College Math Placement Test College Algebra 2 — Questions and Answers
Question 1: Which of the following is the solution set of |2x - 3| < 7?
- -2 < x < 5 (Correct answer)
- -5 < x < 2
- x < -2 or x > 5
- x > 5
Correct answer: -2 < x < 5
Solving |2x-3| < 7 gives -7 < 2x-3 < 7, so -4 < 2x < 10, meaning -2 < x < 5.
Question 2: What is the vertex of the parabola y = 2(x - 3)² + 5?
- (3, 5) (Correct answer)
- (-3, 5)
- (3, -5)
- (-3, -5)
Correct answer: (3, 5)
The vertex form y = a(x-h)² + k has vertex (h, k), so the vertex is (3, 5).
Question 3: If f(x) = x² - 4 and g(x) = x + 2, what is f(g(x))?
- x² + 4x (Correct answer)
- x² + 4x + 4
- x² + 4x + 4 - 4
- x² - 2
Correct answer: x² + 4x
f(g(x)) = (x+2)² - 4 = x² + 4x + 4 - 4 = x² + 4x.
Question 4: What is the domain of f(x) = √(x² - 9)?
- x ≤ -3 or x ≥ 3 (Correct answer)
- -3 ≤ x ≤ 3
- x ≥ 3
- All real numbers
Correct answer: x ≤ -3 or x ≥ 3
The radicand x²-9 ≥ 0 factors as (x-3)(x+3) ≥ 0, giving x ≤ -3 or x ≥ 3.
Question 5: Solve for x: log₂(x) + log₂(x - 2) = 3
- x = 4 (Correct answer)
- x = 2
- x = 8
- x = -2
Correct answer: x = 4
Combining logs gives log₂(x(x-2)) = 3, so x(x-2) = 8, x²-2x-8 = 0, giving x = 4 (rejecting x = -2).
Question 6: Which expression is equivalent to (x² - 5x + 6) / (x² - 4) for x ≠ ±2?
- (x - 3)/(x + 2) (Correct answer)
- (x - 2)/(x + 3)
- (x + 3)/(x - 2)
- (x - 3)/(x - 2)
Correct answer: (x - 3)/(x + 2)
Factoring gives (x-2)(x-3) / ((x-2)(x+2)), and canceling (x-2) leaves (x-3)/(x+2).
Question 7: An arithmetic sequence has first term 5 and common difference 3. What is the 20th term?
- 62 (Correct answer)
- 65
- 59
- 60
Correct answer: 62
The nth term is a₁ + (n-1)d = 5 + 19(3) = 5 + 57 = 62.
College Math Placement Test College Algebra 2
Which of the following is the solution set of |2x - 3| < 7?