College Math Placement Test Intermediate Algebra 4 — Questions and Answers
Question 1: Which of the following is equivalent to (x² − 9)/(x² − x − 6)?
- (x + 3)/(x + 2) (Correct answer)
- (x − 3)/(x − 2)
- (x + 3)/(x − 2)
- (x − 3)/(x + 2)
Correct answer: (x + 3)/(x + 2)
Factor: (x−3)(x+3)/[(x−3)(x+2)] = (x+3)/(x+2) for x ≠ 3.
Question 2: Solve: √(x + 7) = 4
- x = 9 (Correct answer)
- x = 3
- x = 23
- x = −3
Correct answer: x = 9
Squaring both sides: x+7 = 16, so x = 9; check: √16 = 4 ✓.
Question 3: What are the x-intercepts of f(x) = x² + 2x − 15?
- x = 3 and x = −5 (Correct answer)
- x = −3 and x = 5
- x = 3 and x = 5
- x = −3 and x = −5
Correct answer: x = 3 and x = −5
Factor: (x+5)(x−3) = 0, giving x = 3 or x = −5.
Question 4: If f(x) = 2x − 1, what is f⁻¹(x)?
- (x + 1)/2 (Correct answer)
- (x − 1)/2
- 2x + 1
- 1/(2x − 1)
Correct answer: (x + 1)/2
Let y = 2x−1, swap x and y: x = 2y−1, solve for y: y = (x+1)/2.
Question 5: Which value of k makes 4x² + kx + 9 a perfect square trinomial?
- 12 (Correct answer)
- −12
- 6
- 36
Correct answer: 12
(2x+3)² = 4x²+12x+9, so k = 12 (or −12 for (2x−3)²; 12 listed first).
Question 6: What is the simplified form of (3x⁻²y)/(x³y⁻¹)?
- 3y²/x⁵ (Correct answer)
- 3x/y²
- 3/(x⁵y²)
- 3x⁵/y²
Correct answer: 3y²/x⁵
Combine exponents: 3 · x^(−2−3) · y^(1−(−1)) = 3x⁻⁵y² = 3y²/x⁵.
Question 7: An investment doubles every 6 years. Which equation models the amount A after t years starting at $1,000?
- A = 1000 · 2^(t/6) (Correct answer)
- A = 1000 · 2^(6t)
- A = 1000 · 6^(2t)
- A = 1000 · (t/6)²
Correct answer: A = 1000 · 2^(t/6)
Doubling every 6 years means A = 1000 · 2^(t/6), since at t=6 we get 2¹=2 doublings.
College Math Placement Test Intermediate Algebra 4
Which of the following is equivalent to (x² − 9)/(x² − x − 6)?