2012 Math Challenge for Mathematics I Score: ________ Name: _________________________________________ School: ____________________________________________ Solve each item and write the answer on the blank before the number. Write equations in the form ax + by + c = 0; use = 3.14 ___________________ 1. Find the greatest common factor of 12x4y6z5, 9x2y3z2, 6x2y2z4. ___________________ 2. What is the greatest common factor of 210 and 330? ___________________ 3. What is the least common multiple of 210 and 330? ___________________ 4. Find the next number in the sequence: 1, 3, 8, 16, ____. ___________________ 5. Which of the following is/are not rational numbers? { a. 1/4 b. -1/7 c. 0.020020002... d. 0.435435435...} ___________________ 6. What is the least common multiple of 168 and 420? ___________________ 7. Which is larger, 11/13 or 13/16? ___________________ 8. What is the sum of 1/4 + 2/7 + 1/2? ___________________ 9. If a = 14/15 and b = 7/3, what is a/b? ___________________ 10. What is the product of 7 3/5 and 3 3/4? ___________________ 11. Change 0.0625 to a fraction in lowest terms. ___________________ 12. Simplify (10x2y-1z) / (5x-2yz-2) into an expression with positive exponents. ___________________ 13. Write 324 500 000 in scientific notation. ___________________ 14. To allow for sewing and overlap, an 18 dm diameter piece is cut from a 2m by 2m material. How much clothing material is wasted? ___________________ 15. A temperature of 77OF is how many degrees in Celsius? ___________________ 16. In a school with a population of 600, 2.5 out of 10 belong to the Math Club. How many members has the Math Club? ___________________ 17. A building casts a 7.7 m shadow at the same time that a 4 m pole casts a shadow of 2.2 m. How high is the building? ___________________ 18. A salesman receives a basic salary of P 10, 000 and a commission of 5% on all sales. Find his total sales in a month when he earned P 25 000? ___________________ 19. Kate had P 800. She used 20% of it to buy school supplies and 35% to buy a
blouse. She saved 50% of the remainder. How much did she save? ___________________ 20. What is the absolute value of 2x2-8x+2 at x=5/2? ___________________ 21. Add 3x2y2 + 4xy2 – 7xy + 2x2y + 5 to 3x2y2 – xy2 – 2x2y + 4xy – 2. ___________________ 22. Find all real numbers for which (7-x) (4x + 3) > 2 4 ___________________ 23. Solve for x: (2x + 5) (3x – 2) = 3 4 ___________________ 24. For what values of x is (3x-1)/4 < (2x+5)/3? ___________________ 25. For what values of x is 4x – 7 < 9? ___________________ 26. For what values of x is 2x + 7 > 8? ___________________ 27. Write 0.00145 in scientific notation. ___________________ 28. One square kilometer is equal to how many hectares? ___________________ 29. Write an equation of the line through (-2 , 3) and (1 , 4). ___________________ 30. Solve for x and y: 7x – 3y = 23 and x + 2y = 13. ___________________ 31. Factor by grouping terms: x2 + 6x + xy + 6y. ___________________ 32. Factor 6k2 + 13k + 6. ___________________ 33. Factor completely: x4 – y4. ___________________ 34. What two numbers have a product of 56 and a sum of -15? ___________________ 35. What is the equation of the line with a y-intercept of 4 and makes a triangle with the axes in Q1 with an area of 18 square units? ___________________ 36. Simplify: (x2 + 7x – 18) (5x2 – 13x + 6) ___________________ 37. Multiply (8x2 – 16xy) (x2- 4xy + 4y2) ___________________ 38. Divide:
x2
2 2) (4x y 2– 8xy 2x y3
5 and 5x – 10 –9 x–3
___________________ 39. Pete is 12 years old and his grandfather is 63 years old. In how many years will Pete’s age be 1/4 that of his grandfather? ___________________ 40. A trapezoid ABCD has an area of 25 sq. units. Three of its coordinates are
B(1,8) , C(2,3) and D(-6,3). Find the coordinates of A. ___________________ 41. ABC has its coordinates at A(a,-1) , B(8,-1) and C(5,4). If the base is twice the height, find a. ___________________ 42. Find an equation of the line parallel to 2x – 3y – 3 = 0 and passing through (-2 , 3). ___________________ 43. What is the surface area of a beach ball with a radius of 7 dm? ___________________ 44. How many cubic feet of water must be pumped into a swimming pool 80 ft long, 45 ft wide to raise the water by 2 ft? ___________________ 45. A man is planning to fence the front part of his property with posts 2 m apart. Short of money, he decides to make the posts 3 m apart and uses 3 posts less. How wide is the property? ___________________ 46. How much pure acid must be added to 2 liters of a 10% solution of acid to obtain a mixture that is 20% acid? ___________________ 47. Which point is not collinear with the others: A(-2, -7) , B(-5, -12) , C(4, 5) or D(2, 1)? ___________________ 48. Find an equation of the line perpendicular to 2x – 3y + 3 = 0 and passing through (2,-5). ___________________ 49. Square MNOP is removed from rectangle PQRS leaving an area of 92 cm2. If MQ = 4 cm and SO = 8 cm, find the area Of PQRS.
P
O
M Q ___________________ 50. Find the area of the region bounded by the x and y-axes and the line y = 2x + 5.
ANSWERS:
S
N R
1. 3x2y2z2 2. 30 3. 2310 4. 27 5. C 6. 840 7. 11/13 8. 1 1/28 9. 2/5 10. 28 ½ 11. 1/16 12. 2x4z3 y2 13. 3.245 x 108 14. 145.66 dm2 15. 25oC 16. 150 17. 14m 18. P 300 000 19. P 180.00 20. 5 1/2 21. 6x2y2 + 3xy2 – 3xy + 3 22. 11/6 > x 23. x = 26 24. x <23 25. -1/2 < x < 4 26. x > 1/2 or x < -15/2 27. 1.45 x 10-3 28. 100 hectares 29. x – 3y + 11 = 0 30. x = 5 y=4 31. (x + y)(x + 6) 32. (3k + 2)(2k + 3) 33. (x2 + y2)(x + y)(x-y) 34. -7 and -8 35. 4x + 9y – 36 = 0 36. x + 9 5x – 3 37. 16 y2 38. _____1______ (x + 3) (x – 2) 39. 5 years 40. (-1, 8) 41. a = -2 42. 2x – 3y + 13 = 0 43. 615.44 dm2
44. 45. 46. 47. 48. 49. 50.
7 200 ft3 18m 1/4 L B(-5, -12) 3x + 2y + 4 = 0 117 cm2 6 1/4
MATHEMATICS II
Score: __________ Name: _________________________________________ School: ____________________________________________ Solve each item and write the answer on the blank before the number. Write equations in the form ax + by + c = 0; use = 3.14 ___________________ 1. Convert 27oC to degree Fahrenheit. _ ___________________ 2. Convert 0.2222.... or 0.2 as a fraction. ___________________ 3. Solve x – 4 = 3 ___________________ 4. Find n in 3n + 9 = 2n + 21. ___________________ 5. A jeepney charges P4.00 for the first 8 kilometres and P0.50 for each additional kilometre or part thereof. How much will you pay if you cover a distance of 12 1/2 km? ___________________ 6. An executive secretary takes home a total of P222, 960 annually in salary. What is his monthly take-home pay? ___________________ 7. What is the value of y in 3x – 2y + 5 = 3 at x = 2? ___________________ 8. What is the quotient when 7x2 – 10x – 8 is divided by x-2? ___________________ 9. Solve 7m – 3 = 2(5m – 2) + 6 by finding the value of the variable. ___________________ 10. Lira can wash and wax one car in 3 hours. Rose can do the same job in 5 hours. If they work together, how long will it take them to wash and wax one car? ___________________ 11. Points B(-2 , 4) , C(5 , 4) and A(-5 , 0) are three vertices of a parallelogram. Find the coordinates of a point D, such that ABCD is a parallelogram. ___________________ 12. Factor 3x2 – 27. ___________________ 13. Factor a3 + 8. ___________________ 14. The square of the largest of the three consecutive integers is equal to the sum of the squares of the other two. Find the smallest integer. ___________________ 15. Find two positive consecutive integers whose product is 132. ___________________ 16. Find the numerical value of 41/2 8-1/3.
___________________ 17. Solve the equation 32x + 1 = 243. ___________________ 18. Simplify √ √ . ___________________ 19. Rationalize the denominator:
3
2 3.
___________________ 20. Simplify the expression: 2√ ___________________ 21. Solve the system:
√
4x – 3y = 11
– 5√
√
8x + 6y = -2 ___________________ 22. Solve x2 – 2x -2 = 0. ___________________ 23. Simplify 5x2 + 10x + 5 3x2 + 6x + 3. ___________________ 24. Solve 12x2 – 7x = 10. ___________________ 25. Give the quotient in simplest form. x2 – 5x + 6 y2
:
x2 – 2x y
___________________26. Simplify 2 – ax + ax 3
___________________ 27. Solve: y + 2
ax 3
-
1
___2y___ y2 – 1
=
2y2 – y - 3
___________________ 28. The diameter of a hydrogen atom is 0.00000001 cm. Express the diameter in scientific notation. ___________________ 29. Divide and simplify the result: √
2
√
3
.
:
___________________ 30. Given 465 918, what is the biggest number that can be formed using the same digits? ___________________ 31. If 2/5 of the Second Year students in a school are boys and there are 165 girls, how many Second Year students are in the school? ___________________ 32. Dan and Ed built a small table which they sold at a profit P 120.00. If Dan contributed P 48.00 and Ed contributed P 80.00 for the materials, how much should be Dan’s share if the profit is divided in the ratio of their contribution? ___________________ 33. A parallelogram has an area of 162cm2. If the base is 18cm, what is its height? ___________________ 34. Evaluate 23 + 32. ___________________ 35. The longest side of a right triangle is 2 more than the shortest side. The middle side is 1 more than the shortest side. Find the length of the longest side. ___________________ 36. One number is 15 greater than a 2nd number. If the lesser number is subtracted from twice the greater number, the difference is 46. Find the greater number. ___________________ 37. The length of a rectangle with an area of (x2 + 10x) square units if the width is x units is ___________. ___________________ 38. The square root of the sum of a number and 10 is 7. The number is _______. ___________________ 39. Divide: y2 – 9
y2 + 8y + 15 : (y + 2y – 15) 2
3y
___________________ 40. Pedro can ride 15 kilometres on his bicycle in the same time it takes him to walk 7 kilometres. If his riding rate is 5 kilometres per hour faster than his walking rate, how fast does he walk? ___________________ 41. Simplify the complex fraction: 1
y
+
y
1
y2 + 1 8 ___________________ 42. Solve : 4c2 – 100 = 0. ___________________ 43. Complete the statement: If 3x = 2y, then x y
= ___.
___________________ 44. A milk can has a diameter of 8 cm and a height of 0.12m. What is the volume of the can in centimetres? ___________________ 45. Fred drives 12 1/2 kilometers from Sta. Ana to San Miguel at 50 km per hour and returns at the rate of 75 km per hour. What is the average rate for the entire round trip? ___________________ 46. Find the equation of the line with slope 2/3 and y-intercept 2. ___________________ 47. Solve:
2x + 1
-
x–3
= 2.
___________________ 48. A househelp receives a salary of P42, 000.00 a year with a contract of P300.00 annual increase for 6 years. What is his total income for 6 years? ___________________ 49. Find the tenth term of the geometric sequence 2, 4, 8, ...... ___________________ 50. The number of books loaned from the library during each day of the week were 36, 31, 25, 42, 53. What is the median?
ANSWERS: 1. 80.60F 2. 2/9 3. x = 1, x =7 4. n = 12 5. P6.25 6. P18, 580.00 7. y = 4 8. 7x + 4 9. m = -5/3 10. 1 7/8 hours 11. (2,0) 12. 3(x + 3)(x – 3) 13. (a + 2)(a2 – 2a + 4) 14. -1 or 3 15. 11 and 12
44. 602.88cm3 45. 60 km/hr 46. 2x – 3y + 6 = 0 47. 4 and 12 48. P256, 500.00 49. 1024 50. 36
16. 1 17. x = 2 18. 4√ 19. √ 3 20. -4x√ 21. (5/4 , -2) 22. x = 1 √ 23. 5/3 24. x = 5/4 and x = -2/3 25. x – 3 xy 26. -2 27. y = 2 28. 1 x 10-8 29. 6√ 2 30. 986 541 31. 275 32. P45.00 33. 9 cm. 34. 17 35. 5 36. 31 37. x + 10 38. 39 39. 3y (y + 5)2 40. 4 3/8 km/hr 41. 8 y 42. 43. 2/3
