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.

ฯ€โ‰ˆ3.14159\pi \approx 3.14159 is always the same (constant). xx can be anything (variable).

Showing a random 20 of 50 problems.

Example 1

challenge
In the equation ax+b=0ax + b = 0 with aโ‰ 0a \ne 0 constant and bb constant, give a formula for the variable xx.

Example 2

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

Example 3

easy
In 9โˆ’2x9 - 2x, list the constants.

Example 4

medium
In A=ฯ€r2A=\pi r^2, classify each symbol.

Example 5

challenge
In y=asinโก(bx+c)+dy = a\sin(bx + c) + d, classify each symbol if you study one specific sine curve.

Example 6

easy
In y=7y=7, can yy vary?

Example 7

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

Example 8

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

Example 9

challenge
In f(x)=cf(x) = c for an unknown constant cc, what is the rate of change of ff, and what is f(100)โˆ’f(7)f(100) - f(7)?

Example 10

easy
In 7yโˆ’47y - 4, identify the variable.

Example 11

easy
In 3x+53x+5, name the constants.

Example 12

easy
In 2r2r, if rr is a length that can change, what is rr?

Example 13

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

Example 14

easy
In C=2ฯ€rC = 2\pi r, identify the constants and variables.

Example 15

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

Example 16

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

Example 17

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

Example 18

medium
A letter cc is a constant in E=mc2E=mc^2 but a variable in y=cxy=cx. Explain in one line.

Example 19

easy
Is ฯ€\pi a constant or a variable?

Example 20

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