CAASPP Algebraic Thinking 4 — Questions and Answers
Question 1: On a graph, a line passes through (0, 2) and (3, 8). What is the rate of change (slope)?
- 2 (Correct answer)
- 3
- 4
- 6
Correct answer: 2
Slope = (8 − 2) ÷ (3 − 0) = 6 ÷ 3 = 2.
Question 2: If p represents pencils and p − 6 = 9, how many pencils are there?
- 3
- 12
- 15 (Correct answer)
- 54
Correct answer: 15
Adding 6 to both sides gives p = 15.
Question 3: Which ordered pair is a solution to y = 3x − 1?
- (2, 4)
- (2, 5) (Correct answer)
- (3, 8)
- (3, 10)
Correct answer: (2, 5)
When x = 2: y = 3(2) − 1 = 5, giving the pair (2, 5).
Question 4: A car travels at a constant speed. After 2 hours it has gone 110 miles. Which equation gives the total distance d after t hours?
- d = 55t (Correct answer)
- d = 110t
- d = t + 55
- d = 2t + 110
Correct answer: d = 55t
The speed is 110 ÷ 2 = 55 mph, so d = 55t.
Question 5: Which expression has the same value as 2(3 + x) − 4?
- 6x − 4
- 2x + 2 (Correct answer)
- 6 + 2x − 4
- x + 6
Correct answer: 2x + 2
2(3 + x) − 4 = 6 + 2x − 4 = 2x + 2.
Question 6: The output of a machine is always 3 less than twice the input. If the input is 10, what is the output?
- 7
- 13
- 17 (Correct answer)
- 23
Correct answer: 17
Output = 2(10) − 3 = 20 − 3 = 17.
Question 7: Which graph best represents the equation y = x?
- A horizontal line at y = 0
- A vertical line at x = 0
- A diagonal line through the origin where x and y are equal (Correct answer)
- A curve that rises quickly
Correct answer: A diagonal line through the origin where x and y are equal
y = x means every point has equal x and y coordinates, forming a diagonal line through the origin.
CAASPP Algebraic Thinking 4
On a graph, a line passes through (0, 2) and (3, 8).
What is the rate of change (slope)?