MDTP Pre-Calculus 2 — Questions and Answers
Question 1: Which expression equals log(AB)?
- log A × log B
- log A + log B (Correct answer)
- log A - log B
- log(A + B)
Correct answer: log A + log B
The product rule of logarithms states log(AB) = log A + log B.
Question 2: If sin(θ) = 3/5 and θ is in the first quadrant, what is cos(θ)?
- 4/5 (Correct answer)
- 3/4
- 5/4
- 2/5
Correct answer: 4/5
Using the Pythagorean identity: cos(θ) = √(1 - sin²θ) = √(1 - 9/25) = √(16/25) = 4/5.
Question 3: Solve: e^x = 7 (round to nearest hundredth)
- x ≈ 1.95 (Correct answer)
- x ≈ 2.17
- x ≈ 1.84
- x ≈ 0.85
Correct answer: x ≈ 1.95
Taking the natural log of both sides: x = ln(7) ≈ 1.946.
Question 4: The graph of y = f(x - 2) is a shift of y = f(x) in which direction?
- 2 units left
- 2 units right (Correct answer)
- 2 units up
- 2 units down
Correct answer: 2 units right
Replacing x with x - 2 shifts the graph 2 units to the right.
Question 5: What is the value of tan(45°)?
- 0
- 1/2
- 1 (Correct answer)
- √3
Correct answer: 1
tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1.
Question 6: How many solutions does 2sin(x) = 1 have on the interval [0, 2π)?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
sin(x) = 1/2 gives x = π/6 and x = 5π/6, two solutions in [0, 2π).
MDTP Pre-Calculus 2
Which expression equals log(AB)?