DCAS Algebraic Reasoning 2 — Questions and Answers
Question 1: What is the slope of the line passing through the points (2, 3) and (6, 11)?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Slope = (y₂ - y₁) ÷ (x₂ - x₁) = (11 - 3) ÷ (6 - 2) = 8 ÷ 4 = 2.
Question 2: Solve for x: 2(x + 3) = 14
- 2
- 4 (Correct answer)
- 5
- 8
Correct answer: 4
Distributing gives 2x + 6 = 14; subtracting 6 gives 2x = 8; dividing by 2 gives x = 4.
Question 3: A function is defined as y = 3x + 1. Which ordered pair is NOT a solution?
- (0, 1)
- (1, 4)
- (2, 7)
- (3, 9) (Correct answer)
Correct answer: (3, 9)
For (3, 9): y = 3(3) + 1 = 10, not 9, so this ordered pair does not satisfy the equation.
Question 4: What property is illustrated by: 3(x + 5) = 3x + 15?
- Commutative property
- Associative property
- Distributive property (Correct answer)
- Identity property
Correct answer: Distributive property
The distributive property states a(b + c) = ab + ac, which is shown by 3(x + 5) = 3x + 15.
Question 5: A car travels at a constant speed and covers 150 miles in 3 hours. What is its speed in miles per hour?
- 40
- 45
- 50 (Correct answer)
- 60
Correct answer: 50
Speed = distance ÷ time = 150 ÷ 3 = 50 miles per hour.
Question 6: Which equation represents 'twice a number decreased by 9 equals 15'?
- 2n + 9 = 15
- 2n - 9 = 15 (Correct answer)
- 9 - 2n = 15
- 2(n - 9) = 15
Correct answer: 2n - 9 = 15
'Twice a number' translates to 2n, and 'decreased by 9' means subtract 9, giving 2n - 9 = 15.
Question 7: What is the value of -2³?
- -8 (Correct answer)
- 8
- -6
- 6
Correct answer: -8
-2³ means -(2³) = -(8) = -8, because the exponent applies only to the base 2, not the negative sign.
DCAS Algebraic Reasoning 2
What is the slope of the line passing through the points (2, 3) and (6, 11)?