DSST Mathematics 4 — Questions and Answers
Question 1: What is the domain of f(x) = √(x² - 9)?
- x ≤ -3 or x ≥ 3 (Correct answer)
- x > 3 only
- -3 ≤ x ≤ 3
- All real numbers
Correct answer: x ≤ -3 or x ≥ 3
We need x² - 9 ≥ 0, so x² ≥ 9, giving x ≤ -3 or x ≥ 3.
Question 2: A car travels 150 miles in 2.5 hours. What is its average speed in miles per hour?
- 60 mph (Correct answer)
- 55 mph
- 65 mph
- 75 mph
Correct answer: 60 mph
Average speed = distance / time = 150 / 2.5 = 60 mph.
Question 3: What is the 10th term of the arithmetic sequence 3, 7, 11, 15, ...?
- 39 (Correct answer)
- 43
- 35
- 41
Correct answer: 39
The common difference is 4; aₙ = 3 + (n-1)·4 = 3 + 9·4 = 39.
Question 4: If f(x) = 2x + 1 and g(x) = x², what is f(g(3))?
- 19 (Correct answer)
- 13
- 49
- 7
Correct answer: 19
g(3) = 9, then f(9) = 2(9) + 1 = 19.
Question 5: Which of the following is equivalent to (x² - 4) / (x - 2) for x ≠ 2?
- x + 2 (Correct answer)
- x - 2
- x² + 2
- 2 - x
Correct answer: x + 2
x² - 4 factors as (x-2)(x+2), so the expression simplifies to x + 2.
Question 6: A rectangle has a perimeter of 36 cm and a width of 6 cm. What is its area?
- 72 cm² (Correct answer)
- 108 cm²
- 36 cm²
- 54 cm²
Correct answer: 72 cm²
Perimeter = 2(l + w): 36 = 2(l + 6), so l = 12; Area = 12 × 6 = 72 cm².
Question 7: What is the probability of rolling a sum of 7 with two standard six-sided dice?
- 1/6 (Correct answer)
- 1/12
- 7/36
- 1/4
Correct answer: 1/6
There are 6 favorable outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 total, giving 6/36 = 1/6.
DSST Mathematics 4
What is the domain of f(x) = √(x² - 9)?