MDTP Pre-Calculus 1 — Questions and Answers
Question 1: What is the period of y = sin(2x)?
- π/2
- π (Correct answer)
- 2π
- 4π
Correct answer: π
The period of y = sin(bx) is 2π/b; with b = 2, the period is 2π/2 = π.
Question 2: What is log₂(64)?
- 4
- 6 (Correct answer)
- 8
- 32
Correct answer: 6
log₂(64) = 6 because 2⁶ = 64.
Question 3: Which of the following is an odd function?
- f(x) = x²
- f(x) = x³ (Correct answer)
- f(x) = x² + 1
- f(x) = |x|
Correct answer: f(x) = x³
f(x) = x³ is odd because f(-x) = (-x)³ = -x³ = -f(x).
Question 4: Find the inverse of f(x) = 2x + 6
- f⁻¹(x) = x/2 - 3 (Correct answer)
- f⁻¹(x) = 2x - 6
- f⁻¹(x) = (x-6)/2
- f⁻¹(x) = x/2 + 3
Correct answer: f⁻¹(x) = x/2 - 3
Swapping x and y: x = 2y + 6, solving gives y = (x - 6)/2 = x/2 - 3.
Question 5: Evaluate: sin(90°)
- 0
- 1/2
- √2/2
- 1 (Correct answer)
Correct answer: 1
sin(90°) = 1 is a standard value from the unit circle.
Question 6: What is the amplitude of y = -3cos(x)?
- -3
- 3 (Correct answer)
- 1/3
- 6
Correct answer: 3
Amplitude is the absolute value of the coefficient, |−3| = 3.
MDTP Pre-Calculus 1
What is the period of y = sin(2x)?