five years. How many times more restaurants will there be in 20 years than there are now?

36

Let a + b = a × b - 2a/b. What is 27 + 3?

37

12 cubes are placed together to form a rectangular solid two cubes by two cubes by three cubes. If the entire outside of the rectangular solid is painted and the solid is taken apart into the 12 individual cubes, what is the total number of faces of the cubes that remain unpainted?

38

With 2 dice, what is the probability of rolling a sum of 6 or 8?

39

Lee is taking a math test. There are 40 questions on the test. He gets 6 points for every correct response, 1.5 points for leaving a question blank, and no points for an incorrect response. If Lee leaves 15 questions blank, how many of the remaining questions would he have to get correct in order to get 130.5 points?

40

At Mt. Rainier High School “D” students are on the debate team, “C” students are on the chess team, and “M” students are on the math team. “X” students are on the math team and the debate team, “Y” students are on the chess team and the debate team, and “Z” students are on the math team and chess team. “A” students are on all three teams. In terms of M, X, Z, and A, how many students are only on the math team?

“Math is Cool” Championships-2003-04 4th Grade - March 12, 2004 Team Multiple Choice Contest

Road

Speed Limit in miles per minute

A

2

B

1

C

2

D

2

E

1

F

1

G

1

The map above is a picture of the roads Mr. Sampson can take to get to school. Each morning he starts from his house and only travels west, southwest, or south. He always drives the speed limit. 1

What is the length of road D? A.12 B.13 C.14 D.15 E. 16

2

How many total miles of road are there on the map above? A. 120 B. 126 C. 128 D. 136 E. Answer not given

3

How long in minutes does is take Mr. Sampson to get from one end of road A to the other end of road A? A. 36 B. 9 C. 18 D. 14 E. Answer not given

4

If Mr. Sampson is traveling 75 miles per hour on road G, how many miles above the speed limit is he traveling, in miles per hour? A. 10 B. 15 C. 20 D. 45 E. Answer not given

5

On his way to school, Sampson notices that all the land enclosed by Roads D, E, F, and G is for sale. If he buys it, how many square miles of land will he have purchased? A. 48 B. 24 C. 96 D. 60 E. Answer not given

6

Sampson is in a hurry one morning, and roads D and F are both closed due to construction. What is his fastest route to school? A. Road A to Road B B. Road A to Road C to Road B C. Road A to Road E to Road B D. Road G E. Answer not given

7

Assuming he only travels toward the school, what is the difference between the maximum number of miles Sampson could take to school and the fewest number of miles Sampson could take to school? A. 8 miles B. 10 miles C. 12 miles D. 14 miles E. Answer not given

8

Sampson signs up for the Neighborhood Road Patrol. As a member, he must drive every mile of road looking for downed power lines and trees. Assuming he always travels to school by turning west, southwest, or south, what is the fewest number of days Sampson will need to drive to school to have driven every mile of road? A. 6 days B. 5 days C. 8 days D. 7 days E. Answer not given

9

Because it’s the day before summer, Mr. Sampson isn’t thinking about his driving. If he takes a random direction at each intersection he comes to, and he always turns west, southwest or south, what is the probability he finds himself at the intersection of roads A and B? A. 1/2 B.1/6 C. 1/9 D. 1/18 E. Answer not given

“Math is Cool” Championships-2003-04 4th Grade -March 12, 2004 Team Contest Express all answers as reduced fractions unless stated otherwise. Leave answers in terms of π where applicable. Do not round any answers unless stated otherwise. Record all answers on the colored cover sheet. 1

Sampson uses i ncorrect grammar 3/4 of the ti me. 1/2 of the remai ni ng ti me, he i s di scussi ng mathemati cs. What percentage of the ti me does Mr. Sampson use correct grammar w hen not di scussi ng math?

2

Ni ki i s four years older than Kei sha. Matt i s three years older than Ni ki . If Kei sha i s 18 now , how many years old w as Matt 10 years ago?

3

Mi ke plays “Worms” 5 hours a day. Aaron plays “Jedi Kni ght” 3 hours a day. Bri an plays “Crystal Chroni cles” 13 hours a day. How many hours of vi deo games do they play i n a w eek, i f Mi ke plays 5 days a w eek, Aaron plays 7 days a w eek, and Bri an plays 2 days a w eek?

4

Fi nd the sum of the next three numbers i n the follow i ng sequence: 1, 5, 9, 13, 17, __, __, __

5

Shaun makes a rectangular cake that has si de lengths 9 i nches and 18 i nches. Ki ersten greedi ly eats a square out of the mi ddle of the cake that has si de lengths of 3 i nches. What i s the area of the remai ni ng cake?

6

On Valenti ne’ s Day (February 14), Di ego buys Kelly one rose for each thi ng he loves about her. Kelly reali zes the number of roses i s 3 ti mes the number of days si nce she met Di ego i ncludi ng today and the day they met. If Kelly and Di ego met on January 11, how many thi ngs does Di ego love about Kelly?

7

Peter meets three new people each day at camp. If he i s at camp for a total of 14 days, how many new people does he meet at camp?

8

Mi chelle sets her alarm clock for 6:00 am but alw ays hi ts the snooze button and sleeps i n unti l 6:13. Mi chelle has to leave for school at 7:35 am. It takes her 15 mi nutes to show er, 12 mi nutes to blow dry her hai r, 13 mi nutes to get dressed and do her make-up, and 10 mi nutes to eat breakfast. If Mi chelle spends the remai ni ng ti me readi ng the new spaper, how many mi nutes does she have each morni ng to read the new spaper?

9

Di ego i s bui ldi ng a tree house. It takes 35 boards to bui ld the floor and 17 nai ls per board to attach them. If he can dri ve i n 5 nai ls per hour , how long, i n hours, w i ll i t take to nai l dow n the floor?

10

Fi nd the product of 456 and 789.

Person #1 Practice Relay

Evaluate 2 x 3

6


Evaluate TNYWG - 3 + 7

10


Find TNYWG divided by 2

5


Five times TNYWG

25

Person #1 Relay #1

Evaluate: 15 - 9 + 4 + 6

16

Person #2 Relay #1

TNYWG divided by the number of miles a car going 2 miles per minute will travel in 2 minutes.

4

Person #3 Relay #1

TNYWG plus the fourth positive odd number.

11

Person #4 Relay #1

Evaluate: 5 × TNYWG × 3

165

Person #1 Relay #2

Find number of sides in a hexagon plus the number of faces on a standard die.

12

Person #2 Relay #2

TNYWG plus 5 × 5

37

Person #3 Relay #2

TNYWG minus the total number of dots on a standard die

16

Person #4 Relay #2

17 + the number of feet in three yards + TNYWG

42

Practi ce Relay Person#1 Evaluate 2 x 3




Practi ce Relay Person#2 Evaluate TNYWG - 3 + 7




Practi ce Relay Person#3 Fi nd TNYWG.di vi ded by 2




Practi ce Relay Person#4 Fi ve ti mes TNYWG




Relay #1 Person#1 15 - 9 + 4 + 6

Relay #1 Person#1 15 - 9 + 4 + 6

Relay #1 Person#1 15 - 9 + 4 + 6

Relay #1 Person#1 15 - 9 + 4 + 6

Relay #1 Person#2 TNYWG di vi ded by the number of mi les a car goi ng 2 mi les per mi nute w i ll travel i n 2 mi nutes.




Relay #1 Person#3 TNYWG plus the fourth posi ti ve odd number.




Relay #1 Person#4 Evaluate: 5 × TNYWG × 3




Relay #2 Person#1 Fi nd number of si des i n a hexagon plus the number of faces on a standard di e.

Relay #2 Person#1 .Fi nd number of si des i n a hexagon plus the number of faces on a standard di e.



Relay #2 Person#2 TNYWG plus 5 × 5




Relay #2 Person#3 TNYWG mi nus the total number of dots on a standard di e




Relay #2 Person#4 17 + the number of feet i n three yards + TNYWG




“Math is Cool” Championships-2003-04 4th Grade - March 12, 2004 Mental Math Contest

Express all answers as reduced fractions in terms of radicals and π, where applicable, unless otherwise instructed. Person #1 1

Evaluate: 4 ti mes 3 plus 4.

16

2

How many di mes are i n tw o dollars and si xty cents?

26 [di mes]

3

What i s one fourth of 12?

3

4

What i s the area of a rectangle w i th si des of lengths 3 and 5?

15[uni ts2]

Person #2 1

Evaluate: 5 halves ti mes four.

20/2, 10

2

If Teddy has four blue socks, 3 green socks, and 7 red socks i n a draw er, how many socks must he draw out randomly to ensure a matchi ng pai r?

4 [socks]

3

Kei sha shoots an average of four free throw s i n each basketball game. If she plays i n 25 games, how many free throw s does she shoot total?

100 [free throw s]

4

What i s the area of a square w i th si de length 2?

4[uni ts2]

Person #3 1

What i s 1 half plus 2 fourths?

1, 2/2, 4/4

2

If Kai has fi ve dollars and gi ves tw o dollars and si xty cents to Peter, how much does he have left, i n dollars?

[$] 2.40

3

What i s the area of a tri angle w i th base 4 and hei ght 8?

16

4

In 1 hour, how many ti mes could a car dri vi ng 30 mi les per hour travel around a ci rcular track 2 mi les long?

15 [ti mes]

Person #4 1

What i s the quoti ent of 42 and 3?

14

2

What i s the volume of a cube w i th si de length 2?

8[uni ts3]

3

If today i s Fri day, w hat day w i ll i t be 22 days from now ?

Saturday

4

What i s 10 percent of 20?

2

“Math is Cool” Championships-2003-04 4th Grade - March 12, 2004 College Knowledge Bowl Questions #1 1

How many zeros are in the product of one hundred eighty thousand and one thousand.

7[zeros]

2

Andy wants to buy 5 cookies at 15 cents and 2 muffins at 35 cents. If he pays for these items with a ten dollars bill, how much change should he get back in dollars?

3

What is the time three-quarters of an hour before 3 PM?

2:15 PM

4

Subtract the smallest 4-digit whole number from the smallest 5-digit whole number.

9000

5

Lewis rolls a standard six-sided die. What is the probability that the number showing is greater than 4?

1/3 or 2/6

6

Twenty seconds is what fraction of a minute?

1/3

7

At a race where people have a choice between racing on unicycles, which have 1 wheel, and racing on bicycles which has two wheels, Colin counts 20 wheels and 12 heads. How many bicycles are there?

8 [bicycles]

[$] 8.55

Number 8 is an extra question. Only use it if needed. 8

Find the sum of the different prime factors of 12.

5

“Math is Cool” Championships-2003-04 4th Grade - March 12, 2004


A regular pentagon has a side length of three inches. If two congruent pentagons this size are placed together along a side without overlapping, how many inches will be in the perimeter of the new figure?

24 [inches]

2

The first three numbers of a sequence are 29, 23, and 17. What is the fifth number of the sequence?

5

3

The Big Saltine is a lake with a bottom that is 420 feet below sea level. If a tower 760 feet tall was placed on the bottom of the Big Saltine, how many feet above sea level would the tower’s top be?

340[feet]

4

What is the result when the greatest common factor of 20 and 95 is subtracted from 16.

11

5

Half a puppy’s weight plus 8 pounds is equal to 15 pounds. How many pounds does the puppy weigh?

14[pounds]

6

How much money in dollars do I have if I have 38 pennies and half as many nickels?

[$]1.33

7

What is the result when you reverse the digits of six thousand twenty four, and then add 30.

4236


What is the perimeter of a rectangle if the area of the rectangle is 128 and one side length is two times the other side length.

48

“Math is Cool” Championships-2003-04 4th Grade - March 12, 2004


What is the largest possible number of Mondays in February if it is not a leap year?

4

2

What is the sum of 914 and 782 rounded to the nearest hundred?

1700

3

Susan reads 46 words every 30 seconds. How many words would she read in 10 minutes?

920[words]

4

A class period is 55 minutes long and the teacher talks for 35 minute. If the remaining time is for work on assignments, how many minutes do the students have to work on their assignment?

20[minutes ]

5

Silas, Rupaul and Colinbob are clowns. If all 3 of them want to perform in the circus and only 2 of them will be chosen, how many different combinations of clown pairs could be chosen?

3[combinati ons]

6

Jon runs a mile in 6 minutes and Elise runs a mile in 5 minutes, how many miles will Elise have run by the time Jon has run 10 miles?

12 [miles]

7

The sum of an even number and an odd number is multiplied by the sum of an odd number and an even number. Is the product even or odd?

Odd


Dan Burger sharpens his pencil an average of 20 times a day. How many times would he sharpen his pencil in one week?

140[times]

“Math is Cool” Championships -- 2003-04

Key

4th grade - March 12, 2004 School Name_____________________________Team #________ Proctor Name____________________________Room #_______

Full Name:____________________________________

1st Score


DO NOT WRITE IN SHADED REGIONS Out of 40 Answer

1 or 0

Answer

1 or 0

1 or 0

1

1605

21

171

2

7

22

89,998

3

3

23

111,122,222

4

15

24

A[is larger]

5

3[people]

25

6 [days]

6

20 [mph]

26

210

7

7

27

-1

8

31.3

28

36[units2]

9

60

29

30[centimeters]

10

60[inches]

30

24 [math textbooks]

11

60 [feet]

31

54[centimeters cubed]

12

Saturday

32

35/36

13

12

33

36[units]

14

2 [miles]

34

9 [green shirts]

15

8/5 or eight-fifths

35

16[times more]

16

200 [sheep]

36

63

17

77

37

40 [faces]

18

40 [minutes]

38

5/18 or 10/36

19

3/8

39

18 [questions correct]

20

1:22 pm

40

M-Z-X+A

1 or 0




Key 1st Score

Correct responses are worth 2 points, incorrect responses are worth -1 point and no response is 0 points. Out of 18


1

E

2

B

3

B

4

B

5

A

6

B

7

C

8

A

9

D

-1, 0 or 2

-1, 0 or 2



Key 1st Score

Team Contest-Score Sheet DO NOT WRITE IN SHADED REGIONS Answer

1

12.5[%]

2

15[years old]

3

72[hours]

4

75

5

153 [square inches]

6

105 [things]

7

42[people]

8

32 [minutes]

9

119 [hours]

10

359,784

1 or 0

1 or 0

Out of 10



Relay Contest - Score Sheet Practice relay 6 10 5 25 Answer for relay #1 16 4 11 165 Answer for relay #2 12 37 16 42

Key

“Math is Cool” Masters-2004

Sponsored by: The Swinging Doors and The Accounting Source 4th Grade - May 15, 2004 Individual Contest Express all answers as fractions unless stated otherwise. Leave answers in terms of π where applicable. Do not round any answers unless stated otherwise. Record all answers on the colored cover sheet. 1

Evaluate 375 + 648

2

True or False: 3/5 < 4/6?

3

Evaluate: 4 + 7 × 3 + 2

4

Evaluate: 57 × 49

5

Homer’ s Doughnut Shop has 200 doughnuts to be put i n boxes that hold a dozen doughnuts at a ti me. How many boxes are needed?

6

What i s 1/3 of 1/2 of 2/3?

7

What i s the area of a ci rcle w i th radi us 5?

8

What i s the area of a ri ght tri angle w i th leg lengths of 8 and 16?

9

What i s the remai nder w hen 51806 i s di vi ded by 9?

10

How many dollars does Luke have i f he has 12 quarters?

11

Fi ll i n the blank: 2 × 7 × 5y + 14 × 3 = 2 ( 35y + __ )

12

What i s the area of a square w i th a peri meter of 60?

13

Out of 91 people, 65 are boys. What fracti on of the people are gi rls?

14

What i s the 7th pri me number?

15

If Peter has 24 cooki es and eats half, gi ves Teddy half of the remai ni ng, then gi ves Kai half of the remai ni ng, and then Peter eats the rest, how many cooki es di d he eat?

16

Kai i s 2 years older than Teddy. The sum of thei r ages i s 34. What i s the di fference of thei r ages i n 17 years?

17

There are lanky ostri ches and mooi ng cow s i n a fi eld. If Farmer Sampson counts 30 heads and 86 legs, how many cow s are there?

18

What i s the sum of the i nteri or angles of a square di vi ded by the sum of the i nteri or angles of a ri ght tri angle?

19

What i s the fi fth non-pri me after zero?

20

How many pri me numbers less than 100,000 are perfect squares?

21

What i s the sum of the fi rst 5 terms of the Fi bonacci sequence?

22

If a tri angle has 2 congruent angle measures and the thi rd angle has a measure of 68E, w hat i s the measure, i n degrees, of one of the congruent i nteri or angles?

23

Li bbey and Kei sha take belly dance lessons on Thursdays. Kei sha pays $8 w eekly w hi le Li bbey takes advantage of a deal of buyi ng four w eeks of lessons for $25. After 16 w eeks of lessons, how much money does Li bbey save, i n dollars?

24

Coli n fi ni shed a math test at 1:45 pm and Kei sha took the same test starti ng at the same ti me and fi ni shed at 2:17 pm. How many seconds separated Coli n’ s ti me from Kei sha’ s?

25

The sum of tw o numbers i s 143. Thei r posi ti ve di fference i s 27. What i s the smaller number?

26

If there are 3 Luz i n 7 Ers and 9 Ers i n 6 Pells, how many Luz are i n 28 Pells?

27

Luke tri es to play tenni s but can only hi t the ball 20% of the ti me. If 60 balls are hi t to Luke, how many balls can you expect hi m to hi t?

28

Kei sha fi lls her w ater bottle each morni ng. Kei sha dri nks 1/3 of her w ater before lunch, one half of the remai ni ng w ater at lunch, tw o cups after lunch and then has tw o cups remai ni ng. How many cups of w ater di d Kei sha have at the begi nni ng of the day?

29

Ingri d’ s phone ri ngs i n tw o classes each day. After three, 5-day school w eeks contai ni ng no days off, how many ti mes w i ll her phone ri ng i n class?


Bi ff i s pushi ng a rock up a 72-foot hi ll. He pushes i t up 7 feet every day, and Eho, at ni ght, pushes i t dow n 2 feet. How many days w i ll i t take Bi ff to push the rock to the top of the hi ll?

31

A ri ght tri angle i s draw n i nsi de a ci rcle. If the hypotenuse has a length of 25 and a leg has a length of 7, w hat i s the other leg length?

32

I’ m thi nki ng of a 2-di gi t number. When I sw i tch the di gi ts, the new number i s 27 less than the ori gi nal, and the sum of the tw o numbers i s 99. What i s my ori gi nal number?

33

A group of math students stands i n a ci rcle. Each i s assi gned one number starti ng at 1 and i ncreasi ng i n order around the ci rcle by 1. Person 57 i s across from Person 163. Who’ s number i s across from Person 33?

34

If the ci rcumference of a ci rcle i nscri bed i nsi de a square i s 6π, then w hat i s the area of the square?

35

Tw o standard 6-si ded di ce are rolled. The probabi li ty of rolli ng a sum of x i s 1/12. Fi nd the product of all possi ble i ntegers of x.

36

On a plane, tw o men together had 135 ki lograms of luggage. The fi rst pai d $1.35 for hi s excess luggage and the second pai d $2.70 for hi s excess luggage. Had all the luggage belonged to one person, the excess luggage charge w ould have been $8.10. At most how many ki lograms of luggage i s each person permi tted to bri ng on the plane free of addi ti onal charge?

37

[ In thi s problem, use the facts that 1 ton = 2000 lbs and 1 mi le = 5280 feet. ] An elephant w ei ghi ng 2.64 tons and a rabbi t w ei ghi ng 1 lb. Are balanced on a very long, perfectly ri gi d teeterboard (seesaw ). If the elephant starts sli di ng tow ard the fulcrum at the uni form rate of 1 foot per mi nute, how many mi les per hour must the rabbi t run i n order to mai ntai n balance?

38

The squash season i s neari ng i ts end and the current i ndi vi dual standi ngs are show n i n the chart. Each of the 8 players must sti ll play 28 games, 4 w i th each of the other players. How many players sti ll have a theoreti cal chance to at least ti e for the champi onshi p? Player:

A

B

C

D

E

F

G

H

Games Won: 92 91 90 71 67 66 44 39 Games Lost: 48 49 50 69 73 74 96 101 39

Some w orkers w ere asked to mow tw o fi elds, one tw i ce as bi g as the other. They all mow ed the larger fi eld for half of a day; then they spli t i n half. One group fi ni shed the larger fi eld at the end of the day. The others mow ed the smaller fi eld; but at the end of the day, there remai ned a part to do. Thi s part w as fi ni shed by one w orker i n a si ngle day. How many w orkers w ere there?

40

A fuel tank recei ves a conti nuous, steady flow of 2000 li ters per hour. The tank experi ences a steady rate of fuel usage w i thi n each of the 6 consecuti ve 4-hour peri ods every day. Every day, usage duri ng these peri ods i s, respecti vely, 6000, 13500, 7300, 10000, 8000 and 3200 li ters. What i s the capaci ty, i n li ters, of the smallest tank w hi ch could ensure there w ould alw ays be at least 200 li ters of fuel i n the tank?

“Math is Cool” Championships-2004

Sponsored by: The Swinging Doors and The Accounting Source 4th Grade - May 15, 2004 Team Multiple Choice Contest M r. Willoughby’s English class has the following summer reading list. Each student of his must read at least one book from the list. As they cannot do math very well, help M r. Willoughby’s English students with their calculations about their summer reading. Title

Author

Price ($)

Pages

Weight (ounces)

“Tom Sawyer”

M ark Twain

5.95

298

18

“Treasure Island”

Robert Louis Stevenson

3.95

224

16

“20,000 Leagues Under The Sea”

Jules Verne

3.99

320

19

“The Time M achine”

H. G. Wells

3.99

144

10

“Robinson Crusoe”

Daniel Defoe

2.50

288

17

“Gulliver’s Travels”

Jonathan Swift

4.95

311

20

Questions 1

If Bob reads half of “Treasure Island” in one night, how many pages did he read? A) 100 B) 112 C) 114 D) 124 E) 212

2

A league is equal to three nautical miles. How many nautical miles are in 20,000 leagues? A) 3,000 B) 6,667 C) 60,000 D) 600,000 E) answer not shown

3

Jamie wants to read the two shortest books on the list. How many pages must she read? A) 6.49 B) 599 C) 26 D) 368 E) answer not shown

4

Bill is reading “Treasure Island.” Assuming that only the pages have weight, how many pages of the book weigh one ounce? A) 12 B) 13 C) 14 D) 15 E) 16

5

If Emily reads “Robinson Crusoe” in four hours, how many pages does she read per hour? A) 72 B) 144 C) 216 D) 288 E) 1152

6

Jeff is planning to buy all six books from his friend. How much will it cost Jeff? A) $21.32 B) $25.00 C) $25.33 D) $26.74 E) answer not shown

7

Carl wants to read all six books in five days. How many pages must he read per day? A) 5 B) 25 C) $25.33 D) 317 E) 1585

8

The Book Shipping Company charges 20 cents per ounce plus a 4 dollar flat rate to ship books. How much will it cost to ship all six books? A) $16 B) $20 C) $24 D) $26 E) $104

9

The Text Transport Company charges 4 dollars and 50 cents per book plus 2 dollars to ship books. How much will they charge to ship all six books? A) $24.00 B) $24.25 C) $24.50 D) $24.75 E) $29.00


Sponsored by: The Swinging Doors and The Accounting Source 4th Grade - May 15, 2004 Team Contest

Leave answers in terms of π where applicable. Do not round any answers unless stated otherwise. Record all answers on the colored cover sheet. 1

What is the smallest positive integer that leaves a remainder of 10 when divided into 90?

2

At the bank, Al exchanged a $10 bill for an equal number of nickels, dimes, and quarters. How many of each type of coin did Al receive?

3

Matt’s hair grows 2 inches per month. If he cuts his hair once every three months and only cuts off half an inch, how long will his hair be after one year? (Assuming that he shaves his head at the beginning of every year)

4

If 94 students and 21 adults are going to Mexico to build houses, how many houses can be built if at least 10 students and exactly 2 adults must work on each house the entire time? Each group of people can build one house in the time they’re in Mexico.

5

Find the sum of the following sequence: 3 + 9 + 15 + .........+ 105 + 111

6

Will has a door that is two and a half feet wide and 8 feet tall. He removes the door and cuts it into two congruent rectangles. He then takes one of the halves and cuts it into two congruent triangles. What is the area of one of the triangles?

7

12 boys and 12 girls attend prom at Columbia High School. If each of the boys dances once with each of the girls, how many dances occur total?

8

Shaun is three times as old as Kayla and four times as old as Rayann. If Rayann will be 4/5 of Kayla’s age in two years, how many years old will Shaun be in 5 years?

9

Aaron fills out college applications at a rate of one application every 77 minutes. Keisha fills out two applications simultaneously every 54 minutes. If Libbey takes 8/7 as long as Aaron to fill out an application, how many more complete applications can Keisha fill out in a 24 hour day than Libbey?

10

The probability Lee dresses as a clown on any given day is 1/9. The probability Colin dresses as a clown is 9/1000000 on any given day. According to these probabilities, Colin and Lee should independently dress as a clown on the same day once every how many years? Answer as a decimal rounded to the nearest hundredth and assumes all years have 365 days.

4th grade Relay 1 (4th) 1

Evaluate: 3 x 7 + 5

26

2

Find TNYWG minus the number of faces on a cube.

20

3

Find the sum of the number of odd numbers between 0 and 10 plus TNYWG.

25

4

Evaluate: TNYWG divided by the sum of 2 and 3.

5

Relay 2 (4th) 1

What is the number of socks in a dozen pairs of socks?

24

2

Find the sum of TNYWG plus the number of sides in a triangle.

27

3

Find the quotient of TNYWG and the number of feet in a yard.

9

4

Evaluate: TNYWG times 50% of 10.

45


Sponsored by: The Swinging Doors and The Accounting Source 4th Grade - May 15, 2004 Mental Math Contest Ex press all answers in terms of radicals and π, where applicable, unless otherwise instructed. Person #1 1

What i s the area of a square w i th a peri meter of 20?

25

2

How many feet are i n 15 yards?

45

3

Solve for x i f x mi nus 3 equals 7.

10

4

What i s the angle measure of an i nteri or angle of a square?

90[E]

Person #2 1

What i s the area of a ri ght tri angle w i th leg lengths of 6 and 8?

24

2

What i s the number of i nches i n 1 yard di vi ded by 12?

3

3

How many quarts are i n 2 gallons?

8

4

If Bi ff pushes a rock 5 feet up a 25-foot hi ll every day and every ni ght Eho pushes i t back 1 foot, how many days w i ll i t take Bi ff to get the rock to the top of the hi ll?

6

Person #3 1

If x equals 3 w hat i s 3x plus 5?

14

2

What i s one- half plus one-fourth?

3/4

3

What i s the mean of the follow i ng set of data? (3,4,5,6,7,8,9)

6

4

Kai has $3.50 i n di mes. How many di mes does he have?

35

Person #4 1

What i s the area of a ci rcle w i th a di ameter of 8 i nches?

16π

2

Solve for x:

6

3

How many i nteri or degrees are i n a pentagon?

54 [E]

4

What i s the angle measure betw een the hour hand and the mi nute on an analog clock w hen i t i s 10:00 am?

60 [E]

2x + 7 = 19


Sponsored by: The Swinging Doors and The Accounting Source 4th Grade - May 14, 2004 College Knowledge Bowl Questions #1 1

How many distinct digits are in Mr. Ross’s fake social security number if it is 539-4105?

6 [digits]

2

If Sampson dresses as a clown 2 days per week, what fraction of the week does he not dress as a clown?

5/7

3

Each day Billybob does 12 more crunches than the day before. If he does 30 crunches on the first day, how many crunches total does he do in a week?

462 [crunche s]

4

Googgy and Jon are filming a ski movie. The movie will 15 be two hours plus an additional one half hour of bloopers. [days] If they film 10 minutes per day, how many days does it take them to film their movie?

5

Katherine and Luke are arguing about whether skiing or snowboarding is better. Katherine thinks skiing is better. If Aaron and Max and Keisha are on Katherine’s side, and Colin is on Luke’s side, what fraction of the group thinks skiing is better?

2/3

6

Elise has weird dreams twice every month. How many weird dreams will she have in a year?

24 [dreams]

7

If Joey has 2 dozen donuts and Ross eats half a dozen, how many does Joey have left?

18 [donuts]

Number 8 is an extra question. Only use it if needed.

8

Googgy has 12 pink jelly beans. If Jon eats 3/4 of Googgy’s jelly beans, how many does Googgy have left?

3 [jelly beans]


Sponsored by: The Swinging Doors and The Accounting Source 4th Grade - May 14, 2004


If today is Friday, what day is it 22 days after the day after yesterday?

Saturday

2

If Max goes to a pool party 3 times a week, how many times does he go to pool parties per year?

156 [times]

3

Luke falls asleep on the couch at 6:30 P.M. If he wakes up at 8:45 P.M., how long was he asleep, in hours? Express your answer as an improper fraction.

9/4 [hours]

4

If Chloe eats one hamburger every half hour, how many hamburgers does she eat in 2 days?

96 [hamburgers ]

5

If a baseball player bats .325 one year, .275 the next, and .303 the third year, what is his average batting for these three years?

.301

6

If Jim makes five shots in a game and gets 12 points, how many 3 point shots did he make (assuming no 1 point shots).

2 [3 point shots]

7

Jack can throw a ball 76 feet and Sarah throws a ball 123 feet, how much farther did Sarah throw than Jack?

47 [feet]


8

If a football place kicker makes 75% of his kicks and over a season he tries 200 field goals, how many does he make?

150 [kicks]


Sponsored by: The Swinging Doors and The Accounting Source 4th Grade - May 14, 2004 College Knowledge Bowl Questions #3 1

If you had 3 apples, 6 oranges, and 5 pears, what is the probability of picking an apple if you pick one fruit?

3/14

2

If 30% of a class has brown hair and 42% has blond hair, how many students out of 100 have neither blond nor brown hair?

28 [students ]

3

If a soccer ball is kicked 72 feet into the air and every 3 time it bounces it loses half of the height of its peak, how [bounces] many bounces will it take for the ball to only rise to 9 feet above the ground?

4

On a building, there are 36 windows and nine rows. How many windows are in each column?

4 [windows ]

5

If John reads an average of 3 books per month, how many books will John read in 2 years?

72 [books]

6

If Jill reads an average of 63 pages a night, how many pages will Jill read in 5 nights?

315 [pages]

7

Tom watches TV from 3:30 P.M. until 5:00 P.M. If there is an average of 40 commercials per hour, how many commercials will Tom watch?

60 [commerc ials]


8

If Jeff runs 7 miles every day and he wants to run 112 miles as soon as possible, how many days will Jeff have to continuously run?

16 [days]

“Math is Cool” Masters -- 2004

Key


Full Name:____________________________________

1st Score


DO NOT WRITE IN SHADED REGIONS Out of 40 Answer

1 or 0

Answer

1 or 0

1

1023

21

12

2

True

22

56[E]

3

27

23

[$] 28

4

2793

24

1920 [seconds]

5

17[boxes]

25

58

6

1/9

26

18[Luz]

7

25π[units squared]

27

12 [balls]

8

64 [units squared]

28

12 [cups]

9

2

29

30 [times]

10

[$] 3

30

14[days]

11

21

31

24

32

63 139[person]

12

225 [units squared]

13

2/7 or 26/91

33

14

17

34

15

15[cookies]

35

40

16

2[years]

36

45[kilograms]

17

13 [cows]

37

60 [mph]

18

2

38

5[players]

19

9

39

8[workers]

20

0

40

7000[ liters]

1 or 0

36 [units squared]

1 or 0




Key 1st Score

Correct responses are worth 2 points, incorrect responses are worth -1 point and no response is 0 points. Out of 18


1

B

2

C

3

D

4

C

5

A

6

C

7

D

8

C

9

E

-1, 0 or 2

-1, 0 or 2



Key 1st Score

Out of 10

Team Contest-Score Sheet DO NOT WRITE IN SHADED REGIONS Answer 1

16

2

25 [coins]

3

22 [inches]

4

9 [houses]

5

1083

6

5 [square feet]

7

144[dances]

8

29[years old]

9

36[applications]

10

2739.73 [years]

1 or 0

1 or 0



Relay Contest - Score Sheet Answer for relay #1 26 20 25 5 Answer for relay #2 24 27 9 45

Key

“Math is Cool” Championships – 2004-05 Hosted by: Moses Lake High School Math Team

4th Grade – April 22, 2005 Individual Contest – Written by Gregg Sampson GENERAL INSTRUCTIONS

Good sportsmanship is expected throughout the competition by all involved. Bad sportsmanship may result in disqualification. Calculators may not be used on any portion of this contest. Express all non-integer answers as fractions unless stated otherwise or it is a problem dealing with money and in that case, a decimal answer should be given. For 5th and 6th grade, all fractions and ratios must be reduced. Units are not necessary unless it is a problem that deals with time and, in that case, am or pm is needed. However, if you choose to use units, they must be correct. Leave all answers in terms of Β where applicable. Do not round any answers unless stated otherwise. Record all answers on the colored cover sheets in the answer column only. Make sure all answer sheets have all the information filled out at the top of the sheet. Tests will be scored as a 0 if answers are not recorded correctly on the answer sheets. Blank answer sheets and answer sheets with no name will also be scored as a 0. INDIVIDUAL TEST - 35 minutes

When you are prompted to begin, tear off the colored sheet and begin testing. Make sure your name and school are recorded on the answer sheet. This test is scored as a 1 or 0. Express all non-integer answers as fractions unless stated otherwise or it is a problem dealing with money and in that case, a decimal answer should be given. For 4th & 4th grade, make sure all fractions and ratios are reduced. Units are not needed except on questions that deal with time and, in that case, a.m. or p.m. is needed. If you choose to use units, you must use them correctly. Record your answers on the score sheet. No talking during the test.


1 2 3 4 5 6

Evaluate: 8 + 5 Evaluate: 181 – 97 Find the product of 8 and 7. Find the quotient of 54 and 6. Biff has 7 goldfish and his friend Eho has 9. How many more goldfish does Eho have than Biff? Each clown holds the same number of balloons. Biff saw 72 balloons being held by 9 clowns. How many balloons was each clown holding?

7 8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Eho found a misfit square checkerboard that had 49 squares on it. How many squares are on each side of the checkerboard? Colin and Josh found a bag of cookies under the bleachers after a math contest. On Monday, they gave the cookies to their friends. They gave half the total amount of cookies to Libbey, and then half of the remaining amount to Keisha. Colin and Josh had one cookie left over and gave it to Lee. How many cookies did Colin and Josh find under the bleachers? Paul spends $2.50 a day for school lunch. How much, in dollars, does he spend in 4 days for school lunch? Kai is planning a trip to Mathwood Theme Park. It is 80 miles to the park and he figures he will be able to travel at 40 miles per hour (mph). How long, in hours, should it take him to get to Mathwood? What is the most number of 7¢ candies I can buy with one dollar? What time is it 17 minutes before 1:08 p.m.? What is the maximum number of times a line can intersect a circle? Write down the largest 4 digit even number using only the digits 5, 7 and 8. Each of the three digits must be used at least once. Sally had a cube that was made up of 125 smaller cubes. The cube was 5 by 5 by 5. Sally painted the outside of the 5 by 5 by 5 cube. How many smaller cubes have paint on only one side? What is the remainder when 38 is divided by 5? The math team decided to triple the number of members they send to English Camp this year. Eho pointed out that even if they triple the number of members going to English camp, it will still be the same number they sent last year. How many members went to English camp last year? The radius of a circle is 3. What is the diameter of the circle? Find the difference of 8371 and 7984. What is the area of a right triangle with legs of length 8 and 7? Is the sum of two odd numbers always odd, always even, or could it be either? What is the mode of the following set of data? {8,8,9,11,11,11} Frank gets 1 out of every 4 math questions correct at math contests. If Frank works out 120 math questions, how many would he expect to get correct? The sum of the ages of Josh, Colin and Keisha is 51. What will be the sum of their ages in 7 years?

25 26 27 28 29

What is the units digit of the product of 829 and 768? Teddy can do a math contest three times as fast as Kai. Kai can do the test in 6 hours and 15 minutes. How many hours and minutes does it take Teddy to do the test? What is the mean of 16 and 80? We know B

< C and A < B. Is A <, >, or = to C?

What is the first prime number greater than 17?

Challenge Questions 30 31 32 33 34 35 36 37 38 39 40

What is the probability of drawing a red 4 out of a standard deck of 52 cards in one draw? What is the sum of the next two numbers in the sequence: 3, 6, 12, 24, 48, … When a certain number is divided by 8 the quotient is 3 and the remainder is 2. What is the number? How many positive 3-digit numbers have at least two digits that are the same? How many ways can you make $20.00 using $10, $5, and $1 dollar bills? Kai, Teddy and Peter run a race. They are the only three running the race. The probability of Kai winning the race is 1/2. The probability of Teddy winning is 1/3. What is the probability that Peter will win the race? Carl is planning a trip. He has figured out it will take him five days. The first day he will travel 150 miles, the second 100 miles, the third 50 miles, the fourth 200 miles, and the last day 100 miles. The rental car company rents cars for $40 per day plus 20 cents per mile. What will Carl’s total car rental bill be, in dollars? Mathville High has 50 students enrolled and every student is taking at least one math or science class. 25 of the students take only a math class while 7 take both math and science. How many students take only science? 256 basketball teams show up for a single elimination tournament. This means once a team loses, it is out of the tournament. What is the minimum number of games needed to be played before a winner is crowned? A piece of paper with four edges is folded over once and then cut into two pieces along the fold. What is the minimum number of edges of the two pieces of paper? A train traveling at 30 mph takes 8 seconds to completely enter a tunnel and 45 seconds to pass completely through the tunnel once it is completely entered. How many feet long is the tunnel?


4th Grade – April 22, 2005 Team Multiple Choice Contest – Written by Amanda Hochstatter TEAM MULTIPLE CHOICE - 15 minutes This test is the only test where you will be penalized for incorrect responses. You will receive 2 points for a correct letter response, 0 points for leaving it blank and -1 point for an incorrect response. When you are prompted to begin, tear off the colored sheet, pass out a copy of the test to each team member, and begin testing. Since this is a multiple choice test, ONLY a letter response should be listed as an answer on the answer sheet.

Sarah is trying to organize her movie collection. Below is a list of all the videos and DVDs she has, how long each one is, and who made the video.

Sarah’s Collection DVD/Video Movie Time Company Video Jurassic Park 2 hrs 7 min Universal Studios DVD Harry Potter 1 2 hrs 32 min Warner Brothers Video Mulan 1 hr 28 min. Disney Video Matrix 2 hrs 16 min Warner Brothers DVD Finding Nemo 1 hr 40 min. Disney Video Titanic 3 hrs 12 min Paramount DVD The Lion King 1 hr 28 min. Disney Video Apollo 13 2 hrs 20 min Universal Studios Video Hook 2 hrs 22 min Columbia Tri-star DVD A little Princess 1 hr 37 min. Warner Brothers The Sound of Music Video 2 hr 52 min. Fox DVD Star Wars 1 2 hr 13 min. Fox Sarah wants to watch all the Disney movies. How long will it take her to watch them, if she takes a 15 minute break between each movie?

1

A) 5 hr 6 min B) 3 hr 26 min

2

E) Answer not given Sarah decides to watch all the DVDs. How long will it take her if she doesn’t take any breaks? A) 34200 sec

B) 93609 sec

C) 3 hr 38 min

C) 36400 sec

D) 4 hr 36 min

D) 46200 sec

E) Answer not given

3

Videos cost $10.00 and DVDs cost $15.00. How much has Sarah spent on her collection?

4

A) $135 B) $140 C) $145 D) $150 E) Answer not given Sarah is thinking of buying her videos in DVDs. The DVDs are discounted by 10%. The original price per DVD was $15. How much would it cost Sarah to replace her videos if she gets the discount of 10%?

5 6

7 8 9

A) $10.50 B) $70.00 C) $95.50 D) $157.40 E) Answer not given Sarah wants to organize her movies on a shelf. How many different arrangements are possible if she wants to keep the DVD’s together and the videos together? A) 12! B) (7!)(5!) C) (12!)(7!)(5!) D) (7!)(5!)(2!) E) Answer not given Sarah wants to make a box for her videos and DVDs. The videos have dimensions of 8 in × 3.5 in × 1 in, and the DVDs have dimensions of 8 in × 5 in × ½ in. What is the box with the smallest volume that will fit all of her DVDs and videos? A) 8 in × 8.5 in × 6 in B) 8 in x 1 in x 39.5 in C) 8 in × 9 in × 1 in D) 10 in × 16 in × 3.5 in E) 8 in x 9.5 in x 5 in What company makes the longest films on average according to Sarah’s collection? A) Warner Brothers B) Universal Studios C) Paramount D) Columbia Tri-star E) Fox What is the mean or average length of the all the movies rounded to the nearest minute? A) 2 hrs 32 min B) 2 hrs 18 min C) 2 hrs 11 min D) 2 hrs 45 min E) Answer not given How many days would it take to watch all the movies in a row? A) 1 day 9 min B) 1 day 2 hrs 7 min C) 1 day 2 hrs 3 min E) Answer not given

D) 2 days 2 hrs 4 min

Sarah’s Collection DVD/Video Video DVD Video Video DVD Video DVD Video Video DVD Video DVD

Movie Jurassic Park Harry Potter 1 Mulan Matrix Finding Nemo Titanic The Lion King Apollo 13 Hook A little Princess The Sound of Music

Star Wars 1

Time 2 hrs 7 min 2 hrs 32 min 1 hr 28 min. 2 hrs 16 min 1 hr 40 min. 3 hrs 12 min 1 hr 28 min. 2 hrs 20 min 2 hrs 22 min 1 hr 37 min. 2 hr 52 min. 2 hr 13 min.

Company Universal Studios Warner Brothers Disney Warner Brothers Disney Paramount Disney Universal Studios Columbia Tri-star Warner Brothers Fox Fox


4th Grade – April 22, 2005 Team Contest – Written by Gregg Sampson TEAM TEST - 15 minutes

When you are prompted to begin, tear off the colored sheet and give a copy of the test to each of your team members and begin testing. This test is scored as a 1 or 0. Express all non-integer answers as fractions unless stated otherwise or it is a problem dealing with money and in that case, a decimal answer should be given. For 4th & 4th grade, make sure all fractions and ratios are reduced. Units are not needed except on questions that deal with time and, in that case, a.m. or p.m. is needed. If you choose to use units, you must use them correctly.

1

Your school won first place today. There were 12 members from your school and each person on the team shook hands with each other exactly once. How many handshakes occurred?

2

Evaluate: 18 + 5 – 4 – 7 + 9

3

Joel rolls three 5-sided dice with faces numbered 1 through 5. How many different sums of the faces are possible?

4

You and three of your friends went to a movie. All of you sat in one row together. How many different ways could you sit?

5

Paul went on a nature walk with his daughter during our yearly math retreat. Each step Paul takes is 3 feet long and each one of his daughter’s steps is 16 inches long. Paul took 200 steps. How many steps did his daughter take?

6

How many edges does a triangular pyramid have?

7

If it is April, what month will it be 2005 months from now?

8

If an equal number of 2’s, 3’s, and 7’s are added together to get 60, what is the total number of 2’s used in the sum?

9

How many whole numbers greater than 12 and less than 55 cannot be written as the sum of two odd numbers?

10

What number, when added to 58, results in a sum of 124?


4th Grade – April 22, 2005 Relay Contest – Written by Cameron Frederick RELAYS - 5 minutes per relay There is no talking during this event and you must always be facing forward. Person #1 will be given an answer sheet(s) and will need to fill out the top. The proctor will hand out a strip of paper to each person. These need to be face down on your desk until it is time for the relay to start. Once the relay begins, everyone may turn over their strip of paper and begin working. You may write on the strip of paper to come up with your answer. However, when person #1 figures out his/her problem, he/she will record just his/her final answer on the answer sheet and pass only the answer sheet back to the person behind. This continues until person #4 puts an answer on the answer sheet and gives it to the proctor. A correct answer from person #1, #2 and #3 is worth 1 point each. A correct answer from person #4 is worth 2 points making each relay worth 5 points. You will see the expression TNYWG [Proctor: write this on the board] which means: “the number you will get”. This is where you put your teammate’s answer that they pass back to you, and then you should be able to solve your question. Once the relay begins, turn over your strip of paper and make sure you have the right person number. Remember, no talking and remain facing forward to avoid being disqualified!

Person 1 Person 2 Person 3 Person 4 Person 1 Person 2 Person 3 Person 4 Person 1 Person 2 Person 3 Person 4

Practice Relay

Answer

How many digits are in the number 74,389?

5

Evaluate: TNYWG + 6

11


2

Evaluate: 6 x TNYWG + 1

13

Relay #1

Answer

Multiply 4 and 3.

12

What is the area of a square with a perimeter of TNYWG?

9

Evaluate: TNYWG/3

3

Evaluate: 4 + TNYWG/3

5

Relay #2

Answer

What is 32?

9

What is TNYWG divided by 3?

3

Evaluate: TNYWG x 16

48


16


4th Grade – April 22, 2005

Final Score:

KEY


Mental Math Contest – Written by Cameron Frederick

When it is time to begin, I will read the first question twice. You may not do any writing or talking while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You may not erase or cross out answers once you have written an answer down. If there are eraser marks or crossed out answers, they will be marked wrong. Once all students have laid their pencils on the desk, another question will be asked. If a student doesn’t lay his/her pencil down, the maximum wait time is 30 seconds from the second reading of the question before another question is asked. The value of each question is a one or zero. Each student will be asked four questions, then another member of your team will come up.

PERSON 1 NAME: 1.1 What is the sum of 8 and 4?

1.2 1.3 1.4

How many sides does a parallelogram have?

4

What is the difference between 17 and 3?

14

Reduce: 16 halves

8

PERSON 2 NAME: 2.1 How many cups are in a gallon?

2.2 2.3 2.4

1

Reduce: 8/12

2/3

True or False. The number 363 is divisible by 3.

True 63

What is the circumference of a circle with a radius of 6?

12π

What is the perimeter of a 7 by 6 rectangle?

26

How many times larger is the number 9 when compared to the number 3?

3

PERSON 4 NAME: 4.1 Find the radius of a circle with an area of 16π.

4.2 4.3 4.4

16 [cups]

What is one-half plus one-half?

PERSON 3 NAME: 3.1 Find the product of 7 and 9.

3.2 3.3 3.4

1 or 0 12

4


8

How many centimeters are in a meter?

100 [cm]

Write one-fourth as a decimal.

0.25



Division 1 COLLEGE KNOWLEDGE BOWL ROUND #1 Written by Kristina & Jie #

Problem

1

One emu can eat 1

2 3 4 5 6 7 7 8

1 cheeseburgers in one day. How many 3 cheeseburgers can three emus eat in three days? What is the side length of a regular octagon with perimeter 32?

Answer 12 [cheeseburgers]

4

Fred’s Friendly Farm has pigs and chickens. There are a total of twelve heads and forty legs. How many pigs are on the farm? A circle of radius four centimeters fits exactly inside a square. Find the perimeter of the square, in centimeters. What is the area of a square with side length seven?

8 [pigs]

What time will it be 233 minutes after 11:27 pm?

3:20 am

How many sides does a decagon have?

10 [sides]

32 [cm] 49

Extra Problem – Only if Needed What is the probability of rolling a number less than three on a six-sided die?

2/6 or 1/3



Division 1

COLLEGE KNOWLEDGE BOWL ROUND #2 Written by Kristina & Jie #

1 2

3 4 5 6 7

7.1 8

Problem How many years are in three and one-quarter centuries?

Answer 325 [years]

Courtney has three shirts: a pink one, a blue one, and a yellow one. She also has two skirts: a black one and a white one. If an outfit consists of one skirt and one shirt, how many different outfits can she make? What is the probability of drawing a heart or the queen of spades from a standard deck of 52 cards? Give your answer as a fraction. 83 is 37 more than what number?

6 [outfits]

How many minutes are in a day?

1440 [minutes] 30

What is the perimeter of a rectangle with sides of length six and nine? Joe is filling up a 30 gallon pool with a hose. The hose can pump five gallons in one minute. However, the pool drain is open while he fills, allowing two gallons of water to escape per minute. How many minutes does it take to fill the pool?

14/52 or 7/26 46

10 [minutes]

Extra Problem – Only if Needed John can answer five questions in one minute, but two of them are always wrong. How many questions will be answered correctly if he answers 20 questions?

12 [questions]



Division 1

COLLEGE KNOWLEDGE BOWL ROUND #3 Written by Kristina & Jie #

1 2 3 4 5 6 7 7.1 8

Problem Three times a number, minus four is equal to eight. What is the number? What is the remainder when eighty-six is divided by seven?

Answer 4

How many different ways can you arrange the letters in the word “MATH”? What is the sum of one-sixth and five-twelfths?

24 [ways]

What is the area in square feet of a plot of land thirteen feet wide by seventeen feet long? If Farmer Bob has six chickens, four cows, and three sheep on his farm, how many animal feet are on the farm? If I count by sevens starting with 12, what will be the fourth number that I say?

221 [square feet] 40 [feet]

2

7/12

33

Extra Problem – Only if Needed If today is Tuesday, what day of the week will it be 17 days from now?

Friday



Division 2 COLLEGE KNOWLEDGE BOWL ROUND #1 Written by Gregg Sampson #

1 2 3 4 5 6 7 7 8

Problem How many sides does a heptagon have?

Answer 7 [sides]

If Peter can ride his bike 10 miles in 20 minutes, what is his speed in miles per hour? What is the probability of rolling a sum of 7 with two six sided dice? What is the product of three-fourths and two-thirds?

30 [mph]


5

How many quarts are in 3 and one-half gallons?

14 [quarts]

What is 3 times 4 times 2?

24

6/36 or 3/18 or 2/12 or 1/6 6/12 or ½

Extra Problem – Only if Needed What is the next number in the sequence 2,5,8,11,….

14



Division 2

COLLEGE KNOWLEDGE BOWL ROUND #2 Written by Cameron Frederick #

1 2

3 4 5

6 7 7.1 8

Problem Brian is making lemonade. It takes 8 lemons to make a pitcher of lemonade. How many lemons will Brian need to make 4 pitchers of lemonade? Isaac has 4 US State quarters in his pocket. One is of Georgia, one is of Pennsylvania, one is of Delaware, and one is of Indiana. What is the probability that Isaac will pull out the Pennsylvania quarter out of is pocket on the first try? What is the product of 11 and 18?

Answer 32 [lemons]

How many days are between and not including the dates March 11, 2004, and September 2, 2004? Erica woke up at 7:34 AM to get ready for a Math is Cool competition. She had a long day figuring out tricky math problems. After the competition, Erica went to sleep that night 14 hours and 27 minutes after she had woken up that morning. What time did Erica go to sleep? What is the remainder when 1876 is divided by 3?

174 [days]

What is the tens digit when you multiply 1234 by 90?

6

¼

198

10:01 PM

1

Extra Problem – Only if Needed Karl watches 7 red cars and 3 blue cars pass his house yesterday. What percentage of the cars he saw were red?

70 [%]



Division 2

COLLEGE KNOWLEDGE BOWL ROUND #3 Written by Cameron Frederick #

1 2 3 4 5

6 7 7.1 8

Problem Amanda’s mom cooked 12 cakes for her family. If Amanda eats 4 of the cakes, what fraction of the cakes is left for the rest of the family? Evaluate: Twelve plus, six times four, minus three

Answer 8/12 or 4/6 or 2/3

A square has a side length of 15. What is the square’s area?

225 [un2]

What is the perimeter of a triangle with sides of length 4, 15, and 13? Jacob is having a party and he invites 4 friends. He shakes the hand of every person as they arrive at the door. Then as people arrive they join Jacob at the door and shake the hands of each person that arrives after that. How many handshakes will have occurred after everyone has arrived? Sarah is sad because her little brother stole half of her stuffed animals. If she now has 27 stuffed animals left, how many stuffed animals did she originally have? What is the difference between the numbers 3882 and 1928?

32 [un]

33

10 [handshakes]

54

1954

Extra Problem – Only if Needed Dino the dinosaur is 130 ft tall. How tall, in inches, is Dino?

1560 [inches]


Final Score:

KEY


School Name__________________________________Team #________

First Score



13 84 56 9 2 [goldfish] 8 [balloons] 7 [squares] 4 [cookies] [$] 10.00 2 [hours] 14 [pieces] 12:51 p.m. 2 or Twice 8758 54 [cubes] 3 0 [members] 6 [un] 387 28 [un2]

1 or 0 1 or 0

Answer 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Even 11 30 [questions] 72 [years] 2 2 hours, 5 minutes 48 < 19 2/52 or 1/26 288 26 252 9 [ways] 1/6 or equivalent [$] 320.00 18 [students] 255 [games] 6 [edges] 1980 [feet]

1 or 0

1 or 0


Final Score:

KEY


School Name__________________________________Team #________ Proctor Name__________________________________Room #_______

First Score (out of 18)

Division:

Team Multiple Choice Contest – Score Sheet Correct responses are worth 2 points, incorrect responses are worth -1 point and no response is 0 points. DO NOT WRITE IN SHADED REGIONS

Answer

1 2 3 4 5 6 7 8 9 10

A A C E D B C C B

-1, 0 or 2

-1, 0 or 2

“Math is Cool” Championships – 2004-05 4th Grade – April 22, 2005

Final Score:

KEY



Div: Team Contest – Score Sheet DO NOT WRITE IN SHADED REGIONS

Answer

1 2 3 4 5 6 7 8 9 10 10

66 [handshakes] 21 13 [sums] 24 450 [steps] 6 [edges] May 5 [2’s] 21 [numbers] 66

1 or 0

1 or 0

“Math is Cool” Championships -- 2004-05 4th Grade – April 22, 2005

KEY


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

5

11

2

13

1 or 0

1 or 0

1 or 0

2 or 0


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

12

9

3

5

1 or 0

1 or 0

1 or 0

2 or 0


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

9

3

48

16

1 or 0

1 or 0

1 or 0

2 or 0



Final Score: (Out of 16)

School Name__________________________________Team #________ Proctor Name_________________________________Room #_______ Division: When it is time to begin, I will read the first question twice. You may not do any writing or talking while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You may not erase or cross out answers once you have written an answer down. If there are eraser marks or crossed out answers, they will be marked wrong. Once all students have laid their pencils on the desk, another question will be asked. If a student doesn’t lay his/her pencil down, the maximum wait time is 30 seconds from the second reading of the question before another question is asked. The value of each question is a one or zero. Each student will be asked four questions, then another member of your team will come up.

PERSON 1 NAME:

1.1 1.2 1.3 1.4 PERSON 2 NAME:

2.1 2.2 2.3 2.4 PERSON 3 NAME:

3.1 3.2 3.3 3.4 PERSON 4 NAME:

4.1 4.2 4.3 4.4

1 or 0


Final Score:


School Name__________________________________Team #________

First Score



13 84 56 9 2 [goldfish] 8 [balloons] 7 [squares] 4 [cookies] [$] 10.00 2 [hours] 14 [pieces] 12:51 p.m. 2 or Twice 8758 54 [cubes] 3 0 [members] 6 [un] 387 28 [un2]

1 or 0 1 or 0

Answer 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Even 11 30 [questions] 72 [years] 2 2 hours, 5 minutes 48 < 19 2/52 or 1/26 288 26 252 9 [ways] 1/6 or equivalent [$] 320.00 18 [students] 255 [games] 6 [edges] 1980 [feet]

1 or 0

1 or 0


Final Score:




Division:


Answer

1 2 3 4 5 6 7 8 9 10

-1, 0 or 2

-1, 0 or 2


Final Score:





Answer

1 2 3 4 5 6 7 8 9 10 10

1 or 0

1 or 0

“Math is Cool” Masters – 2004-05 Sponsored by: American Chemical Society

4th Grade – May 14, 2005 Individual Contest Written by: Cherie Clymer

GENERAL INSTRUCTIONS

Good sportsmanship is expected throughout the competition by all involved. Bad sportsmanship may result in disqualification. Calculators may not be used on any portion of this contest. Express all non-integer answers as fractions unless stated otherwise or it is a problem dealing with money and in that case, a decimal answer should be given. For fifth and sixth grade, all fractions and ratios must be reduced. Units are not necessary unless it is a problem that deals with time and, in that case, am or pm is needed. However, if you choose to use units, they must be correct. Leave all answers in terms of Β where applicable. Do not round any answers unless stated otherwise. Record all answers on the colored cover sheets in the answer column only. Make sure all answer sheets have all the information filled out at the top of the sheet. Tests will be scored as a 0 if answers are not recorded correctly on the answer sheets. Blank answer sheets and answer sheets with no name will also be scored as a 0. INDIVIDUAL TEST - 35 minutes

When you are prompted to begin, tear off the colored sheet and begin testing. Make sure your name and school are recorded on the answer sheet. This test is scored as a 1 or 0. Express all non-integer answers as fractions unless stated otherwise or it is a problem dealing with money and in that case, a decimal answer should be given. For fifth & sixth grade, make sure all fractions and ratios are reduced. Units are not needed except on questions that deal with time and, in that case, a.m. or p.m. is needed. If you choose to use units, you must use them correctly. Record your answers on the score sheet. No talking during the test.


1 2 3 4 5 6 7

How many diagonals can be drawn in a square? Find the sum of the three numbers: 832, 981, and 653 Find the product of 8 and 21. Find the quotient of 126 and 7. Find the difference between 9102 and 8987. It takes four sheep to make one coat. How many sheep does it take to make 20 coats? A circle has diameter 12. What is its radius?

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

I have 56 pieces of candy to divide evenly among my 7 friends. How many pieces of candy does each of my friends get? How many sides does a hexagon have? Biff did a survey of his class to find out how many gold fish are owned by his classmates. In the class of 20 classmates, 17 students didn’t own any. Of the three who did, one owned 17, another 15, and the last classmate owned 12. How many total fish are owned by Biff’s classmates? What is the mean of the data set {8, 3, 7}? At the end of a soccer match, every player shakes hands with every other player. If there are 5 players on each team, how many handshakes will take place? The sum of three consecutive numbers is 27. What is the smallest of the three numbers? The scores on the individual “Math is Cool” test for Math Academy School was 23, 25, 27, 25, 32, 15, 15, 25. What was the mode of the individual score for Math Academy School? What is the sum of the digits of the number you find after you round 38,129,450 to the nearest 10,000? How many counting numbers are between 5 and 20, inclusive? Five people go to a movie and sit together in a row. How many different ways can they sit in a row? When I divide a certain number by 6, the quotient is 7 and the remainder is 4. What is the number? What’s the smallest palindrome larger than 1001? On the first day that I began cross-country skiing, I went 1 km. If I double the distance I ski each day, on which day did I first ski over 20 km in a single day? How many perfect squares are between 10 and 20? What is the largest integer you can add to 43 that yields a result less than 200? When two six-sided dice are rolled, how many different sums are possible? Biff and Eho decided to go backpacking in the Cabinet mountains in Montana, 210 miles away. 60 miles away from home, Eho realized he forgot his backpack, so they went back. How many miles did they travel, total, to get to the Cabinet mountains? What is the area of a right triangle with legs of lengths 3 and 4? Bubble gum costs 7 cents each piece. If I have $2.00, how many pieces of bubble gum can I buy?

27

In the figure shown, what is the measure, in degrees, of angle A? 20° A

28 29

120°

If today is Tuesday, what day was it 70 days ago? An item that originally cost $100.00 was discounted by 30%. What is the new price of the item, in dollars?

Challenge Questions 30 31 32 33 34 35 36 37

38 39 40

The probability that our math team will win a trophy is 7/10. What are the odds in favor of our team winning? [Express answer in the form of a:b.] What is the sum of the next two terms in the following sequence? 1, 8, 27, 64,… The length and width of a rectangular prism are tripled, but the height remains the same. By what factor is the volume increased? The mean average of three numbers is 3. If two of the three numbers are 1, what is the other number? A rectangular playing field is 40 yards wide and 30 yards long. How far is it diagonally across this field, in yards? What is the sum of all integers that make the following inequality true? x < 3 Express 10112 as a base 10 number. Mathland Middle School’s math team members all participate in at least one of three other school activities: band, leadership, and track. Of the 40 members of the team, 15 are in leadership, 23 are on the track team, 4 are in both leadership and band, 6 are in both leadership and track, 3 are in band and track, and 2 students are in all three activities. How many students are in the band, total? The entrance to a railroad tunnel in the Cascade mountains is in the shape of a semi-circle. Seven feet from the center of the tunnel, the height of the entrance is 24 feet. How tall is the tunnel at its center, in feet? What is the volume of a cone, in cubic feet, with a height of 1 foot and a radius of ¼ foot? Dart players are aiming at the bulls eye as shown below. Given that all the dart players will hit the target with a dart, what is the probability their dart will hit the shaded area? The radius of the large circle is 5; the radius of the medium circle is 3, and the radius of the small circle is 1.


4th Grade – May 14, 2005 Team Multiple Choice Contest Written by: Joel Turtle

TEAM MULTIPLE CHOICE - 15 minutes This test is the only test where you will be penalized for incorrect responses. You will receive 2 points for a correct letter response, 0 points for leaving it blank and -1 point for an incorrect response. When you are prompted to begin, tear off the colored sheet, pass out a copy of the test to each team member, and begin testing. Since this is a multiple choice test, ONLY a letter response should be listed as an answer on the answer sheet.

A coach is examining his quarterbacks in order to find out who he should start in the state playoffs. In football, a quarterback is the player who throws the ball to his receivers. A completion is a pass that is caught, and each completion is measured for distance in terms of yards. In the following scenario, quarterbacks may gain yards only by making completions. Below is a chart comparing the three quarterbacks after the team’s first 10 games. Quarterback Completion Percentage

Biff Eho John

1 2 3 4

68.75% 48% 34%

Total Total Yards Minutes Yards Number Number per per per of Passes of Game Game Pass Completed Passes 110 160 242 22 22 120 250 168 42 14 170 500 204 51 12

What is the total number of passes John has thrown? A) 110 B) 120 C) 170 D) 204 E) Answer not given How many passes per 16 throws should Biff complete? A) 21 B) 12 C) 11 D) 19 E) Answer not given How many games should it take Eho to gain 1008 yards? A) 4 B) 6 C) 8 D) 10 E) Answer not given Between Biff, Eho and John, what is the range of the total number of passes completed? A) 50

B) 10

C) 60

D) 115

E) Answer not given

5 6 7 8 9

What is the average number of passes John completes per game? A) 12 B) 17 C) 11 D) 19 E) Answer not given If Biff gets paid $50 per pass completed, how much has he earned? A) $2,300 B) $5,500 C) $6,700 D) $8,975 E) Answer not given Eho makes $100,000 plus $25 for each completed pass and $2 for each minute he plays. How much has Eho earned? A) $103,840 B) $116,790 C) $164,320 D) $183,460 E) Answer not given John is paid $1,000 per game plus $5 per yard gained. How much has he made? A) $15,400 B) $13,970 C) $14,940 D) $20,200 E) Answer not given If Biff throws 32 passes, how many yards would be expected to be gained? A) 318

B) 421

C) 456

D) 484

E) Answer not given


4th Grade – May 14, 2005 Team Contest – Written by Tom Clymer

TEAM TEST - 15 minutes

When you are prompted to begin, tear off the colored sheet and give a copy of the test to each of your team members and begin testing. This test is scored as a 1 or 0. Express all non-integer answers as fractions unless stated otherwise or it is a problem dealing with money and in that case, a decimal answer should be given. For fifth & sixth grade, make sure all fractions and ratios are reduced. Units are not needed except on questions that deal with time and, in that case, a.m. or p.m. is needed. If you choose to use units, you must use them correctly.

1 2 3 4 5 6 7 8 9 10

How many positive three-digit numbers are composed of three different odd digits? A snake’s length is equal to 80 centimeters plus one third of its length. How long is the snake, in centimeters? How many ways can you make change for $2.00 using only quarters, dimes, and/or nickels? What is the result when I begin with the number 12, square it, subtract 50, divide by 2, and add 16? How many diagonals can be drawn in a convex octagon?

3 and 4.8 5 If hamburgers cost $2.15 each, french fries cost $1.50 per order, and beverages cost $0.95 each, how much, in dollars, will a family of four spend on dinner if each person orders a hamburger, french fries, and a beverage? A prime number is a counting number greater than one which does not have any factors other than itself and one. For example, 11 and 13 are prime numbers, but 12 is not. What is the sum of the squares of the prime numbers less than 10? Anand, Bob, and Ciara seat themselves in three of five empty desks. How many ways can they do this? Arrange the letters A-D in increasing order, if A = 4×3+ 9 88 B= 4 C = 52 − 32 Express as a mixed number: 175% of the sum of 9

82 D= 9


4th Grade – May 14, 2005 Relay Contest – Written by Tom Tosch


Person 1 Person 2 Person 3 Person 4

Relay #1

Answer

How many sides does a pentagon have?

5

What is TNYWG squared?

25

What is the smallest prime number larger than TNYWG?

29

What is the remainder when TNYWG is divided by 3?

2

Relay #2

Answer

Person 1 What is 5 + 7 + 9 + 11? Person 2 What is the difference between TNYWG and (8 + 3 – 2 + 11 +

12

Person 3

1/36

Person 4

16 – 16)? What is the probability of rolling a sum of TNYWG with two fair six sided dice? What is the reciprocal of TNYWG?

32

36



Final Score:

KEY


Mental Math Contest


PERSON 1 NAME: 1.1 What is the sum of seventeen and thirty-one?

1.2 1.3 1.4

1 or 0 48

What is the quotient of forty-eight and four?

12

What is 13 squared?

169

The area of a triangle is 18. The height and base are equal. What is the height? PERSON 2 NAME: 2.1 What is the positive difference between nine and fifty-three?

2.2 2.3

6

44

What is the product of seven and twelve?

84

What is the difference between the sum of the first two even positive integers and the product of the first two odd positive integers?

3

2.4

How many different outfits can be made from four shirts, five pairs of pants and three hats? PERSON 3 NAME: 3.1 What is the sum of forty-three and twenty-eight?

3.2 3.3 3.4

[outfits]

71

What is the product of fourteen and six?

84

What is the perimeter of a rectangle with sides measuring four centimeters by nine centimeters? How many sides does a dodecagon have?

26 [cm] 12

PERSON 4 NAME: 4.1 What is the positive difference between sixty-seven and thirty-nine?

4.2 4.3 4.4

60

28

What is the quotient of ninety-one and seven?

13

How many feet are in a mile?

5280 [ft]

What positive number, when multiplied by itself, results in forty-nine?

7



Division 1 & 2 Written by Tom Tosch


1 2 3 4

5 6 7 7 8

Problem Joe has 24 identical math books that weigh a total of 72 pounds. How much, in pounds, does two math books weigh? What is 487 less than 734?

Answer 6 [lbs]

When you flip a fair coin two times, what is the chance of getting two heads? A sunburst star is made by drawing an outward-pointing equilateral triangle on each side of a regular octagon where each side of the equilateral triangle is the same length as each side of the regular octagon. How many sides does this sunburst star have? What is the smallest number that is greater than 1 that has a remainder of 1 when you divide by each of 2, 3 and 5? What is the greatest number of days possible in two consecutive months? The ratio of boys to girls in a classroom is 4:5 and there are 27 students total. How many girls are there in the classroom?

¼

247

16 [sides]

31 62 [days] 15 [girls]

Extra Problem – Only if Needed If “x” equals two, what is three “x” minus ten?

-4



Division 1 & 2 Written by Tom Tosch


1 2 3 4 5 6 7 7.1 8

Problem How many prime numbers are between 20 and 40?

Answer 4 [numbers]

David bought an ocelot for $1.79, and paid for it with a $5 bill. He got as much of his change as possible in quarters. How many quarters did he get? What time is one hour and thirty-nine minutes after 10:43AM?

12 [quarters]

Amy has 3 cats, 2 turtles and 3 birds as pets. How many total feet does her pets have? Mike lives 120 miles from his friend George. His parents drive him to George’s house at 30 miles per hour and they return at 40 miles per hour. How many hours did they spend traveling? What is the sum of the first 5 positive odd numbers?

26 [feet]

12:22 PM

7 [hours]

25

If I double the side length of a square with an area of 9, what is the 36 area of the new square? Extra Problem – Only if Needed What is the total value of three quarters, five dimes, two nickels and four pennies, in cents?

139 [cents]



Division 1 & 2 Written by Cameron Frederick


1 2 3 4 5 6 7 7.1 8

Problem Josh jumps on his trampoline 5 times every 10 seconds. How many times does he jump on his trampoline in 6 minutes? How many fluid ounces are in a quart?

Answer 180 [times]

David buys three DVDs and two boxes of candy for $59.05. If the DVDs cost $17.85 apiece, how much, in dollars, is a box of candy? A football field is 100 yards long. How long, in feet, are 4 football fields? What is the mean of the numbers 28, 25, 33 and 34?

[$] 2.75

How many different ways can I reorder the letters in the word “F-O-O-D”? Roger Rabbit eats 17 carrots, 11 cabbages, 4 radishes, and 8 beets from Farmer Frank’s field. How many vegetables did he eat in all?

32 [ounces]

1200 [ft] 30 12 [ways] 40 [veggies]

Extra Problem – Only if Needed What is the next number in the sequence: 1, 3, 9, 27, …?

81


Final Score:

KEY


School Name__________________________________Team #________

First Score



2 [diag] 2466 168 18 115 80 [sheep] 6 8 [pieces] 6 44 [goldfish] 6 45 [handshakes] 8 25 15 16 120 [ways] 46 1111 th

6 [day]

1 or 0 1 or 0

Answer 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

1 156 11 [sums] 330 [miles] 6 [un2] 28 [pieces] 40 [°] Tuesday [$] 70.00 7:3 341 9 7 50 [yards] 0 11 13 [students] 25 [feet]

40

8/25

1

48

π [ft3]

1 or 0

1 or 0


Final Score:

KEY




Division:


1 2 3 4 5 6 7 8 9 10

Answer E (500) C B C B B A D D

-1, 0 or 2

-1, 0 or 2


Final Score:

KEY




Answer

1 2 3 4 5 6 7 8 9 10 10

60 [numbers] 120 [cm] 97 [ways] 63 20 [diag] 25

1 5

[$] 18.40 87 60 [ways] DCAB

1 or 0

1 or 0


KEY

School:_______________________________Team #________ Proctor: ______________________________ Room #_______Div Written by Tom Tosch


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

5

25

29

2

1 or 0

1 or 0

1 or 0

2 or 0


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

32

12

1/36

36

1 or 0

1 or 0

1 or 0

2 or 0



Final Score: (Out of 16)


PERSON 1 NAME:

1.1 1.2 1.3 1.4 PERSON 2 NAME:

2.1 2.2 2.3 2.4 PERSON 3 NAME:

3.1 3.2 3.3 3.4 PERSON 4 NAME:

4.1 4.2 4.3 4.4

1 or 0


Final Score:


School Name__________________________________Team #________

First Score


STUDENT NAME________________________________Division: Individual Contest – Score Sheet DO NOT WRITE IN SHADED REGIONS Answer

1 or 0 1 or 0

Answer

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

2 [diag] 2466 168 18 115 5 [sheep] 6 8 [pieces] 6 44 [goldfish] 6 45 [handshakes] 8 25 15 16 120 [ways] 46 1111

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

1 156 11 [sums] 330 [miles] 6 [un2] 28 [pieces] 40 [°] Tuesday [$] 70.00 7:3 341 9 7 50 [yards] 0 11 13 [students] 25 [feet]

20

6th [day]

40

8/25

fLt3]

[

1 or 0

1 or 0


Final Score:




Division:


Answer

1 2 3 4 5 6 7 8 9 10

-1, 0 or 2

-1, 0 or 2


Final Score:





Answer

1 2 3 4 5 6 7 8 9 10 10

1 or 0

1 or 0


4th Grade – April 21, 2006 Individual Contest GENERAL INSTRUCTIONS

Good sportsmanship is expected throughout the competition by all involved. Bad sportsmanship may result in disqualification. Calculators may not be used on any portion of this contest. Express all non-integer answers as fractions unless stated otherwise or it is a problem dealing with money, and in that case, a decimal answer should be given. For 5th and 6th grade, all fractions and ratios must be reduced. Units are not necessary unless it is a problem that deals with time and, in that case, am or pm is needed. However, if you choose to use units, they must be correct. Leave all answers in terms of B where applicable. Do not round any answers unless stated otherwise. Record all answers on the colored cover sheets in the answer column only. Make sure all answer sheets have all the information filled out at the top of the sheet. Tests will be scored as a 0 if answers are not recorded correctly on the answer sheets. Blank answer sheets and answer sheets with no name will also be scored as a 0. INDIVIDUAL TEST - 35 minutes

When you are prompted to begin, tear off the colored sheet and begin testing. Make sure your name and school are recorded on the answer sheet. This test is scored as a 1 or 0. Express all non-integer answers as fractions unless stated otherwise or it is a problem dealing with money and in that case, a decimal answer should be given. For 4th & 4th grade, make sure all fractions and ratios are reduced. Units are not needed except on questions that deal with time and, in that case, a.m. or p.m. is needed. If you choose to use units, you must use them correctly. Record your answers on the score sheet. No talking during the test.

Record all answers on the colored cover sheet. Evaluate: 19267 - 17261

1 2 3 4 5 6 7 8

Jolanda bakes three pizzas, each consisting of 8 slices. How many slices did Jolanda bake? If a TI-89 (graphing calculator) has 50 buttons, how many buttons are on 7 TI89’s? How many hours are there in 4 days? Evaluate: 213 times 489 If Ronaldo drove 223 miles from Bainbridge to Walla Walla, how long, in miles, will he have driven round trip if he takes the same route back? What is the difference between the number of months in a year and the number of days in a week? Jimmy paid $3.20 for 4 watermelons. How much did one melon cost, in dollars?

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Pens cost 39 cents each. Tishi wants to buy 9 pens. How much will it cost, in dollars, to buy 9 pens? Evaluate: 555 – 444 + 333 – 222 + 111 To hit a homerun, Roy must hit a baseball 300 feet. Roy hit the ball 138 feet. How much farther, in feet, must he hit the ball next time to hit a homerun? Henry has a rose garden. He plants the roses in rows of 8 with 47 roses in each row. How many roses did he plant? An odd number plus an even will always be even or odd? If the moon is 250,000 miles from the earth, how long, in hours, would it take to get there if you travel at 250 miles per hour? How many positive factors does 23 have? Cheng has 4 lights that together consume 400 watts. After he turns 3 off, how many watts will be consumed if all bulbs consume watts equally? Find the larger of two numbers whose sum is 6 and whose positive difference is 4? Lafondah bought a shirt on sale at 50% off for $25. What was the original cost of the shirt, in dollars? What is the remainder when 37 is divided by 11?

0 1 2 3 + + + 2 2 2 2 Kyl Wellman and his 95 pounds of fighting fury can answer 65 calculus questions per hour. If he enters a calculus contest lasting 6 hours and answers all questions with no time to spare, how many questions did he answer? I am thinking of a two-digit number less than 50. The difference between the digits is four. When the digits are multiplied together, the result is 5. What is the number? What is the probability of rolling a number less than 4 on a fair 6 sided die? Evaluate

What is the area of a circle of radius 9? How many sides does a dodecagon have? Sampson is four times as old as Biggerstaff who is twice as old as Silas. If Silas is 22, how old is Sampson, in years? What is the median of 7, 12, 4, 60, 88, 9, 31, 14, 25, 36, 17? William Faulkner’s The Sound and the Fury is 567 pages long. If Will can read 20 pages a day, on what day after he starts reading will he finish the book? Find two numbers whose product is 30 and whose difference is 13.


A rabbit and cat both run up a set of stairs. The cat takes the stairs 3 at a time and rabbit five at a time. What is the first step they both land on assuming they start on the ground? What is the probability of rolling a sum of 4 on two six-sided fair dice? What number belongs in the blank? 31 + 9 + 6 + 4 = 60 + 5 + 3 - __ Biff and Eho ran a race consisting of two unequal legs. Biff ran his leg in 8 minutes at a constant speed of 125 meters per minute. Eho ran his leg in 4 minutes at a constant speed of 110 meters per minute. How far, in meters, did Biff and Eho run in total? Square “A” has 1/4th the area of square “B” who has a perimeter of 24. What is the perimeter of the smaller square? Shashawnda received an 87%, 93%, 94%, and an 80% on four tests. What is the minimum percentage Shashawnda must get on the next test to have an average of 90% over the five tests? What is the probability of drawing two cards of the same suit (Spades, Hearts, Clubs or Diamonds) from a standard deck of cards? There are 19 heads in a field of ducks and camels and 62 legs. How many camels are in the field? If today is August 27 and the digital clock shows 10:00 in the morning, how many more times will the clock show 10:00 that month? If 3 men can drink 3 glasses of water in 3 minutes, how long will it take 5 men to drink 5 glasses? John woke up at 9 AM. He spent 6 hours at school, followed by half that time at Basketball, and then half of time spent at Basketball was spent at dinner. At what time did John finish eating dinner? (Include AM or PM in the answer.)


4th Grade – April 21, 2006 Team Multiple Choice Contest TEAM MULTIPLE CHOICE - 15 minutes This test is the only test where you will be penalized for incorrect responses. You will receive 2 points for a correct letter response, 0 points for leaving it blank and -1 point for an incorrect response. When you are prompted to begin, tear off the colored sheet, pass out a copy of the test to each team member, and begin testing. Since this is a multiple choice test, ONLY a letter response should be listed as an answer on the answer sheet.

Andy’s marbles Andy has 200 marbles. 1/2 of them are red 1/4 of them are blue 1/8 of them are green 1/8 of them are yellow

1 2 3

How many red marbles does Andy have? A) 50 B) 100 C) 200 D) 400 E) Answer not given Andy’s friend, Mandy, tells him that his marbles are worth a lot of money. She says that if he sold all of his blue marbles he would get $25. If every type of marble costs the same, how much is his whole collection worth? A) $25 B) $75 C) $100 D) $200 E) Answer not given What pie chart represents Andy’s marble collection? yellow

green

red

red

B) green

A) blue yellow red green

blue

yellow green red

4 5

blue blue D) E) Answer not given C) If Andy wanted to give Mandy exactly half of his yellow marbles, how many would he give? A) 12 B) 13 C) 25 D) 4 E) Answer not given Andy wants to play a game of marbles where blue marbles are not allowed. How many marbles can he use? A) 150 B) 200 C) 175 D) 50 E) Answer not given

6

Andy wonders how much bigger his yellow marbles are than his green marbles. He lines up some green marbles next to some yellow marbles. How many times bigger across are the yellow marbles?. green yellow

7 8

9

A) 1 B) 2 C) 3 D) 4 E) 5 Late at night one night, Andy needs two marbles of the same color – and he doesn’t care what color. How many marbles does he need to pull out of the bag (he can’t see them and they are the same size) to be sure he has at least two of the same color? A) 5 B) 2 C) 26 D) 1 E) 200 Andy lets Mandy borrow his marbles. She decides to make triangles out of them. She makes a triangle by putting down one marble, then two below it, then three below those, like the picture on the right. If she keeps going until she makes a row with six marbles, how many marbles will it take? A) 6 B) 15 C) 21 D) 36 E) 58 When Mandy is done playing with marbles, she writes the numbers 1 2 3 4 5 6 7 8 9 very big on a sidewalk. She wants to jump over one number at a time, so she steps on 2, then 4, then 6. What number does she want to step on next? A) 1 B) 3 C) 8 D) 9 E) 4


4th Grade – April 21, 2006 Team Contest TEAM TEST - 15 minutes

When you are prompted to begin, tear off the colored sheet and give a copy of the test to each of your team members and begin testing. This test is scored as a 2 or 0. Express all non-integer answers as fractions unless stated otherwise or it is a problem dealing with money and in that case, a decimal answer should be given. For 5th & 6th grade, make sure all fractions and ratios are reduced. Units are not needed except on questions that deal with time and, in that case, a.m. or p.m. is needed. If you choose to use units, you must use them correctly.

1 2 3 4 5 6 7 8

9 10

Ten fish can eat 10 worms in 10 seconds. At this rate, how many seconds would it take 30 fish to eat 30 worms? In writing the counting numbers 1 through 100, what is the 50th digit you would write? A sign points north toward Motown with a distance of 92 miles, and south toward Notown, with a distance of 41 miles. Motown and Notown are along the same straight road. How many miles apart are Motown and Notown? The rule for a certain number pattern or sequence is to subtract 3 from a number of the sequence to get the next number of the sequence. If the first number of the sequence is 13, what is the 4th number of the sequence? Terry buys a dozen cookies for $4, then sells them again at 2 for $1. How many dollars profit does Terry make? (Profit is the amount of money you get to keep after you have paid your expenses out of your income.) In a certain year, September had 5 Mondays but only 4 Tuesdays. On what day of the week was September 20th of that year? Adding 30 to my number then subtracting 21 gives the same result as subtracting 81 from my number then adding what? In the Kingdom of Boredom, the unit of money is the “duller” (symbol: D). There are 1-D bills, 2-D bills, and 3-D bills, but no 4-D or 5-D bills. In how many ways can you make exactly 6 dullers using these bills? (Consider two ways to be the same if they use the same bills, even if they are in a different order.) Laura arrived at school at 8:23 AM. If Laura had arrived at school half an hour earlier, she would have arrived 19 minutes before the start of school. What time does Laura’s school start? What is the perimeter, in inches, of a square with area 49 square inches?


4th Grade – April 21, 2006 Relay Contest RELAYS - 5 minutes per relay There is no talking during this event and you must always be facing forward. Person #1 will be given an answer sheet(s) and will need to fill out the top. The proctor will hand out a strip of paper to each person. These need to be face down on your desk until it is time for the relay to start. Once the relay begins, everyone may turn over their strip of paper and begin working. You may write on the strip of paper to come up with your answer. However, when person #1 figures out his/her problem, he/she will record just his/her final answer on the answer sheet and pass only the answer sheet back to the person behind. This continues until person #4 puts an answer on the answer sheet and gives it to the proctor. A correct answer from person #1, #2 and #3 is worth 1 point each. A correct answer from person #4 is worth 2 points making each relay worth 5 points. You will see the expression TNYWG [Proctor: write this on the board] which means: “the number you will get”. This is where you put your teammate’s answer that they pass back to you, and then you should be able to solve your question. Once the relay begins, turn over your strip of paper and make sure you have the right person number. Remember, no talking and remain facing forward to avoid being disqualified!

Person 1 Person 2 Person 3 Person 4 Person 1 Person 2 Person 3 Person 4 Person 1

Practice Relay

Answer

4x2x3

24

TNYWG ÷ 3

8

TNYWG x 4

32

TNYWG - 25

7

Relay #1

Answer

23 - 17

6

The number of inches in TNYWG feet.

72

TNYWG ÷ 3

24

The number of feet in TNYWG inches.

2

Relay #2

Answer

If NASA can launch a space shuttle for 1/2 billion dollars, how many can it launch with 3 billion dollars? If 2/3 of all scheduled launches are cancelled due to inclement weather, how many of TNYWG launches will actually launch?

6 [shuttles]

Person 3 If a space shuttle carries 7 people, how many people will be

2 [launches/ shuttles] 14 [people]

Person 4

7 [people]

Person 2

launched into space in TNYWG launches? If half of all people launched into orbit space walk, how many people out of TNYWG will actually space walk?



Final Score:

KEY


Mental Math Contest


PERSON 1 NAME: 1.1 What is the product of 9 and 8?

1.2 1.3 1.4

What is the average of 15, 20 and 25?

20


3

What is the perimeter of a pentagon with side length 5?

25


2.2 2.3 2.4

2


9

How many pints are in a gallon?

8 [pints] 42

What is the difference between 34 and the product of 2 and 12?

10


8

How many feet are in three and one-third yards?

10 [feet]


4.2 4.3 4.4

28

What is the remainder when three hundred seventy two is divided by five?


3.2 3.3 3.4

1 or 0 72

36

What is three-quarters of 200?

150


76

How many nickels are in 4 dollars?

80 [nick]



Division 1 COLLEGE KNOWLEDGE BOWL ROUND #1 #

Problem

1

If an elevator can hold 13 people, how many can 3 elevators hold?

Answer 39 [people]

2 A new parking garage can hold one and a half times the

750 [cars]

3 What is the area of a square with perimeter 32?

64

4 I’m thinking of a number between 1 and 23 that is

12

5 How many days have passed in 96 hours?

4 [days]

6 How many sides does a heptagon have?

7 [sides]

7 When will it be 2 hours and 17 minutes past 7:54 pm?

10:11 pm

number of cars as the old garage, which held 500 cars. How many cars will the new garage hold?

divisible by 2, 3, 4, and 6. What is it?

7

Extra Problem – Only if Needed

8 How many digits are in 9 squared?

2 [digits]



Division 1


Problem

1

If the digits in 2006 are multiplied, what is the resulting product?

2

If Sean was born in 1987, what is his youngest possible age at any time in 2005, in years?

17 [years]

3

A piano has 88 keys, with 36 of them being black. How many are white?

52 [keys]

4

How many faces does a cube have?

6 [faces]

5

Nine consecutive numbers have a sum of 99. What is the average of these numbers?

11

6

A man walks 3 feet into a street and is 1/8 the way to the other side. How much farther, in feet, must he walk to get the other side?

21 [feet]

7

What is the probability of rolling an 8 on a fair 8 sided die?

1/8

7.1 8

Answer 0

Extra Problem – Only if Needed What is the largest two digit prime number?

97



Division 1


Problem

1

A house has 27 windows, only one-third are open. How many windows are closed?

2

How many odd numbers are between 10 and 40?

3

A three ring binder has 42 pages contained in the rings. How many holes were punched?

4

The light in a lighthouse revolves 20 times a minute. How many revolutions will be completed in one hour?

1200 [rev]

5

What is 64 minus the quantity 8 times 8?

0

6

Today, Frank is 4 years older than Tom. In five years how many years older will Frank be than Tom?

4 [years]

7

What is the perimeter of a regular octagon with side length of four and one-half?

36

7.1 8

Answer 18 [win]

15 [numbers] 126 [holes]

Extra Problem – Only if Needed What is 24 x 3?

72




Problem

Answer

1

What is the sum of 8 nines and 3 squared?

81

2 What is 33 + 55 + 25 + 2 = _____?

115

3 Sam won the fifty meter freestyle race with a time of 2 2.5 [min] minutes. He then won his next race with a time of 3 minutes. What was his average time for the two races, in minutes? [Express answer as a decimal.]

4 What is the perimeter of a rhombus with side length 11? 44 5 During a basketball game, Jones scored 3 points. Henry

18 [points]

6 What do I get if I divide 12 by 12 and then multiply by

12

7 Evaluate: 128 plus the quantity 82 divided by 2

169

scored twice as many points as Jones and Tina scored 3 times as many points as Henry. How many points did Tina score?

12?

7

Extra Problem – Only if Needed

8 What is the units or ones place of 99 times 996

4



Division 2


Problem

Answer

1

Eleven times what number is 132?

12

2

Jim has five different pairs of shorts and 5 different shirts. How many different combinations can be made?

25 [comb]

3

What time is it 2 hours and 17 minutes before 4:37 pm?

2:20 pm

4

133 is 47 more than what number?

86

5

What is 8 divided by 2 divided by 2 times 1?

2

6

What is the circumference, in inches, of a circle with radius of 8 inches?

16π [inches]

7

What do I get if I divide 20 by 10 and then multiply by 11? 22

7.1 8

Extra Problem – Only if Needed Johnny bought new socks at the Gap that cost $4.40. Before he paid for the socks, he realized he only had quarters. To the nearest whole quarter, how many quarters did Johnny need to pay?

18 [quarters]



Division 2


Problem

Answer

1

What is the area of a triangle with a base of 7 and a height of 10?

35

2

Demitri left for school at 8 am. He walked to Jim’s house which took 13 minutes and then walked to the basketball court which took him 15 minutes. He and Jim played for 20 minutes and then walked the remainder of the distance to school which took 8 minutes. At what time did they arrive at school?

8:56 AM

3

While signing copies of her new book, Harry Potter and the 14 [letters] Half Blood Prince, J.K. Rowling used all letters of the alphabet that came after I but before X. How many letters did she use?

4

What is 17 minus 16 plus 12 minus 4 minus 4 minus 3?

2

5

What is the probability of rolling an even number on a six sided die?

½ or 3/6

6

What time is it 2 hours and 23 minutes after 10:35 pm?

12:58 AM

7

James gets a monthly allowance of $7.50. How much money total does he get in allowance each year, in dollars?

[$] 90

7.1 8

Extra Problem – Only if Needed What is the sum of all the one digit prime numbers?

17


Final Score:

KEY


School Name__________________________________Team #________

First Score



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

2006 24 [slices] 350 [buttons] 96 [hours] 104,157 446 [miles] 5 [$] 0.80 [$] 3.51 333 162 [ft] 376 [roses] Odd 1,000 [hours] 2 [factors] 100 [watts] 5 [$] 50 4 3

1 or 0 1 or 0

Answer

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

390 [questions] 15 1/2 or 3/6 81π 12 [sides] 176 [years] 17 29th [day] 2 and 15 15 [th Step] 1/12 or 3/36 18 1440 [meters] 12 96 [%] 12/51 or 4/17 12 [camels] 9 [times] 3 [minutes] 7:30 PM

1 or 0

1 or 0


Final Score:

KEY



First Score

(out of 18)

Division:


1 2 3 4 5 6 7 8 9 10

Answer B C D E (he can’t) A B A C C

-1, 0 or 2

-1, 0 or 2


Final Score:

KEY



First Score

(out of 20)


1 2 3 4 5 6 7 8 9 10 10

Answer 10 [seconds] 3 133 [miles] 4 [$] 2 Friday 90 7 [ways] 8:12 AM 28 [inches]

2 or 0

2 or 0


4th Grade – May 20, 2006 Individual Contest GENERAL INSTRUCTIONS

Good sportsmanship is expected throughout the competition by all involved. Bad sportsmanship may result in disqualification. Calculators or any other aids may not be used on any portion of this contest. On all tests, except multiple choice, express all rational, non-integer answers as reduced common fractions unless stated otherwise or it is a problem dealing with money and in that case, a decimal answer should be given. For fifth and sixth grade, all fractions and ratios must be reduced. Units are not necessary unless it is a problem that deals with time and, in that case, am or pm is needed. However, if you choose to use units, they must be correct. Leave all answers in terms of π where applicable. Do not round any answers unless stated otherwise. Record all answers on the colored cover sheets in the answer column only. Make sure all answer sheets have all the information filled out at the top of the sheet. Tests will be scored as a 0 if answers are not recorded correctly on the answer sheets. Blank answer sheets and answer sheets with no name will also be scored as a 0. INDIVIDUAL TEST - 35 minutes



1 2 3 4 5 6 7


8

Sally bought 12 “Math is Cool” t-shirts for $144. How much did each t-shirt cost, in dollars? [Express answer as a decimal.]

9

Marcy went to the pet store and bought a rabbit and a goldfish, she spent $24.00. The rabbit cost twice as much as the goldfish, how much, in dollars, did she pay for the rabbit? [Express answer as a decimal.]

If one clown can hold 4 balloons, how many clowns does it take to hold 32 balloons? Find the product of 78 and 27. Find the quotient of 221 and 13. Evaluate: 5(3 + 5) - 6 In 1997 Don was 29 years old. On the same day in 2007, how many years old is Don? Diesel costs $3.29 a gallon. How much, in dollars, will it cost to fill a diesel tank that holds 33 gallons? [Express answer as a decimal.]

10 11 12 13

It takes the sound of thunder five seconds to travel a mile. How far away, in miles, is the thunder if it takes the sound 55 seconds to reach you?

5 8 Write the following reduced fraction as a mixed number: 11/4 Write the following mixed number as a reduced fraction: 3

Compare the following pairs of numbers using <, = or >. 5/6

7/8

14

Joe wants to buy the largest number of pieces of candy as possible. One type of candy sells for 18¢ for 5 pieces and another type sells for 13¢ for 4 pieces. What is the largest number of pieces of candy he can buy for 77¢ if the candy must be bought in those increments?

15

On the first day Eho walked for 3 hours 32 minutes. On the second day he walked for 6 hours 55 minutes and on the last day he walked for 2 hours and 48 minutes. How many total hours did he walk? [Express answer as a mixed number.]

16

Joe has a garden that was 30 feet by 40 feet. He put a sidewalk around the garden that was 3 feet wide. What is the outside perimeter of the sidewalk, in feet?

17

For every 100 families with TV sets, 12 families like watching sports. In a town of 23,400 families who all have TV sets, how many families would like watching sports?

18

At the end of a board game, Al had $57 of game dollars. During the game he had won $200, lost $150, won $25, lost $10, and lost $35. How much money did Al have at the start, in dollars? [Express answer as a decimal.]

19

If a notebook holds 70 pages, how many pages would eight and one-half notebooks hold?

20 21

How many lines of symmetry does a square have?

22

A school charges $7.00 for adult tickets and $4.00 for student tickets to a school play. The cost of the production of the play was $800. The drama club made $1140 after the cost of the production was deducted. How many student tickets were sold if 410 tickets were sold in all?

23

Biff and Eho were tossing fair coins. Biff tossed his fair coin 23 times while Eho tossed his fair coin 22 times. What is the probability that Biff gets more heads than

Bill spent $34.26 on shoes and $74.26 on a skate board. After his purchases he had $18.26. How much money, in dollars, did he have when he started shopping? [Express answer as a decimal.]

Eho?

24

A clothing store is selling shirts for $20.00. They decided to raise the price of the shirt by 20%. A few days later they decided to raise the price another 20%. What is the new price of the shirt, in dollars? [Express answer as a decimal.]

25

Annie bought a calculator for $121.17. She paid $125.00. The store was out of dollar bills and all they had was quarters, dimes, nickels and pennies. What is the smallest number of coins she could receive as change?

26

Mara bought some flowers to plant in her garden. When she separated the plants into groups of three, she had one plant left over. When she separated the plants into groups of five, she had one plant left over. When she separated the plants into groups of eight, she had none left over. What is the smallest number of plants that Mara could have bought?

27

Patrick, Tony and Neil live in a row of three houses on the same street. Walking past their houses, they pass a white house first, then a green house, then a blue house. Patrick lives next door to the green house. Tony does not live next door to his friend who lives in the blue house. Who lives in the blue house?

28

Two numbers have a sum of 9 and a product of 20. What is the smallest of these two numbers?

29

A 6-inch diameter pizza costs $8.00 while a 12-inch diameter pizza costs $16.00. Which pizza is the better deal? If you feel the 6-inch diameter pizza is the better deal write down 6 as you answer. If you feel the 12-inch diameter pizza is the best deal write down 12 as your answer. If you feel neither is a better deal (they are the same value), write down neither.


Fred and Ed went on a three day hike. Each day they hiked 10 miles. The first day it took them 3 hours of hiking to travel 10 miles. The next day it took 5 hours. If the average rate of speed for the entire trip was 2.5 miles per hour, how many hours did it take them to hike the 10 miles on the third day?

31 32

How many numbers between 10 and 50 (inclusive) are divisible by 2, 3 or 5?

33

A bag contains red, green and blue marbles. Joe is told 60% of the marbles are blue and that the bag contains 23 red marbles and 33 green marbles. How many

A ball returns to one-half its dropped height. By the time it hits the ground the fourth time, it has traveled up and a down a total of 66 feet. From what height was it dropped, in feet?

blue marbles are in the bag?

34

Write the four letters from smallest to greatest given the following are true: A+B=B+B+B A+A
35

A 200 acre wheat field averaged 40 bushels per acre. A 150 acre wheat field averaged 60 bushels per acre. What was the overall average, bushels per acre, on the 350 acres? [Express answer as a decimal to the nearest whole number.]

36

Of the 64 proctors volunteering today, all are on the Mt. Spokane Math Team. 36 are taking AP Calculus, 18 are taking AP Biology, 16 are taking AP English, 4 are taking AP Biology and AP Calculus, 7 are taking AP Biology and AP English and 5 are taking AP Calculus and AP English. Seven are not taking any AP courses. How many are taking all three courses AP Biology, AP Calculus and AP English at the same time?

37

Each time the two hands on a certain standard 12-hour clock form a 180° angle, a bell chimes once. From noon today until noon tomorrow, how many chimes will be heard?

38

Let A = the area of a trapezoid with a height of 6 and one base length of 8 and another base length of 5. Let B = the area of a rectangle with diagonal of length 13 and a side length of 5. Find A + B.

39

In a river with a steady current, it takes a frog 20 minutes to swim a certain distance upstream, but it takes her only 10 minutes to swim back. How many minutes would it take a stick to float this same distance downstream?

40

At a grade school, only two students have the same (two letter) initials. What is the largest number of students that could possibly attend this school with different names?


4th Grade – May 20, 2006 Team Multiple Choice Contest TEAM MULTIPLE CHOICE - 15 minutes


Water flows into the reservoir at 5,000 cubic feet per minute (cfm). When all 20 adjustable spillway gates, gates at the base of the dam that allow water to flow out of the reservoir, are open one foot, a total of 1000 cfm of water is released. Reservoir

Face of Dam

750 feet 4,000 feet

10,000 feet

1

How tall, in feet, is the dam? A) 10,000

2

B) 4,000

C) 750

D) 500

E) Answer not given

What is the area of the bottom floor of the reservoir, in square feet? A) 7,500,000

B) 3,000,000

E) Answer not given

C) 30,000,000,000

D) 100,000,000

3

What is the maximum volume of water the reservoir will hold, in cubic feet? A) 100,000,000

4

B) 7,500,000

C) 3,000,000

D) 30,000,000,000

E) Answer not given A new hydro-electric power plant was added to the dam, consuming 1,000 cfm to produce 10 mega watts of power for the nearby town. During the summer, however, 20 mega watts are needed for the heavy air conditioning use. How many cfm of water must flow through the power plant to accommodate this need?

5

A) 2,000 B) 2,500 C) 2,200 D) 2,400 E) Answer not given What consistent height, in feet, must all the spillway gates be open to keep the reservoir level constant?

6

A) 4.5 B) 5 C) 6 D) 4 E) Answer not given If the reservoir water level is at 700 feet but needs to be raised to 725 feet, how many minutes will it take with all the spillway gates open at 1 foot?

7

A) 250,000 B) 275,000 C) 2,000 D) 30,000 E) Answer not given Divers have realized that only 15 of the 20 spillway gates are operating. What consistent height, in feet, must the 15 gates be open to allow the reservoir to remain at a constant height?

8

A) 6 B) 20/3 C) 7 D) 7.5 E) Answer not given How many minutes would it take a full reservoir to empty if all the gates are open 10 feet?

9

A) 3,000,000 B) 4,500,000 C) 6,000,000 D) 7,500,000 E) Answer not given How many tons of water is in a full reservoir, if 1 cubic foot of water equals 8 gallons, 1 gallon equals 8 pounds, and 2,000 pounds equals 1 ton? A) 900,000,000 B) 960,000,000 C) 860,000,000 D) 800,000,000 E) Answer not given


4th Grade – May 20, 2006 Team Contest TEAM TEST - 15 minutes (note change in point value!)


1 2

3 4

My favorite math book is the seventeenth book from the left and the fourth book from the right on the bottom shelf of my bookcase. How many books are on the bottom shelf of my bookcase? Tom, along with his mother, father, grandmother, and younger siblings (his brother and his twin sisters), went out to dinner to celebrate his 13th birthday. The females of the family all ordered the $8.99 seafood special, and the males all ordered the $9.99 tofu mixed grill. In addition, the kids each had ice cream at $2.39, while the adults each had coffee at $1.79. In dollars, what was the total bill, ignoring tax? If you add my number to 93, then subtract that sum from 2006, the answer is the product of 18 and 80. What is my number? A B Rectangle ABCD is divided by straight line segments into 4 regions as in the diagram (not drawn to scale). The areas of 3 of the regions 40 56 are given. What is the area (in square units) of rectangle ABCD? 15 D

5 6 7 8 9 10

C

The number 8330 (which is written in standard notation) can be written in scientific notation as 8.33 x 103, where 103 means 10 x 10 x 10. Write in standard notation the number which is written in scientific notation as 2.4 x 105. Find the value of (9344 x 201) – (199 x 9344). In this problem, the symbol # between two numbers means to subtract the sum of the two numbers from the product of the two numbers. As in ordinary arithmetic, do operations inside the parentheses before operations outside the parentheses. Find (9 # 7) # 2. Tina needs two meters of ribbon to make a fancy bow. She has 12 meters of ribbon. How many cuts will it take for her to cut all the ribbon into lengths for making fancy bows? Annette travels 1 kilometer in 2 minutes. Babette travels 2 kilometers in 1 minute. How many minutes longer does it take the slower person to travel 10 kilometers than the faster person? Each of my 4 cards is one color on one side and a different color on the other side in the following combinations: red/green, green/purple, purple/orange, and orange/blue. I lay 3 of the cards out on the table and hide the 4th card. The cards on the table are showing the colors orange, purple, and blue. Name the 2 colors on the card I hid.


4th Grade – May 20, 2006 Relay Contest RELAYS - 5 minutes per relay

There is no talking during this event and you must always be facing forward. Person #1 will be given an answer sheet(s) and will need to fill out the top. The proctor will hand out a strip of paper to each person. These need to be face down on your desk until it is time for the relay to start. Once the relay begins, everyone may turn over their strip of paper and begin working. You may write on the strip of paper to come up with your answer. However, when person #1 figures out his/her problem, he/she will record just his/her final answer on the answer sheet and pass only the answer sheet back to the person behind. This continues until person #4 puts an answer on the answer sheet and gives it to the proctor. A correct answer from person #1, #2 and #3 is worth 1 point each. A correct answer from person #4 is worth 2 points making each relay worth 5 points. You will see the expression TNYWG [Proctor: write this on the board] which means: “the number you will get”. This is where you put your teammate’s answer that they pass back to you, and then you should be able to solve your question. Once the relay begins, turn over your strip of paper and make sure you have the right person number. Remember, no talking and remain facing forward to avoid being disqualified!

Relay #1 Person 1 Person 2 Person 3 Person 4

Person 1

Answer

Find the perimeter of an equilateral triangle with side length of 24 8. TNYWG + 6 10 Evaluate: + 32 − 5 5 If you live TNYWG miles away from school, how many miles is 20 [miles] the round trip? Find the sum of the factors of TNYWG. 42

Relay #2

Answer

Given a jar of 4 yellow, 3 red and 7 blue marbles, find the probability of drawing a red or yellow marble with one draw. Evaluate: TNYWG + TNYWG

7/14 or 1/2

Person 2 Person 3 Evaluate: TNYWG x (4 + 5 + 6 + 7 - 10) Person 4 Evaluate: TNYWG ÷ 3!

1 12 2



Final Score:

KEY


Mental Math Contest

When it is time to begin, I will read the first question twice. You may not do any writing or talking while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You may not change or cross out answers once you have written an answer down. If there are eraser marks, write-overs, or crossed out answers, they will be marked wrong. Once all students have laid their pencils on the desk, another question will be asked. If a student doesn’t lay his/her pencil down, the maximum wait time is 30 seconds from the second reading of the question before another question is asked. You may continue to work on a problem while the next question is being read. The value of each question is a one or zero. Each student may answer only four questions, and then another member of your team will come up, until each team member has had a turn. If your team has fewer than 4 members, missing team members will receive a zero.

PERSON 1 NAME: 1.1 Find the sum of twenty-one and twenty-two.

1.2 1.3 1.4

What is the greatest common factor of 24 and 30?

6

What is 4 factorial?

24

What is the sum, in degrees, of the exterior angles of a regular hexagon?

360 [°]

PERSON 2 NAME: 2.1 What is the product of twenty and two?

2.2 2.3 2.4

1 or 0 43

40

What quadrant is the point 8 comma 2 located?

1st

What is the least common multiple of 12 and 16?

48

How many times is the digit 2 used in the numbers 1 through 20, including 1 and 20? PERSON 3 NAME: 3.1 How many positive numbers less than forty are divisible by seven?

3 [times]

3.2 3.3

What day of the week will it be twenty days from next Saturday?

Friday

What is the area of a trapezoid whose height is 8 and bases have a sum of 12? What is the smallest integer greater than the square root of 110?

48

3.4

PERSON 4 NAME: 4.1 How many perfect squares are between 10 and 103?

4.2 4.3 4.4

5

11 7

What is the sum of the absolute value of negative 7 and 5 factorial?

127

Find the result after 20 is divided by 1/2 and 10 is added to the quotient.

50

Find the hypotenuse of a right triangle if the two legs are 5 and 12?

13



Division 1 & 2 COLLEGE KNOWLEDGE BOWL ROUND #1 #

Problem

1

A string of length 12 is cut into 3 pieces of equal length. What is the sum of the lengths of the three pieces? I have 17 cents. If I double the number of pennies I have, I would have 29 cents. How many pennies do I have? If I roll a regular 6-sided die two times, what is the probability I will roll the same number? What is the difference between the number that is 23 more than 49, and the number 17? The Hochstatter family went out to dinner. Each of the two parents’ meal cost $10. Each of the three teenagers’ meal cost $12 and, finally, Grace’s meal cost $15. What was the total cost, in dollars, of the meals for the Hochstatter family? A certain tree trunk splits into three large branches. Each large branch splits into four small branches. Each small branch splits into five twigs. What is the total number of twigs on this tree? Spongebob Squarepants wants to power his house with electric eels. Spongebob needs 117 watts of electricity. Each eel produces 3 watts of electricity. How many eels does Spongebob need?

2 3 4 5

6

7

Answer 12

12 [pennies]

1/6 55 [$] 71

60 [twigs]

39 [eels]

Extra Problem – Only if Needed 8 How many diagonals can be drawn in a regular quadrilateral?

2 [diagonals]



Division 1 & 2


Problem

1

Triscia was supposed to meet Annie at 2:13 PM. If Annie arrived 20 minutes early, then Annie arrived at what time? On a class test, everyone took the test and everyone got a different grade. Ali’s grade was both the 10th highest and the 10th lowest grade in the class. How many students were in the class? In how many different ways can the letters in the word CLOCK be arranged? What is the sum of the digits of the number representing the year 10 years from now? The average of two numbers is 8 and their product is 55. What is the larger of the two numbers? The year “1988” contains two equal digits. Of the years from 1988 through 2006, how many have three equal digits? The perimeter of a regular hexagon is 54. What is the length of each side?

2

3 4 5 6 7

Answer 1:53 PM

19 [students]

60 [ways] 9 11 2

9

Extra Problem – Only if Needed 8

Evaluate: Three cubed minus the product of the first two prime numbers.

21



Division 1 & 2


Problem

1

Grace read all pages in a chapter of a book, starting with page 20 and finishing with page 40. How many pages did Grace read? David paints twice as fast as Caleb. If it took Caleb 6 hours to paint a room, how long, in minutes, would it have taken if both had painted the room together? If today were Monday, the day after tomorrow would be what day? Evaluate: 1 + 11 + 111 + 1111

2 3 4 5 6

7 7.1 8

Answer 21 [pages]

120 [min]

Wednesday 1234

24 Find the product of the number of interior angles in a triangle and the number of sides in an octagon. Each time Tom’s phone rings, it rings for 3 seconds, then it’s 23 [sec] silent for 2 seconds before the next ring. If Tom’s phone rings 5 times, how many seconds does it take from the beginning of the first ring until the end of the final ring? A line and a circle are drawn on a piece of paper so that the 2 [times] line passes through the center of the circle. How many times does the line intersect the circle?

Extra Problem – Only if Needed What is one thousand nine hundred ninety rounded to the nearest hundred?

2000


Final Score:

KEY


School Name__________________________________Team #________

First Score



1 or 0 1 or 0

Answer

1

1617

21

[$] 126.78

2

8 [clowns]

22

310 [tickets]

3

2106

23

1/2

4

17

24

[$] 28.80

5

34

25

19 [coins]

6

39 [yrs]

26

16 [plants]

7

[$] 108.57

27

Patrick

8

[$] 12

28

4

9

[$] 16.00

29

12

10

11 [miles]

30

4 [hours]

11

29/8

31

29 [num]

12

2 3/4

32

24 [ft]

13

<

33

84 [blue mar]

14

22 [pieces]

34

D, B, A, C Order matters

15

13 1/4 [hrs]

35

49 [bus/acre]

16

164 [ft]

36

3 [stu]

17

2808 [fam]

37

22 [chimes]

18

[$] 27

38

99

19

595 [pgs]

39

40 [mins]

20

4 [lines]

40

677 [students]

1 or 0

1 or 0


Final Score:

KEY



First Score

(out of 18)

Division:


Answer

1 2 3 4 5 6 7 8 9 10

C E

(40,000,000)

D A B A B C B

-1, 0 or 2

-1, 0 or 2


Final Score:

KEY



First Score

(out of 20)


Answer

1 2 3 4 5 6 7 8 9 10 10

20 [books] [$] 80.86 473 132 [sq units or un2] 240,000 18,688 45 5 [cuts] 15 [minutes] red/green

2 or 0

2 or 0


KEY


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

24

10

20 [miles]

42

1 or 0

1 or 0

1 or 0

2 or 0


7/14 [or ½] 1 or 0

Answer for person

Answer for person

Answer for person

#2

#3

#4

1

12

2

1 or 0

1 or 0

2 or 0


Final Score:


School Name__________________________________Team #________

First Score



1 or 0 1 or 0

Answer

1

1617

21

[$] 126.78

2

8 [clowns]

22

310 [tickets]

3

2106

23

1/2

4

17

24

[$] 28.80

5

34

25

19 [coins]

6

39 [yrs]

26

16 [plants]

7

[$] 108.57

27

Patrick

8

[$] 12

28

4

9

[$] 16.00

29

12

10

11 [miles]

30

4 [hours]

11

29/8

31

29 [num]

12

2 3/4

32

24 [ft]

13

<

33

84 [blue mar]

14

22 [pieces]

34

D, B, A, C Order matters

15

13 1/4 [hrs]

35

49 [bus/acre]

16

164 [ft]

36

3 [stu]

17

2808 [fam]

37

22 [chimes]

18

[$] 27

38

99

19

595 [pgs]

39

40 [mins]

20

4 [lines]

40

677 [students]

1 or 0

1 or 0


Final Score:



First Score

(out of 18)

Division:


Answer

1 2 3 4 5 6 7 8 9 10

C E

(40,000,000)

D A B A B C B

-1, 0 or 2

-1, 0 or 2


Final Score:



First Score

(out of 20)


Answer

1 2 3 4 5 6 7 8 9 10 10

20 [books] [$] 80.86 473 132 [sq units or un2] 240,000 18,688 45 5 [cuts] 15 [minutes] red/green

2 or 0

2 or 0



Final Score:

(Out of 16)


PERSON 1 NAME:

1.1 1.2 1.3 1.4 PERSON 2 NAME:

2.1 2.2 2.3 2.4 PERSON 3 NAME:

3.1 3.2 3.3 3.4 PERSON 4 NAME:

4.1 4.2 4.3 4.4

1 or 0

Relay Answers 4th Grade

Mental Math 4th Grade

College Bowls

4th Grade Division 1 & 2









1 2 3 4 5

Subtract 29 from 42.

6 7 8

Find the sum of 70,000 and 50,000.

What is the product of 16 and 9? What is 2 + 2 + 2 + 2 + 2 + 2? Find the value of: 8 + 3 – 2 – 5 – 11 + 10 Trevor has sand in his shoes. He has 5.5 cubic centimeters of sand in his left shoe and a total of 8.2 cubic centimeters of sand in both shoes. How many cubic centimeters of sand does he have in his right shoe? [Express your answer as a decimal.]

In square units, what is the area of a square with perimeter 4 units? The 38 students attending Science Camp visit the aquarium. They walk around in pairs to see the exhibits. How many pairs of students are there?

9 10

Find the next number in the sequence: 57, 53, 49, 45, …

11 12

The grocery store sells boxes of one dozen eggs. For Easter, I need 70 eggs. How many boxes of eggs should I buy?

13

Annie and Gregg left for North Cascades Base Camp for the yearly math retreat at 9:00 AM and they arrived at 5:00 PM the same day. The trip is 200 miles. What was their average speed in miles per hour?

Find the sum of

2

3

. Give your answer as a fraction. 6 6 The side length of a square is 10 centimeters. A rectangle has the same area as this square. The length of the rectangle is 20 centimeters. What is the width of the rectangle, in centimeters? +

14

It takes Tom 7 minutes to drink a glass of lemonade and 30 seconds to eat a licorice stick. How many minutes will it take him to drink 3 glasses of lemonade and eat 6 licorice sticks if he does not eat and drink at the same time and does not pause?

15 16

How many cups are in two and a half quarts? Two consecutive counting numbers add up to 41. What is four times the larger of these two numbers? (“Consecutive” means in a row, without skipping any, or next to each other, in order.)

17

Yesterday in Hawaii, it was 86 degrees Fahrenheit outside. Today in Seattle, the temperature is half that number of degrees. How many degrees Fahrenheit cooler must it be tonight in Seattle in order for it to snow, if snow cannot fall at temperatures above 32 degrees Fahrenheit?

18

Jill bought 25 notebooks costing 99¢ each. What was the total cost of the notebooks, in dollars? [Express your answer as a decimal.]

19 20

Find the mean or average of the following set of numbers: 1, 6, 8, 3, 0, 6, 4, 2, 7, 3.

21 22 23

How many 6-inch square tiles does it take to cover a 6-foot by 8-foot rectangular floor?

24

A frog eats 2 flies every 45 seconds. How many flies would the frog eat in 5 minutes and 15 seconds?

25

Mario drives his golf cart at its maximum speed, which is 15 miles per hour. How many minutes will it take him to drive through a 5-mile golf course?

26

Anna owes Trevor $150. If she pays him $10 the first day, $20 the second day, $30 the third day and so on, how many days will it take Anna to pay Trevor?

What time is it 40 hours and 5 minutes before 3:15 PM? All students in Ms. Smith’s math class are either on the math team or in choir, or both. 25 of her students in all are on the math team and 20 of her students in all are in choir. If 11 students are in both groups, how many students total does Ms. Smith have in her math class?

B

A

C

D

If AB = 2, AD = 4 and BC = 3, what is the number of square units in the area of ABCD? (“AB” means the length of the line segment from vertex A to vertex B. A and B are right angles.)

27

Amy got 12 words correct out of 15 on this week’s spelling test. What percentage of the words did she miss?

28

Biff and Eho went on a backpacking trip. The first day they hiked 10 miles, the second day they hiked 12 miles, and the third day they hiked 11 miles. How many miles would they need to hike on the fourth day in order to hike an average of 12 miles per day?

29

I am tossing a fair coin. In the last 20 tosses, there were 17 heads and 3 tails. What is the probability of getting tails on my next toss? Give your answer as a reduced common fraction.

Challenge Questions 30 31

What is the sum of the digits of the sum of the digits of the product of 13 and 6?

32

Jack Sprat weighs 155 pounds and his wife weighs 213 pounds. If there are 250 grams in half a pound, how many more kilograms does Jack’s wife weigh than Jack?

33

Tom loves pumpkin pie. He ate

Cherie and Katie were looking at elephants and ostriches in the Children’s Zoo. Cherie saw 12 heads, and Katie saw 30 legs. How many elephants did they see?

1 4

of a pie for dessert last night and

breakfast this morning. What fraction of the pie was left?

1 3

of the pie for

34

Cam is building a straight post-and-rail fence for his parents. They need 120 feet of fencing with a post at each end and posts spaced 10 feet apart along the fence. It takes Cam one hour to dig each post-hole and set a post, and 45 minutes to assemble each 10 feet of fencing. How many hours will it take Cam to build the fence?

35

The hour hand on a clock has moved 75 degrees since I last looked at the clock. How many hours have gone by? Express your answer as a mixed number.

36 37

Adding 736 to 1428 gives the same result as subtracting what number from 3000?

38

A 1-gallon can of paint costs $23.75 and covers 250 square feet. How much will it cost (in dollars) to buy enough paint to paint the walls of a room that has four rectangular walls, each 15 feet by 9 feet? Assume that the room has no doors or windows, and that paint is sold only in 1-gallon cans. [Express your answer as a decimal.]

39

List the following in order of increasing size (smallest first). Your answer should consist of 4 letters in the correct order.

When Amy says 1, Bob says 2. When Amy says 3, Bob says 10. When Amy says 5, Bob says 26. When Amy says 9, Bob says 82. Following this pattern, what will Bob say when Amy says 7?

A)

5+3 12 − 10

x 100

B) The number of inches in 10 yards C) The total number of days in 13 consecutive months D) The number of coins in a collection of equal numbers of nickels and quarters worth a total of $63.90

40

Nine years ago, Sol was twice as old as Cam. In three years, Cam will be three-fourths of Sol’s age. How many years old is Sol right now?


4th Grade – March 23, 2007 Team Multiple Choice Contest Three high schools are going to a track meet. In each event, a first place receives 5 points, a second place receives 3 points, and a third place receives 1 point. The first table gives information about the schools and number of participants, and the second table gives the winners of four races and their schools. High School name Mt. Rainier Highline Renton Place 1st 2nd 3rd

1

2 3

School abbreviation MRHS HHS RHS

Race 1 R. Runner (MRHS) E. Fudd (HHS) P. Bear (RHS)

Number of athletes 51 49 62 Race 2 B. Bailey (HHS) B. Bunny (MRHS) G. Field (MRHS)

Race 3 R. Runner (MRHS) D. Mitchell (RHS) C. Brown (MRHS)

Race 4 Z. Harris (MRHS) S. Bear (RHS) W. Coyote (HHS)

How many more athletes does the Renton team have than the Mt. Rainier team? A) 2 B) 11 C) 12 D) 13 E) Answer not given How many athletes are at the meet altogether? A) 150 B) 162 C) 170 D) 182 E) Answer not given How many total points did Mt. Rainier receive from the first four races?

4

A) 6 B) 11 C) 15 D) 20 E) 36 A van holds 14 passengers. How many vans does Highline need to get to the meet?

5

A) 2 B) 3 C) 4 D) 5 E) Answer not given Josh and Jack are running the 100-meter dash. Josh runs 4 meters per second and Jack runs 5 meters per second. How many seconds after Jack finishes will Josh finish? A) 1

B) 10

C) 20

D) 25

E) Answer not given

6

1/7 of the Highline team lost their shoes during the meet. How many Highline athletes did not lose their shoes?

7

A) 6 B) 7 C) 14 D) 42 E) 43 Each of the athletes from Renton shakes hands once with each of the athletes from Mt. Rainier. How many handshakes take place?

8

9

A) 113 B) 3162 C) 1581 D) 3062 E) 6328 Renton is ordering team uniforms. Company A charges a $50 printing fee plus $7 per uniform. Company B charges a $30 printing fee plus $9 per uniform. What is the lowest amount of money Renton can pay for their uniforms? A) $407 B) $434 C) $484 D) $588 E) $634 The Mt. Rainier team has jumpers, throwers and runners. There are 14 jumpers, 9 throwers and 41 runners. Two people throw and jump, nine people run and jump, and three people throw and run. One person does all three. How many people only run? A) 30

B) 32

C) 28

D) 41

E) Answer not given


4th Grade – March 23, 2007 Team Contest 1

The vertices of a polygon are the points where two sides meet. For example, a square has 4 vertices. How many vertices does the polygon shown at right have?

2

Lucy has three each of all U.S. coins currently in use (penny, nickel, dime, quarter, half-dollar, and dollar). How many cents does she have? Be sure to give your answer in cents, not dollars.

3

Sharon was jogging along a beach. She jogged 135 meters due north, then 380 meters due south, then 210 meters due north. How many meters was she from her starting point?

4

Alex, Billie, and Chris share a plate of 12 cookies. Alex eats more cookies than Billie, and Billie eats more cookies than Chris. If all 12 cookies are eaten, what is the smallest number of cookies Alex could have eaten?

5

David has several cats. Half of them are Manx cats, which have no tail. The other half are ordinary housecats. When he counts all the ears, paws, and tails of all his cats, he finds (correctly) that the total is 39. How many cats does David have?

6

If July 15 was exactly 7 months ago, what month will it be 14 months from today? Give the name of the month, not a number.

7

When Vince, his brother Daren, and their dog Gruff all stood on the scale together, their total weight was 202 pounds. After Gruff ran away and Vince got off the scale to go catch him, the scale with only Daren on it showed 78 pounds. What was the average weight, in pounds, of Vince and Gruff?

8

The minute hand of a broken clock goes twice as fast as it should, while the hour hand goes only half as fast as it should. At noon yesterday, the clock was set correctly. At 6 PM yesterday, what time showed on this broken clock?

9

Sidney was supposed to put a sign reading “FREE COFFEE” on a reader-board at a highway rest stop. However, the letters were slippery and he dropped all 10 of them before he got to the reader-board. Each letter was separate, and he picked them up one by one, at random. What is the probability that the first letter Sidney picked up was just like at least one other letter in the pile? (Give your answer as a fraction.)

10

Figure ABCD is a square, and E, F, G, and H are the midpoints of each side. If side AB = 4 cm, find the shaded area, in square cm.

A E

F B

D H

G C



Practice Relay

Answer

Person 1 What is 2 times 6? Person 2 What is the sum of TNYWG and the quotient of 21 divided by

15

Person 3

2

Person 4

7? What is the positive difference between the number of spades in a deck of cards and TNYWG? Find the product of TNYWG and 30/2.

Relay #1

12

30 Answer

35 [un2] Person 1 What is the area of a rectangle with sides of length 5 and 7? 43 Person 2 Find the sum of TNYWG and the average of 6 and 10. Person 3 Find the number of minutes between 2:37 pm and 3:23 pm, then 3

Person 4

subtract TNYWG. Find the product of TNYWG and the number of multiples of 3 between 17 and 94 Relay #2

Person 1 What is 14 times 6? Person 2 What is the remainder when TNYWG is divided by the number of sides on an octagon? Add TNYWG to 3/4 of 12.

Person 3 Person 4 A prime number has only 2 numbers that divide into it with no remainder (1 and the prime number itself). How many prime numbers are less than or equal to TNYWG?

78 Answer 84 4 13 6



Final Score:

KEY


Mental Math Contest

MENTAL MATH - 30 seconds per question

When it is time to begin, I will read the first question twice. You may not do any writing or talking while arriving at a solution. Once you have a solution, record it on the sheet in front of you. You may not change or cross out answers once you have written an answer down. If there are eraser marks, write-overs, or crossed out answers, they will be marked wrong. Once all students have laid their pencils on the desk, another question will be asked. If a student doesn’t lay his/her pencil down, the maximum wait time is 30 seconds from the second reading of the question before another question is asked. You may continue to work on a problem while the next question is being read. The value of each question is a one or zero. Each student may answer only four questions, and then another member of your team will come up, until each team member has had a turn. If your team has fewer than 4 members, missing team members will receive a zero.

PERSON 1 NAME:

1.1 1.2 1.3 1.4

1 or 0

How many angles does a triangle have?

3 [angles]

Annie worked for 12 hours a day for 5 days last week. How many hours did Annie work last week? What is the difference between 67 and 23?

60 [hrs]

What is 44 divided by 11?

4

44

PERSON 2 NAME:

2.1 2.2 2.3 2.4

Find the difference between 19 and 5.

14

What is 10 minus 4 plus 8 minus 7?

7

Bill got paid 5 dollars for mowing the lawn. Tim got paid 3 times as much as Bill. How many dollars did Tim get paid? What is 100 percent of 10 percent of 100?

[$] 15 10

PERSON 3 NAME:

3.1 3.2 3.3 3.4

Find the diameter of a circle with radius 14.

28 [units]

What is 48 divided by the number of months in a year?

4

Find the product of 11 and 5.

55

What is 36 plus 49?

85

PERSON 4 NAME:

4.1 4.2 4.3 4.4

What is the perimeter of a square with side length 25?

100 [units]


28

If 4 people can sit on each camel, how many people can sit on 6 camels?

24 [people]

What is 30 times 20?

600




Problem What is the tens digit of the product of three and seven?

Answer 2

I have a rope ten feet long. Which shape should I make with my rope in order to surround the greatest area -- a square, a triangle, or a circle?

circle

3

The first four terms of a certain sequence are 1, 3, 5, and 7. Find the ninth term of this sequence.

17

4

My calculator automatically adds ten to every number I enter. I entered two plus thirteen. What number did my calculator show as the answer?

35

5

What is the smallest whole number bigger than the sum of twothirds and two-thirds?

2

6

It snowed steadily all day yesterday at the rate of one inch per hour. How many inches did it snow between seven AM and onefifteen PM? Give your answer as a mixed number.

6

7

Find the remainder when 153 is divided by 7.

6

1 2

7 8

1 4

[inches]

Extra Problem – Only if Needed How many ways can you arrange the letters in the word TACO, spelled T-A-C-O?

24 [ways]



Division 1


1

Problem Rachel is taller than Val, who is shorter than Patty. Patty is shorter than Kerri and Rachel. Kerri is best friends with the shortest of the group. Who is Kerri’s best friend?

Answer Val

2

A rose has 30 petals and a daisy has 21 petals. How many petals are there in a bouquet of two roses and three daisies?

123 [petals]

3

Eric is riding his bike at a speed of 30 miles per hour. At this speed, how many miles will he travel in 4 hours?

120 [miles]

4

An equilateral triangle has equal sides. Find the number of inches in the perimeter of an equilateral triangle with side length one foot.

36 [inches]

5

Find one more than the product of two times nine and add it to one less than the product of three times seven.

39

6

Jamie is 16 years old and Jessica is 12 years old. In years, what will the sum of their ages be 3 years from now?

34 [years]

7

I am counting backwards by fives. The first number I say is 72. What is the fourth number I say?

57

7.1 8

Extra Problem – Only if Needed How many degrees are in the largest angle of a right triangle?

90 [degrees]



Division 1


1

Problem How many circles of radius two inches will fit inside a circle of diameter five inches?

Answer 1 [circle]

2

When 4 copies of the number 10 are multiplied together, how many digits will the product have?

5 [digits]

3

Find the average or arithmetic mean of the following set of numbers: 9, 1, 7, 5, 5, 3

5

4

A pet shop sells cats, dogs and parrots. If there are 3 cats, 4 dogs, 2 parrots and 2 employees, how many legs are there in the pet shop?

36 [legs]

5

What is the probability of rolling a number less than 3 when rolling a standard number cube or die? Give your answer as a fraction.

2/6 [or 1/3]

6

Sam can throw a Frisbee 25 feet and Michael can throw a Frisbee 37 feet. How many feet farther can Michael throw the Frisbee than Sam?

12 [feet]

7

For a spelling quiz, Helen numbered the lines of her paper from 1 through 20. How many digits did Helen write?

31 [digits]

7.1 8

Extra Problem – Only if Needed Find the number of apples Jackie can pick in 45 minutes if she can pick 104 apples in one hour.

78 [apples]




Problem Subtract two from the product of two times two times two.

Answer 6

Joel fed the family dog Slowpoke every day in December and January, and his brother Cam fed Slowpoke every day in February and March. If it is not a Leap Year, how many days more did Joel work than Cam?

3 [days]

3

Fill in the blank: Every rectangle has at least symmetry.

2 [lines of symmetry]

4

Erin counts by twos starting with 1, 3, 5, and so on. How many numbers has she said after she says her first 3-digit number?

51 [numbers]

5

What is the largest possible sum when three standard dice or number cubes are rolled?

18

6

When forty-five thousand eight hundred seventy-seven is rounded to the nearest thousand, what is the last digit of this rounded number that is not zero?

6

7

A cafeteria serves 2 types of lettuce and 5 types of salad dressing. How many possible salads can be served if a salad consists of one type of lettuce and one type of dressing?

10 [salads]

1 2

7 8

lines of

Extra Problem – Only if Needed It is 11:17 AM. What time will it be in 48 minutes?

12:05 PM



Division 2


Problem Halogen light bulbs last 450 hours. How many hours will a pack of three halogen bulbs last if they are used in one socket immediately following one another?

Answer 1350 [hours]

2

Sally cuts a piece of string into ten pieces. If she doesn’t cut through more than one string with each cut, how many cuts did it take?

9 [cuts]

3

I am thinking of a counting number. When I divide it by three, I get a remainder of one. Is my number even, odd, or you can’t tell?

can’t tell

4

Maximus is taller and stronger than Marcus, who is shorter than Quintus. If Cicero is shorter than Marcus, who is the second shortest person in this group?

Marcus

5

Fill in the blank in this sequence: 7, 14, 21,

28

6

Find the number of inches in the perimeter of a triangle with sides of length 21, 17 and 5 inches.

43 [inches]

7

A firefighter is on the fifth floor of a building. She runs up 7 floors and rescues a kitten. She then goes down 9 floors and drops the kitten off. Next she climbs 12 floors up from this spot to put out the fire. On what floor was the fire?

15 [or 15th]

1

7.1 8

.

Extra Problem – Only if Needed Multiply the product of 3 and 4 times the sum of 3 and 4.

84



Division 2


Problem Danny has a penny, a nickel, a dime, and a quarter in his pocket. How many coins would he have to take out to be sure of getting at least five cents?

Answer 2 [coins]

2 3


15

Katie left her bookmark between two pages whose numbers had a sum of 49. What is the number of the larger of these two pages?

[page] 25

4 5

How many digits are in the number one hundred fifty thousand?

6 [digits]

What number would you have to add to the product of zero and seven to get a sum of twelve?

12

6

If today is Wednesday, what day of the week will it be 22 days from today?

Thursday

7

It takes 5 minutes for a horse to chew a carrot. How many carrots can the horse chew in three-quarters of an hour?

9 [carrots]

1

7.1 8

Extra Problem – Only if Needed What is the value of 10 minus 1 plus 9 minus 2 plus 8 minus 3?

21


Final Score:

KEY


School Name__________________________________Team #________

First Score



1 2 3 4 5 6 7 8 9 10 11 12 13

13

14 15 16 17 18 19 20

24 [min]

144 12 3 2.7 [cm3] 120,000 1 [un2] 19 [pairs] 41 25 [mph] 6 [boxes] 5/6 5 [cm]

10 [cups] 84 11 [degrees] [$] 24.75 4 5 [days]

1 or 0 1 or 0

Answer

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

192 [tiles] 11:10 PM 34 [students] 14 [flies] 20 [min] 7 [un2] 20 [%] 15 [miles] 1/2 6 3 [elephants] 29 [kg] 5/12 [or equiv. unreduced fraction] 22 [hours] 2 1 [hrs] [or equiv. mix number] 2

836 50 [$] 71.25 BCAD 21 [years]

1 or 0

1 or 0


Final Score:

KEY


First Score

(out of 18)




Answer

1 2 3 4 5 6 7 8 9 10

B B D C E [5] D B C A

-1, 0 or 2

-1, 0 or 2


Final Score:

KEY


First Score

(out of 20)




Answer

1 2 3 4 5 6 7 8 9 10 10

7 [vertices] 573 [cents or ¢] 35 [meters] 5 [cookies] 6 [cats] April 62 [pounds] 3:00 [PM] 7/10 10 [square cm or cm2]

2 or 0

2 or 0


KEY


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

12

15

2

30

1 or 0

1 or 0

1 or 0

2 or 0


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

35 [un2]

43

3

78

1 or 0

1 or 0

1 or 0

2 or 0


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

84

4

13

6

1 or 0

1 or 0

1 or 0

2 or 0

“Math is Cool” Masters – 2006-07 Sponsored by: Wenatchee Valley Clinic

4th Grade – May 19, 2007 Individual Contest

GENERAL INSTRUCTIONS applying to all tests:






4th Grade – May 19, 2007 Individual Contest

Record all answers on the colored cover sheet. Evaluate: 305 – 184

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17

What is the product of 18 and 12? Evaluate as a decimal: 28.42 ÷ 0.4 What is 60% of 315? How many years are equivalent to 276 months? When two standard six-sided dice are rolled, what is the probability that the sum of the numbers shown is ten? [Give your answer as a reduced common fraction.] Linnea drove 500 [kilometers] at 120 [kilometers per hour]. How many minutes did it take her? A is 92 larger than B, and the sum of A and B is 234. What is the value of A? When a coin is flipped three times, what is the probability that there are exactly two heads? [Give your answer as a reduced common fraction.] Danielle has some cookies with four layers of frosting each and some cookies with only three layers of frosting each. If she has a total of 38 cookies with a total of 120 layers of frosting, how many cookies with four layers of frosting does she have? What is the remainder when 182 is divided by 8? What is the next term in the sequence 6, 12, 24, 48, ___ ? What is the area, in square centimeters, of a circle with a diameter measuring 18 cm? What is the perimeter, in centimeters, of a triangle with sides measuring 17, 41, and 46 cm? What is the total surface area, in square centimeters, of a right circular cylinder with a base radius of 3 cm and a height of 12 cm? What is the volume, in cubic centimeters, of a right circular cylinder with a base radius of 12 cm and a height of 4 cm? When two cards are drawn from a standard 52-card deck [without replacing the first card], what is the probability that they are the same suit? [Give your answer as a reduced common fraction.]

18 19 20 21 22 23 24 25 26 27 28 29

What value(s) of g satisfy 2(4g - 3) - 3(g + 8) = -75 ? How many squares of any size are there in a four-by-four grid of unit squares? When one card is drawn from a standard 52-card deck, what is the probability that it is a red card or a Jack? When I double my age, in years, and then add 19 years, the result is 85 years. How old am I in years? In how many ways can first, second, and third-place medals be awarded in a competition involving nine people, if no ties are allowed? A rectangular picture measuring 13 cm by 18 cm is to be glued to a rectangular piece of paper measuring 19 cm by 24 cm so that 3 cm of paper shows on all sides of the picture. What is the area, in square centimeters, of the paper that is not covered by the picture? How many diagonals can be drawn in a convex decagon (10-gon)? In how many distinguishable ways can five people be seated at a round table? How many distinguishable arrangements are there of the letters in the word “letters”? How many positive three-digit numbers contain exactly two distinct digits (e.g. 343 or 772, but not 589 or 111)? Pat can build a house in 6 weeks, while Tom can build one in 15 weeks. How many days would it take the two of them to build a house working together? [Assume that there are 7 work-days in a work-week.] Two marbles are drawn without replacement from a bag of marbles containing 4 red, 6 green and 3 purple marbles. What is the probability both marbles are green.


Biff ran 4 times as fast as Eho. In fact, he ran 80 miles in 2 hours less than it took Eho to run 28 miles. How fast did Eho run? Tickets on a bus were $4.00 and $6.00. A total of 45 tickets were sold and $230 earned. How many $4.00 tickets were sold? A cow is tied to an external corner of a rectangular barn with sides measuring 15 and 25 m. If the cow’s tether is 30 m long, what is the area, in square meters, of the region the cow can graze? [Give your answer as a reduced common fraction in terms of π.] If eight “aarghs” are worth six “blahs”, and ten “blahs” are worth three “crikeys”, how many “crikeys” would 120 “aarghs” be worth? Anne’s Game Farm has only ten-point bucks and six-point bucks. If there are a total of 87 bucks with a total of 602 points between them, how many six-point bucks are there? If P pizzas can be purchased for D dollars, how many cents would be necessary to purchase 3 pizzas? When the digits of a positive two-digit number are reversed, the result is a positive two-digit number 18 greater than the original number. What is the smallest possible value of the original number? If it takes two chickens three days to lay five eggs, how many eggs will nine chickens lay in fourteen days? How many positive two-digit numbers contain at least one digit of 1 but not the digit2? Circles A and B are concentric, and a chord of circle B that is tangent to circle A measures 14 m. What is the area, in square meters, of the region between the two circles? Biff, Eho and Frank are tossing a coin to see who can gets the first head. As soon as a head appears (even if each has not had an equal number of tosses) the game is over. If Biff tosses first, then Eho, then Frank, with the order repeated (possibly indefinitely) until the first head appears, what is the probability that Frank will win? [Express your answer as a reduced common fraction.]


4th Grade – May 19, 2007 Team Multiple Choice Contest

Four married couples (Kelly & Jacob, Mary & Nick, Carla & Danny, Brenda & Ted) visit the Lake de Puddle Resort for lunch and a day of boating. The lunch menu is shown in the table on the left, and the boat rental prices in the table on the right. For the lunch menu, on any given day only one kind of each item is available (for example, only one kind of sandwich or one kind of pie). Main Dish Chef’s Salad Pizza Sandwich Side Orders French Fries Bacon

1 2 3 4 5 6 7 8 9

Cost $2.50 $4.00 $5.50

$1.00 $0.75

Drinks Milk Soda

Cost $1.50 $___

Dessert Cake Pie

$2.00 $2.50

Type of boat Rowboat

Cost Flat fee of $30, plus $8 per hour

Canoe

$18 for the first hour, plus $6 for each additional half-hour

Motorboat

$45 per hour plus $1.50 per mile

How much do 3 glasses of milk cost? A) $3.00 B) $4.50 C) $5.00 D) $6.00 E) answer not given A side order of bacon consists of one slice. Jacob ordered a chef’s salad, 3 slices of bacon and a glass of milk. How much did he pay? A) $5.75 B) $6.00 C) $6.25 D) $7.00 E) answer not given Jacob added a 15% tip to his lunch bill, rounding off the tip to the nearest nickel. He then paid for his lunch plus tip with a $10 bill. How much change did he get? A) $3.80 B) $1.95 C) $2.20 D) $2.80 E) answer not given Mary ordered a chef’s salad and Nick ordered 3 pieces of cake. They each had a soda. How much less did Mary’s lunch cost than Nick’s? A) $3.50 B) $3.65 C) $3.75 D) $4.00 E) answer not given Carla and Danny together order one of everything on the lunch menu. If the average price of the 9 items they order is $2.40, what is the price of one soda? A) $1.50 B) $2.40 C) $2.00 D) $1.75 E) answer not given Brenda definitely wants one main dish, one drink, and one dessert. She might have one side order, or she might not have any side order. If one possible drink is water (free), how many different lunches could Brenda order? A) 12 B) 54 C) 48 D) 18 E) answer not given Kelly and Jacob plan a boat trip to Deer Glade, which is 12.5 miles away. If they rent a rowboat and travel at 5 miles per hour, how many minutes long will the one-way trip be? A) 120 B) 135 C) 150 D) 165 E) answer not given Kelly and Jacob want to spend exactly an hour at Deer Glade before heading back. How much would it cost them to rent a rowboat for their trip to Deer Glade and back, assuming they row at a constant rate of 5 miles per hour? A) $54 B) $70 C) $38 D) $90 E) answer not given Kelly and Jacob might rent a motorboat instead for their trip to Deer Glade and back (again spending exactly one hour at Deer Glade before returning). How much would it cost them if the motorboat’s speed is a constant 25 miles per hour? A) $108.75 B) $82.50 C) $127.50 D) $90 E) answer not given


4th Grade – May 19, 2007 Team Contest

1

Jeff adds 3 counting numbers (w + x + y) and correctly gets an even sum. Karen adds 2 of the same numbers as Jeff added, plus a different third number (w + x + z) and correctly gets an odd sum. Is the sum of y + z even or odd? If there is not enough information to be sure, answer “can’t tell”.

2

The faces of a cube are labeled 1, 2, 3, and so on. When three such cubes are rolled, the product of the numbers showing is 90. What is the sum of the numbers showing?

3

The display on my calculator scrambles the digits of the numbers I enter but it gives the correct sum of the original unscrambled numbers. I tried to add two 4-digit numbers, which the display shows as 5126 + 7831 = 3003. I remember that the hundreds digit of one of my numbers is a multiple of the hundreds digit of the other number. What were my two numbers?

4

My number is an even counting number with an even number of even digits and an odd number of odd digits. All its digits are different. What’s the smallest my number could be if it has at least 5 digits?

5

List the following in order of increasing size (smallest first). (Your answer should consist of 4 letters in the correct order.) A = the number of hours in a month B = the number of days in a decade C = the number of milligrams in a gram D = the number of ounces in a ton

6

Stephen’s number is 1/3 of Tyler’s number and is 2 more than twice Joe’s number. What is Tyler’s number if Joe’s number is 17?

7

Every time a straight line crosses either another line or a circle, an intersection point is created. What could be the largest number of intersection points created with one circle and 3 lines?

8

For lunch, Clair chooses 1 sandwich (ham, cheese, or turkey), 1 bag of chips (potato chips or vegetable chips), 1 piece of fruit (apple or banana), and 1 drink (milk or orange juice). However, Claire never chooses milk when she has a cheese sandwich. How many different lunches can Claire choose?

9

Three identical rectangles, each 5 inches long and n inches wide, are put together with their sides lined up to form a new, larger rectangle. The perimeter of this new rectangle is 34 inches. What is the sum, in inches, of the two possible values for n?

10

Fifty years ago, the oak tree in my yard was twice as old as the spruce tree. In 30 years, the spruce tree will be 100 years old. How many years old is the oak tree now?


4th Grade – May 19, 2007 Relay Contest


Person 1 Person 2 Person 3 Person 4

Relay #1

Answer

Joe walked 5 hours at 3 miles per hour. How many miles did Joe walk? A field has chickens and cows in it. There are 28 cows and TNYWG chickens. How many feet are in the field? What is the difference between the TNYWG and the product of 12 and 11? What is the probability of drawing a red marble from a bag that contains 7 green marbles, 4 purple marbles and TNYWG red marbles? Relay #2

15 [miles] 142 [feet] 10 10/21

Answer

Person 1 What is the mean of 5, 7, 9, 11, and 13? Person 2 What is the next number in the sequence 1, TNYWG, 17, 25,

33

Person 3

22 [cats]

Person 4

____? The ratio of dogs to cats was 1 to 2. There was a total of TNYWG dogs and cats. How many cats were there? Keith traveled at 30 mph for 6 hours and then TNWG mph for 3 hours. How many miles did Keith travel?

9

246 [miles]



Final Score:

KEY


Mental Math Contest

PERSON 1 NAME: 1.1 What is the sum of two-thirds and one-sixth?

1.2 1.3

What is 11 times 12?

1 or 0 5/6 132

Charlie is taller than Dan, but is shorter than Jacob. Who is the shortest of the three? 1.4 The ratio of horses to cows in a field was 2 to 5. There were a total of 35 horses and cows in the field, how many were cows? PERSON 2 NAME: 2.1 What is the sum of 67 and 48?

Dan

2.2 2.3

78


25 [cows]

115

Jim needs 1000 signatures to get a ballot passed. Jim has 654 signatures, how many more does he need? 2.4 The number of boys in Triscia’s class exceeded the number of girls by 7. If there were a total of 29 pupils in her class, how many were boys? PERSON 3 NAME: 3.1 What is 9 squared?

346 [sig]

3.2 3.3 3.4

What is the positive square root of 121?

11

How many minutes have passed between 11 o’clock am and 1:17pm?

137[min]

4.2

Jill made 8 dozen brownies. How many brownies did she make?

4.3

108 doughnuts are put into boxes with a dozen in each box. How many boxes are needed to hold the doughnuts? The average of the first 7 numbers was 21. The average of the next 3 numbers was only 11. What was the over all average of the all the numbers?

18 [boys]

81

Joe made 60% more points at his basketball game this time than he did at his 20 [pts] last basketball game. If he made 32 points this game, how many points did he make at the last game? PERSON 4 NAME: 10 4.1 How many sides does a decagon have?

4.4

96 [brownies] 9 [boxes] 18


May 19, 2007


Problem What is 12 times 5 plus 10?

Answer 70

What is the perimeter of a square with a side of length 14?

56

How many feet are in a field if there are 4 elephants, 7 people and 13 chickens in the field?

56[feet]

4 5

What is 2997 rounded to the nearest 10?

3000

There are 10 fish in a pond. Every time a fish dies or is removed, it is replaced with two new fish. On Monday raccoons ate 3 fish. On Wednesday little Timmy added 4 more fish to the pond. How many fish are now in the pond?

17 [fish]

6

Joe is selling lemonade. He sells a cup of lemonade for 25 cents. Joe spent ten dollars on supplies to get started. In addition, the cost of the lemons for each cup is 5 cents. How many cups of lemonade does Joe need to sell to break even?

50 [cups]

7

Four consecutive even numbers add to 84. What is the largest of the four numbers?

24

1 2 3

7 8

Extra Problem – Only if Needed The average of six, eight, and some number is five. What is that number?

1


May 19, 2007



1

Problem What is the measure in degrees of the interior angle of a regular quadrilateral?

Answer 90 [°]

2

Jacob is building a 4-foot by 4-foot pen with posts at the corners and between every foot of fencing. How many posts are needed?

16 [posts]

3

If one crate can hold four and a half pounds, how many pounds can be held in sixteen crates?

72 [pounds]

4 5

How many sides does a dodecagon have?

12 [sides]

Two numbers sum to 84 and have a difference of 18. What is the larger of the two numbers?

51

6

What is the area, in square units, of a square with perimeter 24?

7

A coloring book has 28 pages numbered 1, 2, 3 and so on through page 28. How many times does the digit 2 occur in the page numbers?

36 [square units] 12 [2’s]

7.1 8

Extra Problem – Only if Needed If 7 clowns can hold 28 balloons, how many balloons can 4 clowns hold?

16 [balloons]


May 19, 2007



Problem What is the least amount of money, in cents, I can have with four coins if all of them are different?

Answer 41 [cents]

2

Helly Hansen ordered three-dozen pairs of ski gloves for the upcoming winter. However, the store clerk lost two pairs. How many induvidual gloves are left in the order?

68 [gloves]

3 4

What time is it 35 minutes after 6:35 pm?

7:10 pm

If today is the 15th of June and Timmy’s birthday is in 45 days, what is the date of Timmy’s birthday?

July 30th

5

44 clowns can fit in a car. If there are 17 clowns currently in the car there is room for how many more?

27 [clowns]

6

The area of a triangle is 20 square inches. If the height of the triangle is 10 inches, what is the length of the base of the triangle in inches?

4 [units]

7

A 3-by-3-by-3 cube is painted blue and then cut into 27 unit cubes. How many cubes have only one painted face?

6 [cubes]

1

7.1 8

Extra Problem – Only if Needed A flight of fifteen stairs raises ten feet. If all the steps are equally tall, how many inches high is each step?

8 [inches]


Final Score:

KEY


School Name__________________________________Team #________

First Score



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

121 216 71.05 189 23 [yrs] 1/12 250 [min] [A =] 163 3/8 6 [cookies] 6 96 81π [cm2] 104 [cm] 90π [cm2] 576π [cm3] 4/17 -9 30 [Squares] 7/13

1 or 0 1 or 0

Answer

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

33 [yrs] 504 [ways] 222 [cm2] 35 [diagonals] 24 [ways] 1260 [ways] 243 [numbers] 30 [days] 5/26 4 [mph] 20 [tickets] 1475π/2 [m2] 27 [crikeys] 67 [6 pt bucks] 300D/P 13 105 [eggs] 16 [numbers] 49π [m2] 1/7

1 or 0

1 or 0


Final Score:

KEY






1 2 3 4 5 6 7 8 9 10

Answer B C D A E [$1.85] B C D C

-1, 0 or 2

-1, 0 or 2


Final Score:

KEY






Answer

1 2 3 4 5 6 7 8 9 10 10

odd 14 1625 & 1378 (either order) 10,246 ACBD 108 9 [points] 20 [lunches] 6 [inches] 90 [years]

2 or 0

2 or 0


KEY

School:_______________________________Team #________ Proctor: ______________________________ Room #_______Div RELAY # 1 Answer for person #1

15 [miles] 1 or 0

Answer for person

Answer for person

#2

142 [feet] 1 or 0

Answer for person

#3

#4

10

10/21

1 or 0

2 or 0


Answer for person

#1

#2

9

33

1 or 0

1 or 0


22 [cats] 1 or 0


246 [miles] 2 or 0









1 2 3 4 5 6 7

How many sides does a square have?

8 9

What is the product of 7 × 10 ?

10 11 12 13 14 15 16 17 18

Find the difference between 39 and 17. Nicky is carrying two packages. One weighs 6 pounds and the other weighs 7 pounds. How many pounds do Nicky’s two packages weigh together? What digit is in the hundreds place of the number 63,548? How many months are in three years? Add 100 plus 1000 plus 10. Sally is listing the counting numbers (1, 2, 3, and so on) in order. How many counting numbers go in the box between 5 and 11? 1, 2, 3, 4, 5, ? , 11, 12, 13,…

I have a math book, a science book, and a history book in a row on the shelf. In how many different orders can I arrange them if I want to keep the math book and the science book next to each other? If you multiply an odd counting number by an even counting number, will the result be even or odd? Answer “can’t tell” if there is not enough information to be sure. If A is a square with a side length of 10 inches, and B is a circle with diameter 10 inches, which has the larger area, A or B? Answer “same” if the areas are equal. What is the missing number in this sequence? 5, 12, 19, __, 33 Larry is putting 38 eggs in 6 baskets. If each basket has the same number of eggs, what is the least (smallest) number of eggs that could be left over? How many triangles can be drawn following the lines of this figure?

Stephanie uses two carrots and one tomato to make one cup of carrot-tomato juice. What is the total number of vegetables (carrots and tomatoes) of this size that she would need to make a quart of carrot-tomato juice? A fence is to be placed around a rectangular garden that is 8 feet by 5 feet. How many feet of fencing are needed? Sandy practiced the flute 10 days in December and 20 days in January. How many total days in December and January did Sandy NOT practice the flute? If you sleep for 8 hours a day and are awake the rest of the day, what fraction of the day are you awake?

19 20 21 22 23 24 25 26 27 28 29 30

A coat costs $47. George has enough money to pay the exact price without using coins. If George has just one $20 bill and no $2 bills, what is the smallest total number of bills he could have? What is the sum of the first five odd counting numbers? Karen has 64 cookies. She puts them into 4 bags, with an equal number of cookies in each bag. Lauren takes 3 of those bags. How many cookies does Lauren take? One fish can eat four bugs in one hour. At this rate, how many bugs can three fish eat in two hours? What is the product of 98 times 76? A bird flies at ten feet per second. How many seconds will it take for the bird to reach Andrew, who is standing 30 yards away? April had 18 apricots, Beryl had 118 berries, and Cheryl had 218 cherries. Each girl ate half her fruit (always eating whole fruits). How many pieces of fruit did the three girls have left? When I triple my number, subtract 6, then divide by 2, I get 12. What is my number? Steve filled his car’s gas tank and then drove 200 miles before running out of gas. If the gas tank holds 8 gallons, how many miles per gallon does Steve’s car get? One MathSnack has 170 calories. How many MathSnacks can Jody eat without going over 2,000 calories? The sum of my number and 18 is the same as the product of my number and 7. What is my number? Aly is twice as old as her brother today. When she is 25 years old, her brother will be 20 years old. How many years old is Aly today?

Challenge Problems on next page.

Challenge Questions 31 32 33 34

35 36 37 38 39 40

A lollipop costs a quarter and a candy bar costs 75¢. If I spent $9.25 and bought eight candy bars, how many lollipops did I buy? A tea bag can make 3 cups of tea, where each cup is 8 fluid ounces. How many fluid ounces of tea can 27 tea bags make? Lucy took two-dozen pencils to school on Monday. By the end of the day, she had lost one of these pencils. She lost the same number of pencils on Wednesday as she did on Tuesday. On Thursday she lost 7 pencils. On Friday she lost at least one pencil, but not as many as she lost on Wednesday. If she still had 6 pencils when she left school on Friday, how many pencils did she lose on Tuesday? Dave has invented a new throwing toy for his dog. The toy, called a Frismerang, is shown at right. Each side of the shaded triangle in the middle is 3 inches. Each other part of the toy is either a square or a triangle with the same side lengths as the shaded triangle. What is the 3 length in inches of the outline (perimeter) of the Frismerang?

Biff and Eho are buying ice cream at Dairy Queen. Biff buys a Blizzard for $2.73. Eho buys a Brownie Earthquake for $3.19. Before they paid for the ice cream, they had three times as much money as they had left after they paid for the ice cream. How much money, in dollars, did they have before buying ice cream? A mountain is 9000 feet high. A mountain-climber is 72 inches tall. The mountain is how many times as tall as the climber? A pen and a note pad together cost 60 cents. The pen costs 40 cents more than the note pad. At these prices, how much money (in dollars) would you have left from a $5 bill after buying 13 of the note pads? Cory has 5 pairs of Nike shoes, 4 pairs of Adidas shoes, and 6 pairs of Puma shoes. If she picks shoes without looking, how many shoes does she need to pick in order to be sure that she has one right and one left shoe of the same brand? Put the following five values in order of size, starting with the smallest, and give the letters matching that order. Your answer should consist of 5 letters in the correct order. A = 1000 hours, B = 1 week, C = 10,000 minutes, D = 9 days, E = 1 month For how many of the first 600 counting numbers is the sum of their digits less than 20?


4th Grade – March 28, 2008 Team Multiple Choice Contest In some places, fire is a natural part of a forest’s life and the forest can recover if burned. If all fires are prevented, the forest may become unhealthy and overgrown. Sometimes it is necessary for forest managers (foresters) to cut down sick trees in order to restore the forest to its natural state. Mark, the forester, is doing this work on the one-acre plot of forest described below. NOTES: “Range” is the difference between the largest and smallest of a group of numbers. One square mile is equal to 640 acres. 99

65 height in feet

Tree species present Ponderosa Pine Douglas-Fir

Number of trees 30

TOTAL

298

tallest shortest

1

All the trees on the plot are either ponderosa pines or Douglas-firs. How many of the trees are Douglas-firs? A) 30 B) 298 C) 328 D) 268 E) answer not given

2

Approximately what fraction of the trees are ponderosa pines? 3 9 1 1 3 A) B) C) D) E) 10 10 3 10 100

3

Mark the forester is checking five trees for insects. He starts with the two trees shown in the diagram above (the tallest and shortest tree in the plot). The third tree he looks at is 7 feet taller than the shortest tree. The height of the fourth tree is the average of the heights of the first three trees. The fifth tree is five feet taller than the fourth tree. What is the probability that a tree picked at random from among these five trees is taller than 75 feet? 1 3 4 5 7 A) B) C) D) E) 3 5 5 6 5

4

When Mark decides what trees to cut, he looks at the health of each tree. Healthy trees are straight and tall. The heights of five trees are: 33 yards 824 inches 25 yards 83 feet 10 inches 70 feet All five are perfectly straight. He will definitely not cut down the tallest one. How tall is the tree he will definitely not cut down? A) 33 yards B) 824 inches C) 25 meters D) 83 feet 10 inches E) 70 feet

5

A river runs through the middle of the acre. Mark notices that along one bank of the river, nine trees grow in a very definite pattern. The first tree is 67 ft, the second is 70 ft, the third is 73 ft, and so on. How many feet tall is the sixth tree? A) 64 B) 79 C) 82 D) 85 E) 86

In some places, fire is a natural part of a forest’s life and the forest can recover if burned. If all fires are prevented, the forest may become unhealthy and overgrown. Sometimes it is necessary for forest managers (foresters) to cut down sick trees in order to restore the forest to its natural state. Mark, the forester, is doing this work on the one-acre plot of forest described below. NOTES: “Range” is the difference between the largest and smallest of a group of numbers. One square mile is equal to 640 acres. 99

65 height in feet

Tree species present Ponderosa Pine Douglas-Fir

Number of trees 30

TOTAL

298

tallest shortest

6

Trees grow slowly in the winter and quickly in summer, so inside the trunks there are circular ‘rings’, a dark ring for every winter and a light ring for every summer. How many years old is this tree? (Remember that it is still growing!) A) 1 B) 2 C) 4 D) 8 E) 9

7

When Mark has finished cutting down the less healthy trees, there are 171 trees left. He cut down 3 30% ( ) of the ponderosa pines. How many Douglas-fir trees did he cut down? 10 A) 118 B) 80 C) 90 D) 157 E) 97

8

Now that Mark has finished cutting trees, the range of tree heights is 27 feet. How many feet tall is the shortest tree that was not cut down? A) 27 B) 66 C) 72 D) 78 E) answer not given

9

Which number represents the closest estimate of the number of trees you would expect to find in two square miles of this forest, if the plot described (before any trees are cut down) is a good sample of the entire forest? A) 596 B) 400,000 C) 192,000 D) 38,144 E) 1,280


4th Grade – March 28, 2008 Team Contest 1

Biff made 5 trips from the grocery store to his car to carry out the watermelons he bought for a picnic. On one trip he carried 2 watermelons, on one trip he carried 3 watermelons, and on each of the other trips he carried one watermelon. Eho made a single trip, using a cart to take out all 5 of the watermelons he bought. How many watermelons did Biff and Eho buy altogether?

2

Put the following five values in order from smallest to largest. Your answer should consist of five letters in the correct order.

A=

1 4

B=

1 2

C =

1 5

D=

3 4

E =

3 8

3

Subtract 18 from the sum of 8 and 80.

4

Give the letters of all of the following statements that are true. If none are true, answer “none”. A) The three sides of a triangle must be equal. B) The radius of a circle is twice its diameter. C) All squares are rectangles. D) A trapezoid is a type of quadrilateral.

5

Seven students stayed for a while after school to work on a poster for Math Team. Chris left before Mary. Allison left before Henry, who left after Kitty. Robin and Chris left together. Kitty left before Jim. Robin left after Henry. List the name of every student who could possibly have been the last to leave.

6

I have 90 cents. What is the largest number of 3-cent jellybeans I could buy, if I also buy at least one 5-cent gumball and end up with no money left over?

7

The positive multiples of 3 are the numbers you say when counting by threes starting with 3. How many of the first 100 counting numbers have at least one digit that is a positive multiple of 3?

8

Sherry adds her favorite counting number to Terry’s favorite counting number and gets an even sum. When Sherry divides her number by 4, the remainder is 2. Is Terry’s number even or odd? Answer “can’t tell” if there is not enough information to be sure.

9

My pet bunny rabbit hops 2.5 feet with each hop, and hops 100 hops per hour. On average, how many inches does my bunny hop each minute? If your answer is not a whole number, give it as a decimal.

10

At the beginning of day 1 (before any mosquitoes hatch or get eaten), twenty rainbow trout are swimming in a pond with 1000 adult mosquitoes. Each trout eats 15 adult mosquitoes every evening, but 325 new adult mosquitoes are hatched every day at noon. No other mosquitoes die. On day number n , the population of adult mosquitoes first reaches 1500. What is n ?



Person 1 Person 2 Person 3 Person 4 Person 1 Person 2 Person 3

Person 4 Person 1 Person 2 Person 3 Person 4

Practice Relay

Answer

Evaluate 3 + 5 – 2.

6

Evaluate TNYWG + 17.

23

Find the product of TNYWG and 4.

92

Find the difference between TNYWG and 90.

2

Relay #1

Answer

There are 4 chickens and 3 cows in a field. How many feet are in the field altogether? From the wool of one sheep, you can knit TNYWG caps. How many caps can you knit from the wool of 4 sheep? The temperature outside yesterday was TNYWG degrees F. Overnight last night, the temperature dropped 30 degrees F. This morning, the temperature rose 20 degrees F. It is now noon. What is the temperature outside now, in degrees F? Find the product of 17 and 11, and then add TNYWG.

20 [feet]

Relay #2

Answer

What is the number of units in the perimeter of a rectangle with side lengths of 3 units and 6 units? Evaluate 2 × TNYWG × 5.

18 [units]

Paula makes TNYWG cupcakes, and Brad puts these cupcakes into boxes. Each box holds 3 rows of cupcakes, with 5 cupcakes in each row. How many boxes will Brad need? Multiply TNYWG by the 9th term in the following sequence: 65, 60, 55, and so on.

12 [boxes]

80 [caps] 70 [degrees F] 257

180

300



Final Score:

KEY


MENTAL MATH - 30 seconds per question PERSON 1 NAME:

1.1 1.2 1.3 1.4

1 or 0

How many inches are in two feet?

24 [in]

Find the sum of seven plus eight, then subtract five.

10

To find the square of a number means to multiply the number by itself. What is the square of 6? What time will it be two hours and fifteen minutes after 6:00 AM?

36 8:15 AM

PERSON 2 NAME:

2.1 2.2 2.3 2.4

Subtract twelve from twenty-nine.

17

The area of a rectangle is twenty-four square inches, and one side length is six inches. What is the number of inches in the other side length? How many seconds are in half a minute?

4 [inches]

Yesterday was Saturday. What day will it be the day after tomorrow?

Tuesday

30 [sec]

PERSON 3 NAME:

3.1 3.2 3.3 3.4

How many days are in three weeks?

21 [days]

Joel has four chocolate cookies and one peanut butter cookie. If Joel picks one cookie at random, what is the probability that Joel picks a peanut butter cookie? Give your answer as a fraction. How many cents are left if you start with one dollar’s worth of change, and then spend a dime, a nickel, and a penny? Miya is six years older than Henry. Miya is sixteen years old. How many years old is Henry?

1/5

84 [cents] 10 [years]

PERSON 4 NAME:

4.1 4.2 4.3 4.4

What is the average of three, seven, and five?

5

Baby Danelle is one and one-twelfth years old. How many months old is Baby Danelle? What is the digit in the tens place of the product of 8 and 7?

13 [months]

Find the fourth number of the sequence whose first three numbers are nine, eighteen, and twenty-seven.

36

5




Problem

1

The year 2008 is a Leap Year. How many months in 2008 will have an odd number of days? What is 165 minus 79? Miya has eight candies. Helen gives Miya six candies. They now have equal numbers of candies. How many candies did Helen begin with? How many meters are in three kilometers? Cam drives to Canada at sixty miles per hour. If the distance is one hundred fifty miles, how many hours does he drive? If your answer is not a whole number, give it as a mixed number. How many cups are in two and one-half pints? The Incredible Shrinking Woman is five feet two inches tall. If she shrinks two inches every year, how many years will it take for her to reach four feet in height?

2 3

4 5

6 7

7 8

Answer 8 [months]

86 20 [candies]

3000 [m] 2

2

[hours]

5 [cups] 7 [years]

Extra Problem – Only if Needed Find the ones-place digit of the product of the first ten counting numbers.

1

0



Division 1


Problem

1

A bag has three red marbles, five blue marbles, and seven green marbles. I take one marble from the bag at random. What is the probability that I will get a blue marble? Give your answer as a fraction. Today is Wednesday. What day of the week will it be twenty-three days from today? If one half of my number is one hundred, what is twice my number? It is now seven-forty PM. If your bedtime is eightthirty PM, how many more minutes do you have before your bedtime? There are a dozen eggs in a carton. George eats onehalf of the eggs, and Martha eats one-third of the eggs. How many eggs are left in the carton? Nemo flaps his fin twenty times per minute. How many times does he flap his fin in five minutes and thirty seconds? The Sled-Dogs football team has two wins and six losses. What is the smallest number of additional games they need to play to win at least half of their game this season, if they don’t lose any more games and there are no ties?

2 3 4

5

6

7

7.1 8

Answer 5 15

or

3

Friday 400 50 [minutes] 2 [eggs]

110 [times]

4 [wins]

Extra Problem – Only if Needed What is 47 times 27?

1

1269



Division 1


Problem

1

Anna is forcing me to write math questions. If I need to write 14 questions and I write 2 questions in each hour, how many hours will I need to spend writing problems to finish all the questions? What is 37 plus 14 minus 29? What is the smallest whole number greater than zero that can be divided with no remainder by both 8 and 12? There are 95 kids in the cafeteria who are actually eating their lunches. If that is one-third of all the kids in the cafeteria, how many kids in the cafeteria are not eating their lunches? What is the largest 4-digit counting number that has three digits the same and one different? How many ways can you arrange the letters in the word bank, spelled B-A-N-K, if all your arrangements must start with B? Ian likes to count by 8’s. What is the fifth number he will say if the first number he says is 3?

2 3

4

5 6

7 7.1 8

Answer 7 [hours]

22 24

190 [kids]

9998 6 [ways]

35

Extra Problem – Only if Needed What is the median of the values 7, 13, 4, and 11?

12




Problem

1 What is the average of 30 and 18? 2 Each angle of an equilateral triangle is the same number of degrees. All the angles of a triangle add up to 180 degrees. How many degrees are in each angle of an equilateral triangle? 3 There are 2 bugs in a rug and 3 rugs in a jug. How many bugs are in 4 jugs? 4 I plan to study mental math one day next week. If I choose the day at random, what is the probability that it will be EITHER Monday OR Tuesday? Give your answer as a fraction. 5 How many ounces are in a pound? 6 When my number is added to 10, the sum is the same as the product of two times 20. What is my number? 7 Angela has eight coins. None of them are pennies. She has less than 50 cents. What is the value in cents of the most valuable coin she could have? 7 Extra Problem – Only if Needed 8

If a large Tetris piece consists of 4 small pieces and it takes 10 small pieces to clear a row, how many large pieces are needed to clear 2 rows?

Answer 24 60 [degrees]

24 [bugs]

2 7

16 [ounces] 30

10 [cents]

5 [pieces]



Division 2


Problem

1

What is the mode of the following set of numbers: three, two, three, two, three, and four? 2 A pudding recipe calls for 2 cups of milk and one egg. If you use two eggs to make a larger pudding with this recipe, how many pints of milk should you use? 3 What is the largest possible 3-digit counting number that has all its digits different? 4 What fraction is equal to one-half of one-half? 5

What is the difference when you subtract the product of 3 times 11 from the product of 17 times 2? 6 If it was Monday one week and two days ago, what day was it yesterday? 7 Lewis is counting by threes. The first number he says is four. What is the first odd two-digit number he will say? 7.1 8

Answer 3

2 [pints]

987

1 4

1

Tuesday

13

Extra Problem – Only if Needed Is the number of days in 7 weeks closer to the number of days in one month or in two months?

2 [months]



Division 2


Problem

1

Jinglin had fifty cents. Then she spent a dime and a quarter. How many cents did she have left? The last time I poured a cup of coffee for myself was this morning at 8 AM. It is now 20 minutes before 9 AM. How many minutes have gone by since I poured myself a cup of coffee? The area of a square is 4 square centimeters. What is the number of centimeters in the perimeter of the square? What is the sum of the largest two-digit whole number and the smallest three-digit whole number? A horse runs at 12 miles per hour. If it keeps up this rate, how many miles will it travel in three and one-half hours? What digit is in the ones place of the sum of 854 and 389? Cam is trying to learn a list of 100 spelling words. Every hour he spends studying, he learns 25% of the words on the list. How many hours will he need to study to learn 100% of the words on the list?

2

3

4 5

6 7

7.1 8

Answer 15 [cents] 40 [minutes]

8 [centimeters] 199 42 [miles]

3 4 [hours]

Extra Problem – Only if Needed Anna’s favorite number is a whole number that can be divided by 3 with no remainder. What is her favorite number if it is greater than 129 and less than 135?

132


Final Score:

KEY


School Name__________________________________Team #________

First Score



4 [sides} 22 13 [pounds] 5 36 [months] 1110 5 [numbers] 70 4 [orders] even A 26 2 [eggs] 5 [triangles] 12 [vegetables] 26 [feet] 32 [days] 16/24 or 2/3 6 [bills] 25

1 or 0 1 or 0

Answer 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

48 [cookies] 24 [bugs] 7448 9 [seconds] 177 [pieces] 10 25 [miles per gallon] 11 [MathSnacks] 3 10 [years] 13 [lollipops] 648 [ounces] 4 [pencils] 72 [inches] [$] 8.88 1500 [times] [$] 3.70 16 [shoes] CBDEA 580 [numbers]

1 or 0

1 or 0


Final Score:

KEY


First Score

(out of 18)




Answer

1 2 3 4 5 6 7 8 9 10

D D B A C C A C B

-1, 0 or 2

-1, 0 or 2


Final Score:

KEY


First Score

(out of 20)




Answer

1 2 3 4 5 6 7 8 9 10 10

13 [watermelons] CAEBD 70 C, D [either order] Jim, Mary [either order] 25 [jellybeans] 51 [numbers] even 50 [inches] [n=] 8

2 or 0

2 or 0


KEY


Answer for person

Answer for person

Answer for person

#1

#2

#3

#4

6

23

92

2

1 or 0

1 or 0

1 or 0

2 or 0


20 [feet] 1 or 0

Answer for person

Answer for person

#2

#3

80 [caps] 70 [deg F] 1 or 0

1 or 0


257 2 or 0


Answer for person

#1

#2

18 [un]

180

1 or 0

1 or 0


12 [boxes] 1 or 0


300 2 or 0

Math+is+Cool+Four

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