Math exam

Prompt

UPCAT Reviewer - Review Masters - Mathematics_hGasT2y.pdf PDF copy all questions Sure. I copied all 100 mathematics questions from the uploaded UPCAT Reviewer, including the choices and mathematical expressions. UPCAT Mathematics — All Questions 1–10 1. 15 3 1 ​ −5 2 1 ​ = A. 8 3 2 ​ B. 9 3 1 ​ C. 9 6 5 ​ D. 10 3 1 ​ 2. 5 16 ​ = A. 3.2% B. 3.25% C. 32.5% D. 320% 3. 5.75=______ A. 11/2 B. 17/3 C. 23/4 D. 29/5 4. Divide 42 by 3 3 1 ​ . A. 12 5 3 ​ B. 14 3 2 ​ C. 15 D. 16 5 1 ​ 5. ∣2−7∣−∣8−14∣= A. −11 B. −1 C. 1 D. 11 6. What is the product of −1.54 and −1.64? A. 252.56 B. 25.256 C. 2.5256 D. −2.5256 7. −4[8−(5−2)]−3= A. 15 B. 17 C. −17 D. −23 8. (x 3 y 2 ) 4 = A. x 7 y 6 B. x 12 y 8 C. x 8 y 6 D. x 3 y 8 9. Which of the following has the lowest value? A. 8 3 ​ B. 0.2 2 C. 25 2 ​ D. 10% 10. Which of the following has the largest value? A. 0.7 B. 0.77 C. 0.777 D. 0.077 11–20 11. (4 2 )(5 2 ) A. 9 2 B. 9 4 C. 200 D. 400 12. Which of the following has the greatest value? A. 3 2 ​ B. 8 5 ​ C. 4 3 ​ D. 0.675 13. Which of the following fractions has the smallest value? A. 4 7 ​ B. 5 8 ​ C. 20 27 ​ D. 60 67 ​ 14. 5 3 ​ × 7 5 ​ × 9 7 ​ × 11 9 ​ = A. 11 3 ​ B. 99 15 ​ C. 35 63 ​ D. 385 105 ​ 15. 32 ? ​ =0.875 A. 16 B. 18 C. 24 D. 28 16. 5 4 ​ + 2 1 ​ + x 3 ​ = 20 41 ​ , x=? A. 4 B. 5 C. 6 D. 7 17. If 24 m ​ =0.625, what is the numerical value of m? A. 12 B. 13 C. 14 D. 15 18. What part of y is x? A. xy B. y x ​ C. x y ​ D. xy 1 ​ 19. Which of the following groups of numbers are multiples of 6 between 81 and 100? A. 84, 90 B. 86, 92 C. 84, 90, 96 D. 86, 92, 98 20. What is the value of m+n m−n ​ when m equals 3 1 ​ and n equals 4 3 ​ ? A. − 7 2 ​ B. − 13 5 ​ C. −3 2 1 ​ D. −2 5 3 ​ 21–30 21. 20 is 125% of what number? A. 7 B. 9 C. 10 D. 16 22. 4 2 +4 0 +4 −4 = A. 16 4 1 ​ B. 17 4 1 ​ C. 12 D. 13 23. 0.489×0.592×0.798×0.875×0.23 is approximately equal to A. 25 2 ​ B. 125 7 ​ C. 5 1 ​ D. 625 27 ​ 24. What is 75% of 3 2 ​ ? A. 3 2 ​ B. 4 3 ​ C. 2 1 ​ D. 3 1 ​ 25. The product of −3 and −6 is how much larger than the sum of −2 and −7? A. 9 B. 12 C. 15 D. 27 26. Which expression has the largest value? A. ∣7∣ B. ∣7−2∣ C. 2−∣7∣ D. ∣−7∣+2 27. What is the weight, in kilograms, of 26 sacks of sugar if 156 sacks weigh 12 kg? A. 2 B. 3 C. 4 D. 5 28. 64x 7 ​ = A. 8x 3 B. 4x 3 C. 8x 2 x ​ D. 8x 3 x ​ 29. If m−4=9, then 3m−5= A. 10 B. 17 C. 20 D. 34 30. The point with coordinates (−5,3) is in quadrant A. I B. II C. III D. IV 31–40 31. If a and b are both odd numbers, then which of the following must be an odd number? A. a+b B. ab+1 C. 2a+4b D. a+b+3 32. Last week, Vince read from page 139 to page 225 inclusive in his History book. How many pages did he read? A. 86 B. 87 C. 88 D. 89 33. Anne will be P years old in Q years. Her age R years ago was A. P+Q−R B. P−Q+R C. P+Q+R D. P−Q−R 34. If a jeepney ride costs ₱8.50 for the first four kilometers and ₱1.50 for each additional kilometer or fraction thereof, then how much would a passenger pay for a 12 km ride? A. ₱10.00 B. ₱18.00 C. ₱18.50 D. ₱20.50 35. (5x 2 −4x+3)−(3x 2 +4x−3)= A. 2x 2 B. −2x 2 C. 2x 2 −8x D. 2x 2 −8x+6 36. If 6x−15<4+5, then A. x>6 B. x<6 C. x<4 D. x<−4 37. How far can Jaiah go on her scooter from 3:35 p.m. to 4:15 p.m. at 30 km per hour? A. 20 km B. 18 km C. 17½ km D. 16 km 38. b a ​ − c a ​ = A. bc 1 ​ B. b−c a ​ C. bc ab−ac ​ D. bc ac−ab ​ 39. 1, 8, 27, 64, 125, ? A. 175 B. 201 C. 216 D. 225 40. Which equation is not satisfied by x=−3? A. x 2 −x−6=0 B. x 2 +x−6=0 C. x 2 −9=0 D. x 2 +6x+9=0 41–50 41. What percent profit was made on a pair of pants that was bought for ₱250 and sold for ₱350? A. 10% B. 20% C. 30% D. 40% 42. If y<−2, which of the following must have the greatest value? A. y 2 ​ B. 2 y ​ C. y+1 2 ​ D. y−1 2 ​ 43. (3x+2)(4x−5)= A. 12x 2 −10x B. 12x 2 +10x−0 C. 12x 2 −7x−10 D. 12x 2 −23x−10 44. If 0.002x=2, then 2.2x= A. 2002 B. 2020 C. 2200 D. 2202 45. Find the value of m m−n ​ + n n−m ​ if m is 20 and n is 10. A. − 2 1 ​ B. 0 C. 2 1 ​ D. 1 46. y 2 −1 y−1 ​ A. y 1 ​ B. y+1 1 ​ C. y−1 1 ​ D. y 2 1 ​ 47. What is the average of all even integers from 2 to 40? A. 20 B. 21 C. 22 D. 23 48. Review Masters increases its enrollees by 25% yearly. What is the ratio of the enrollees in one year to the enrollees in the previous year? A. 1:4 B. 4:1 C. 5:4 D. 4:5 49. Mark Caguioa scored an average of 29 for his first three games and an average of 32 for his next four games; then his average so far is about A. 28 B. 29 C. 30 D. 31 50. Ning is 8 years younger than her brother Michael. Twenty-eight years ago, she was half as old as Michael. How old is Michael now? A. 44 B. 42 C. 40 D. 36 51–60 51. If the triangle below is an isosceles with a as the vertex angle, which set of numbers could be values of a,b,c, respectively? A. (50, 65, 65) B. (50, 50, 80) C. (50, 60, 70) D. (70, 60, 60) 52. What is the area of a square inscribed in a circle having a diameter of 4 cm? A. 4 cm 2 B. 8 cm 2 C. 4π cm 2 D. 8π cm 2 53. A triangle has the following points as vertices: (0, 0), (3, 4), and (6, 0). This triangle is A. a scalene triangle B. an isosceles triangle C. a right triangle D. an equilateral triangle 54. The diameter of a wheel is 6 cm. How many complete revolutions will the wheel make if it rolls a distance of 108π cm? A. 6 B. 12 C. 18 D. 24 55. The length, width, and height of a large box are thrice those of a smaller box. The volume of the large box is A. thrice that of the smaller box B. 6 times that of the smaller box C. 9 times that of the smaller box D. 27 times that of the smaller box 56. On a number line, if one endpoint of a line segment is at −12, and its midpoint is at −4, then the other endpoint is at A. 0 B. 12 C. 8 D. 4 57. A telephone pole is 9 meters tall. What is the length of a piece of wire which extends from the top of the pole to a point that is 12 meters from the base of the pole? A. 21 B. 18 C. 15 D. 12 58. If the measures of the angles of a triangle are in the ratio 2:3:4, what is the degree measure of the smallest angle? A. 20 B. 30 C. 40 D. 60 59. The width of a rectangular rug is 4 feet. If the perimeter is 20 feet, what is the length of the rug? A. 4 feet B. 5 feet C. 6 feet D. 16 feet 60. If AC=18, BE=13, DE=3 and D is the midpoint of CE, what is AB? A. 10 B. 11 C. 12 D. 13 61–70 61. If four lines are drawn in a plane, what is the maximum possible number of points of intersection of the lines? A. 4 B. 5 C. 6 D. 7 62. The perimeter of a triangle is 90 cm. The measure of the longest side is 6 less than the sum of the measures of the other two sides. Four times the measure of the shortest side equals the sum of the measures of the other two sides. What is the length in cm of the shortest side of the triangle? A. 30 cm B. 24 cm C. 20 cm D. 18 cm 63. In the figure, KLMN is a parallelogram with angle measures as marked. Find x+y. A. 75 B. 105 C. 115 D. 120 64. What is the sum of the measures of the angles of this polygon? A. 720° B. 900° C. 1080° D. 1260° 65. When the length of a rectangle is divided by 4 and the width is tripled, the area of the new rectangle is the area of the original one multiplied by _____. A. 4 B. 3 C. 2 D. 4 3 ​ 66. In parallelogram WXYZ, V is the midpoint of ZY. The area of △WZV is what percent of the area of WXYZ? A. 20% B. 25% C. 30% D. 33% 67. The figure has four squares placed side by side. How many rectangles are in the figure? A. 6 B. 8 C. 10 D. 12 68. An isosceles triangle with base 10 cm has an area of 60 cm². Find its perimeter. A. 18 cm B. 36 cm C. 40 cm D. 48 cm 69. If the sides of a quadrilateral are 8, 14, 12, and 20 cm and the longest side of a similar quadrilateral is 30 cm, how long is the shortest side of this quadrilateral? A. 5 cm B. 12 cm C. 15 cm D. 16 cm 70. In the figure, the ratio of the area of triangle LEA to the area of rectangle LAST is A. 1:2 B. 2:1 C. 1:4 D. 4:1 71–80 71. Point A(5,3) is the midpoint of line OAK, where O is at the origin. The coordinates of K are: A. (2.5, 1.5) B. (8, 8) C. (−5, −3) D. (10, 6) 72. The perimeter of a square is 24. What is the length of a diagonal of this square? A. 6 6 ​ B. 6 2 ​ C. 2 ​ D. 24 2 ​ 73. If a triangle has sides 4, 8 and 11, which could be the sides of a similar triangle? A. (2, 4, 5½) B. (8, 16, 24) C. (7, 11, 14) D. (2, 6, 9) 74. The area of the whole figure below is 42. If four congruent squares each with a perimeter of 8 are cut out to form a cross as shown, what is the area of the cross? A. 20 B. 24 C. 26 D. 30 75. In the figure, if AO=5 and OB=3, what is the area of the shaded region? A. 16π B. 25π C. 39π D. 64π 76. If x=1− 1− 2 1 ​ 1 ​ , then x=______. A. −2 B. −1 C. 0 D. 1 77. Given: f(x)=5x 4 −3x 3 −x 2 +2x+5. Find f(−1)−f(1). A. −1 B. 0 C. 1 D. 2 78. A biker took 2 hours to ride 24 km and then returned by the same route. If he rode at an average speed of 8 km/hr on the return trip, what was his average speed in km/hr for the round trip? A. 8 B. 9.6 C. 10 D. 10.5 79. If the sum of two positive integers is 16 and the difference of their squares is 64, what is the difference of the two integers? A. 32 B. 16 C. 8 D. 4 80. Find the value of q so that x q ​ −2x=3 has 4 as a root. A. 4 B. 20 C. 38 D. 44 81–90 81. If 2≤a≤4 and 3≤b≤6, what is the greatest value of a 2 −b 2 ? A. −32 B. −20 C. 5 D. 7 82. The expression (x 2 +9)(x−5) x ​ represents a real number for all real values of x EXCEPT _____. A. −3 B. 3 C. 5 D. −5 83. If (6 3 )(5 5 )=25(30 k ), then what is the value of k? A. 3 B. 4 C. 6 D. 8 84. Simplify: 4 27x 2 ⋅ 9x 4 ​ ​ A. 3x 3x ​ B. 3x C. 3x ​ D. 4 3x ​ 85. What is the remainder when 2x 4 −x 3 +3x−1 is divided by x+2? A. 0 B. 2 C. −2 D. 33 86. If x=y+4 and x=20−y, then what is the value of x 2 −y 2 ? A. 24 B. 80 C. 16 D. 5 87. The sum of squares of two numbers is 225 and the square of their sum is 441. What is the reciprocal of their product? A. 108 B. 108 1 ​ C. 216 D. 216 1 ​ 88. If log 10 ​ x+log 10 ​ 8=log 10 ​ 16, then x is equal to _____. A. 2 B. 4 C. 8 D. 16 89. The solution set of 3y+2x≥2 does NOT include points in quadrant _____. A. I B. II C. III D. IV 90. Find the fourth term of the arithmetic progression x,y,2y−x,… A. 2x−y B. 3x−y C. 3y−2x D. 2x−3y 91–100 91. For any real number x, (x−3) 5 −(x−2)(x−3) 4 =______. A. −1 B. (x−3) 4 C. −(x−3) 4 D. −5(x−3) 4 92. Which of the following has the same value as i 62 ? A. i B. −1 C. 1 D. −i 93. The product of (−x m+1 ) and (−x m−1 ) is A. x 2m B. −x 2m C. x m−1 D. −x m+1 94. If y is an integer and y+3>0, what is the least possible value of y? A. −3 B. −2 C. −1 D. 2 95. 2(2x 3 ) is equal to __________. A. 4x 3 B. 2x 3 C. 2x 3 +1 D. 2x 3 +2 96. For what value of k does the graph of y=x 2 −3x−k pass through the point (−1,2)? A. 6 B. 2 C. 0 D. −2 97. If the ratio of x to y is 3:7, what is the ratio of x+y to x? A. 3:10 B. 7:10 C. 10:3 D. 10:7 98. What is the x-intercept of the line 2x+7y+15=0? A. 7 15 ​ B. 15 2 ​ C. − 2 15 ​ D. 15 99. If the reciprocal of x+1 is x−1, then what is x? A. ± 2 ​ B. 2 ​ C. 0 D. 2 100. If xy+yz+xz=−10 and xyz=8, then x 1 ​ + y 1 ​ + z 1 ​ =______. A. −80 B. − 4 5 ​ C. − 5 4 ​ D. 5 4 If you cant answer,reformat it.also add a feature where i could upload a pdf