Practice Constant vs Variable in Math

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

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Quick Recap

Constants are symbols with fixed, unchanging values; variables are symbols whose values can change or are yet to be determined.

π≈3.14159 is always the same (constant). x can be anything (variable).

Showing a random 20 of 50 problems.

Example 1

challenge
In the equation ax+b=0 with a≠0 constant and b constant, give a formula for the variable x.

Example 2

medium
In y=mx+b, which symbols are parameters once a specific line is chosen?

Example 3

easy
In 9−2x, list the constants.

Example 4

medium
In A=πr2, classify each symbol.

Example 5

challenge
In y=asin⁡(bx+c)+d, classify each symbol if you study one specific sine curve.

Example 6

easy
In y=7, can y vary?

Example 7

medium
In P=4s for a square, classify P, s, and 4.

Example 8

easy
Is the speed of light c a constant or variable in physics?

Example 9

challenge
In f(x)=c for an unknown constant c, what is the rate of change of f, and what is f(100)−f(7)?

Example 10

easy
In 7y−4, identify the variable.

Example 11

easy
In 3x+5, name the constants.

Example 12

easy
In 2r, if r is a length that can change, what is r?

Example 13

medium
In a chemistry formula PV=nRT, identify the constant.

Example 14

easy
In C=2πr, identify the constants and variables.

Example 15

easy
In V=lwh, classify each symbol if a box's dimensions can change.

Example 16

challenge
In y=ax+b, explain why a and b are constants for one line yet behave like variables across the family of all lines.

Example 17

hard
Given y=kx with k a fixed proportionality constant. If (x,y)=(4,12) lies on this graph, find k and then y when x=9.

Example 18

medium
A letter c is a constant in E=mc2 but a variable in y=cx. Explain in one line.

Example 19

easy
Is π a constant or a variable?

Example 20

medium
In h(x)=3, what is the rate of change of the output?
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