NCDAP Elementary Algebra 5 — Questions and Answers
Question 1: What is the value of x if 4x + 3 = 2x + 11?
- 2
- 3
- 4 (Correct answer)
- 7
Correct answer: 4
Subtracting 2x and 3 from both sides gives 2x = 8, so x = 4.
Question 2: A store sells notebooks for $3 each. Maria has $20 and spends d dollars on other items. Which inequality shows how many notebooks n she can buy?
- 3n ≤ 20 + d
- 3n ≥ 20 - d
- 3n ≤ 20 - d (Correct answer)
- 3n + d ≥ 20
Correct answer: 3n ≤ 20 - d
Maria has 20 - d left after other purchases, so 3n ≤ 20 - d.
Question 3: What is the GCF of 12x³ and 18x²?
- 6x
- 6x² (Correct answer)
- 12x²
- 6x³
Correct answer: 6x²
GCF of 12 and 18 is 6; GCF of x³ and x² is x²; so GCF = 6x².
Question 4: If the ratio of boys to girls in a class is 3:4 and there are 21 boys, how many girls are there?
- 24
- 28 (Correct answer)
- 16
- 18
Correct answer: 28
Setting up 3/4 = 21/g gives g = 28.
Question 5: Which equation represents a line parallel to y = 3x - 5?
- y = -3x + 2
- y = 3x + 7 (Correct answer)
- y = (1/3)x - 5
- y = -3x - 5
Correct answer: y = 3x + 7
Parallel lines have the same slope; y = 3x + 7 has slope 3, matching the given line.
Question 6: Simplify: (x² - 4) / (x - 2), assuming x ≠ 2
- x - 2
- x + 2 (Correct answer)
- x² + 2
- x
Correct answer: x + 2
x² - 4 = (x+2)(x-2); dividing by (x-2) cancels that factor, leaving x + 2.
Question 7: A plumber charges a $45 flat fee plus $30 per hour. Which equation gives the total cost C for h hours?
- C = 30 + 45h
- C = 45h - 30
- C = 45 + 30h (Correct answer)
- C = 75h
Correct answer: C = 45 + 30h
Total cost = flat fee + hourly rate × hours = 45 + 30h.
NCDAP Elementary Algebra 5
What is the value of x if 4x + 3 = 2x + 11?