NCDAP Algebraic Concepts & Quantitative Reasoning 3 — Questions and Answers
Question 1: Simplify: (x³ · x⁵) / x⁴
- x⁴ (Correct answer)
- x⁶
- x²
- x¹²
Correct answer: x⁴
x³ · x⁵ = x⁸, then x⁸ / x⁴ = x⁴.
Question 2: Two cars start at the same point. Car A travels north at 55 mph and Car B travels south at 65 mph. How far apart are they after 2 hours?
- 240 miles (Correct answer)
- 120 miles
- 110 miles
- 130 miles
Correct answer: 240 miles
They move in opposite directions: (55 + 65) × 2 = 240 miles.
Question 3: What is the value of |−8| + |3|?
- 11 (Correct answer)
- 5
- -5
- -11
Correct answer: 11
Absolute value gives distance from zero: 8 + 3 = 11.
Question 4: Which of the following equations has a graph that is a horizontal line?
- y = 5 (Correct answer)
- x = 5
- y = 5x
- y = x + 5
Correct answer: y = 5
y = 5 is a horizontal line where every point has y-coordinate 5.
Question 5: Factor completely: x² - 9
- (x - 3)(x + 3) (Correct answer)
- (x - 3)²
- (x + 9)(x - 1)
- (x - 9)(x + 1)
Correct answer: (x - 3)(x + 3)
x² - 9 is a difference of squares: (x - 3)(x + 3).
Question 6: A gym charges a $30 enrollment fee plus $25 per month. Which equation gives total cost C after m months?
- C = 25m + 30 (Correct answer)
- C = 30m + 25
- C = 55m
- C = 25 + 30m
Correct answer: C = 25m + 30
Monthly cost is 25m and the one-time fee is 30, so C = 25m + 30.
Question 7: If 3/5 of a number is 24, what is the number?
- 40 (Correct answer)
- 14.4
- 72
- 8
Correct answer: 40
(3/5)x = 24 → x = 24 × (5/3) = 40.
