College Math Placement Test College Algebra 3 — Questions and Answers
Question 1: What are the zeros of f(x) = x³ - x² - 6x?
- 0, 3, -2 (Correct answer)
- 0, -3, 2
- 1, 3, -2
- 0, 6, -1
Correct answer: 0, 3, -2
Factoring gives x(x-3)(x+2) = 0, so the zeros are x = 0, 3, -2.
Question 2: What is the inverse of the function f(x) = (2x + 1) / (x - 3)?
- f⁻¹(x) = (3x + 1)/(x - 2) (Correct answer)
- (x + 1)/(3x - 2)
- (3x - 1)/(x + 2)
- (2x - 3)/(x + 1)
Correct answer: f⁻¹(x) = (3x + 1)/(x - 2)
Swapping x and y gives x(y-3) = 2y+1, then solving for y yields y = (3x+1)/(x-2).
Question 3: A system of equations has 2x + 3y = 12 and 4x - y = 5. What is the value of x?
- x = 27/14 (Correct answer)
- x = 3
- x = 2
- x = 41/14
Correct answer: x = 27/14
Multiplying the second equation by 3 and adding: 14x = 27, so x = 27/14.
Question 4: Which of the following is a factor of x³ + 8?
- x + 2 (Correct answer)
- x - 2
- x² - 2x + 4
- x² + 2x - 4
Correct answer: x + 2
x³+8 = (x+2)(x²-2x+4) using the sum of cubes formula a³+b³ = (a+b)(a²-ab+b²).
Question 5: If 3^(2x) = 81, what is x?
- 2 (Correct answer)
- 4
- 3
- 1
Correct answer: 2
Since 81 = 3⁴, we have 3^(2x) = 3⁴, so 2x = 4 and x = 2.
Question 6: What is the sum of the geometric series 3 + 6 + 12 + ... + 384?
- 765 (Correct answer)
- 768
- 762
- 384
Correct answer: 765
With a₁=3, r=2, and last term 384=3·2^7, n=8 terms; S = 3(2⁸-1)/(2-1) = 3·255 = 765.
Question 7: The graph of which equation is a circle with center (-1, 4) and radius 5?
- (x+1)² + (y-4)² = 25 (Correct answer)
- (x-1)² + (y+4)² = 25
- (x+1)² + (y-4)² = 5
- (x-1)² + (y-4)² = 25
Correct answer: (x+1)² + (y-4)² = 25
The standard form (x-h)²+(y-k)²=r² with h=-1, k=4, r=5 gives (x+1)²+(y-4)²=25.
College Math Placement Test College Algebra 3
What are the zeros of f(x) = x³ - x² - 6x?