College Math Placement Test Elementary Algebra 2 — Questions and Answers
Question 1: Solve for x: 3(x − 4) = 2x + 1
- x = 13 (Correct answer)
- x = 11
- x = 5
- x = −11
Correct answer: x = 13
Distribute: 3x − 12 = 2x + 1, then subtract 2x and add 12 to get x = 13.
Question 2: Which expression is equivalent to (2x²)(3x³)?
- 5x⁵
- 6x⁵ (Correct answer)
- 6x⁶
- 5x⁶
Correct answer: 6x⁵
Multiply coefficients (2·3 = 6) and add exponents (2+3 = 5) to get 6x⁵.
Question 3: If 4 − 2y = 10, what is the value of y?
- −3 (Correct answer)
- 3
- 7
- −7
Correct answer: −3
Subtract 4 from both sides: −2y = 6, then divide by −2 to get y = −3.
Question 4: Factor completely: x² − 9
- (x − 3)²
- (x + 3)(x − 3) (Correct answer)
- (x − 9)(x + 1)
- (x + 9)(x − 1)
Correct answer: (x + 3)(x − 3)
x² − 9 is a difference of squares: a² − b² = (a+b)(a−b), so it factors as (x+3)(x−3).
Question 5: A number is 5 more than twice another number. If the larger number is 17, what is the smaller number?
- 6 (Correct answer)
- 7
- 9
- 12
Correct answer: 6
Set up: 17 = 2n + 5, so 2n = 12 and n = 6.
Question 6: Simplify: (x + 3)²
- x² + 9
- x² + 6x + 9 (Correct answer)
- x² + 3x + 9
- x² − 6x + 9
Correct answer: x² + 6x + 9
(x+3)² = x² + 2(x)(3) + 3² = x² + 6x + 9 using the perfect square trinomial formula.
Question 7: Which value of x satisfies |2x − 6| = 4?
- x = 1 or x = 5 (Correct answer)
- x = 5 or x = 1
- x = 5 only
- x = 1 only
Correct answer: x = 1 or x = 5
Set 2x − 6 = 4 (giving x = 5) and 2x − 6 = −4 (giving x = 1), so both x = 1 and x = 5 are solutions.
College Math Placement Test Elementary Algebra 2
Solve for x: 3(x − 4) = 2x + 1