Download PERT Practice Exam... and more Exams Technology in PDF only on Docsity!
Question 1. Which of the following numbers is both rational and an integer? A) √ B) 1/ C) - 4 D) π Answer: C Explanation: An integer like - 4 is also rational because it can be represented as - 4/1. Question 2. What is the value of |–7|? A) – 7 B) 7 C) 0 D) 14 Answer: B Explanation: The absolute value of – 7 is 7, as absolute value measures distance from zero. Question 3. Which of the following is the product of (3/5) × (10/9)? A) 1/ B) 2/ C) 2/ D) 1/ Answer: B Explanation: (3/5) × (10/9) = (3×10)/(5×9) = 30/45 = 2/3. Question 4. What is the result of 2 – 3 × 4 + 5? A) 3 B) – 5 C) – 7 D) 9
Answer: B Explanation: Order of operations gives 2 – (3×4) + 5 = 2 – 12 + 5 = – 10 + 5 = – 5. Question 5. Which of the following is an irrational number? A) 0. B) 3/ C) √ D) – 2 Answer: C Explanation: √3 cannot be written as a fraction and has a non-repeating, non-terminating decimal. Question 6. Which set contains only whole numbers? A) {0, 2, 5, 7} B) {–2, 0, 3} C) {1/2, 1, 2} D) {0, – 1, 2} Answer: A Explanation: Whole numbers are 0 and all positive integers. Set A fits. Question 7. What is the value of (–2)³? A) – 6 B) 8 C) – 8 D) 6 Answer: C Explanation: (–2) × (–2) × (–2) = 4 × (–2) = – 8. Question 8. What is the sum of 0.6 and 1.25? A) 1.
Question 12. Simplify: (8/27)^(1/3) A) 2/ B) 8/ C) 3/ D) 4/ Answer: A Explanation: Cube root of 8 is 2, cube root of 27 is 3, so 2/3. Question 13. Which of the following correctly shows the use of the distributive property? A) 2(x + 3) = 2x + 6 B) x² + x² = 2x C) (x + 2)(x + 3) = x² + 5x + 6 D) (x + 2)² = x² + 4x + 4 Answer: A Explanation: Distributive: a(b + c) = ab + ac. Question 14. Simplify the expression: 3x – 2y + 5x + y A) 8x – 3y B) 8x – y C) 2x – y D) 3x + 2y Answer: B Explanation: 3x + 5x = 8x, – 2y + y = – y, so 8x – y. Question 15. Evaluate the expression 2a² – 3b when a = 2 and b = – 1. A) 11 B) 7 C) 10
D) 5
Answer: A Explanation: 2(2)² – 3(–1) = 2*4 + 3 = 8 + 3 = 11. Question 16. Which translates “the sum of twice a number and 7 is 15” into an equation? A) 2x + 7 = 15 B) 2x – 7 = 15 C) 7x + 2 = 15 D) x/2 + 7 = 15 Answer: A Explanation: “Twice a number” is 2x, “sum with 7” is 2x + 7. Question 17. Solve for x: 3x – 5 = 10 A) 15 B) 5 C) 3 D) – 5 Answer: B Explanation: 3x = 15, x = 5. Question 18. Solve for y: 2y + 4 = 10 A) 3 B) 7 C) 2 D) 4 Answer: A Explanation: 2y = 6, y = 3. Question 19. If x + y = 7 and x – y = 3, what is x?
D) x > 4 Answer: B Explanation: 3x ≤ 12 ⇒ x ≤ 4. Question 23. What is the value of 2³ × 2²? A) 2⁶ B) 2⁵ C) 2⁴ D) 2³ Answer: B Explanation: Add exponents: 2³ × 2² = 2^(3+2) = 2⁵. Question 24. Which of the following simplifies to x? A) x²/x B) x/x² C) x⁰ D) x¹ Answer: D Explanation: x¹ = x. Question 25. Simplify √50. A) 25 B) 5√ C) 10 D) 2√ Answer: B Explanation: √50 = √(25×2) = 5√2. Question 26. Add: (2x² + 3x + 1) + (x² – 5x + 4)
A) 3x² – 2x + 5 B) 3x² + 2x + 5 C) x² – 2x + 5 D) 3x² – 2x + 4 Answer: A Explanation: 2x² + x² = 3x², 3x – 5x = – 2x, 1 + 4 = 5. Question 27. Subtract: (5x³ – 2x² + x) – (2x³ + x² – 3x) A) 3x³ – 3x² + 4x B) 7x³ – 3x² – 2x C) 3x³ – 3x² + 4x D) 7x³ – x² + 2x Answer: A Explanation: Subtract like terms: 5x³ – 2x³ = 3x³, – 2x² – x² = – 3x², x – (–3x) = 4x. Question 28. Multiply: (x + 2)(x – 3) A) x² – 6 B) x² – x – 6 C) x² + x – 6 D) x² – x + 6 Answer: B Explanation: (x + 2)(x – 3) = x² – 3x + 2x – 6 = x² – x – 6. Question 29. Factor: x² – 9 A) (x – 9)(x + 1) B) (x – 3)(x + 3) C) (x + 9)(x – 1) D) (x – 3)² Answer: B
Explanation: Factors of 12 that add to 7 are 3 and 4. Question 33. Factor by grouping: x³ + 3x² + 2x + 6 A) (x² + 2)(x + 3) B) (x + 1)(x² + 6) C) (x² + 3)(x + 2) D) (x + 2)(x² + 3) Answer: D Explanation: Group: (x³ + 3x²) + (2x + 6) = x²(x + 3) + 2(x + 3) = (x² + 2)(x + 3). Correction: Answer: A Explanation: Factoring by grouping: x³ + 3x² + 2x + 6 = (x³ + 3x²) + (2x + 6) = x²(x + 3) + 2(x + 3) = (x² + 2)(x
- 3). Question 34. Solve the equation x² – 5x = 0 A) x = 0, x = – 5 B) x = 0, x = 5 C) x = 5 D) x = – 5 Answer: B Explanation: x(x – 5) = 0 ⇒ x = 0 or x = 5. Question 35. Which of the following is a function? A) {(1, 2), (2, 3), (1, 4)} B) {(1, 2), (2, 3), (3, 4)} C) {(1, 2), (1, 3), (2, 4)} D) {(1, 2), (2, 2), (1, 3)} Answer: B
Explanation: Each input has only one output. Question 36. What is the domain of the function f(x) = 1/(x – 2)? A) x ≠ 0 B) x ≠ 2 C) x > 2 D) x < 2 Answer: B Explanation: The denominator cannot be zero, so x ≠ 2. Question 37. Evaluate f(x) = 3x – 1 for x = – 2 A) – 5 B) – 7 C) – 6 D) 5 Answer: B Explanation: 3(–2) – 1 = – 6 – 1 = – 7. Question 38. Which graph best represents y = x² – 4? A) A parabola opening upwards with vertex at (0, – 4) B) A straight line through (0, – 4) C) A parabola opening downwards with vertex at (0, 4) D) A circle centered at (0, – 4) Answer: A Explanation: y = x² – 4 is a parabola opening upwards. Question 39. Which function is the inverse of f(x) = 2x + 3? A) f⁻¹(x) = (x – 3)/ B) f⁻¹(x) = 2x – 3
D) 8
Answer: A Explanation: Area = (1/2) × base × height ⇒ 24 = (1/2)(8)h ⇒ h = 6. Question 43. If you invest $500 at 4% simple interest for 3 years, what is the interest earned? A) $ B) $ C) $ D) $ Answer: A Explanation: I = Prt = $500 × 0.04 × 3 = $60. Question 44. A car rental charges $25 per day plus $0.15 per mile. If you rent for 4 days and drive 200 miles, what is the total cost? A) $ B) $ C) $ D) $ Answer: C Explanation: Cost = 4×25 + 0.15×200 = 100 + 30 = $130. Correction: Answer: $130 is missing from choices; correct answer is $130. Question 45. Which figure is a quadrilateral? A) Triangle B) Pentagon C) Rectangle D) Hexagon
Answer: C Explanation: A rectangle has four sides, making it a quadrilateral. Question 46. Which of the following statements is true about parallel lines? A) They intersect at one point B) They never intersect C) They intersect at two points D) They form a right angle Answer: B Explanation: Parallel lines never intersect. Question 47. Which angle is obtuse? A) 30° B) 60° C) 90° D) 120° Answer: D Explanation: An obtuse angle is more than 90° and less than 180°. Question 48. Which triangle has all sides of equal length? A) Scalene B) Isosceles C) Equilateral D) Right Answer: C Explanation: An equilateral triangle has all sides equal. Question 49. The sum of the interior angles of a quadrilateral is: A) 360°
Question 53. What is the area of a circle with radius 3? A) 9π B) 6π C) 3π D) 12π Answer: A Explanation: Area = πr² = π × 9 = 9π. Question 54. What is the perimeter of a rectangle with length 8 and width 5? A) 26 B) 40 C) 13 D) 12 Answer: A Explanation: Perimeter = 2(8 + 5) = 26. Question 55. What is the area of a parallelogram with base 7 and height 4? A) 28 B) 14 C) 11 D) 21 Answer: A Explanation: Area = base × height = 7 × 4 = 28. Question 56. What is the volume of a cube with side length 5? A) 25 B) 125 C) 30
D) 15
Answer: B Explanation: Volume = s³ = 5³ = 125. Question 57. What is the surface area of a cube with side length 6? A) 36 B) 216 C) 72 D) 144 Answer: D Explanation: Surface area = 6s² = 6 × 36 = 216. Correction: Answer: B Explanation: 6 × 36 = 216. Question 58. What is the volume of a cylinder with radius 2 and height 10? A) 40π B) 20π C) 80π D) 10π Answer: A Explanation: Volume = πr²h = π × 4 × 10 = 40π. Question 59. What is the area of a sector of a circle with radius 4 and central angle 90°? A) 4π B) 8π C) π D) 16π
B) y = – 2x + 3 C) y = 3x + 2 D) y = 2x – 3 Answer: A Explanation: y = mx + b, m = 3, b = – 2. Question 64. Which equation is parallel to y = 4x + 5? A) y = 4x – 2 B) y = – 4x + 1 C) y = x + 4 D) y = – x + 2 Answer: A Explanation: Parallel lines have equal slopes. Slope = 4. Question 65. Which equation is perpendicular to y = – 1/2 x + 3? A) y = 2x + 1 B) y = – 2x + 1 C) y = 1/2 x – 3 D) y = – 1/2 x – 1 Answer: A Explanation: Perpendicular slope is negative reciprocal of – 1/2, which is 2. Question 66. The graph below shows the number of books read by students in a month. What type of graph is it? A) Pie chart B) Bar graph C) Line graph D) Histogram Answer: B
Explanation: Bar graphs are used to display categorical data. Question 67. What is the mean of the data set: 2, 4, 6, 8, 10? A) 6 B) 5 C) 7 D) 4 Answer: A Explanation: (2+4+6+8+10)/5 = 30/5 = 6. Question 68. What is the median of the set: 3, 5, 7, 9, 11? A) 7 B) 5 C) 9 D) 11 Answer: A Explanation: Middle value in ordered set is 7. Question 69. What is the mode of the set: 1, 2, 2, 3, 4? A) 1 B) 2 C) 3 D) 4 Answer: B Explanation: Mode is the value that appears most often, which is 2. Question 70. What is the range of the set: 12, 15, 20, 25, 30? A) 15 B) 18
