College Math Placement Test College Math Placement Algebra 3 — Questions and Answers
Question 1: Solve the system: x + y = 7 and x − y = 3
- x=2, y=5
- x=5, y=2 (Correct answer)
- x=4, y=3
- x=3, y=4
Correct answer: x=5, y=2
Adding the equations: 2x=10 → x=5; substituting back: y=7−5=2.
Question 2: Which equation represents a line parallel to y = 3x − 4?
- y = −(1/3)x + 2
- y = 3x + 7 (Correct answer)
- y = (1/3)x − 4
- y = −3x + 4
Correct answer: y = 3x + 7
Parallel lines have the same slope; only y=3x+7 has slope 3.
Question 3: Simplify: (x² − 4)/(x − 2)
- x − 2
- x + 2 (Correct answer)
- x² + 2
- x(x−2)
Correct answer: x + 2
x²−4=(x−2)(x+2); dividing by (x−2) cancels to give x+2, for x≠2.
Question 4: If 3^(2x) = 81, what is x?
- 4
- 2 (Correct answer)
- 3
- 1
Correct answer: 2
81=3⁴, so 3^(2x)=3⁴ means 2x=4, giving x=2.
Question 5: A store sells pencils for $0.25 each. If you spend $3.75, how many pencils did you buy?
- 12
- 13
- 15 (Correct answer)
- 16
Correct answer: 15
3.75 ÷ 0.25 = 15 pencils.
Question 6: What are the roots of x² − 5x + 6 = 0?
- x=1 and x=6
- x=−2 and x=−3
- x=2 and x=3 (Correct answer)
- x=−1 and x=−6
Correct answer: x=2 and x=3
Factor as (x−2)(x−3)=0, so x=2 or x=3.
Question 7: Evaluate: (2³ × 2⁻¹) / 2²
- 2
- 1 (Correct answer)
- 4
- 1/2
Correct answer: 1
2³×2⁻¹=2²; then 2²/2²=2⁰=1.
College Math Placement Test College Math Placement Algebra 3
Solve the system: x + y = 7 and x − y = 3