Algebra 1 Slope and Rate of Change Test with Point Values (PDF)

Algebra 1 math test: Slope and Rate of Change – Maths PDF

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This slope rate of change test for Algebra 1 covers slope and rate of change (Common Core F-IF.B.4, F-IF.B.6, F-LE.A.1b), with a free PDF to print.

This test checks slope and rate of change for Common Core F-IF.B.6, F-IF.B.4, and F-LE.A.1b. It has 9 questions worth 20 points in all, and you have 45 minutes. Write clear steps, because points are awarded for method as well as for the final answer. Leave a few minutes to review.

Time and points

About this test

Grade: Algebra 1
Chapter: Slope and Rate of Change
Standards: F-IF.B.4, F-IF.B.6, F-LE.A.1b
Time: 45 minutes
Total: 20 points

Slope rate of change test: questions

Question 1 – Slope of two points [2 pts]

Find the slope of the line through \((-3, 4)\) and \((5, -2)\). State whether the line rises or falls from left to right.

Question 2 – Slope from a graph [2 pts]

Line for question 2.

Find the slope of the line shown.

Question 3 – Slope from a table [2 pts]

The table shows a linear function: \((1, 10), (3, 4), (5, -2), (7, -8)\). Find its slope.

Question 4 – Missing coordinate [2 pts]

The slope of the line through \((-4, 1)\) and \((4, y)\) is \(\frac{3}{4}\). Find \(y\).

Question 5 – Gas tank rate [2 pts]

Gas in a tank.

Find the rate of change of the gas in the tank and explain what it means.

Question 6 – Average rate of change [2 pts]

A bike’s distance from home in miles is modeled by \(d(t) = t^{2} + 3t\), where \(t\) is in hours. Find the average speed from \(t = 2\) to \(t = 6\).

Question 7 – Canoe trip [3 pts]

A canoe trip.

The graph shows a canoe trip.

On which interval is the canoe not moving? (1 point)
Find the rate of change from hour 2 to hour 4. (1 point)
Find the rate of change from hour 4 to hour 5 and explain its sign. (1 point)

Question 8 – Compare rates [3 pts]

Ethan’s walk.

Ethan’s walk is shown in the table. Priya walks according to \(d = 3.2t\) miles after \(t\) hours.

Find Ethan’s speed. (1 point)
State Priya’s speed. (1 point)
Who walks faster, and by how much? (1 point)

Question 9 – Interpret an equation [2 pts]

A gym charges \(y = 45 + 12x\) dollars for \(x\) months. Interpret the number 12 and the number 45 in this context.

Key facts behind this slope rate of change test

Key facts

Slope = rise ÷ run = (y₂ – y₁)/(x₂ – x₁).
Positive slope rises, negative slope falls, horizontal lines have slope 0, vertical lines are undefined.
In a context, slope is a rate of change with units like dollars per hour.
A linear function has the same rate of change between any two points.
Average rate of change over [a, b] is (f(b) – f(a))/(b – a).

How to use this slope rate of change test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 1 chapters: Algebra 1 math.

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