Accuplacer College Placement ACCUPLACER Advanced Algebra and Functions Test 1 — Questions and Answers
Question 1: What are the solutions to x² − 5x + 6 = 0?
- x = 1 and x = 6
- x = 2 and x = 3 (Correct answer)
- x = −2 and x = −3
- x = −1 and x = −6
Correct answer: x = 2 and x = 3
Factor as (x − 2)(x − 3) = 0, giving x = 2 and x = 3.
Question 2: Which of the following is the inverse function of f(x) = 3x − 6?
- f⁻¹(x) = (x + 6)/3 (Correct answer)
- f⁻¹(x) = (x − 6)/3
- f⁻¹(x) = 3x + 6
- f⁻¹(x) = x/3 − 6
Correct answer: f⁻¹(x) = (x + 6)/3
Swap x and y in y = 3x − 6, then solve for y: x = 3y − 6 → y = (x + 6)/3.
Question 3: What is the vertex of the parabola y = (x − 3)² + 5?
- (3, 5) (Correct answer)
- (−3, 5)
- (3, −5)
- (−3, −5)
Correct answer: (3, 5)
In vertex form y = (x − h)² + k, the vertex is (h, k) = (3, 5).
Question 4: Evaluate: log₂(32)
- 4
- 5 (Correct answer)
- 6
- 8
Correct answer: 5
2⁵ = 32, so log₂(32) = 5.
Question 5: If f(x) = x² + 1 and g(x) = 2x, what is f(g(3))?
- 13
- 19
- 37 (Correct answer)
- 49
Correct answer: 37
g(3) = 6, then f(6) = 6² + 1 = 37.
Question 6: Which expression is equivalent to (2x³y²)²?
- 4x⁵y⁴
- 4x⁶y⁴ (Correct answer)
- 2x⁶y⁴
- 4x⁶y²
Correct answer: 4x⁶y⁴
Square each factor: 2² = 4, (x³)² = x⁶, (y²)² = y⁴, giving 4x⁶y⁴.
Accuplacer College Placement ACCUPLACER Advanced Algebra and Functions Test 1
What are the solutions to x² − 5x + 6 = 0?