College Math Placement Test College Algebra 4 — Questions and Answers
Question 1: Which of the following represents a one-to-one function?
- f(x) = x³ (Correct answer)
- f(x) = x²
- f(x) = |x|
- f(x) = sin(x)
Correct answer: f(x) = x³
f(x) = x³ is strictly increasing, so each output corresponds to exactly one input, making it one-to-one.
Question 2: What is the remainder when x⁴ - 3x² + 2 is divided by (x - 1)?
- 0 (Correct answer)
- 1
- 2
- -1
Correct answer: 0
By the Remainder Theorem, substitute x=1: 1 - 3 + 2 = 0, so the remainder is 0.
Question 3: Simplify: (2i)(3 - 4i) where i = √(-1)
- 8 + 6i (Correct answer)
- 6i - 8i²
- 6 - 8i
- -6 + 8i
Correct answer: 8 + 6i
(2i)(3-4i) = 6i - 8i² = 6i + 8 = 8 + 6i, since i² = -1.
Question 4: What is the horizontal asymptote of f(x) = (3x² + 2) / (x² - 5)?
- y = 3 (Correct answer)
- y = 0
- y = -2/5
- No horizontal asymptote
Correct answer: y = 3
When degrees are equal, the horizontal asymptote is the ratio of leading coefficients: y = 3/1 = 3.
Question 5: Solve: 2^(x+1) = 5^x
- x = ln(2)/(ln(5) - ln(2)) (Correct answer)
- x = ln(5)/ln(2)
- x = ln(10)
- x = 1
Correct answer: x = ln(2)/(ln(5) - ln(2))
Taking ln: (x+1)ln2 = x·ln5, so x·ln2 + ln2 = x·ln5, giving x = ln2/(ln5 - ln2).
Question 6: A polynomial has roots x = 2 (multiplicity 2) and x = -1. What is the lowest-degree polynomial with these roots?
- x³ - 3x² + 4 (Correct answer)
- x³ - 3x + 2
- x³ + 3x² - 4
- x² - x - 2
Correct answer: x³ - 3x² + 4
(x-2)²(x+1) = (x²-4x+4)(x+1) = x³-3x²+4, accounting for multiplicity.
Question 7: If log₁₀(x) = 2.5, what is the value of log₁₀(x²)?
- 5 (Correct answer)
- 6.25
- 1.25
- 12.5
Correct answer: 5
log₁₀(x²) = 2·log₁₀(x) = 2(2.5) = 5 by the power rule of logarithms.
College Math Placement Test College Algebra 4
Which of the following represents a one-to-one function?