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Covers arithmetic, elementary algebra, and college-level math. Tests numerical operations, algebraic problem-solving, and quantitative reasoning. Results guide placement into appropriate college math courses.
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Question 1. What is the sum of 237 and 468? A) 705 B) 695 C) 725 D) 715 Answer: A Explanation: Adding 237 + 468 yields 705, as 200 + 400 = 600, 30 + 60 = 90, 7 + 8 = 15; total 600 + 90 + 15 = 705. Question 2. Subtract 583 from 1000. A) 417 B) 423 C) 387 D) 413 Answer: A Explanation: 1000 - 583 equals 417, subtracting each part: 1000 - 500 = 500; 500 - 80 = 420; 420 - 3 = 417. Question 3. Multiply 36 by 7. A) 252
Answer: A Explanation: 36 × 7 = 252, calculated directly or using distributive property: 30×7=210, 6×7=42, sum=252. Question 4. Divide 144 by 12. A) 12 B) 14 C) 11 D) 13 Answer: A Explanation: 144 ÷ 12 = 12, since 12×12=144. Question 5. Simplify 3 + 4 × 2. A) 14 B) 11 C) 10
Explanation: Find common denominator 12: 8/12 + 9/12=17/12=1 5/12; but note the correct sum is 8/12 + 9/12=17/12, which simplifies to 1 5/12; the closest option is B, assuming a typo, but actual sum is 17/12. Question 8. Subtract 5/8 from 7/4. A) 9/ B) 11/ C) 3/ D) 13/ Answer: A Explanation: Convert to common denominator 8: 7/4=14/8; 5/8=5/8; 14/8 - 5/8=9/8. Question 9. Multiply 3/4 by 2/5. A) 3/ B) 6/ C) 1/ D) 3/ Answer: A
Explanation: Multiply numerators: 3×2=6; denominators: 4×5=20; simplified as 6/20=3/10. Question 10. Divide 3/4 by 2/3. A) 9/ B) 1/ C) 8/ D) 2/ Answer: A Explanation: Dividing fractions involves multiplying by the reciprocal: (3/4) ÷ (2/3)= (3/4)×(3/2)=9/8. Question 11. Convert 0.75 to a fraction. A) 3/ B) 1/ C) 2/ D) 4/ Answer: A Explanation: 0.75 equals 75/100, simplified to 3/4.
Answer: A Explanation: 0.3×0.4=0.12. Question 15. Divide 0.9 by 3. A) 0. B) 0. C) 0. D) 0. Answer: A Explanation: 0.9 ÷ 3=0.3. Question 16. What is 25% of 200? A) 50 B) 25 C) 75 D) 100 Answer: A
Explanation: 25% of 200 = 0.25×200=50. Question 17. Convert 0.2 to a percentage. A) 20% B) 2% C) 0.2% D) 200% Answer: A Explanation: 0.2=20%. Question 18. Which of the following is equivalent to 3/4? A) 0. B) 0. C) 0. D) 0. Answer: A Explanation: 3/4=0.75. Question 19. Which number is greater?
Answer: A Explanation: - 1/2=-0.5, which is less than 0, 1/3≈0.33, 2/5=0.4. Question 22. Compare - 3/4 and 1/2. A) - 3/4 is less than 1/ B) - 3/4 is greater than 1/ C) They are equal D) Cannot determine Answer: A Explanation: - 3/4 ≈ - 0.75, which is less than 0.5. Question 23. Find the absolute value of - 7/3. A) 7/ B) - 7/ C) 7/ D) - 7/ Answer: A Explanation: Absolute value of - 7/3 is 7/3.
Question 24. If the ratio of apples to oranges is 3:4 and there are 12 apples, how many oranges are there? A) 16 B) 12 C) 9 D) 8 Answer: A Explanation: Ratio 3:4, so 3 corresponds to 12; 1 unit equals 4; thus, oranges = 4×4=16. Question 25. Solve for x: 2x=10. A) 5 B) 20 C) 8 D) 12 Answer: A Explanation: Divide both sides by 2: x=10/2=5. Question 26. Solve for x: x/3=4.
D) 6x + 4 Answer: A Explanation: Distribute 2: 2×3x=6x, 2×(-4)=-8. Question 29. Factor the expression x^2 + 5x + 6. A) (x + 2)(x + 3) B) (x + 1)(x + 6) C) (x + 3)^ D) x(x + 5) + 6 Answer: A Explanation: Factoring quadratic: find two numbers that multiply to 6 and add to 5, which are 2 and 3. Question 30. Solve for x: x - 7=3. A) 10 B) 4 C) 3 D) - 10 Answer: A
Explanation: Add 7 to both sides: x=3+7=10. Question 31. Solve for x: 3x + 4=19. A) 5 B) 7 C) 15 D) 23 Answer: A Explanation: Subtract 4: 3x=15; divide by 3: x=5. Question 32. Solve the system: x+ y=10 and x - y=4. A) x=7, y= B) x=6, y= C) x=5, y= D) x=8, y= Answer: A Explanation: Add equations: (x + y) + (x - y)=10+4→2x=14→x=7; substitute into x + y=10: 7 + y=10→ y=3.
Answer: A Explanation: Set y=0: 0=2x+4→2x=-4→x=-2. Question 36. What is the y-intercept of y=2x + 4? A) 4 B) - 4 C) 2 D) 0 Answer: A Explanation: y-intercept is the constant term: 4. Question 37. Which of the following lines are parallel? A) y=2x + 3 and y=2x - 5 B) y=3x + 2 and y=-3x + 4 C) y=x + 1 and y= - x + 3 D) y=4x + 1 and y=2x + 5
Answer: A Explanation: Parallel lines have the same slope; both have slope 2. Question 38. Which line is perpendicular to y=1/2 x + 3? A) y= - 2x + 1 B) y= 2x + 4 C) y= - 1/2 x - 1 D) y= 1/2 x - 2 Answer: A Explanation: Perpendicular lines have slopes that are negative reciprocals; - 2 is the reciprocal of 1/2 with opposite sign. Question 39. Simplify the radical √50. A) 5√ B) 25 C) 10 D) √25 + √ Answer: A Explanation: √50=√(25×2)=5√2.
B) x^5 y^ C) x^6 y^ D) x^3 y^ Answer: A Explanation: Apply power of a power: x^(3×2)=x^6, y^(2×2)=y^4. Question 43. Simplify (2x^2 y)^3. A) 8x^6 y^ B) 2x^6 y^ C) 8x^2 y^ D) 2x^2 y^ Answer: A Explanation: Distribute the 3: 2^3=8, x^(2×3)=x^6, y^3. Question 44. Expand: (x + 3)^2. A) x^2 + 6x + 9 B) x^2 + 3x + 9 C) x^2 + 9 D) x^2 + 6x + 3
Answer: A Explanation: Use (a + b)^2 = a^2 + 2ab + b^2: x^2 + 6x + 9. Question 45. Factor: x^2 - 16. A) (x + 4)(x - 4) B) (x + 8)(x - 2) C) (x + 2)(x - 8) D) (x + 16)(x - 1) Answer: A Explanation: Difference of squares: x^2 - 16 = (x + 4)(x - 4). Question 46. Solve for x: 2x + 5= 3x - 4. A) 9 B) - 9 C) 1 D) - 1 Answer: A Explanation: Subtract 2x from both sides: 5= x - 4; add 4: 9= x.
