DCAS Algebraic Reasoning 2

Question 1

What is the slope of the line passing through the points (2, 3) and (6, 11)?

Accepted Answer

2

Answer

Slope = (y₂ - y₁) ÷ (x₂ - x₁) = (11 - 3) ÷ (6 - 2) = 8 ÷ 4 = 2.

Question 2

Solve for x: 2(x + 3) = 14

Accepted Answer

4

Answer

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?

Accepted Answer

(3, 9)

Answer

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?

Accepted Answer

Distributive property

Answer

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?

Accepted Answer

50

Answer

Speed = distance ÷ time = 150 ÷ 3 = 50 miles per hour.

DCAS - Delaware Comprehensive Assessment System Practice Test