College Math Placement Test College Math Placement Algebra 4 — Questions and Answers
Question 1: Which inequality is represented by the graph of a dashed line y = 2x + 1 with shading above it?
- y ≤ 2x + 1
- y < 2x + 1
- y > 2x + 1 (Correct answer)
- y ≥ 2x + 1
Correct answer: y > 2x + 1
A dashed line means the boundary is excluded, and shading above means y is greater than the line, so y > 2x+1.
Question 2: Simplify: √(50x²)
- 5x√2 (Correct answer)
- 5x²√2
- 10x
- 25x√2
Correct answer: 5x√2
√50=√(25×2)=5√2, and √(x²)=|x|, so the simplified form is 5|x|√2, typically written 5x√2 assuming x≥0.
Question 3: Solve for x: (x/3) + 5 = 9
- x = 12 (Correct answer)
- x = 42
- x = 4
- x = 24
Correct answer: x = 12
Subtract 5: x/3=4; multiply by 3: x=12.
Question 4: What is the vertex of the parabola y = (x − 2)² + 5?
- (2, 5) (Correct answer)
- (−2, 5)
- (2, −5)
- (5, 2)
Correct answer: (2, 5)
The vertex form y=(x−h)²+k gives vertex (h,k)=(2,5).
Question 5: Which value of x satisfies 5x + 3 > 18?
- x = 2
- x = 3
- x = 2.5
- x = 4 (Correct answer)
Correct answer: x = 4
5x > 15 → x > 3; only x=4 satisfies this.
Question 6: Simplify: (4x³ − 8x² + 2x) / (2x)
- 2x² − 4x + 1 (Correct answer)
- 4x² − 4x + 1
- 2x³ − 4x + 1
- 2x² + 4x − 1
Correct answer: 2x² − 4x + 1
Divide each term by 2x: 4x³/2x=2x², −8x²/2x=−4x, 2x/2x=1.
Question 7: If y varies directly with x and y = 12 when x = 4, what is y when x = 7?
- 21 (Correct answer)
- 28
- 14
- 16
Correct answer: 21
The constant k=y/x=12/4=3; when x=7, y=3×7=21.
College Math Placement Test College Math Placement Algebra 4
Which inequality is represented by the graph of a dashed line y = 2x + 1 with shading above it?