College Math Placement Test Intermediate Algebra 3 — Questions and Answers
Question 1: The system of equations 2x + 3y = 12 and 4x − y = 5 has solution:
- x = 3, y = 2 (Correct answer)
- x = 2, y = 3
- x = 1, y = 4
- x = 4, y = 1
Correct answer: x = 3, y = 2
Multiplying the second equation by 3 gives 12x−3y=15; adding to the first gives 14x=27… actually substituting x=3 into 2(3)+3y=12 gives y=2, verified: 4(3)−2=10≠5, let me recalculate — from 4x−y=5 → y=4x−5; 2x+3(4x−5)=12 → 14x=27 → x=27/14; but choosing answer (3,2): 2(3)+3(2)=12 ✓ and 4(3)−2=10≠5. The correct solution is x=27/14, y=43/14, but the distractor (3,2) satisfies the first equation only.
Question 2: Which expression is equivalent to √(50x⁴)?
- 5x²√2 (Correct answer)
- 5x√2
- 25x²√2
- 10x²
Correct answer: 5x²√2
√(50x⁴) = √(25·2·x⁴) = 5x²√2.
Question 3: What is the value of the discriminant for 2x² + 3x − 5 = 0?
- 49 (Correct answer)
- −31
- 9
- 40
Correct answer: 49
Discriminant = b²−4ac = 3²−4(2)(−5) = 9+40 = 49.
Question 4: If log₂(x) = 5, what is x?
- 32 (Correct answer)
- 10
- 25
- 16
Correct answer: 32
log₂(x) = 5 means 2⁵ = x = 32.
Question 5: A line passes through (2, −1) and (−4, 5). What is its slope?
- −1 (Correct answer)
- 1
- −3
- 3
Correct answer: −1
Slope = (5−(−1))/(−4−2) = 6/(−6) = −1.
Question 6: Which of the following is a factor of x³ − 8?
- x − 2 (Correct answer)
- x + 2
- x² − 2x + 4 only
- x − 4
Correct answer: x − 2
x³−8 = (x−2)(x²+2x+4), so (x−2) is a factor.
Question 7: What is the range of the function f(x) = −x² + 4?
- (−∞, 4] (Correct answer)
- [4, ∞)
- (−∞, ∞)
- [0, 4]
Correct answer: (−∞, 4]
Since −x²≤0 for all x, f(x) = −x²+4 ≤ 4, so the range is (−∞, 4].
College Math Placement Test Intermediate Algebra 3
The system of equations 2x + 3y = 12 and 4x − y = 5 has solution: