Practice Rate of Change (Algebraic) in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The ratio of how much one quantity changes to how much another quantity changes — measured over an interval.

Miles per hour, dollars per item, degrees per minute — change per unit.

Showing a random 20 of 50 problems.

Example 1

hard

A population grows from 5000 to 8000 in 6 years. Express the average growth rate as a percent per year.

Example 2

medium

A line passes through

(a,3)

and

(a+5,18)

. Find the rate of change.

Example 3

medium

A tank drains from 50 L to 20 L in 6 minutes. Find the rate of change of volume.

Example 4

easy

A water tank gains 24 gallons in 8 minutes. Find the rate of change.

Example 5

medium

Two points give

\frac{\Delta y}{\Delta x}=\frac{8}{-4}

. Simplify the rate and interpret its sign.

Example 6

easy

A car travels 150 miles in 3 hours. What is its average rate of change (speed)?

Example 7

medium

Find the average rate of change of

f(x)=2^x

from

x=1

x=4

Example 8

hard

Find the average rate of change of

f(x)=x^2+3x

from

x=a

x=a+h

, in simplest form.

Example 9

challenge

A line through

(1,k)

and

(4,10)

has rate of change 2. Find

k

Example 10

hard

Find the average rate of change of

g(x) = 2x^2 - 3

from

x = -1

x = 3

Example 11

easy

Find the rate of change of the line through

(2,4)

and

(2,9)

Example 12

easy

y=\dfrac{1}{3}x-2

, what is the rate of change?

Example 13

hard

Why can't

f(x)=x^2

have a constant rate of change?

Example 14

easy

A bike rider covers 15 km in 1.5 hours. Average rate of change of distance?

Example 15

easy

A car goes 120 miles in 2 hours. What is its rate (speed)?

Example 16

medium

Find the average rate of change of

f(x)=\dfrac{1}{x}

from

x=1

x=4

Example 17

hard

Find the average rate of change of

f(x)=x^2-4x+1

[-1,3]

Example 18

challenge

On what interval

[1,b]

does

f(x)=x^2

have average rate of change equal to

7

Example 19

medium

Find the rate of change of the line through

(-2,4)

and

(3,-6)

Example 20

easy

Find the rate of change of the line through

(-1,5)

and

(3,5)

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Slope Derivative