NCDAP Algebraic Concepts & Quantitative Reasoning 5 — Questions and Answers
Question 1: A train travels 360 miles in 4.5 hours. What is its average speed in miles per hour?
- 80 mph (Correct answer)
- 75 mph
- 90 mph
- 60 mph
Correct answer: 80 mph
Speed = distance/time = 360/4.5 = 80 mph.
Question 2: What is the solution set of |2x - 6| = 10?
- x = 8 or x = -2 (Correct answer)
- x = 8 or x = 2
- x = -8 or x = 2
- x = 4 or x = -2
Correct answer: x = 8 or x = -2
2x - 6 = 10 gives x = 8; 2x - 6 = -10 gives x = -2.
Question 3: If y varies directly with x and y = 15 when x = 3, what is y when x = 7?
- 35 (Correct answer)
- 21
- 45
- 5
Correct answer: 35
k = y/x = 15/3 = 5, so y = 5 × 7 = 35.
Question 4: Which graph best represents the inequality y > 2x - 1?
- Dashed line with shading above (Correct answer)
- Solid line with shading above
- Dashed line with shading below
- Solid line with shading below
Correct answer: Dashed line with shading above
Strict inequality (>) uses a dashed boundary line, and 'greater than' shades above the line.
Question 5: Evaluate: 2⁰ + 3⁻¹ + 4¹
- 5 1/3 (Correct answer)
- 8
- 4 1/3
- 6
Correct answer: 5 1/3
2⁰ = 1, 3⁻¹ = 1/3, 4¹ = 4; total = 1 + 1/3 + 4 = 5 1/3.
Question 6: A rectangular garden has a perimeter of 54 feet. If the length is 3 more than twice the width, what is the width?
- 8 feet (Correct answer)
- 13 feet
- 11 feet
- 19 feet
Correct answer: 8 feet
Let w = width, l = 2w + 3; 2(w + 2w + 3) = 54 → 6w + 6 = 54 → w = 8.
Question 7: Which of the following represents a proportional relationship?
- y = 4x (Correct answer)
- y = 4x + 2
- y = x² + 4
- y = 4/x
Correct answer: y = 4x
A proportional relationship has the form y = kx (passes through the origin with no constant).
NCDAP Algebraic Concepts & Quantitative Reasoning 5
A train travels 360 miles in 4.5 hours.
What is its average speed in miles per hour?