NCDAP Elementary Algebra 4 — Questions and Answers
Question 1: Solve for x: x/3 + 4 = 9
- 15 (Correct answer)
- 13
- 39
- 5
Correct answer: 15
Subtracting 4 gives x/3 = 5, then multiplying by 3 gives x = 15.
Question 2: Which expression represents 'twice the sum of a number and 6'?
- 2n + 6
- 2(n + 6) (Correct answer)
- 2n + 12
- n + 12
Correct answer: 2(n + 6)
'Twice the sum' means you multiply the entire sum (n + 6) by 2, giving 2(n + 6).
Question 3: If f(x) = x² - 2x + 1, what is f(3)?
- 2
- 4 (Correct answer)
- 6
- 10
Correct answer: 4
f(3) = 3² - 2(3) + 1 = 9 - 6 + 1 = 4.
Question 4: What is the product of (x + 5)(x - 2)?
- x² - 3x - 10
- x² + 3x - 10 (Correct answer)
- x² + 7x - 10
- x² - 3x + 10
Correct answer: x² + 3x - 10
Using FOIL: x² - 2x + 5x - 10 = x² + 3x - 10.
Question 5: A rectangle has a perimeter of 36 feet. If the width is w, which equation shows the length l?
- l = 36 - w
- l = 18 - w (Correct answer)
- l = 36/w
- l = 18w
Correct answer: l = 18 - w
Perimeter = 2l + 2w = 36, so l + w = 18, giving l = 18 - w.
Question 6: Simplify: (3x³)(4x²)
- 7x⁵
- 12x⁶
- 12x⁵ (Correct answer)
- 7x⁶
Correct answer: 12x⁵
Multiply coefficients: 3 × 4 = 12; add exponents: x³ · x² = x⁵; result is 12x⁵.
Question 7: Which number is NOT a solution to |x - 3| < 2?
- 2
- 4
- 1
- 5 (Correct answer)
Correct answer: 5
|5 - 3| = 2, which is not less than 2, so x = 5 is not a solution.
