College Math Placement Test College Math Placement Algebra 2 — Questions and Answers
Question 1: Simplify: (3x²y)(4xy³)
- 7x³y⁴
- 12x³y⁴ (Correct answer)
- 12x²y³
- 7x²y³
Correct answer: 12x³y⁴
Multiply coefficients (3×4=12) and add exponents for like bases: x^(2+1)=x³, y^(1+3)=y⁴.
Question 2: Solve for x: 2(x - 3) = 4x + 6
- x = -6 (Correct answer)
- x = 6
- x = -3
- x = 3
Correct answer: x = -6
Distribute to get 2x−6=4x+6, then −12=2x, so x=−6.
Question 3: Which of the following is a factor of x² − 9?
- (x − 3)²
- (x + 9)
- (x − 3)(x + 3) (Correct answer)
- (x − 9)(x + 1)
Correct answer: (x − 3)(x + 3)
x²−9 is a difference of squares: a²−b²=(a−b)(a+b), so x²−9=(x−3)(x+3).
Question 4: If f(x) = 3x² − 2x + 1, what is f(−1)?
- 6 (Correct answer)
- 2
- 0
- 4
Correct answer: 6
f(−1)=3(1)−2(−1)+1=3+2+1=6.
Question 5: Solve: |2x − 5| = 9
- x = 7 only
- x = −2 only
- x = 7 or x = −2 (Correct answer)
- x = 2 or x = −7
Correct answer: x = 7 or x = −2
Set 2x−5=9 → x=7, and 2x−5=−9 → x=−2; both solutions are valid.
Question 6: What is the slope of the line passing through (−2, 3) and (4, −1)?
- 2/3
- −2/3 (Correct answer)
- 3/2
- −3/2
Correct answer: −2/3
Slope = (−1−3)/(4−(−2)) = −4/6 = −2/3.
Question 7: Factor completely: 2x² + 10x + 12
- 2(x+2)(x+3) (Correct answer)
- (2x+4)(x+3)
- 2(x+1)(x+6)
- (x+2)(2x+6)
Correct answer: 2(x+2)(x+3)
Factor out 2 first: 2(x²+5x+6)=2(x+2)(x+3).
College Math Placement Test College Math Placement Algebra 2
Simplify: (3x²y)(4xy³)