Government of the Republic of Trinidad and Tobago MINISTRY OF EDUCATION Curriculum Planning and Development Division
for the Secondary Entrance Assessment (SEA)
(2017)
TABLE OF CONTENTS HOW TO USE THIS BOOKLET ....................................................................................................................................... i Workbook ................................................................................................................................................................... 1 SECTION I................................. ................ ................................... .................................... ................................... .................................. ................................... ................................... ................................... .......................... ........ 2 A - Number ............................................................................................................................................................. 2 SECTION I................................. ................ ................................... .................................... ................................... .................................. ................................... ................................... ................................... ........................ ...... 12 B - Measurement and Money .............................................................................................................................. 12 SECTION I................................. ................ ................................... .................................... ................................... .................................. ................................... ................................... ................................... ........................ ...... 22 C - Geometry ........................................................................................................................................................ 22 SECTION I................................. ................ ................................... .................................... ................................... .................................. ................................... ................................... ................................... ........................ ...... 28 D – – Statistics ......................................................................................................................................................... 28 SECTION II................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 33 A - Number ........................................................................................................................................................... 33 SECTION II................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 47 B – Measurement – Measurement and Money ............................................................................................................................. 47 SECTION II................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 64 C – – Geometry ....................................................................................................................................................... 64 SECTION II................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 76 D- Statistics ................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ................................ ............... 76 SECTION III .................................. ................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 78 A - Number ........................................................................................................................................................... 78 SECTION III .................................. ................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 86 B – Measurement – Measurement and Money ............................................................................................................................. 86 SECTION III .................................. ................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 96 C - Geometry ........................................................................................................................................................ 96 SECTION III .................................. ................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... .................... 101 D - Statistics ........................................................................................................................................................ 101 Appendices ............................................................................................................................................................. 107 Appendix A SECONDARY ENTRANCE ASSESSMENT GUIDELINES ................................. ............... ................................... .................................. ...................... ..... 108 TABLE OF SPECIFICATIONS – SPECIFICATIONS – MATHEMATICS MATHEMATICS................................. ............... ................................... .................................. ................................... .................................. ................ 109 ASSESSMENT OBJECTIVES – OBJECTIVES – MATHEMATICS MATHEMATICS .................................. ................ ................................... .................................. ................................... .................................. ................ 110 Appendix B STRATEGY FOR SOLVING PROBLEMS .................................. ................ ................................... .................................. ................................... ............................ .......... 116
TABLE OF CONTENTS HOW TO USE THIS BOOKLET ....................................................................................................................................... i Workbook ................................................................................................................................................................... 1 SECTION I................................. ................ ................................... .................................... ................................... .................................. ................................... ................................... ................................... .......................... ........ 2 A - Number ............................................................................................................................................................. 2 SECTION I................................. ................ ................................... .................................... ................................... .................................. ................................... ................................... ................................... ........................ ...... 12 B - Measurement and Money .............................................................................................................................. 12 SECTION I................................. ................ ................................... .................................... ................................... .................................. ................................... ................................... ................................... ........................ ...... 22 C - Geometry ........................................................................................................................................................ 22 SECTION I................................. ................ ................................... .................................... ................................... .................................. ................................... ................................... ................................... ........................ ...... 28 D – – Statistics ......................................................................................................................................................... 28 SECTION II................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 33 A - Number ........................................................................................................................................................... 33 SECTION II................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 47 B – Measurement – Measurement and Money ............................................................................................................................. 47 SECTION II................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 64 C – – Geometry ....................................................................................................................................................... 64 SECTION II................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 76 D- Statistics ................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ................................ ............... 76 SECTION III .................................. ................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 78 A - Number ........................................................................................................................................................... 78 SECTION III .................................. ................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 86 B – Measurement – Measurement and Money ............................................................................................................................. 86 SECTION III .................................. ................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... ..................... ... 96 C - Geometry ........................................................................................................................................................ 96 SECTION III .................................. ................. ................................... ................................... ................................... ................................... ................................... ................................... ................................... .................... 101 D - Statistics ........................................................................................................................................................ 101 Appendices ............................................................................................................................................................. 107 Appendix A SECONDARY ENTRANCE ASSESSMENT GUIDELINES ................................. ............... ................................... .................................. ...................... ..... 108 TABLE OF SPECIFICATIONS – SPECIFICATIONS – MATHEMATICS MATHEMATICS................................. ............... ................................... .................................. ................................... .................................. ................ 109 ASSESSMENT OBJECTIVES – OBJECTIVES – MATHEMATICS MATHEMATICS .................................. ................ ................................... .................................. ................................... .................................. ................ 110 Appendix B STRATEGY FOR SOLVING PROBLEMS .................................. ................ ................................... .................................. ................................... ............................ .......... 116
Appendix C SOME WORKED WORKED EXAMPLES WITH “TIPS”........................................................................................... “TIPS”........................................................................................... 117 Appendix D ANSWERS TO PROBLEMS ................................................. ............................... ................................... .................................. ................................... ............................... ............. 133 Section 1 A - Number ..................................................................................................................................... 133 Section 1 B – B – measurement measurement & Money ........................................................................................................... 135 Section 1 C - Geometry .................................................................................................................................. 136 Section 1 D - Statistics .................................................................................................................................... 137 Section 11 A - Money ..................................................................................................................................... 138 Section 11 B- Measurement and Money ....................................................................................................... 140 Section 11 C - Geometry ................................................................................................................................ 142 Section 11 D - Statistics .................................................................................................................................. 145 Section 111 A - Number ................................................................................................................................. 146 Section 111 B – B – Measurement Measurement & Money ....................................................................................................... 147 Section 111 C - Geometry .............................................................................................................................. 149 Section 111 D - Statistics ................................................................................................................................ 150
HOW TO USE THIS BOOKLET This booklet was created to support students who are preparing for the Mathematics Paper of the Secondary Entrance Assessment (SEA). It comprises of a workbook and appendices. The Workbook contains items from SEA past papers (2010 – 2015), arranged according to sections (1, 11 and 111), topics (Number-A, Measurement and Money-B, Geometry-C and Statistics-D) and according to difficulty level (simple to difficult). The table below shows the number of items in each section and for each topic.
TOPICS SECTIONS
1 11 111
A NUMBER
B MEASUREMENT AND MONEY
C GEOMETRY
D STATISTICS
39 40 10
35 34 10
12 18 5
9 4 5
Students are to solve the problems in the workbook. Before solving the problems in the workbook, students may find it helpful to study Appendix B – Strategy for Solving Problems (with two worked examples) and Appendix C – Some worked Examples with “Tips”. Teachers and Parents may find Appendix A useful as it provides the guidelines and objectives for the Mathematics paper of the SEA. Appendix D provides the answers for the problems contained in the workbook and as such can be used as a means of checking the correctness of the answers obtained while solving the problems.
i|Page
Workbook
1|Page
SECTION I A - Number
Each question is worth 1 mark. Show ALL working in the Working Column.
No. 1.
TEST ITEMS Write in words :
12 540
Answer________________________
2.
Write in figures: Two hundred and five thousand and seventythree. Answer _____________
3.
State the VALUE of the underlined digit in the following numeral. 753 291 Answer _____________
4.
Write the numeral which represents (2 x 10 000) + (6 x 1000) + (3 x 10) + (7 x 1). Answer________________________________
5.
Write the number 263 to the NEAREST hundred. Answer_________________________________
6.
Write 8.74 to the NEAREST tenth. Answer_________________________________
2|Page
WORKING COLUMN
No. 7.
TEST ITEMS Write the number in the box that CORRECTLY completes the following sentence.
×
= 20
Answer ______________
8.
Write the following numbers in descending order (starting with the GREATEST in value). 5173,
5731,
5317
Answer _______________________________
9.
Write
as a mixed number.
Answer _________________
10.
Calculate: 1996
−
684 _______________
Answer
11.
________________
MULTIPLY:
6.03 x 0.04 Answer ___________________
3|Page
WORKING COLUMN
No. 12.
TEST ITEMS A star fish has 5 arms as shown below.
How many arms will 16 starfish have?
Answer___________________arms
13.
Ken eats four plums each day. How may plums would he eat in TWO weeks?
Answer________________________
14.
A chocolate factory produces 250 boxes of chocolate in a day. Each box contains 30 chocolate bars. How many chocolate bars are produced in a day? Answer __________________ bars
15.
At a school bazaar, every seventh student who entered in the first hour was admitted free. If 46 students entered in the first hour, how many of them entered free?
Answer ____________________
4|Page
WORKING COLUMN
No. 16.
TEST ITEMS The first four shapes in a pattern are shown below. EACH shape is made from squares of the same size.
How many squares would form the 6 th shape?
Answer ________________________ squares
17.
Complete the following number sequence. 4, 9, 15, 22, 30, 39, ______ Answer __________________
18.
Complete the number pattern below.
Answer 5|Page
_______________________________
WORKING COLUMN
No. 19.
TEST ITEMS What number, N, should go in the circle to make the operation CORRECT?
N Subtract 8 Divide by 4 8
Answer N =________________
20.
Write the correct number in the circle to give the result shown.
21.
What FRACTION of the whole shape is shaded?
Answer ___________________________
6|Page
WORKING COLUMN
No. 22.
TEST ITEMS Express the SHADED PART as a COMMOM FRACTION of the whole shape.
Answer ____________________
23.
24.
Shade of the shape below.
A pizza was cut into 12 equal slices as shown below.
Shade of the pizza.
25.
At the market, a mother bought some fruits: 3 oranges, 4 pears and 5 mangoes. What FRACTION of the fruits were pears? Answer ____________________
7|Page
WORKING COLUMN
No. 26.
TEST ITEMS Complete the sequence below by filling in the missing fraction in the box.
27.
, ,
Write in the box the number that CORRECTLY completes the number sentence.
28.
,
=
Write ONE of the following symbols
>
=
<
In the box below so that the number sentence is correct
29.
Arrange the fractions below in ASCENDING order. (Begin with the SMALLEST).
1 1 1 1 4 12 3 6 Answer _____________________
30.
A piece of ribbon is
m long.
A piece measuring m is cut off. What is the length, in metres, of the remaining piece? Answer ____________________________m
8|Page
WORKING COLUMN
No. 31.
TEST ITEMS
Express 5 as an IMPROPER fraction.
Answer_________________
32.
Jamie divides an orange into 12 equal slices.
She gives
to her friend. How many slices does
Jamie give to her friend?
Answer __________________________slices
33.
Kerry has 120 oranges. He sells
of them.
How many oranges does Kerry sell?
Answer _______________________oranges
9|Page
WORKING COLUMN
No. 34.
TEST ITEMS
WORKING COLUMN
Complete the table below.
Common Fraction
Percentage
15%
3 5
35.
60%
The whole shape below is divided into the portions shown
30%
10%
x%
x %
x %
What number does x represent? Answer ________________________________%
36.
A netball team played 16 games. The team lost 3 games, drew 1 and won the others. What percentage of games did they win? Answer________________________________%
37.
In a spelling contest, Peter was given 40 words to spell. He spelt 32 words correctly. What fraction of the total number of words did he spell correctly? Answer _________________________
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No. 38.
TEST ITEMS
WORKING COLUMN
Ms Mohammed is paying cash for the TV and receives a 20% discount.
Cash Price $520
TV •••
Calculate the amount of this discount.
Answer $ _______________________
39.
A laptop was advertised as shown below.
Calculate the VAT to be paid. Answer $_____________________
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SECTION I B - Measurement and Money
Each question is worth 1 mark. Show all working in the Working Column. No. 1.
TEST ITEMS Amy has the coins shown in the diagram below.
25 cents
25 cents 5 cents
10 cents
25 cents 5 cents
10 cents
10 cents
What is the TOTAL value of all the coins? Answer $_________________________
2.
Chad buys a bag of oranges for $9.50. How much change should he get if he pays with a $20.00 bill? Answer $_____________________
3.
How many quarters (25¢ coins) will Tori get in exchange for a $5.00 note? Answer ______________________quarters
4.
Nikki has a total of $7.00 in her piggy bank. If she only saves 25¢ coins, how many 25¢ coins does she have? Answer_______________________
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WORKING COLUMN
No. 5.
TEST ITEMS Lisle has $6.00. Pencils are sold a $1.25 each. What is the GREASTEST number of pencils that Lisle can buy?
Answer_______________________pencils
6.
Shari has 4 coins on her desk. They have a total value of 50 c. The value of 2 coins is shown in the diagram below.
10 ¢
5¢
Write the correct value on EACH of the other 2 coins.
7.
Maya buys some of the apples and plums advertised below.
She buys 4 apples and pays with a $10 bill. How many plums can she buy with the remainder of the money?
Answer _________________________plums
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WORKING COLUMN
No. 8.
TEST ITEMS
WORKING COLUMN
Ron purchased 4 mangoes from Stall A and Mac purchased 5 mangoes from Stall B.
Stall A
Stall B
4 for $3.00
5 for $4.00
Who bought the mangoes at a cheaper rate?
Answer ____________________________
9.
A sales clerk is preparing a tag to show the selling price for a television.
Complete the tag below.
Cost Price
$1 740.00
Discount
$174.00
Selling Price
10.
Jessica bought a blouse for $80.00 and sold it for $60.00. Calculate the percentage loss on the sale. Answer__________________________
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No. 11.
TEST ITEMS
WORKING COLUMN
The length of a carrot is measured below.
0
1
2
3
4
5
6
cm
What is the length to the NEAREST centimetre? Answer ________________cm
12.
How many pieces of string 25 cm long can be cut from a piece of string length 2 m? Answer __________________pieces
13.
+
kg 6 3
g 763 286
Answer
14.
The shape below has sides that are all equal.
15cm
What is the perimeter of this shape? Answer _________________cm
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No.
TEST ITEMS
15.
WORKING COLUMN
A garden has the shape shown below with all its sides of equal length. The perimeter is 72 metres.
What is the length of ONE side of the garden? Answer ___________________metres
16.
A piece of board has the shape shown below. The perimeter of the board is 40 cm. 10 cm 7 cm d cm
9 cm
3 cm 6 cm
Calculate the length of the side marked d cm.
Answer d = ________________cm
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No. 17.
TEST ITEMS
WORKING COLUMN
Indira awoke at quarter past seven. Draw in the hands on the clock below to show the time Indira awoke.
11
12
1 2
10 9
3 4
8 7
18.
6
5
The clock shown below is 25 minutes slow. 11
12
1 2
10 9
3 4
8 7
6
5
To which number should the longer hand point to show the correct time? Answer _________________
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No.
TEST ITEMS
19.
Write the time shown on Clock A, in digital notion, on Clock B.
20.
Karen’s journey from Rio Claro to Port-of-Spain took 205 minutes. How many HOURS did her journey take? Answer _________________hours
21.
Allan sets out to run three laps without stopping. He starts at 10:15 a.m. and each lap takes 15 minutes. At what time does he finish?
Answer __________________a.m.
22.
Sally began reading a book at 8:17 p.m. She took a break after reading for half an hour. At what time did she take a break?
Answer ___________________p.m.
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WORKING COLUMN
No. 23.
TEST ITEMS School starts at 8:45 a.m. Sally arrived half an hour late. What time did she arrive at school? Answer ________________a.m.
24.
Which of the two sacks has the SMALLER mass?
Answer __________________
25.
A bag of flour weighs 4.1 kg and a bag of corn meal weighs 3985 g. By how much is one bag heavier than the other? Answer _________________g
26.
A square sheet of paper has sides of 11 cm. What is its area? Answer_________________cm2
27.
The area of a square is 121 cm 2. Calculate the length of ONE of its sides. Answer______________ cm
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WORKING COLUMN
No. 28.
TEST ITEMS
WORKING COLUMN
A rectangular garden bed is 5 metres long and has an area of 18 square metres.
5m
How wide is the garden bed? Answer_______________metres(m)
29.
A square, labeled S, and a rectangle, labeled R, are shown below. (The shapes are not drawn to scale.) 10 cm
25 cm
R
S
w
Both shapes have the same area. Calculate the width, w , of rectangle R? Answer
30.
________________________________
The width of the rectangular card below is 4 cm. the length, x cm, of the card is twice the width.
4 cm x cm
Calculate the area of the card. Answer____________________ cm2
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No. 31.
TEST ITEMS Two containers are shown below. Which container holds more?
Answer __________________________
32.
Convert 2.369 kilometres to metres. Answer __________________ metres
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WORKING COLUMN
SECTION I C - Geometry
Each question is worth 1 mark. Show ALL working in the Working Column. No. 1.
TEST ITEMS The triangle shown below has ONLY two sides of equal length.
What type of triangle is it? Answer ______________________________
2.
A picture of a solid is shown below.
What is the name of the solid? Answer _________________________
3.
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Circle the pyramid from the set of solids below.
WORKING COLUMN
No. 4.
TEST ITEMS What is the name of the solid that will be formed when the net below is folded?
Answer __________________________
5.
How many lines of symmetry are there in the following shaded shape?
Answer _________________ lines
6.
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Complete the drawing below to show the net of the triangular- based prism.
WORKING COLUMN
No. 7.
TEST ITEMS
WORKING COLUMN
The diagram below show the net of a cuboid.
4 cm
z 2 cm 10 cm
What is the area of the shaded face, Z? Answer ___________________cm2
8.
The diagram below is a rectangle. The points B, D, F and H are midpoints of its sides. A
B
D
H
G
C
F
E
Name ONE line of symmetry of the rectangle Answer __________________________
9.
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Draw the line or lines of symmetry in the plane shape below.
No. 10.
TEST ITEMS
WORKING COLUMN
Complete the shape below so the XY is a line of symmetry.
X
Y
11.
Tyson is facing West and makes THREE a clockwise direction.
turns in
N
W
E
S
In which direction will Tyson now be facing? Answer _____________________
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No. 12.
TEST ITEMS Sunil changes the position of the arrow on the circular dial shown below.
He makes a quarter turn ANTI-CLOCKWISE. At which number is the arrow now pointing?
Answer _______________________
13.
The following net is for a cube with edges of 5 cm. Calculate the perimeter of this net.
Answer ____________ cm
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WORKING COLUMN
No. 14.
TEST ITEMS What is the name of the solid shape that can be made with the following net?
Answer ______________________
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WORKING COLUMN
SECTION I D – Statistics
Each question is worth 1 mark. Show ALL working in the Working Column. No. 1.
TEST ITEMS
WORKING COLUMN
The pictograph below is to be completed to show the favourite brand of cellphones for 30 students in a class. If represents 2 students, complete the pictograph to show how many students prefer Nokia.
MOTOROLA NOKIA SONY
2.
The table below show the number of goals that a team scored in football games.
Games A B
Goals Scored 4 goals 2 goals
C D
The team scored a total of 42 goals. Complete the table to show the number of goals scored in Game C.
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No. 3.
TEST ITEMS The graph below shows the number of haircuts a barber did on five days of a particular week.
Day
Number of Haircuts
Monday Tuesday Wednesday Thursday Friday
The total number of haircuts done in the five days is 75. How may haircuts were done by the barber on Monday?
Answer _______________ haircuts
4.
A bowler obtained the following number of wickets in 9 matches: 3, 1, 4, 6, 4, 2, 4, 1, 3
What is the MODAL number of wickets? Answer __________________________
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WORKING COLUMN
No. 5.
TEST ITEMS
WORKING COLUMN
The graph below shows the number of children buying ice-cream from Monday to Friday.
l i
y a d n o
y a d s e u T
y a d s e n d e
y a d s r u h T
y a d i r F
represents 14 children
How many MORE children bought ice-cream on Monday and Wednesday? Answer _______________children
6.
The incomplete bar graph shows the number of marbles owned by 3 of 4 boys in a club.
s l 12 r 10 f 8 r 6
4 2 Sam
Tim
Sid
Roy
Boy
Together the 4 boys owned 30 marbles. How many marbles did Tim own? Answer _____________________marbles
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No. 7.
TEST ITEMS Altogether, four pupils own 39 marbles. Complete the following chart to show the tally for Tom’s marbles.
8.
Cookies were packaged in three bags as shown below.
What is the mean number of cookies in a bag? Answer _______________________cookies
9.
The mean of 20 and 10 is the same as the mean of 16 and
.
What number does
represent?
Answer ________________________
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WORKING COLUMN
No. 10.
TEST ITEMS The table below shows Adam’s cricket scores for five days in a week. Days of the Week Cricket Scores Monday
9
Tuesday
11
Wednesday
17
Thursday
28
Friday
15
Calculate his mean score for that week. Answer _______________________
11.
The following bar graph represents some TV shows viewed by the pupils in a Standard 3 class.
How many more pupils need to view Smallville for it to be as popular as Goodluck Charlie? Answer __________________ pupils
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WORKING COLUMN
SECTION II A - Number
Each question is worth 2 or 3 marks. Show ALL working in the Working Column. No.
TEST ITEMS
WORKING COLUMN
1. Four digits are shown below.
3
9
8
7
Using EACH digit only ONCE, write the
a) SMALLEST four-digit number Answer ___________________
b) LARGEST four-digit EVEN number. Answer _______________________
2.
2
7 1 + 4 8 3
Answer __________________
3. Maria has 413 stamps. Her brother has 49 stamps fewer than she has. How many stamps do they have ALTOGETHER?
Answer __________________ stamps
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No.
TEST ITEMS
4. Sammy planted 526 heads of lettuce. Don planted 98 more than Sammy and 49 more than Linda. a) How many heads of lettuce did Don plant? Answer _____________________
b) How many heads of lettuce did Linda plant? Answer__________________________
c) Calculate the number of heads of lettuce planted ALTOGETHER. Answer _________________________
5. Ravi has 56 marbles. Scott has half as many as Ravi. How many marbles do they have ALTOGETHER?
Answer_____________________________ marbles 6. The following diagram shows a wall that is to be covered with identical square tiles. The shaded area is already tiled.
Express the area of the tiled portion as a decimal fraction of the area of the ENTIRE wall. Answer ____________________
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WORKING COLUMN
No.
TEST ITEMS
7. The table below shows the number of marks awarded for EACH correct answer in Sections A, B and C of a test.
Section
Number of Marks for Each Correct Answer
A
1 mark
B
3 marks
C
5 marks
Jessica got 16 items correct in Section A and 8 items correct in Section B. How many items must Jessica get correct in Section C to earn a score of 50 on the test?
Answer ___________________________
8.
Express as a SINGLE decimal fraction.
+
Answer ________________
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WORKING COLUMN
No.
TEST ITEMS
WORKING COLUMN
9. The table below shows the points scored for hitting three different coloured targets in a video game.
Colour
Number of Points
White
2
Blue
3
Gold
5
Ana scored 53 points in playing the game. She hit the blue target 4 times and the white target 3 times. How many times did she hit the GOLD target? Answer _______________times
10. A team earns 2 points for a win, 1 point for a draw and no points for a loss. The table below shows the points earned by the team.
Results
Points
Won
16
Draw
10
Loss
0
The team played 25 games. How many games did the team lose? Answer _______________games
36 | P a g e
No.
TEST ITEMS
WORKING COLUMN
11. Tia is required to multiply 579 by 31. Instead she multiplies 579 by 21 correctly.
a) What is Tia’s answer? Answer _______________________
b) Complete the statement below. The difference between the required answer and Tia’s answer is equal to 579 x
.
c) What is the CORRECT answer that was required of Tia?
Answer __________________________
12. A school received 25 boxes of pencils. Each box contained 36 pencils. The pencils were distributed EQUALLY among 9 classes. How many pencils did EACH class receive? Answer ________________________
13. Jerry has 40 stickers that are either red, yellow or blue in colour. There are 24 red ones and equal numbers of blue and yellow. Calculate the percentage of his stickers that are yellow. Answer _________________%
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No.
TEST ITEMS
14. Sasha used 55% of her savings to buy a game. She has $135 remaining. How much was her savings before buying the game? Answer $_________________
15. Lisa buys some sweets for a party. She fills 20 bags with 14 sweets each. She has 10 sweets left over. a) How many sweets did Lisa buy?
Answer _______________sweets
b) How may bags could she fill if she puts 12 sweets in EACH bag?
Answer ____________bags
16. What are the next TWO numbers in the sequence 16, 19, 23, 28, , ? Answer __________and ______________
17.
Brian and his father went fishing on the weekend (Saturday and Sunday). They caught 120 fishes on Saturday. Their catch decreased by 25% on Sunday. (a)
Calculate the number of fishes that they caught on Sunday? Answer ________________ fishes
(b)
How many fishes did they catch ALTOGETHER on the weekend?
Answer ________________ fishes
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WORKING COLUMN
No.
TEST ITEMS
WORKING COLUMN
18. Study the number pattern below.
1
4
9
36
a) Write in the TWO missing numbers. Answer _________________________
b) What is the NINTH number in this number pattern? Answer _____________________
19. In a speed-reading competition, Anna read 10 pages for every 7 pages that Kevin read. At the end of the competition, Kevin read 140 pages. How many pages did Anna read? Answer ___________________pages
20. Jack tried to climb 20 m up a coconut tree. For every 5 m he climbed, he fell back 2 m. how far up the tree would he have reached after falling 3 times? Answer _______________ m
21. There were 15 weeks in the school term. Paul went to school for the first 2 weeks and was absent the next week. This pattern was repeated throughout the whole term. For how many weeks was Paul present during the term? Answer __________________weeks
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No.
TEST ITEMS
WORKING COLUMN
22. Ian doubles a certain number and then adds 6. The result is 24. What is the number? Answer ______________________
23. Which of the following fractions is the LARGEST?
5 , 8
2 , 3
7 12
Answer _________________________
24. a) Write in the box below the sign, > or <, the CORRECTLY completes the number sequence.
b) Find the difference between
and
Answer _________________________
25. Three mixed numbers from the set given below will produce a WHOLE number when added.
3
1 2
1
1 8
2
7 12
What are the THREE numbers? Answer ________________________
40 | P a g e
4
3 8
No.
TEST ITEMS
26.
WORKING COLUMN
5 − 2
Answer ________________________
27. Dad had a piece of rope that was
4 m long. He cut
3 m of it to make a swing. What is the length of the remaining piece of rope?
Answer ___________________m
28. (a) Mummy cuts 8 pizzas into SIXTHS. Kori gets
of ONE pizza.
How many SIXTHS of pizza does he get? Answer ______________ sixths
(b)
How many SIXTHS of pizza does mummy have remaining? Answer ______________ sixths
29.
Tom sets out on a journey of 1 km. He ran km and
then he walked km. what fraction of the journey did Tom still have to travel to complete 1 km? Answer__________________________
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No.
TEST ITEMS
30. Carrie had $60 as an allowance for the week. She
spent of it on snacks, of it on stickers and saved the remainder.
a) What fraction did she spend on snacks and stickers together? Answer ___________________________________ b) How much money did she save? Answer $________________________
31. Calculate:
3
2 5 ÷ 3 6
Answer _______________________________
32. Calculate:
16
1 7 ÷ 2 5 10
Answer _____________________________
33. Three quarters of a number is 60.
What is of the SAME number?
Answer _____________________
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WORKING COLUMN
No.
TEST ITEMS
34. The product of two numbers is 9. One of them
is 3 . What is the other number?
Answer__________________________
35. Five years ago, Paul was
his father’s age. Paul’s
father is now 37 years old. How old is Paul now?
Answer ____________________________
36. If 75% of a class of 32 students are present, how many students are absent from the class?
Answer_______________________
37. Susan had gained 20 points for being neat and tidy. On Friday, she lost 10% of these points for untidy work. How many points did she have left?
Answer _______________ points
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WORKING COLUMN
No.
TEST ITEMS
38. A fruit vendor transported 360 mangoes to the market. While transporting the mangoes, 10% of them were damaged.
a) How many mangoes were damaged? Answer ______________________mangoes
b) The mangoes that were not damaged were packed into boxes of 12. How many boxes were used to pack these mangoes? Answer ____________________boxes
39. There are 60 donuts in a glass case. Eighteen of them are chocolate coated. What percentage of donuts is NOT chocolate coated? Answer ____________________________
40. In a car park,
of the cars are blue and the
remainder are white. What percentage of the cars are white?
Answer _____________________%
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WORKING COLUMN
No.
TEST ITEMS
41. Alim collected seashells over the weekend. He collected 45 seashells on Saturday and three times as many on Sunday. a) How many seashells did Alim collect on Sunday? Answer______________________seashells b) What percentage of the seashells collected over the weekend did he collect on Saturday? Answer ___________________________%
42. Jasmine went to the market and purchased 32 fruits consisting of 6 apples, some oranges and some guavas. She purchased twice as many oranges as apples. She recorded her purchases as shown in the table below. a) Complete the table Fruit Apples
I. II.
Number Purchased 6
Oranges Guavas Total
32
b) What percentage of the fruits purchased was apples? Answer ______________________%
43. Simplify, using decimal notation,
7 +
+
Answer ____________________________
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WORKING COLUMN
No.
TEST ITEMS
WORKING COLUMN
44. Complete the table below by writing in the CORRECT percentage at (a) and fraction at (b).
Fraction
Percentage
Decimal
(lowest term)
2 3
(a) %
(b)
0.005
45. How many pieces of string length 0.3 m can be cut from a piece 10.5 m long?
Answer ___________________pieces
46. Mr Singh planted a tree. Each week, the tree grew by 0.24 m. how many weeks did the tree take to grow to 6 m?
Answer ___________________weeks
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SECTION II B – Measurement and Money
Each question is worth 2 or 3 marks. Show ALL working in the Working Column. No. 1.
TEST ITEMS Sam bought 2 snacks at 65¢eash and 1 drink for $1.25. What is his change from a $5 note? Answer _______________________________
2.
Jane bought the 3 items shown below at the supermarket.
a) What is the TOTAL cost of the 3 items? Answer $ _______________________________
b) Calculate Jane’s EXACT change if she paid for the items with a $20.00 bill. Answer $ ________________________________
3.
A table and four chairs together cost $540. The cost of each chair is $70. Calculate the cost of the table. Answer $ ______________________________
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WORKING COLUMN
No. 4.
TEST ITEMS
WORKING COLUMN
The entrance fee to a cricket match was $12 for a teacher and half-price for a student. A group of 20 students and 3 teachers went to the match. Calculate the TOTAL entrance fee for the group. Answer$ ___________________________
5.
Jane has an EQUAL number of $20, $10, $5 and $1 bills. a) What is the LEAST amount of money that Jane could have? Answer __________________________________
b) If Jane has $144.00, how many of EACH type of bill does she have? Answer __________________________________
6.
Karie’s father promised to give her $4.00 for every $10.00 she saved. Karie saved $60.00. a) How much money does her father have to give her? Answer $ ______________________________ b) How much money ALTOGETHER?
would
she
have
Answer $ ________________________________
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No. 7.
TEST ITEMS Tom works for eight hours each day and is paid $12 per hour. a) If he works for five days, calculate the total amount that he is paid. Answer $ _________________________________
b) When Tom works on Saturdays, he is paid
per hour at 1 times the week-day rate. How much is Tom paid per hour on a Saturday?
Answer $ ________________________________
8.
A discount of 15% was given for each cash purchase at a shoe store. How much will Derrick pay cash for a pair of shoes marked at $600.00? Answer ________________________________
9.
Gina buys the blouse below which is priced at $180.00.
After discount, how much money does she pay for the blouse? Answer $ _____________________________
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WORKING COLUMN
No.
TEST ITEMS
10.
WORKING COLUMN
Chelsea bought some items at Reflex Clothing Store. Her bill is shown below. Some values are not stated. Reflex Clothing Store Quantity
Item
Unit
Cost
Cost 1
Track Pants
@
$55.00
3
T-shirts
@
$20.00
5
Handkerchiefs @
$4.00
Total before VAT
Total Cost after VAT
(a)
The cost of the 3 T-shirts
Answer $______________
(b)
The VAT on her total bill
Answer $______________
(c)
The total cost after VAT. Answer $______________
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$20.00 $135.00
VAT 15%
Calculate
$55.00
No. 11.
TEST ITEMS The school cafeteria bought 5 dozen silly bands at $15 per dozen and sold them for $2 EACH. (a) What was the profit, in dollars, made by the school cafeteria? Answer $______________
(b) Calculate the profit as a percentage of the cost price. Answer ______________%
12.
The cost price of a television is $1200. VAT is calculated at 15% of the cost price. (a) Calculate the amount of VAT. Answer $______________
(b) Calculate the TOTAL amount that a customer pays for the television. Answer $______________
(c) Larry bought one of the televisions but later sold it for $980. Calculate his lost as a percentage of the cost price. Answer ______________%
13.
Mr Lee borrowed $8000 from the bank to buy a used car. He paid simple interest at a rate of 12% per year for a period of 3 years. How much simple interest did Mr Lee pay? Answer $______________
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WORKING COLUMN
No. 14.
TEST ITEMS Ali borrowed $5000.00 from the bank for a period of 3 years at a rate of 8% per annum.
(a) Calculate the simple interest that Ali must repay. Answer $______________
(b) How much money must Ali repay the bank at the end of 3 years
Answer $______________
15.
Tony borrowed $12000 from a bank at a rate of 8% per annum.
(a) Calculate the simple interest if he agreed to repay the loan in 2 years.
Answer ______________
(b) How much will Tony have to repay the bank?
Answer ______________
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WORKING COLUMN
No. 16.
TEST ITEMS Mrs. Chin got a loan of $6000 from a credit union. She took 3 years to repay the loan at the simple interest rate of 5% per annum. Calculate the TOTAL amount of money that Mrs. Chin repaid.
Answer $__________________ 17.
Burns ran the following distances over a 2-week period while training for the Olympics.
Week
Distance Ran
1
3 km 800 m
2
2.75 km
What is the TOTAL distance covered by Burns over the 2 weeks? Answer ______________
18.
The diagram below shows the distances that David covered in a triathlon.
How many kilometers did David cover during the entire event? Answer ______________Kilometers
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WORKING COLUMN
No. 19.
TEST ITEMS The sides of triangle PQR are equal in length. The perimeter of PQR is 21cm.
(a) What is the length of PQ? Answer ______________cm
(a) Two triangles identical to PQR are combined as shown in Diagram II to form a new shape. Find the perimeter of the new shape. Answer ______________cm
20.
The semicircle PQRT with radius 7cm fits inside the rectangle PRSU as shown in the diagram below.
Calculate the perimeter of the rectangle PRSU. Answer ______________cm
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WORKING COLUMN
No. 21.
TEST ITEMS
WORKING COLUMN
The diagram below shows a cycling track consisting of a rectangle and two semicircles.
A cyclist starts at point A and cycles in the direction of the arrows to point B. What distance did he cover?
( =
)
Answer ______________meters
22.
Shae designed a gold chain by using 20 thin gold circles arranged as shown below. Each circle has a radius of 1.5 cm.
(a) What is the diameter of EACH circle? Answer Diameter = ______________cm
(b) Calculate the length, L cm, of the chain. Answer L= ______________cm
(c) Shae needs a matching bracelet to measure 18cm in length. How many circles are needed? Answer ______________
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No. 23.
TEST ITEMS An examination began at 8:30 a.m. and was done in two parts. The first part lasted for 1 hour 50 minutes. The second part lasted for 1 hour 15 minutes. At what time did the examination finish if there was a 20-minute break after the first part?
Answer ______________
24.
Michael left home at 7:37 a.m. and arrived at school 43minutes later. He reached school 5 minutes before the bell rang. At what time did the bell ring? Answer ______________
25.
Mr. Ben had to be at work at 9:00 a.m. He must get dressed, eat and walk to work. After getting out of bed, it takes him 15 minutes to get dressed, then 20 minutes to eat, and a further 35 minutes to walk to work. (a) How long does it take Mr. Ben to get dressed, eat and walk to work? Answer ______________ (b) What is the LATEST time Mr. Ben should get out of bed in order to get to work on time? Answer ______________
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WORKING COLUMN
No. 26.
TEST ITEMS The time shown on Clock A is 15 minutes AHEAD of the correct time.
(a) Insert the correct time on Clock B.
Answer _____________
(b) At the end of the next hour, Clock A gained an additional 5 minutes ahead of the correct time. What time will be shown on Clock A? Answer _____________ 27.
A pumpkin weighing 2.6 kilograms is placed on the scale below.
(a) Draw the new position of the pointer when the pumpkin is placed on the scale. (b) How many GRAMS does the pumpkin weigh? Answer _______________
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WORKING COLUMN
No. 28.
TEST ITEMS The combined weight of Jane and her sister, Nora, is 51.4 kg. If Jane is 5.6 kg heavier than Nora, how much does Nora weigh? Answer _______________kg
29.
In the diagram below, the area of the shaded triangle is 36 cm².
What is the area of the rectangle? Answer _______________ 30.
The side of a square is 11cm. (a) What is the area of the square? Answer _______________cm² (b) What is the perimeter of the same square? Answer _______________cm (c) Two sides of the square are extended by 3cm as shown below
What is the area of the NEW shape? Answer _______________cm²
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WORKING COLUMN
No. 31.
TEST ITEMS The side of each square on the following grid is 3 cm.
Complete EACH of the following statements. (a)
The area of ONE square on the grid is _______________ cm2
(b)
The TOTAL shaded area on the grid is _______________ cm2
32.
The following diagram shows a wall that is to be covered with identical square tiles. The shaded area is already tiled.
Express the area of the tiled portion as a decimal fraction of the area of the ENTIRE wall. Answer ____________________
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WORKING COLUMN
No. 33.
TEST ITEMS The following diagram represents the floor space of the library (A) and the computer room (B) at Central Government School. The diagram consists of identical squares.
(a)
What is the MOST suitable unit for measuring the area of the floor? Answer ___________________
(b)
Each floor space has to be covered with carpet. Which room has the SMALLER floor space to be covered? Answer ___________________
(c)
Which room has the floor with the SMALLER perimeter? Answer ______________________
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WORKING COLUMN
No. 34.
TEST ITEMS (a) Ram’s garden plot is 12 m long and 8 m wide. What is the area of the garden? Answer _______________m²
(b) Ram makes a path 1 m wide around the garden as shown below.
Calculate the area of the path (shaded) Answer _______________m²
35.
The following diagram shows a rectangular box with dimensions 6 cm x 9 cm x 18 cm and a small cube with sides 3 cm.
How many small cubes are needed to completely fill the rectangular box?
Answer _____________________ cubes
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WORKING COLUMN
No. 36.
TEST ITEMS
WORKING COLUMN
Calculate the area of the following shape.
Answer ____________________ cm2
37.
A food vendor made 7
litres of soup for sale. She
sells the soup in servings of 375 ml.
How many servings of soup can she get from the 7
litres? Answer _______________servings
38.
The volume of the cuboid shown below is 48cm ³. The length of the cuboid is 3cm, the width is 2cm and the height is h cm.
Calculate the value of h. Answer _______________
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No.
TEST ITEMS
39.
The volume of the cuboid fish tank shown below is 72 000 cm³.
(a) What is the area of its base labeled B? Answer _______________ cm²
(b) How deep is the fish tank? Answer _______________cm
(c) Calculate the area of the shaded side A. Answer _______________cm²
40.
The container shown below is used to fill the fish tank next to it.
(a) What is the volume, in LITRES, of the fish tank? (1000 cm³ = 1 litre) Answer _______________ (b) How many full containers are needed to fill the tank completely? Answer _______________
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WORKING COLUMN
SECTION II C – Geometry
Each question is worth 2 or 3 marks. Show ALL working in the Working Column. No. 1.
TEST ITEMS Use the diagram below to answer the questions that follow.
State the names of: (a) ONE plane shape in the diagram above Answer_______________________
(b) ONE solid that would be needed to make a model of the building Answer________________________
2.
Sheldon has the following plane shapes.
Draw a diagram to show how Sheldon can fit the three shapes together to form a new rectangle.
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WORKING COLUMN
No. 3.
TEST ITEMS The diagram below shows three triangles labeled W,X and Y. The line segments marked with the double strokes (II) are equal in length.
(a) Which triangle is (i) Right-angled? Answer______________
(ii) Equilateral? Answer______________
4.
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Complete the table below.
WORKING COLUMN
No.
TEST ITEMS
5.
WORKING COLUMN
(a) Draw a net of a cube in the space provided below.
(b) Complete the table below. Shape
Edges
Vertices
Faces
8
6
Cube
6.
The diagram below shows a cylindrical package closed at both ends.
(a) How many faces does the package have? Answer______________
(b) Draw the net of the package.
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No. 7.
TEST ITEMS (a)
The following diagram is incomplete.
Complete the diagram to represent the net of a triangular prism. (b)
How many edges does a triangular prism have? Answer ______________ edges
8.
XY is a line of symmetry of the incomplete figure ABCD shown below
(a) Complete the drawing of ABCD. (b) Circle the term from the list below that BEST describes ABCD
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Parallelogram
Square
Quadrilateral
Rhombus
WORKING COLUMN
No. 9.
TEST ITEMS The diagram below shows an incomplete shape.
Complete the shape so that XY is a line of symmetry.
10.
The diagram below shows an incomplete plane shape and one of its lines of symmetry, RS.
(a) Complete the drawing of the shape. (b) Draw another line of symmetry, PQ, for the completed shape.
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WORKING COLUMN
No. 11.
TEST ITEMS The triangle XYZ is moved to the position of triangle PQR.
(a) Name the movement. Answer__________________________ (b) Describe this movement FULLY. Answer___________________________ _________________________________
12.
The shaded triangle T below was moved to the position of triangle S.
(a) Name the movement. Answer______________
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WORKING COLUMN
No.
TEST ITEMS (b) How many shaded triangles EXACLTY like T would completely cover the rectangle ABCD? Answer______________
(c) Circle the term from the list below which BEST describes the triangle formed when T and S are combined as shown above. Right-angled Isosceles Equilateral
13.
Three triangles, P, Q and R are shown below.
(a)
Which of the triangles is equilateral?
Answer _________________
(b)
Which of the triangles have AT LEAST ONE line of symmetry? Answer _________________
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WORKING COLUMN
No. 14.
TEST ITEMS The shape ABCD below is moved from its position at P to the position at Q so that Corner A is now at A' and Corner D is now at D’ .
(a) What is the name of this movement?
Answer______________
(b) Describe the movement in (a) FULLY.
Answer______________
(c) Under the same movement in (a), describe what happens to Corner B.
Answer____________________________ __________________________________
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WORKING COLUMN
No. 15.
TEST ITEMS Refer to the diagram below to answer the questions that follow.
(a) Name an angle less than 90° Answer______________ (b) Which angle is APPROXIMATELY one-third of a whole turn? Answer______________ (c) Which angles TOGETHER have the SAME measure as half a turn? Answer______________
16.
The following diagram shows a flat shaded shape, ABCD.
(a)
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Circle the word from the following list which BEST describes the angle at C. Acute
Right-angled
Obtuse
Reflex
WORKING COLUMN
No.
TEST ITEMS (b)
(c)
17.
On the diagram of ABCD, tick (✓) the sides which are PARALLEL to each other.
On the diagram, draw ONE line to divide the shape ABCD into TWO triangles.
The minute hand of a clock moved from 9 to 2 in the direction of the arrow shown.
Through how many degrees did the minute hand move?
Answer______________
18.
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The angle formed between the hands of the clock shown below is marked with ‘y’
WORKING COLUMN
No.
TEST ITEMS
WORKING COLUMN
(a) Circle the term listed below that BEST describes angle y. Right angled;
acute;
obtuse;
reflex
(b) Complete the following statement. Angle y measures _______________ degrees. 19.
Sasha is facing SE. She turns in a clockwise direction to face NW.
(a) What fraction of a whole turn does Sasha make? Answer______________
(b) How many MORE degrees must she turn in order to face North? Answer______________°
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No. 20.
TEST ITEMS The gauge needle on a welder’s gas tank moves in the direction of the arrow shown below.
(a) How many degrees does the needle turn through from START to 8
Answer______________
(b) The needle moves from 0 through 135 degrees. Where is the new position of the needle?
Answer______________
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WORKING COLUMN
SECTION II D- Statistics
Each question is worth 2 or 3 marks. Show ALL working in the Working Column. No. 1.
TEST ITEMS
WORKING COLUMN
The pictograph shows the first choice of sports for boys in Standard 5.
Volleyball
= 10 boys
Football Cricket
How many boys indicated their choice of sports? Answer_____________
2.
The incomplete graph below shows the marks that John scored in Mathematics each day during a particular week.
John scored a total of 80 marks for that week. Complete the graph to show how many marks he scored on Friday.
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No. 3.
TEST ITEMS The pie chart below shows how Mr. Samuel spends his salary for the month.
FOOD
OTHER
RENT
Calculate his monthly salary if he spends $1800.00 on food. Answer $_____________
4.
The pie chart below shows the favourite pets of the pupils in Standard 3.
15% 10% dogs
parrots
sheep rabbits
25% goats 5% cats
a) Which TWO pets are EQUALLY favoured? Answer _________________
b) What percentage of the pupils in Standard 3 favour parrots? Answer _________________
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WORKING COLUMN
SECTION III A - Number
Each question is worth 5 marks. Show ALL working in the Working Column. No. 1.
TEST ITEMS At a fair, four plastic bottles with numbers on them are lined up as shown below.
For every turn, a person is given three balls to knock down three bottles. The numbers are added and a toy is given for some EXACT scores as shown on the table below. Toy Rabbit Bear Parrot Monkey
Score 49 46 40 39
(a) Candy knocks down three bottles marked 18, 9 and 12. Which toy did she win? Answer______________ (b) Candy wants to win the bear. Which THREE bottles should she knock down? Answer______________ (c) Candy knocks down the bottled marked 9. Which toy will she NOT be able to win. Answer______________
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WORKING COLUMN
No. 2.
TEST ITEMS The pupils in Standard Five are seated on benches which can seat either 4 pupils (four-seaters) or a 3 pupils (three-seaters). Five four-seaters and fifteen three-seaters are available. (a) What is the LAGREST number of pupils that can be seated if ONLY the four-seaters are used? Answer______________ (b) On Tuesday, 38 pupils are to be seated and ALL the four-seaters MUST be used. What is the SMALLEST number of three-seaters that are needed? Answer______________ (c) On Thursday, 48 pupils are to be seated. How many of EACH type of benches are needed so that ALL seats are occupied and BOTH types of benches are used? Answer______________ four-seaters ______________ three-seaters
3.
There are 168 students in a school. There are twice as many girls as there are boys. (a) Calculate the number of girls in the school. Answer______________ girls (b) The students are to be divided into 7 classes so that each class had the same number of girls and the same number of boys. Calculate the number of girls and the number of boys in EACH class. Answer______________ girls ______________ boys
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WORKING COLUMN
No.
TEST ITEMS (c) Apples are sold in boxes each containing one dozen. How many boxes will the teacher have to buy so that EACH student receives ONE apple? Answer______________ boxes
4.
Nine light posts are evenly spaced along a highway. A total of 144 plastic pipes of the same length are placed EQUALLY between the 9 posts.
(a) How many pipes are placed between the first and second posts? Answer______________ pipes (b) Each pipe is 7m long. The pipes are connected end-to-end (just touching each other) between the posts. What is the distance between the first and second posts? Answer______________ m
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WORKING COLUMN
No. 5.
TEST ITEMS The following incomplete table shows the number of Standard 4 pupils in a school who qualified for the Mental Mathematics Competition. Mathematics Competition Standard 4 4J
Number of Pupils who Qualified 17
4K 4L
18
4M
17
4N
21
The mean number of pupils who qualified from Standard 4 is 19. How many pupils qualified from Standard 4K? Answer ____________________ pupils 6.
Jamie used dots to create a set of patterns as shown below.
(a) How many dots are there in the FOURTH (4 th) pattern? Answer______________ dots (b) Draw the FIFTH and SIXTH patterns in the space on the diagram. Answer______________ (c) How many dots are in the EIGHT pattern? Answer______________ dots
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WORKING COLUMN
No. 7.
TEST ITEMS
WORKING COLUMN
Richie’s marks for the three subjects in an examination are shown on his report below. Richie’s Report
Subject
Maximum Marks
Marks Obtained
Essay
100
70
Mathematics
100
80
Language Arts
100
60
Total
300
(a) Calculate the TOTAL marks RICHIE obtained for the examination. Answer______________ marks (b) Express the total marks that Richie obtained as a percentage of the maximum marks for the test. Answer______________% (c) How many MORE marks did Richie need in order to get 80% on the test? Answer______________ marks
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No. 8.
TEST ITEMS
WORKING COLUMN
A farmer harvested 600 peppers from his garden. He sold 90% of the peppers and gave the remainder to a children’s home. (a) (I) Calculate the number of peppers the farmer sold. Answer______________ peppers (iii)
How many peppers did he give away?
Answer______________ peppers
(b) The farmer sold the peppers at 5 for $8.00. Calculate how much money he made from the peppers sold in Part (a). Answer$ ______________
9.
Mr. Green bought a box of mangoes. 60% were ripe, 25% were green and the remainder had to be thrown away. The box contained 300 mangoes. (a) How
many
mangoes
were
ripe?
Answer______________ mangoes (b) How many mangoes had to be thrown away? Answer______________ mangoes (c) Mr. Green paid $60 for the box of mangoes. Calculate the amount of money he lost. Answer$ ______________
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No. 10.
TEST ITEMS
WORKING COLUMN
At a school fair, 30% of the pies sold had cheese filling, 25% had beef filling and the remaining 90 pies had potato filling. (a) What percentage of pies had potato filling? Answer______________ (b) How many pies were sold at the fair? Answer______________ (c) How many MORE cheese pies than beef pies were sold at the fair? Answer______________
11.
A fruit vendor has 160 fruits in his stall. Of these,
are mangoes and 20% are plums. The remainder are avocados. (a) How many mangoes does he have? Answer______________ mangoes (b) Express the number of fruits that are plums as a DECIMAL fraction. Answer______________ (c) Calculate the number of avocados in the stall. Answer______________ avocados
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No. 12.
TEST ITEMS Use the numbers given in the box below to complete the statements which follow.
6 11
21 49
(a)
36
24
The SQUARE numbers in the box are ________________________
(b)
The SQUARE ROOT of 121 is ________________________
(c)
The TWO numbers which have a product that is equal to the SQUARE of 12 are __________ and _________
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WORKING COLUMN
SECTION III B – Measurement and Money
Each question is worth 5 marks. Show ALL working in the Working Column. No. 1.
TEST ITEMS The price list in a cafeteria is shown below.
Price List Hot Dog
$5.50
Drink
$2.25
Apple
$1.75
Sean bought 2 hot dogs, a drink and 2 apples. Sade bought a hot dog, 3 drinks and an apple. (a) What is the TOTAL amount spent by Sean and Sade? Answer$______________ (b) How much more than Sade did Sean spend? Answer$______________ (c) Which item(s) can be bought with the difference in the amount spent by Sean and Sade? Answer______________
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WORKING COLUMN
No. 2.
TEST ITEMS
WORKING COLUMN
The diagrams below show the cost of a slice of pizza, a scoop of ice-cream and a drink.
(a) Mark has 3 slices of pizza, 1 drink and 2 scoops of ice-cream. Calculate the cost of his meal. Answer$______________
(b) Sandy wishes to get exactly $20.00 in change from a $50.00 note after purchasing a meal. Suggest a possible combination of the THREE items that she can buy. ______________ slice(s) of pizza
$
______________ scoop(s) of ice-cream $ ______________ drink(s) Total
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$ ____ $____
No. 3.
TEST ITEMS The pictures below show the cost of notebooks, erasers and pencils.
Use the information to complete the table below.
4.
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Complete Akeem’s shopping bill below.
WORKING COLUMN
No. 5.
TEST ITEMS
WORKING COLUMN
An appliance store offers 33 % discount on cash purchases. The original price of a refrigerator is $8400 (a) What is the refrigerator?
discounted
price
on
the
Answer$______________ (b) VAT at 15% is calculated on the discounted price. How much is the VAT? Answer$______________ (c) What is the FINAL cost of the refrigerator when purchased for cash? Answer$______________
6.
Ms Brown borrowed $1200 at 20% simple interest for 2 years. (a) How much interest did she pay?
Answer$______________
(b) How much money did she repay ALTOGETHER?
Answer$______________
(c) Ms Brown repaid the TOTAL amount in EQUAL monthly payments. How much did she pay EACH month?
Answer$______________
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No. 7.
TEST ITEMS Lance’s weekly wage is calculated using the rates in the table below. Lance works for 8 hours daily.
Wage Rates $10 per hour during week (Monday to Friday) $15 per hour weekends (Saturday and Sunday)
(a) During one week, Lance worked on Monday, Wednesday, Friday and Saturday. How many hours did Lance work in that week? Answer______________ hours
(b) Using the rates in the table above, calculate Lance’s wage for that week. Answer$______________
(c) Lance’s wage last week was $400. He worked on Saturday and Sunday. How many HOURS did he work from Monday to Friday? Answer______________ hours
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WORKING COLUMN
No. 8.
TEST ITEMS
WORKING COLUMN
The shape of a floor shown below has two portions, an equilateral triangle (A) attached to one side of a square (B) with sides of 12 m.
(a) Complete the following statement: The perimeter of the ENTIRE ________________ m.
floor
is
(b) The square portion (B) ONLY is to be covered with tiles. (i)
The area of B is _________m²
(ii)
B is to be covered using square tiles with sides measuring 30 cm. How many tiles are needed? Answer$______________
(iii)
One of the tiles to be used for covering B costs $4.00. How much will the tiles cost if 10 extra ones are added in case any break? Answer$______________
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No. 9.
TEST ITEMS Daniel is making tickets for his drama club from sheets of bristol board measuring 60cm by 45 cm. (a) Calculate the area of ONE sheet of bristol board Answer______________ (b) What is the LARGEST number of tickets measuring 9 cm by 3 cm that Daniel can make from ONE sheet of bristol board? Answer______________ (c) A ticket costs $10.00 Daniel collected $5000.00 when all the tickets were sold. How many sheets of bristol board did he use? Answer______________
10.
The bottle in the diagram holds 2 litres of soda when full.
Jita fills 4 glasses with 180 ml of soda. (a) How many litres of soda are left in the bottle? Answer______________ litres (b) How many MORE full glasses can she pour from the remaining soda? Answer______________ glasses 92 | P a g e
WORKING COLUMN
No. 11.
TEST ITEMS
WORKING COLUMN
Akil saved $50 at the end of each week to buy the pair of roller skates shown below.
(a)
How many weeks did it take him to save $500? Answer _______________ weeks
(b)
He paid in cash and received a discount. After discount, he paid $400. What was the percentage discount he received? Answer _______________ %
(c)
Akil paid the cashier the EXACT $400 which included ONE or more of EACH bill. Complete the table below to find the LEAST number of bills that Akil gave the cashier.
Bill Number of Bills
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$100
$50
$20
$10
$5
$1 5
No. 12.
TEST ITEMS The following diagram shows the number of long mats (L) and short mats (S) arranged around a rectangular playing field.
The length and width, in metres, of each type of rectangles mat are shown below.
Calculate: (a)
The length of the playing field Answer __________________ m
(b)
The width of the playing field Answer __________________ m
(c)
The area of a short mat Answer __________________ m2
(d)
The number of short mats that would be needed to cover the area of the playing field COMPLETELY Answer ___________________ short mats
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WORKING COLUMN
No. 13.
TEST ITEMS The following diagram shows a triangle PQR, and the position of its image after a movement.
(a)
(b)
Circle the word from the following list which BEST describes triangle PQR. Right-angled
Isosceles
Scalene
Equilateral
Identift the type of movement. Answer ________________________
(c)
Describe the movement FULLY. Answer ________________________ _______________________________ _______________________________
(d)
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Label the image of Point Q as Q’.
WORKING COLUMN
SECTION III C - Geometry
Each question is worth 5 marks. Show ALL working in the Working Column. No.
TEST ITEMS
1.
(a) Draw TWO lines on the figure above so that it forms the net of a solid.
(b) Name the solid formed when the net is folded. Answer______________
(c) The solid forms as ________________ edges and ______________ vertices.
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WORKING COLUMN
No. 2.
TEST ITEMS On the grid below are 2 triangles labeled A and B.
Triangle A slides to the right until the corner at P touches the corner R.
(a) How many units did triangle A slide? Answer______________ (b) Draw the combined shape on the new grid. Triangle B is drawn in position for you.
(c) What is the name given to the combined shape of the two triangles? Answer______________ (d) How many right angles are there in the combined shape? Answer_______________
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WORKING COLUMN
No. 3.
TEST ITEMS The positions of triangles ABC, DBC and FEC are shown below.
(a) What term is used to describe the movement of triangle ABC to the position of triangle FEC? Answer______________ (b) The triangle ABC moves to the position of triangle BDC. Describe the movement FULLY. Answer______________ (c) What type of triangle is the combined shape, triangle ADC? Answer______________
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WORKING COLUMN
No. 4.
TEST ITEMS Four points, A, B, C, D, are equally spaced around the edge of a circular spinner and connected to the centre O as shown in the diagram below.
(a) Raj turns the spinner so that A moves in an anticlockwise direction to the position of B. What was the size of the angle through which the spinner moved? Answer______________
(b) Describe FULLY how Raj can turn the spinner so that B moves to the position of D. Answer____________________________ __________________________________ __________________________________
(c) Raj turned the spinner so that C moves 225° in a clockwise direction to a point M. Label the point M on the diagram above.
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WORKING COLUMN
No. 5.
TEST ITEMS The shaded triangle at P is moved to various positions, Q, R, and S.
Describe CAREFULLY the movements in EACH of the following:
(a) P to Q
Answer______________
(b) R to S
Answer______________
(c) P to S
Answer______________
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WORKING COLUMN
SECTION III D - Statistics
Each question is worth 5 marks. Show ALL working in the Working Column. No. 1.
TEST ITEMS The incomplete bar graph below shows the favourite subjects of the 30 pupils in a Standard 5 class.
a) How many more pupils favour Social Studies than Maths? Answer_________pupils
b) What percentage of the class chose Maths as their favourite subject? Answer ____________________%
c) How many pupils chose English as their favourite subject? Answer ___________________pupils
d) Complete the graph by drawing the bar to represent the number of pupils whose favourite subject is English.
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WORKING COLUMN
No. 2.
TEST ITEMS Six boys ran the 100 m race. The time (in seconds) taken by each boy is shown in the graph below. Time taken for six boys to run a 100m race
) s d n o c e s ( e m i T
0 Al
Ben Che Don Boys
Eze Fred
a) Who won the race? Answer ___________________________ b) For which position were the two boys tied? Answer _____________________________ c) Who was the SLOWEST runner? Answer _____________________________ d) How long did the race last? Answer _____________________________ e) How much longer than the first-place runner did the slowest boy take to run the race? Answer _______________________________
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WORKING COLUMN
No.
TEST ITEMS
3.
WORKING COLUMN
Jeff is playing a game in which he scores points by spinning a pinwheel similar to the one shown below. It is possible to score 1, 2, 3, or 4 points.
1
4
2
3
Jeff spins the pinwheel twenty times and records his scores in the tally chart below. The tally chart is incomplete.
Points Scored 1 2 3 4
Tally
Frequency
I
1
III
3 9
Total Points 1 14 9 36
a) Complete the tally chart above by filling in the missing information. b) What are the modal points scored? Answer ___________________________
c) How many points did Jeff score for the twenty spins? Answer ____________________________
d) Calculate the mean number of points Jeff scored for the twenty spins. Answer ____________________________
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No. 4.
TEST ITEMS
WORKING COLUMN
The heights of a group of students in Standard 1 are given in the table below.
Name of Student Height (cm)
Amina
Betty
Jon
Avi
Ela
Sunil
75
64
84
86
47
64
a) What is the modal height? Answer _____________________cm
b) Calculate the mean height of the group. Answer _____________________cm
c) Amina left the group. What is the mean height of the new group? Answer _____________________cm
5.
The points scored by Sam for 5 games are given in the table below. Game 1
Game 2
Game 3
Game 4
Game 5
34
29
43
34
55
a) What is the modal number of points scored? Answer ____________________________ b) Calculate the mean number of points scored for a game. Answer ____________________________ c) His mean score for 6 games was 42. Calculate his score on Game 6. Answer ______________________________
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No. 6.
TEST ITEMS
WORKING COLUMN
Suri and Mali played a game of darts. Each made six strikes. The following diagram shows the number of points earned for striking the patterns on the dart board.
Stripes = 10 points Dots = 20 points Black = 30 points
(a)
Suri made two strikes on stripes, three on dots and one on black. What is her total score?
Answer ______________ points
(b)
Mali scored 150 points by striking each pattern AT LEAST ONCE. Complete the following score sheet to show how she scored 150 points.
Pattern
Number of Strikes
Score
1
20
6
150
Stripes Dots Black Total
(c)
What is the LOWEST score possible if in the six strikes, a player hits EACH pattern at LEAST ONCE?
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No. 7.
TEST ITEMS
WORKING COLUMN
The following table shows the number of chairs rented and returned to Zippy Party Rentals for the period Monday to Friday of a week in May. Chair Rentals
Number of chairs rented Number of chairs returned
(a)
Mon 113
46
Tue 367
Wed 258
Thur 969
96
Fri 1083
62
On which day was the rental of chairs CLOSEST to 1000? Answer ________________________
(b)
The number of chairs returned for the week was 306. Calculate the number of chairs returned on Thursday if twice as many were returned on Tuesday as returned on Thursday. Answer _______________________ chairs
(c)
What is the mean number of chairs rented over that period in May? Answer _______________________ chairs
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Appendices
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Appendix A SECONDARY ENTRANCE ASSESSMENT GUIDELINES
The Mathematics Paper consists of (46) items and encompasses the four strands of the syllabus.
Number
Measurement and Money
Geometry
Statistics
This paper is divided into three sections with 20 questions in Section I, 20 questions in Section II, and 6 questions in Section III.
Questions in Section I are worth one (1) mark each; questions in section II are worth (2) or three (3) marks each and questions in Section III are worth five (5) marks each (Table 1 & 2)
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TABLE OF SPECIFICATIONS – MATHEMATICS
Table 1: Distribution of Items and Marks by Section and Skill level SECTION
NO. OF ITEMS
SKILL LEVEL (MARKS) AT 10
TOTAL PS 5
20
I
20
KC 5
II
20
12
26
12
50
III
6
8
14
8
20
46
25
50
15
100
*KC – Knowledge Computation
AT – Algebraic Thinking
PS - Problem Solving
Table 2: Distribution of Marks by Strands and Sections
STRAND Number Measurement and Money Geometry Statistics
Total
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Number of Items
Section I
Section II
Section III
Total
18
8 (8 items)
20 (8 items)
10 (2 items)
38 (18 items)
16
7 (7 items)
18 (7 items)
10 (2 items)
35 (16 items)
8
3 (3 items)
10 (4 items)
5 (1 item)
18 (8 items)
4
2 (2 items)
2 (1 item)
5 (1 item)
9 (4 items)
46
20
50
30
100
ASSESSMENT OBJECTIVES – MATHEMATICS
A. NUMBER Whole Numbers
1. Represent any number up to one million using numerals or word names. 2. State the value or place value of a digit in any whole number up to one million. 3. Express a whole number up to one million using expanded notation. 4. Order and compare whole numbers. 5. Add whole numbers. 6. Subtract whole numbers. 7. Multiply by up to four digit numbers by one or two-digit multipliers. 8. Divide up to four digit numbers by one or two digit divisors. 9. Solve one-step word problems involving any one of the four basic operations on whole numbers. 10. Solve multi-step word problems involving any combination of the four basic operations on whole numbers. 11. Calculate the square of a number and the square root of a perfect square. Fractions
12. Represent a fraction using diagrams, word names or numerals. 13. Express a fraction in an equivalent form. 14. Order and compare fractions. 15. Convert improper fractions to mixed numbers and mixed numbers to improper fractions. 16. Add two or more fractions (including whole/mixed numbers) 17. Subtract two fractions (including whole/mixed numbers. 18. Calculate the fraction of a quantity. 19. Express one quantity as a fraction of another. 20. Represent or calculate the whole given a fractional part. 21. Multiply two fractions (including whole/mixed numbers). 22. Divide two fractions (including whole/mixed numbers). 23. Solve word problems involving concepts and operations on fractions.
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Decimals
24. State the value or place value of any digit in a decimal fraction up to hundredths (decimal fractions refer to fractions written in decimal notation).
25. Express decimal fractions using expanded notation. 26. Order and compare decimal fractions. 27. Add decimal fractions (including whole numbers). 28. Subtract two decimal fractions. 29. Multiply two decimal fractions. 30. Divide two decimal fractions. 31. Solve word problems involving measures expressed in decimals. 32. Express decimal fractions, as common fractions and vice versa. Approximation and Computational Estimation
33. Approximate whole numbers to the nearest ten, hundred or thousand. 34. Approximate decimal fractions to the nearest tenths or hundredths. 35. Estimate the result of a computation involving any of the four operations on whole numbers, decimals or fractions. Percent
36. Calculate the percent of a quantity. 37. Express a percent as a fraction and a fraction as a percent. 38. Express a percent as a decimal and a decimal as a percent. 39. Express one quantity as a percent of another. 40. Calculate the whole (or part) given a part expressed as a percent. 41. Solve one – step and multi – step problems involving percentages.
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B. MEASUREMENT Money
42. Identify coins, bills, their value and the value of a set of coins/bills. 43. Determine the possible combination of coins, bills, which are equal to the given amount. 44. Add and subtract quantities expressed in dollars and cents. 45. Calculate total cost and the change in money transactions. 46. Solve problems involving payments (for example salaries) and charges (for ex ample rentals, given a unit rate. 47. Calculate profit or loss given cost price and selling price. 48. Express profit or loss percent as a percent of the cost price. 49. Calculate the VAT on an item when given as a percent. 50. Calculate the discount on an item when given a percent. 51. Calculate the simple interest and amount of an investment or loan given principal, rate and time. 52. Solve problems involving direct proportions. 53. Determine the best buy comparing rates.
Linear Measure
54. Name an appropriate standard metric unit for measuring the length of an object. 55. Convert units of length within the metric system. 56. Compare two lengths. 57. Measure lengths of lines using standard or non-standard units. 58. Read and record linear measures using decimal notation. 59. Estimate the length of an object to the nearest centimeter. 60. Solve problems involving addition and subtraction of measures in (a) metres and centimetres (b) kilometres and metres. 61. (a) Calculate the perimeter of polygons. (b) Calculate unknown sides of polygons given the perimeter. 62. State the relationship between the circumference and diameter (or radius) of a circle. 63. Solve problems involving perimeter of polygons and circumferences of circles.
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Area
64. Name an appropriate standard metric unit for measuring the area of a region. 65. Compare the area of surface. 66. Measure the area of a region using square units and record measures to the nearest unit. 67. Estimate the area of a region to the nearest square unit. (a) calculate the area of squares, rectangles and triangles using formulae. (b) Calculate the total area of a compound shape. (c) Calculate an unknown side of a square or rectangle given its area. 68. Solve problems involving area of plane shapes. 69. Solve problems involving area and perimeter of plane shapes. 70. Solve problems involving area and money, for example, the cost of tiling.
Volume
71. Name an appropriate standard metric unit for measuring capacity or volume of a given container/solid. 72. Compare the sizes of containers. 73. Measure the capacity of containers in standard and non-standard units. 74. Measure the volume of a solid by counting cubic units. 75. (a) Calculate the volume of cubes and cuboids using the formulae. (b) Calculate unknown sides of cubes or cuboids given the volume. 76. State the relationship between the metric units of volume and capacity. 77. Solve problems involving volume/capacity.
Mass
78. Name an appropriate standard metric unit for measuring the mass of a given object. 79. State the relationship between the gram and the kilogram. 80. Compare the masses of objects. 81. Measure the mass of an object using appropriate metric units. 82. Read measuring scales and record masses using decimal notation. 83. Make reasonable estimations of the mass of objects in the environment in kilograms. 84. Add and subtract measurement in kilograms and grams. 85. Solve problems involving mass and money, mass and volume. 113 | P a g e
Time
86. State the various units for measuring time and the relationships between these units. 87. Tell time using analog and digital notation. 88. Convert analog notation to digital notation and vice versa. 89. Solve problems involving calculation of total time and elapsed time in hours and minutes. 90. Solve problems involving time using both digital and analog notations. 91. Solve problems involving time and rate.
C. GEOMETRY Solids and Plane Shapes
92. Identify solids from drawings. 93. Describe the properties of solids with respect to the number of vertices and the number and type of edges and faces. 94. Draw solids given models or descriptions. 95. Name a solid given its net. 96. Draw nets of cube, cuboids, cylinders, triangular prisms, pyramids and cones. 97. Identify plane shapes from drawings. 98. Describe the properties of plane shapes with respect to (a) The number of sides and angles (b) The number of equal sides, and (c) The number of pairs of parallel sides. 99. Describe the properties of isosceles, equilateral and right-angled triangles. 100.Construct a plane shape given specific properties. 101.Describe a plane shape as a composition of other plane shapes.
Symmetry
102. Identify and draw lines of symmetry in plane shapes, including shapes with curved edges. 103. Complete a plane shape using the property of line of symmetry. 104. Determine the number of lines of symmetry in plane shapes.
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Slides, Flips and Turns
105.
Identify and describe slides, flips and turns.
106.
Determine the type of movement (slide, flip, turn), which transforms a plane shape from one position to another.
107.
Perform a slide, flip or turn on a plane shape to create another plane shape.
108.
Perform slides, flips and turns on a plane shape to create patterns.
109.
Complete and describe patterns made by simple transformations.
110.
Solve problems involving, recognizing and describing slides, flips and turns.
Angles
111.
Use ‘larger’, ‘smaller’ and ‘same’ to compare the size of two angles.
112.
Arrange a set of angles in order of size.
113.
Explain what is an angle.
114.
Represent angles using drawings.
115.
Measure angles using standard and non-standard units.
116.
Identify the degree as the unit for measuring angles.
117.
Solve problems using a whole turn (360ᵒ)
118.
Solve problems involving simple fractions of a whole turn.
119.
Estimate the size of an angle given a unit.
120.
Compare angles using 90ᵒ as a benchmark.
121.
Identify angles in shapes and solids in the environment.
D. STATISTICS
122.
Interpret data presented in simple frequency tables or tally charts.
123.
Construct tally charts and simple frequency tables from raw data.
124.
Interpret pictographs, block graphs and pie charts.
125.
Construct pictographs, block graphs and bar graphs from given data.
126.
Calculate the mode and the mean from a set of raw scores.
127.
Determine the mode and the mean from data presented in frequency tables, bar graphs or block graphs.
128.
Solve problems involving the mean.
129.
Summarize data presented in tables of graphs.
130.
Solve problems involving interpretation of the data in tables and graphs.
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Appendix B STRATEGY FOR SOLVING PROBLEMS
-Step Problem Solving Strategy Apply Polya’s Four -Step 1.
Read the problem at least twice so as to understand the problem.
2.
Draw a picture or diagram Create an organized table or list Work backwards Look for a pattern
Guess and check
3.
Solve the problem
Carry out or implement the plan using the selected problem solving strategy.
Write the solution in a sequential, logical manner.
If no solution is obtained, repeat steps 1 to 3.
Review the problem
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What key words are there? Ensure the meanings of key words are understood.
Devise a plan to solve the problem. What problem solving strategy can I use?
3.
Read the problem aloud if desired. What am I being asked? What do I need to find out? What important information was I given? Make jottings about what you need to find and important information given.
Look back at the solution process and double check your work. Ensure that all relevant data are used. Check on the reasonableness of the answer obtained. Ensure that appropriate units of measure are stated.
Appendix C SOME WORKED EXAMPLES WITH WITH “TIPS”
Section Section 1 A
Question, Tips or Points to Consider and Solution No. 33
Tips
To find the answer multiply
by 120. Express Express 120 as a fraction, that is,
before multiplying. When solving, divide the denominator 8 and the numerator 120 by the same number or numbers. You can also multiply the numerators, multiply the denominators and then divide.
Consider 120 as the whole, that is, eight-eighths. Using the unitary method, find one-eighth of 120 by dividing 120 by 8. Then to find fiveeighths, multiply the answer by 5.
Solution 5 120 ⨯ = 5 ⨯ 15 = 75 orange nges 8 1 OR Eight-eighths = 120 One-eighth = 120 ÷ 8 = 15 Five-eighths = 15 ⨯ 5 = 75 oranges
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Section Section 1 B
Question, Tips or Points to Consider and Solution No. 26
Tips
To find the answer subtract 3985g from 4.1kg.
Express 4.1kg as 4100g; the answer is required in grams.
When subtracting ensure that numbers are placed under u nder each other according to the appropriate place value position.
Be careful when regrouping in order to subtract.
Solution
Section 1 C
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No. 12
Section
Question, Tips or Points to Consider and Solution Tips
There are 4 quarter turns in a circle. For example, in the diagram turning from 0 to 2, from 2 to 4, from 4 to 6 and from 6 to 0 each represent a quarter turn. This also holds for moving from 1 to 7, from 7 to 5, from 5 to 3 and from 3 to 1.
Anti-clockwise refers to the movement that is opposite to the movement of the hands in a clock.
Solution
The arrow will point to 7.
Section 1 D
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No. 3
Section
Question, Tips or Points to Consider and Solution Tips Count the number of
represented in the table. Compare this with
the number of haircuts stated.
Figure out how many haircuts
represents.
Locate the information related to Monday.
Solution There are 15
in the table.
These represent 75 haircuts. represents 75 ÷ 15 = 5 haircuts. You can also solve this by asking, “What
number when multiplied by 15 equals 75?” You may also try to “guess and check” and count in 5s.
There is only one
for Monday.
So, 5 haircuts were done on Monday.
Section 11 A
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No. 10
Section
Question, Tips or Points to Consider and Solution Tips
You may draw a column in the table and write the number of games played that match the number of points given.
Remember the number of games cannot be more than the number of points for “won” and “draw”.
Find the total number of games “won” and “draw”.
Subtract the total from the number of games played.
Solution Results Won Draw Loss
Points 16 10 0
Number of Games Played 8 10 ?
The total number of games “won” and “draw” = 8 + 10 = 18 Number of games “loss” = 25 – 18 = 7
Section 11 B
No.13
Tips
You may use the formula for finding simple interest or find the amount of interest for one year and then use the answer to find for three years.
When using the formula SI = P ⨯ R ⨯ T remember to write R as
Solution Simple Interest for 1 year =
⨯ $8000 = 12 ⨯ $80 = $960
Simple Interest for 3 years = $960 ⨯ 3 = $2880
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.
Section
Question, Tips or Points to Consider and Solution OR Using the formula: SI = P ⨯ R ⨯ T = $8000 ⨯
Section 11 C
⨯ 3 = $80 ⨯ 12 ⨯ 3 = $2880
No. 12
Tips (a)
You may review the different types of movements you learnt – slides/translation, flips/reflection and turns/rotation, and their properties.
Try to picture the movement in your mind and decide which of the above was done.
(b)
Divide the rectangle into parts to determine how many Ts can fit. You can shade Ts in the drawn rectangle.
(c)
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Review the different types of triangles and their properties.
Remember to combine T and S to form one triangle.
Section
Question, Tips or Points to Consider and Solution Solution (a) Flip or reflection.
(b)
Two of Triangle T will cover one-quarter of rectangle ABCD. So, 8 will cover the entire rectangle. OR Triangle T covers one-eighth of rectangle ABCD. So, 8 will cover the entire rectangle. OR 2 “blocks” are used to make T. There are 16 blocks in rectangle ABCD. So, 8
of Triangle T will cover the rectangle ABCD.
Isosceles (Triangles T and S are right-angled triangles of the same size. The “slanted” lines in T and S are the same length and they are longer than the vertical and horizontal lines in T and S.)
Section 11 D
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No.3
Section
Question, Tips or Points to Consider and Solution Tips
Remember a circle is used to make a pie chart.
There are 4 quarter turns in a circle. (Four quarters form the whole.)
A quarter turn forms a right angle.
The pie chart represents the whole or the entire salary.
Each part or fraction of the pie chart represents how the money was used.
Solution Food represents one-quarter of the pie chart. $1800 was spent on food. So, one-quarter of the salary is equal to $1800. The entire/whole salary = four-quarters = $1800 ⨯ 4 = $7200
Section 111 A
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No. 4
Section
Question, Tips or Points to Consider and Solution Tips (a)
Remember the number of spaces is 1 less than the number of posts. This can be counted in the diagram.
The pipes are divided equally among the 8 spaces.
(b)
Picture the situation in your mind or draw a diagram that shows the given information.
You need to use whatever answer you obtain in part (a) to solve part (b).
Solution (a) Number of pipes = 144 Number of spaces = 8 Number of pipes in each space = 144 ÷ 8 = 18 pipes (between the first and second posts) OR Number of pipes = 144 Number of spaces = 8 If 10 pipes are placed in each space then a total of 80 pipes would have been used.
Number of pipes remaining to be shared = 144 – 80 = 64 Now, divide the 64 remaining pipes among the 8 spaces: 64 ÷ 8 = 8 So, the number of pipes in each space = 10 + 8 = 18 OR Use the same idea above to share the 64 pipes and placing 5 pipes in each space (using 40 pipes), subtracting to obtain the remainder (64 – 40 = 24) and then sharing the remainder (24) among the 8 spaces (3 per space).
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Section
Question, Tips or Points to Consider and Solution
Number of pipes in each space = 10 + 5 + 3 = 18 (b) Number of pipes between 1st and 2nd posts = 18 pipes Length of 1 pipe = 7 m Distance between 1st and 2nd posts = length of 18 pipes = 18 ⨯ 7 = 126 m OR Using a drawing:
You can use addition or multiplication or both: 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 126 m 18 ⨯ 7 = 126 m 7 ⨯ 10 + 7 ⨯ 8 = 70 + 56 = 126 m
Section 111 B
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No. 9
Section
Question, Tips or Points to Consider and Solution Tips (a)
The bristol board is in the shape of a rectangle.
Draw and label a rectangle.
The area of rectangle = L ⨯ B.
Use any rules you know to solve the problem easily, e.g.
commutative rule: 3 ⨯ 5 = 5 ⨯ 3 (the order in which the numbers are multiplied does not change the answer)
multiplying by 10: “add-on” a 0
The unit of measure for area (in this problem) is sq. cm or cm2.
(b)
The tickets are rectangular in shape.
Draw tickets within the drawn rectangle.
Decide how best to draw tickets within the rectangle by considering which lengths are easily divisible by 9 or 3. This would ensure that the entire sheet of bristol board is used. (There would be no spaces or wastage.) OR
Calculate the area of each ticket.
Divide the area of the rectangle by the area of a ticket.
(c)
It would be helpful to calculate the amount of money Daniel would get for the tickets created from one sheet of bristol board. OR
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You can calculate the number of tickets sold by Daniel.
Section
Question, Tips or Points to Consider and Solution Solution (a)
Area of rectangle = L ⨯ B = 60 ⨯ 45 = 45 ⨯ 6 ⨯ 10 = 2700 cm2
(b) Draw tickets within the rectangle. Both numbers (60 and 45) are divisible by 3, however, only 45 is completely divisible by 9.
45 ÷ 9 = 5 (rows of tickets) 60 ÷ 3 = 20 (tickets in each row)
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Section
Question, Tips or Points to Consider and Solution
To find the number of tickets you can use addition or multiplication: Number of tickets = 20 + 20 + 20 + 20 + 20 = 100 tickets Number of tickets = 20 ⨯ 5 = 100 tickets OR Area of rectangle = 2700 cm2 Area of each ticket = 9 ⨯ 3 = 27 cm2 Number of tickets = 2700 ÷ 27 = 100 tickets (c) 1 sheet of bristol board is used to make 100 tickets. Each ticket costs $10. So, 100 tickets would cost: $10 ⨯ 100 = $1000 $1000 represents the cost of tickets from 1 sheet of bristol board. $5000 (which is 5 times the amount above) represents the cost of tickets from 5 sheets of bristol board. OR Daniel collected $5000. Each ticket cost $10. Number of tickets sold by Daniel = Amount of money collected ÷ Cost of 1 ticket = $5000 ÷ $10 = 500 tickets. 100 tickets are made from 1 sheet of bristol board. 500 tickets would be made from 5 times the number of sheets = 5 129 | P a g e
Section Section 111 C
Question, Tips or Points to Consider and Solution No. 1
Tips (a) and (b) Review the different solids and their nets.
This net can only be made using four-sided shapes. The only solids formed using squares and/or rectangles are cubes and cuboids.
Once you have an answer, try folding the net in your mind so as to form a solid.
A cube is the only solid with 6 square faces.
Picture in your mind any cube you know, e.g. box and die.
(c)
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Review the different solids and their properties.
Section
Question, Tips or Points to Consider and Solution Solution (a)
(b) Cube (c) The solid formed has 12 edges and 8 vertices.
Section 111 D
No. 5
Tips (a)
Mode represents the most frequent score, so look for the number that is recorded the most number of times.
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Section
Question, Tips or Points to Consider and Solution (b)
The mean is a number that represents the scores if they were equally distributed.
To calculate the mean add all the scores together and then divide by the number of scores.
(c)
Remember the mean score for six games was obtained by dividing by 6.
Multiply the mean score by 6 to find the total of the 6 scores.
Subtract the total for the 5 games from the total of the 6 games to obtain the score on Game 6.
Solution (a) 34 (b) 34 + 29 + 43 + 34 + 55 =
195 ÷ 5 = 39 (c) 42 ⨯ 6 = 252 (total score for 6 games) Score for Game 6 = Total score for 6 games – Total score for 5 games = 252 – 195 = 57
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Appendix D ANSWERS TO PROBLEMS Section 1 A - Number
Question
Answer
1. 2. 3. 4. 5. 6. 7. 8. 9.
Twelve thousand five hundred and forty 205 073 3 000 26 037 300 8.7 240 5731, 5317, 5173
10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
1 312 0.2412 80 arms 56 plums 7 500 6 students 36 squares 49 25 40 10
22.
9
3 4
3 8 7 15
23. Any 4 blocks can be shaded. 24.
Any 4 parts can be shaded. 133 | P a g e
Question 25. 26.
27. 28. 29.
30.
31.
32. 33. 34.
35.
Answer 4 1 = 12 3 5 9 8 >
1 1 1 1 12 6 4 3 m
23 4 9 slices 75 oranges 3 20
20%
36. 37.
75%
38. 39.
$104 $675
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32 16 8 4 or or or 40 20 10 5
Section 1 B – measurement & Money
Question
Answer
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.
$1.15 $10.50 20 quarters 28 coins $10.50 4 pencils 25¢ 10¢ 6 plums Stall A $1566.00 25% 5 cm 8 pieces 10kg 049g 60 cm 12 cm 5cm
19. 20. 21.
10 3:40 3
22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 135 | P a g e
hours
11:00 a.m. 8:47 p.m. 9:15 a.m. Flour 115 g 121 cm2 11 cm 3.6m 4 cm 32 cm2 The container with the Orange Juice. 2369m
Section 1 C - Geometry
Question
Answer
1. 2. 3.
Isosceles Triangle Cylinder
4. 5. 6.
Square-based pyramid or pyramid 4
7. 8. 9.
40 cm BF or HD
10.
11. 12. 13. 14.
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South 7 70cm Triangular-based pyramid or pyramid
Section 1 D - Statistics
Question
Answer
1.
2.
3. 4. 5. 6. 7. 8. 9. 10. 11.
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5 haircuts 4 wickets 42 children 5 marbles IIII IIII I 11 cookies 14 16 4 pupils
Section 11 A - Money
Question 1. 2.
Answer (a) 3789 (b) 9738
3. 4.
5. 6. 7. 8. 9. 10. 11.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
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777 (a) 624 heads of lettuce (b)575 heads of lettuce (c)1725 heads of lettuce 84 marbles 0.25 2 items 35 7 = 100 20
7 gold 7losses (a)12 159 (b) 10 (c) 17949 100 20% $300 (a) 290 sweets (b) 24 bags 34, 41 (a) 90 fishes (b) 210 fishes (a) 16 , 25 (b) 81 200 pages 9m 10 weeks
9 2 3
(a) >
(b) 25.
or 7
1 3 , 2
1 3 1 4 8 8
Question 26.
27.
Answer 23 7 =2 8 8 11 1 =1 10 10
28.
(a) 2 sixths (b) 46 sixths
29.
1 15
30.
(a)
(b) $21
31.
4
32. 33. 34. 35. 36. 37. 38.
6 16 2.5 17 8 students 18 points (a) 36 mangoes (b) 27 boxes 70% 40% (a) 135 shells (b) 75%
39. 40. 41. 42.
Fruit
Number purchased 6 12 14 32
Apples Oranges Guavas TOTAL
(c) 18.75% 43. 44.
7.53 Fraction (Lowest terms)
2 3
(b)
45. 46.
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35 pieces 25 weeks
Percentage
Decimal
(a) 66.67% 0.005
Section 11 B- Measurement and Money
Question 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
11. 12.
Answer $2.45 (a) $7.65 (b) $12.35 $260 $156 (a) $36 (b) 4 (a) $24 (b) $84 (a) $480 (b) $18 $510 $153 (a) $60 (b) $20.25 (c) $155.25 (a) $45 (b) 60% (a) $180 (b) $1380 (a) 33
13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
23. 24. 25. 140 | P a g e
%
$2880 (a) $1200 (b) $6200 (a) $1920 (b) $13920 $6900 6550 m or 6.55 km 15.1 km (a) 7 cm (b) 28 cm 42 cm 354 m (a) 3 cm (b) 60 cm (c) 6 circles 11:55 a.m. 8:25 a.m. (a) 70 mins or 1 hr 10 mins
Question
Answer
26.
(b) 7:50 a.m. (a) 8:00 (b) 9:20 or
27.
(a)
28. 29. 30.
31. 32. 33. 34. 35. 36. 37. 38. 39.
40.
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(b) 2600 g 22.9 kg 72 cm (a) 121 cm2 (b) 44 cm (c) 154 cm2 (a) 9
(b) 58.5
1 4
(a) (a) 96 m2 (b) 44 m2 36 cubes 120 20 servings 8 cm (a) 1800 cm (b) 40 cm (c) 1200 cm2 (a) 30 litres (b) 120 containers
(b) B
(c) A
Section 11 C - Geometry
Question 1. 2.
3. 4. 5.
6.
Answer (a) Square or rectangle or triangle (b) Cuboid or cube or triangular-based prism Examples of solution
(a) (i) W (ii) Y (b) Cone (c) 2 faces (a) Examples of solution
(b) 12 (a) 3 faces (b) Examples of solution
7.
(c) 9 edges 8.
(a)
(b) Quadrilateral 142 | P a g e
Question
Answer
9.
10.
(a)
(b)
11. 12.
13. 14.
15.
16. 143 | P a g e
(a) Slide (b) XYZ moved 2 units to the left and 3 units down. (a) Flip or reflection (b) 8 triangles (c) Isosceles (a) R (b) P and R (a) Flip or reflection (b) ABCD is reflected in the mirror line BC or flipped about the line BC. (c) Corner B remains in the same position. (a) r or p (b) q or t or s (c) t and r (a) Acute (b) AB and DC (iii) AC or DB
Question 17. 18.
Answer 1500 (a) Reflex (b) 240 degrees
19. (a)
20.
(b) 450 (a) 240 degrees
(b) 4 or as shown below
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Section 11 D - Statistics
Question
Answer
1. 2.
165 boys
3. 4.
$7200 (a) Rabbits and goats (b) 20%
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Section 111 A - Number
Question 1.
2.
3.
4. 5. 6.
7.
8.
9.
10.
11.
12.
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Answer (a) Monkey (b) 19 18 9 (c) Rabbit (a) 20 pupils (b) 6 three-seaters (c) 3 four-seaters 12 three-seaters (a) 112 girls (b) 16 girls 8 boys (c) 2 boxes (a) 18 pipes (b) 126 m 22 pupils (a) 10 dots (b)
(c) 36 dots (a) 210 marks (b) 70% (c) 30 marks (a)(i)540 peppers (ii) 60 peppers (b)$864 (a) 180 mangoes (b) 45 mangoes (c) $9 (a) 45% (b) 200 pies (c) 10 pies (a) 60 mangoes (b) 0.2 or .2 (c) 68 avocados (a) 49, 36 (b) 11 (c) 6,24
Section 111 B – Measurement & Money
Question 1.
2.
3. 4.
5.
6.
7.
8.
9.
10. 11.
12.
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Answer (a) $30.75 (b) $2.75 (c) A drink or an apple (a) $38 (b) One combination is shown below
(a) $10.50 (b) 5 (a) $13.50 (b) 20 $8.00 (c) $2.15 (a) $5600 (b) $840 (c) $6440 (a) $480 (b) $1680 (c) $70 (a) 32 hours (b) $360 (c) 16 hours (a) 60 m (b)(i)144 m2 (ii) 1600 tiles (iii) $6440 (a) 2700 cm2 (b) 100 tickets (c) 5 sheets (d) (a) 1.28 litres (b) 7 glasses (a) 10 weeks (b) 20% $100 $50 $20 $10 $5 3 1 1 2 1 (a) 12m (b) 6m (c) 1 (d) 72 mats
$1 5
Question 13.
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Answer (a) Scalene (b) Rotation or turn (c) Turn 90° about P clockwise direction (d)
Section 111 C - Geometry
Question 1.
2.
3.
4.
5.
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Answer (a)
(b) Cube (c) 12 edges and 8 vertices (a) 6 units (b)
(c) Trapezium (d) 2 right angles (a) Turn or rotation (b) Triangle ABC is reflected or flipped about line BC. (c) Equilateral triangle (a) A right angle or 90 0 or a quarter turn (b) Turn the spinner either clockwise or anti-clockwise a half of a complete turn or two right angles or 180 0. (c)
(a) Slide 3 units to the right and 2 units up. (b) Half turn or 1800 turn. (c) Reflect P about line OX to move to R then turn R 180 0 to move to S. (There may be other answers.)
