NCDAP Elementary Algebra 3 — Questions and Answers
Question 1: What is the solution to the inequality 2x + 5 > 11?
- x > 3 (Correct answer)
- x < 3
- x > 8
- x ≥ 3
Correct answer: x > 3
Subtracting 5 gives 2x > 6, then dividing by 2 gives x > 3.
Question 2: Factor the expression: x² - 9
- (x - 3)(x - 3)
- (x + 3)(x - 3) (Correct answer)
- (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 3: If 5 - 2x = -3, what is x?
- 1
- 4 (Correct answer)
- 3
- -4
Correct answer: 4
Subtracting 5 gives -2x = -8, then dividing by -2 gives x = 4.
Question 4: A train travels at 60 mph. Which equation shows the distance d after t hours?
- d = 60 + t
- d = 60t (Correct answer)
- t = 60d
- d = 60 / t
Correct answer: d = 60t
Distance = rate × time, so d = 60t.
Question 5: Which pair of values (x, y) satisfies both x + y = 7 and x - y = 3?
- (4, 3)
- (5, 2) (Correct answer)
- (6, 1)
- (3, 4)
Correct answer: (5, 2)
Adding the equations gives 2x = 10, so x = 5; then y = 7 - 5 = 2.
Question 6: Evaluate: -3² + (−3)²
- 0 (Correct answer)
- -18
- 18
- -9
Correct answer: 0
-3² = -9 and (-3)² = 9, so -9 + 9 = 0.
Question 7: What is the y-intercept of the line y = -4x + 7?
- -4
- 4
- 7 (Correct answer)
- -7
Correct answer: 7
In slope-intercept form y = mx + b, the y-intercept is b = 7.
NCDAP Elementary Algebra 3
What is the solution to the inequality 2x + 5 > 11?