NCDAP Algebraic Concepts & Quantitative Reasoning 4 — Questions and Answers
Question 1: Solve the system: x + y = 10 and x - y = 4. What is x?
- 7 (Correct answer)
- 3
- 6
- 4
Correct answer: 7
Adding the equations: 2x = 14 → x = 7.
Question 2: What is the y-intercept of the line 3x - 2y = 12?
- -6 (Correct answer)
- 6
- 4
- -4
Correct answer: -6
Set x = 0: -2y = 12 → y = -6.
Question 3: A population of bacteria doubles every 3 hours. If there are 200 bacteria now, how many will there be in 9 hours?
- 1600 (Correct answer)
- 800
- 1200
- 400
Correct answer: 1600
After 9 hours = 3 doubling periods: 200 × 2³ = 200 × 8 = 1600.
Question 4: Which expression is equivalent to (2x²)³?
- 8x⁶ (Correct answer)
- 6x⁵
- 8x⁵
- 6x⁶
Correct answer: 8x⁶
(2x²)³ = 2³ · x^(2·3) = 8x⁶.
Question 5: Maria scored 78, 85, 92, and 89 on her first four tests. What score does she need on the fifth test to have an average of 87?
- 91 (Correct answer)
- 87
- 85
- 89
Correct answer: 91
(78 + 85 + 92 + 89 + x)/5 = 87 → 344 + x = 435 → x = 91.
Question 6: Which of the following is NOT a function?
- x = y² (Correct answer)
- y = x²
- y = 2x + 1
- y = |x|
Correct answer: x = y²
x = y² fails the vertical line test because one x-value maps to two y-values.
Question 7: Simplify: (4x² - 8x) / (4x)
- x - 2 (Correct answer)
- x + 2
- 4x - 8
- x² - 2x
Correct answer: x - 2
Factor and cancel: 4x(x - 2) / 4x = x - 2.
NCDAP Algebraic Concepts & Quantitative Reasoning 4
Solve the system: x + y = 10 and x - y = 4.
What is x?