College Math Placement Test College Math Placement Algebra 5 — Questions and Answers
Question 1: Which expression is equivalent to (x + 3)²?
- x² + 9
- x² + 6x + 9 (Correct answer)
- x² + 3x + 9
- x² + 6x + 6
Correct answer: x² + 6x + 9
(x+3)²=x²+2(3)x+3²=x²+6x+9 using the perfect square formula.
Question 2: Solve: √(2x + 1) = 5
- x = 12 (Correct answer)
- x = 13
- x = 24
- x = 8
Correct answer: x = 12
Square both sides: 2x+1=25 → 2x=24 → x=12; verify √(25)=5 ✓.
Question 3: What is the domain of f(x) = 1/(x − 4)?
- All real numbers
- All real numbers except x = 4 (Correct answer)
- All real numbers except x = −4
- x > 4
Correct answer: All real numbers except x = 4
The denominator cannot be zero, so x−4≠0, meaning x≠4.
Question 4: Which of the following is the solution to the system: y = 2x and y = x + 3?
- (3, 6) (Correct answer)
- (1, 2)
- (3, 3)
- (6, 3)
Correct answer: (3, 6)
Set 2x=x+3 → x=3; then y=2(3)=6, giving (3, 6).
Question 5: Factor: x³ − 8
- (x − 2)(x² + 4)
- (x − 2)(x² + 2x + 4) (Correct answer)
- (x + 2)(x² − 2x + 4)
- (x − 2)³
Correct answer: (x − 2)(x² + 2x + 4)
x³−8 is a difference of cubes: a³−b³=(a−b)(a²+ab+b²)=(x−2)(x²+2x+4).
Question 6: A line has a y-intercept of −3 and passes through (2, 1). What is its equation?
- y = 2x − 3 (Correct answer)
- y = x − 3
- y = 3x − 3
- y = 2x + 1
Correct answer: y = 2x − 3
Slope m=(1−(−3))/(2−0)=4/2=2; using y=mx+b: y=2x−3.
Question 7: Simplify: (3a²b)³
- 9a⁶b³
- 27a⁵b³
- 27a⁶b³ (Correct answer)
- 9a⁵b
Correct answer: 27a⁶b³
Apply the power to each factor: 3³=27, (a²)³=a⁶, b³=b³, giving 27a⁶b³.
College Math Placement Test College Math Placement Algebra 5
Which expression is equivalent to (x + 3)²?