- 1. In a school the total enrollment of class 8th is 115. If the number of boys exceeds the number of girls by 33, find the number of boys in a class 8th.
A) 74
B) 89
C) 32
D) 50
- 2. One of the angles of a triangles is equal to the sum of the remaining tow angles. If the ratio of these angles is 4:5, find the angles of the given triangle.
A) 40, 60, 80
B) 70,80,90
C) 90, 50, 40
D) 60, 70, 80
- 3. Two equal sides of a triangle are each 4 m less than three times the third side.Find the dimensions of a triangle,if its perimeter is 55 m.
A) 12, 12, 5
B) 15,15,8
C) 23, 23, 9
D) 13,13,8
- 4. If a + 1/a = 2, find the value of a3 + (1/a)3
A) 14
B) 11
C) 12
D) 13
- 5. A gardener bought twice the number of Lilly plants that he had in his garden but had to throw 3 bad plants. When the new Lilly plants were planted, he had in all 48 plants in the garden.Find the number of Lilly plants he had originally.
A) 17
B) 13
C) 7
D) 5
- 6. Simplify a3 - b3 ÷ (a-b)
A) a2 - ab + b2
B) a3-ab+b2
C) a2 + ab + b2
D) (a+b)(a-b)
- 7. If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2
A) 15
B) 12
C) 35
D) 10
- 8. What must be added to each of the numerator and the denominator of the fraction 7/11 to make it equal to 3/4
A) 2
B) 8
C) 5
D) 7
- 9. Simplify: 2(3)2 - 3(2)3 + (1 - 4)3
A) 20
B) 12
C) -23
D) -33
- 10. By how much is 3 – 1/3 greater than 2 and 1/2?
A) 1 1/6
B) 3 1/4
C) 3 1/2
D) 1 1/2
- 11. If water pours into a tank at a rate of 100 liters per minute, at what rate is the tank being filled in kiloliters per hour?
A) 9 kiloliters per hour
B) 5 kiloliters per hour
C) 7 kiloliters per hour
D) 6 kiloliters per hour
- 12. Subtract the sum of a + 2b + c and 3a - b - c from 6a + b - 2c.
A) 4a - c
B) 3a - c
C) 2a - c
D) 5a - c
- 13. The sum of the interior angles of a polygon is 1620 degrees. How many sides has the polygon?
A) 9
B) 10
C) 12
D) 11
- 14. The sum of the two angles of a triangle is three times the third angle. What is the sum of the first two angles?
A) 115
B) 125
C) 145
D) 135
- 15. Danny had some stickers. He gave 1/3 of the stickers plus 1 sticker to his brother. Then, he gave 1/3 of the remaining stickers plus 4 stickers to his sister. Finally, he gave ½ of what remained plus 3 stickers to best friend. He found that he had 4 stickers left. How many stickers did Danny have at first?
A) 43
B) 42
C) 40
D) 41
- 16. What number is 2/5 of the way from – 3 to 5?
A) 1/5
B) 4/5
C) 3/5
D) 2/5
- 17. What is the smallest positive integer that must be multiplied to 60 to get a perfect cube?
A) 550
B) 650
C) 450
D) 350
- 18. What three-digit number is both a square of an integer and a cube of an integer?
A) 729
B) 329
C) 529
D) 829
- 19. Sandra is 18 years older than Paulo. In 13 years, Sandra will be as twice as old as Paulo will be then. How old is Sandra now?
A) 24
B) 21
C) 22
D) 23
- 20. The average of five numbers is 14. The average of the three of the numbers is 12. What is the average of the other two numbers?
A) 19
B) 15
C) 16
D) 17
- 21. A car leaves P at 8 AM and travels to Q at a constant speed. A bus leaves Q at 8:45 AM and travels to P at a speed three times that of the car. If they meet at 10 AM, find the ratio of the distance traveled by the bus to the distance traveled by the car when they meet?
A) 8:15
B) 9:15
C) 7:15
D) 10:15
- 22. What is the quotient when 3x5 + 5x4 - 4x3 + 7x + 3 is divided by x + 2?
A) 3x4+x3+2x2+4x-1
B) 3x4-x3-2x2+4x+1
C) 3x4-x3-2x2+4x-1
D) 3x4-x3-3x2+4x-1
- 23. A man is walking away from a lamppost with a light source 6 meters above the ground. The man is 2 meters tall. How long is his shadow when he is 110 meters from the lamppost?
A) 65 m
B) 45 m
C) 55 m
D) 35 m
- 24. Factor completely the expression x3 - 7x + 6.
A) (x -1) (x - 2) (x - 3)
B) (x +1) (x - 2) (x + 3)
C) (x -1) (x + 2) (x + 3)
D) (x -1) (x - 2) (x + 3)
- 25. How many different three-digit numbers less than 300 can be formed with the digits 1,2,3 and 5 if repetition of digits is not allowed?
A) 12
B) 11
C) 10
D) 13
- 26. z varies directly as x and varies inversely as the square of y. If z = 7/2 when x = 14 and y = 6, find z when x = 37 and y = 9.
A) 2
B) 5
C) 7
D) 3
- 27. The diagonals of parallelogram JKLM intersect at P. If PM = 3x – 2, PK = x + 3 and PJ = 4x – 3, find the length of PL?
A) 11
B) 7
C) 9
D) 5
- 28. The difference of two numbers is 22. Find the numbers so that their product is to be minimum.
A) -7,10
B) -10,9
C) -11,11
D) -17,19
- 29. Herald can do the carpentry job in 20 minutes while Lexter can do the job in 28 minutes. How long will it take them to finish the job Herald and Lexter work together?
A) 13 minutes
B) 10 minutes
C) 15 minutes
D) 12 minutes
- 30. Find the solution set of the linear system: (1) 2x + 5y = -6 (2) 5x - 2y = 14
A) (1, -1)
B) (-9, 3)
C) (2, -2)
D) (3, -3)
- 31. The length of the rectangular lot is 3 less than twice its width, and its height is 2 inches shorter than its width. If the height of the box is x - 3, give the volume of of the box in terms of x.
A) V = (x -1) (x + 8) (x - 3)
B) V= (x -1) (x + 8) (x + 3)
C) V = (x +1) (x + 8) (x +3)
D) V= (x -1) (x - 8) (x - 3)
- 32. A sack of rice weighs 25 kilograms. If the rice is to be divided equally among 8 families, how many grams of rice would each family receive?
A) 3215
B) 3115
C) 3125
D) 3512
- 33. In a class, half of the students took Geography while three-fifths took Statistics. If 8 students took both and four students did not choose any of the two subjects, how many students are there in class?
A) 30
B) 60
C) 40
D) 20
- 34. A natural number is 5 less than four times another natural number. If the larger number is between 15 and 55, find the difference between the largest and smallest possible values of the smaller number.
A) 8
B) 7
C) 5
D) 6
- 35. Find the difference between 6/7 and its reciprocal.
A) 11/42
B) 17/42
C) 13/42
D) 15/42
- 36. An isosceles triangle with perimeter 80 cm is cut in half through a line passing through its vertex angle. If each resulting triangle has a perimeter of 70 cm, find the height of the original triangle.
A) 20 cm
B) 50 cm
C) 30 cm
D) 40 cm
- 37. The sum of two positive integers is 9 and the sum of their cubes is 243. What is the product of the two numbers?
A) 15
B) 16
C) 17
D) 18
- 38. The following set of observations is arranged in ascending order: 12, x, 16, 17, y, 27, 32, 33 Find x and y if the mean of the data set is 21.25 while its median is 18.5.
A) x = 13; y = 25
B) x = 12; y = 20
C) x = 13; y = 20
D) x = 13; y = 30
- 39. Find the coordinates of the vertex of the parabola y = 2x2 + 4x − 3.
A) (-1, -5)
B) (-1,-3)
C) (1, -5)
D) (-1, 3)
- 40. What is the probability of getting exactly two heads in flipping a fair coin four times?
A) 5/8
B) 7/8
C) 3/8
D) 1/4
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