College Math Placement Test Intermediate Algebra 2 — Questions and Answers
Question 1: Which of the following is the solution set of |2x − 5| = 9?
- x = 7 or x = −2 (Correct answer)
- x = 7 or x = 2
- x = 14 or x = −4
- x = 2 or x = −7
Correct answer: x = 7 or x = −2
Setting 2x−5=9 gives x=7, and setting 2x−5=−9 gives x=−2.
Question 2: What is the vertex of the parabola y = 2(x − 3)² + 4?
- (3, 4) (Correct answer)
- (−3, 4)
- (3, −4)
- (−3, −4)
Correct answer: (3, 4)
In vertex form y = a(x−h)²+k, the vertex is (h, k) = (3, 4).
Question 3: If f(x) = x² − 4 and g(x) = x + 2, what is (f/g)(x) for x ≠ −2?
- x − 2 (Correct answer)
- x + 2
- x² − 2
- (x−2)(x+2)
Correct answer: x − 2
f(x)/g(x) = (x²−4)/(x+2) = (x−2)(x+2)/(x+2) = x−2 for x ≠ −2.
Question 4: Solve for x: 3^(2x) = 27
- x = 3/2 (Correct answer)
- x = 3
- x = 9
- x = 1/2
Correct answer: x = 3/2
27 = 3³, so 3^(2x) = 3³ means 2x = 3, giving x = 3/2.
Question 5: Which inequality is equivalent to −3x + 6 < 0?
- x > 2 (Correct answer)
- x < 2
- x > −2
- x < −2
Correct answer: x > 2
Subtracting 6 gives −3x < −6, then dividing by −3 (flip sign) gives x > 2.
Question 6: What is the sum of the solutions of x² − 6x + 8 = 0?
- 6 (Correct answer)
- 8
- −6
- 2
Correct answer: 6
By Vieta's formulas, the sum of roots equals −(−6)/1 = 6.
Question 7: Simplify: (2x²y³)³
- 8x⁶y⁹ (Correct answer)
- 6x⁵y⁶
- 8x⁵y⁶
- 6x⁶y⁹
Correct answer: 8x⁶y⁹
Apply the power rule: 2³=8, (x²)³=x⁶, (y³)³=y⁹, giving 8x⁶y⁹.
College Math Placement Test Intermediate Algebra 2
Which of the following is the solution set of |2x − 5| = 9?