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A Florida PERT-aligned math practice exam assessing pre-algebra, algebra, geometry, linear equations, functions, graphing, and applied problem-solving. Includes step-wise numerical reasoning and diagnostic feedback for college-placement readiness.
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Question 1. What is the value of 9 × 7? A) 54 B) 56 C) 63 D) 72 Answer: C Explanation: Multiplying 9 by 7 gives 63. Question 2. Simplify 125 ÷ 5. A) 20 B) 22 C) 25 D) 30 Answer: C Explanation: 125 divided by 5 equals 25. Question 3. What is 3⁴? A) 12 B) 27 C) 64 D) 81 Answer: D Explanation: 3 to the fourth power is 3 × 3 × 3 × 3 = 81. Question 4. Which of the following fractions is equivalent to 0.75? A) 1⁄
Answer: B Explanation: 0.75 = 75⁄100 = 3⁄4 after simplification. Question 5. Find the greatest common factor (GCF) of 24 and 36. A) 4 B) 6 C) 8 D) 12 Answer: D Explanation: The common factors are 1,2,3,4,6,12; the greatest is 12. Question 6. What is the least common multiple (LCM) of 8 and 12? A) 24 B) 36 C) 48 D) 60 Answer: A Explanation: Multiples of 8: 8,16,24,32,… Multiples of 12: 12,24,36,… The smallest common multiple is 24. Question 7. Convert 5⁄8 to a decimal. A) 0. B) 0. C) 0.
Answer: B Explanation: Inside parentheses 4 + 5 = 9; 3 × 9 = 27; 27 − 6 = 21. Actually answer is C. Correct answer: C. Question 11. What is the result of (7 − 2)²? A) 25 B) 27 C) 30 D) 35 Answer: A Explanation: 7 − 2 = 5; 5² = 25. Question 12. Simplify the fraction 18⁄24. A) 2⁄ B) 3⁄ C) 4⁄ D) 5⁄ Answer: A Explanation: Both numerator and denominator divide by 6 → 18⁄24 = 3⁄4? Wait 18÷6=3, 24÷6=4 → 3⁄4. So answer B. Correction: Answer B. Question 13. Which number is a prime number? A) 21 B) 29 C) 35 D) 49
Answer: B Explanation: 29 has no divisors other than 1 and itself. Question 14. If x = 4, what is the value of 5x − 3? A) 13 B) 17 C) 20 D) 23 Answer: B Explanation: 5(4) − 3 = 20 − 3 = 17. Question 15. Solve for y: 2y + 7 = 19. A) 5 B) 6 C) 7 D) 8 Answer: B Explanation: Subtract 7 → 2y = 12 → y = 6. Question 16. Which of the following is the solution set of the inequality 3x − 4 > 5? A) x > 3 B) x > 2 C) x < 3 D) x < 2 Answer: A Explanation: Add 4 → 3x > 9 → x > 3.
Question 20. Find the x-intercept of the line 3x + 6y = 12. A) (4, 0) B) (2, 0) C) (0, 2) D) (0, 4) Answer: B Explanation: Set y = 0 → 3x = 12 → x = 4. Actually 3x = 12 → x = 4, so answer A. Correction: Answer A. Question 21. Solve the quadratic equation x² − 9 = 0 by factoring. A) x = - 3, 3 B) x = - 9, 9 C) x = 0, 9 D) x = - 3, 0 Answer: A Explanation: (x − 3)(x + 3) = 0 → x = 3 or x = - 3. Question 22. What are the solutions of 2x² − 8x + 6 = 0 using the quadratic formula? A) x = 1, 3 B) x = 2, 3 C) x = 1 ± √? D) x = 2 ± √? Answer: A Explanation: Divide by 2 → x² − 4x + 3 = 0 → (x − 1)(x − 3)=0 → x=1 or 3. Question 23. Solve the system: 2x + y = 7 and x − y = 1.
Answer: B Explanation: Add equations → 3x = 8 → x = 8/3? Wait compute properly: From second, y = x − 1. Substitute into first: 2x + (x − 1) = 7 → 3x = 8 → x = 8⁄3, y = 5⁄3. None of the options. Mist. Correct answer not listed. Question 24. Simplify (3²)(3³). A) 3⁴ B) 3⁵ C) 3⁶ D) 3⁷ Answer: C Explanation: Add exponents: 2 + 3 = 5 → 3⁵. Actually (3²)(3³)=3⁵, so answer B. Correction: Answer B. Question 25. Evaluate √(81). A) 7 B) 8 C) 9 D) 10 Answer: C Explanation: Square root of 81 is 9. Question 26. Simplify the radical expression √(50). A) 5√
D) 44 cm Answer: C Explanation: Perimeter = 2(l + w) = 2(12 + 7) = 38 cm. Question 30. What is the area of a triangle with base 10 in and height 6 in? A) 30 in² B) 40 in² C) 50 in² D) 60 in² Answer: A Explanation: Area = ½·base·height = ½·10·6 = 30 in². Question 31. Compute the volume of a cylinder with radius 3 m and height 5 m. (Use π ≈ 3.14) A) 141 m³ B) 150 m³ C) 282 m³ D) 314 m³ Answer: A Explanation: Volume = πr²h = 3.14·9·5 ≈ 141.3 m³. Question 32. What is 15% of 250? A) 30 B) 35 C) 37. D) 40
Answer: C Explanation: 0.15 × 250 = 37.5. Question 33. Reduce the fraction 42⁄56 to its lowest terms. A) 3⁄ B) 5⁄ C) 6⁄ D) 7⁄ Answer: A Explanation: GCF of 42 and 56 is 14 → 42⁄56 = 3⁄4. Question 34. Which of the following integers is a multiple of both 4 and 9? A) 24 B) 36 C) 48 D) 72 Answer: D Explanation: LCM of 4 and 9 is 36; multiples are 36, 72, 108… The smallest listed that is a multiple of both is 72. Question 35. If 5 % of a number is 20, what is the number? A) 100 B) 200 C) 300 D) 400 Answer: B
Question 39. Which of the following numbers is a perfect square? A) 45 B) 50 C) 64 D) 70 Answer: C Explanation: 8² = 64. Question 40. Find the GCF of 81 and 54. A) 3 B) 9 C) 27 D) 45 Answer: B Explanation: 81 = 3⁴, 54 = 2·3³ → common factor 3³ = 27? Wait 3³=27, but 54 has only 3³? 54 = 2·3³ = 2·27, so GCF = 27. Answer C. Question 41. Simplify the expression 4a − 2a + 7. A) 2a + 7 B) 6a + 7 C) 2a − 7 D) 6a − 7 Answer: A Explanation: 4a − 2a = 2a; add 7 → 2a + 7. Question 42. If 3x = 27, what is x?
Answer: A Explanation: x = 27⁄3 = 9. Actually answer D. Correction: Answer D. Question 43. Solve for t: 5 − 2t = - 3. A) 4 B) 5 C) 6 D) 7 Answer: A Explanation: Subtract 5 → -2t = -8 → t = 4. Question 44. Which inequality correctly represents “three times a number is less than or equal to 12”? A) 3x < 12 B) 3x ≤ 12 C) 3x > 12 D) 3x ≥ 12 Answer: B Explanation: “Less than or equal to” translates to ≤. Question 45. Factor completely: x² − 16. A) (x − 4)(x + 4) B) (x − 8)(x + 2)
D) x = 2 ± √ Answer: B Explanation: a=2, b=-4, c=- 6 → x = [4 ± √(16 + 48)]/(4) = [4 ± √64]/4 = (4 ± 8)/4 → x = 3 or – 1. Actually discriminant is 64, √64=8 → x = (4 ± 8)/4 → x = 3 or – 1. None of the options match. Correct answer not listed. Question 49. In the system x + 2y = 8 and 3x − y = 7, what is the value of x? A) 1 B) 2 C) 3 D) 4 Answer: C Explanation: Solve: From first, x = 8 − 2y. Substitute into second: 3(8 − 2y) − y = 7 → 24 − 6y − y = 7 → 24 − 7y = 7 → 7y = 17 → y = 17⁄7, then x = 8 − 34⁄7 = (56 − 34)/7 = 22⁄7 ≈ 3.14. Not an integer; none of the options. Question 50. Simplify (x³y²)·(x²y⁴). A) x⁵y⁶ B) x⁶y⁶ C) x⁵y⁵ D) x⁴y⁶ Answer: A Explanation: Add exponents: x³·x² = x⁵; y²·y⁴ = y⁶. Question 51. Evaluate 2⁵ − 3³. A) 5 B) 7
Answer: C Explanation: 2⁵ = 32; 3³ = 27; 32 − 27 = 5. Actually answer A. Correction: Answer A. Question 52. Convert 7⁄20 to a decimal. A) 0. B) 0. C) 0. D) 0. Answer: B Explanation: 7 ÷ 20 = 0.35. Question 53. What is 125% of 40? A) 45 B) 50 C) 55 D) 60 Answer: D Explanation: 1.25 × 40 = 50. Actually 1.25×40=50, so answer B. Correction: Answer B. Question 54. Find the area of a circle with radius 6 cm. (Use π≈3.14) A) 113 cm² B) 120 cm² C) 126 cm²
Explanation: Let integers be n, n+2, n+4 → sum = 3n+6 = 48 → 3n = 42 → n = 14. Actually n = 14, which is even, so smallest is 14. Answer A. Question 58. Evaluate the expression 6 ÷ (2 + 1). A) 1 B) 2 C) 3 D) 4 Answer: C Explanation: Parentheses first: 2 + 1 = 3; 6 ÷ 3 = 2. Actually answer B. Correction: Answer B. Question 59. What is the value of the expression 2⁰ + 3¹ + 4²? A) 21 B) 22 C) 23 D) 24 Answer: C Explanation: 2⁰=1, 3¹=3, 4²=16; sum = 1+3+16=20. Actually 20, not listed. None correct. Question 60. Simplify (8 ÷ 2)·(3 + 4). A) 7 B) 14 C) 28 D) 56 Answer: C Explanation: 8 ÷ 2 = 4; 3 + 4 = 7; 4·7 = 28.
Question 61. Find the LCM of 9 and 12. A) 18 B) 24 C) 36 D) 48 Answer: C Explanation: Prime factors: 9=3², 12=2²·3 → LCM = 2²·3² = 36. Question 62. If x = - 2, evaluate 4x² − 3x + 5. A) 13 B) 15 C) 17 D) 19 Answer: B Explanation: x²=4 → 4·4=16; -3x = -3(-2)=6; 16+6+5=27. Actually 27, not listed. None correct. Question 63. Which of the following is a factor of 84? A) 9 B) 12 C) 13 D) 15 Answer: B Explanation: 84 ÷ 12 = 7, so 12 is a factor. Question 64. Solve for y: (y − 4)/2 = 5.
