COMPASS College Algebra and Trigonometry 2 — Questions and Answers
Question 1: If log(x) = 3, what is x?
- 1000 (Correct answer)
- 30
- 300
- 100
Correct answer: 1000
log₁₀(x) = 3 means 10³ = x = 1000.
Question 2: What is the value of tan(45°)?
- 1 (Correct answer)
- √3
- 1/√3
- √2/2
Correct answer: 1
tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1.
Question 3: Which conic section is described by the equation x² + y² = 25?
- Circle (Correct answer)
- Parabola
- Ellipse
- Hyperbola
Correct answer: Circle
An equation of the form x² + y² = r² represents a circle with radius r.
Question 4: Simplify: log(100) + log(10)
- 3 (Correct answer)
- 2
- 1
- 4
Correct answer: 3
log(100) = 2 and log(10) = 1, so 2 + 1 = 3.
Question 5: What are the solutions to x² + 4x + 4 = 0?
- x = −2 (double root) (Correct answer)
- x = 2 and x = −2
- x = −4 and x = 0
- x = 2 (double root)
Correct answer: x = −2 (double root)
x² + 4x + 4 = (x + 2)² = 0, so x = −2 is a repeated root.
Question 6: What is the range of f(x) = x²?
- y ≥ 0 (Correct answer)
- All real numbers
- y > 0
- y ≤ 0
Correct answer: y ≥ 0
x² is always non-negative, so the range is y ≥ 0.
COMPASS College Algebra and Trigonometry 2
If log(x) = 3, what is x?