DSST Mathematics 2 — Questions and Answers
Question 1: What is the derivative of f(x) = 3x⁴ - 2x² + 5x - 7?
- 12x³ - 4x + 5 (Correct answer)
- 12x³ - 4x + 5 - 7
- 3x³ - 2x + 5
- 12x⁴ - 4x² + 5
Correct answer: 12x³ - 4x + 5
Using the power rule, the derivative is 12x³ - 4x + 5; the constant -7 drops to zero.
Question 2: Which of the following is the solution set of |2x - 3| < 7?
- -2 < x < 5 (Correct answer)
- x < -2 or x > 5
- -5 < x < 2
- x < 5 only
Correct answer: -2 < x < 5
Solving -7 < 2x - 3 < 7 gives -4 < 2x < 10, so -2 < x < 5.
Question 3: A savings account earns 4% annual interest compounded quarterly. What is the effective annual rate (APY)?
- Approximately 4.06% (Correct answer)
- Exactly 4.00%
- Approximately 4.16%
- Approximately 3.96%
Correct answer: Approximately 4.06%
APY = (1 + 0.04/4)⁴ - 1 ≈ 1.0406 - 1 = 4.06%.
Question 4: If sin θ = 3/5 and θ is in the first quadrant, what is tan θ?
- 3/4 (Correct answer)
- 4/3
- 3/5
- 5/3
Correct answer: 3/4
With sin θ = 3/5, cos θ = 4/5 (Pythagorean theorem), so tan θ = sin/cos = 3/4.
Question 5: What is the sum of the infinite geometric series 8 + 4 + 2 + 1 + ...?
- 16 (Correct answer)
- 12
- 8
- Diverges
Correct answer: 16
The common ratio is 1/2, so S = a/(1-r) = 8/(1 - 1/2) = 16.
Question 6: Which matrix operation is NOT generally commutative?
- Matrix multiplication (Correct answer)
- Matrix addition
- Scalar multiplication
- Element-wise addition
Correct answer: Matrix multiplication
Matrix multiplication AB ≠ BA in general, unlike addition which is always commutative.
Question 7: A line has slope -2/3 and passes through (6, 1). What is the y-intercept?
- 5 (Correct answer)
- -3
- 3
- -5
Correct answer: 5
Using y = mx + b: 1 = (-2/3)(6) + b → 1 = -4 + b → b = 5.
DSST Mathematics 2
What is the derivative of f(x) = 3x⁴ - 2x² + 5x - 7?