NCDAP Algebraic Concepts & Quantitative Reasoning 2 — Questions and Answers
Question 1: Which of the following is equivalent to 3(2x - 4) + 5x?
- 11x - 12 (Correct answer)
- 11x - 4
- 6x - 12
- 11x + 12
Correct answer: 11x - 12
Distribute: 6x - 12 + 5x = 11x - 12.
Question 2: A store sells notebooks for $2.50 each. If a student buys n notebooks and pays with $20, which expression represents the change received?
- 20 - 2.50n (Correct answer)
- 2.50n - 20
- 20 + 2.50n
- 2.50 - 20n
Correct answer: 20 - 2.50n
Change = amount paid minus total cost = 20 - 2.50n.
Question 3: What is the slope of the line passing through (1, 3) and (4, 9)?
- 2 (Correct answer)
- 3
- 1/2
- 6
Correct answer: 2
Slope = (9 - 3)/(4 - 1) = 6/3 = 2.
Question 4: Solve for x: 4x + 7 = 2x - 3
- x = -5 (Correct answer)
- x = 5
- x = -2
- x = 2
Correct answer: x = -5
4x - 2x = -3 - 7 → 2x = -10 → x = -5.
Question 5: If f(x) = x² - 3x + 2, what is f(4)?
- 6 (Correct answer)
- 10
- 14
- 2
Correct answer: 6
f(4) = 16 - 12 + 2 = 6.
Question 6: Which inequality represents 'five less than twice a number is at most 11'?
- 2n - 5 ≤ 11 (Correct answer)
- 2n + 5 ≤ 11
- 5 - 2n ≤ 11
- 2n - 5 ≥ 11
Correct answer: 2n - 5 ≤ 11
'Twice a number' is 2n, 'five less than' subtracts 5, 'at most 11' means ≤ 11.
Question 7: A recipe requires 3/4 cup of sugar per batch. How many cups are needed for 8 batches?
- 6 (Correct answer)
- 5.5
- 7
- 8.25
Correct answer: 6
3/4 × 8 = 24/4 = 6 cups.
NCDAP Algebraic Concepts & Quantitative Reasoning 2
Which of the following is equivalent to 3(2x - 4) + 5x?