COMPASS College Algebra and Trigonometry 1 — Questions and Answers
Question 1: What is log₂(32)?
- 5 (Correct answer)
- 4
- 6
- 3
Correct answer: 5
log₂(32) = 5 because 2⁵ = 32.
Question 2: Solve: e^x = 20 (round to the nearest hundredth)
- 2.996 (Correct answer)
- 1.301
- 4.605
- 2.303
Correct answer: 2.996
Taking the natural log of both sides: x = ln(20) ≈ 2.996.
Question 3: Which of the following is the reciprocal of sin(θ)?
- csc(θ) (Correct answer)
- sec(θ)
- cot(θ)
- tan(θ)
Correct answer: csc(θ)
The reciprocal of sine is cosecant: csc(θ) = 1/sin(θ).
Question 4: What is sin(30°)?
- 1/2 (Correct answer)
- √3/2
- √2/2
- 1
Correct answer: 1/2
sin(30°) = 1/2, a standard value from the unit circle.
Question 5: Find the inverse function of f(x) = 3x + 6
- f⁻¹(x) = (x − 6)/3 (Correct answer)
- f⁻¹(x) = 3x − 6
- f⁻¹(x) = (x + 6)/3
- f⁻¹(x) = x/3 + 6
Correct answer: f⁻¹(x) = (x − 6)/3
Swap x and y, then solve: x = 3y + 6 → y = (x − 6)/3.
Question 6: What is the period of y = cos(2x)?
- π (Correct answer)
- 2π
- π/2
- 4π
Correct answer: π
The period of y = cos(bx) is 2π/b = 2π/2 = π.
COMPASS College Algebra and Trigonometry 1
What is log₂(32)?