DSST Mathematics 5 — Questions and Answers
Question 1: What is the slope of a line perpendicular to y = (3/4)x - 2?
- -4/3 (Correct answer)
- 3/4
- 4/3
- -3/4
Correct answer: -4/3
Perpendicular slopes are negative reciprocals; the reciprocal of 3/4 negated is -4/3.
Question 2: Which expression is equal to (2³)⁴?
- 2¹² (Correct answer)
- 2⁷
- 8⁴
- 2³⁴
Correct answer: 2¹²
Using the power-of-a-power rule: (2³)⁴ = 2^(3×4) = 2¹².
Question 3: What is the median of the data set {4, 8, 15, 16, 23, 42}?
- 15.5 (Correct answer)
- 16
- 18
- 15
Correct answer: 15.5
With six values, the median is the average of the 3rd and 4th: (15 + 16)/2 = 15.5.
Question 4: Simplify: (3x²y)(4xy³)
- 12x³y⁴ (Correct answer)
- 7x³y⁴
- 12x²y³
- 12x³y³
Correct answer: 12x³y⁴
Multiply coefficients (3×4 = 12) and add exponents: x^(2+1) = x³ and y^(1+3) = y⁴.
Question 5: A poll of 200 people shows 60% prefer option A. What is the 95% confidence interval half-width if the margin of error is ±7%?
- 53% to 67% (Correct answer)
- 55% to 65%
- 50% to 70%
- 60% to 67%
Correct answer: 53% to 67%
With a margin of error of ±7%, the interval extends from 60% - 7% = 53% to 60% + 7% = 67%.
Question 6: What is the value of i⁴ where i = √(-1)?
- 1 (Correct answer)
- -1
- i
- -i
Correct answer: 1
i¹ = i, i² = -1, i³ = -i, i⁴ = 1; the powers of i cycle with period 4.
Question 7: What type of conic section is described by x²/9 + y²/4 = 1?
- Ellipse (Correct answer)
- Circle
- Hyperbola
- Parabola
Correct answer: Ellipse
This is the standard form of an ellipse with semi-major axis 3 and semi-minor axis 2.
DSST Mathematics 5
What is the slope of a line perpendicular to y = (3/4)x - 2?