Practice Variables in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

A symbol (usually a letter like x) that represents an unknown or changing quantity in a mathematical expression.

Like a box that can hold any number. 'x+5=12' asks: what's in the box?

Showing a random 20 of 50 problems.

Example 1

medium
Evaluate 2x+6x when x=2.

Example 2

easy
Do 2x and x⋅2 mean the same thing?

Example 3

medium
Why does x−x=0 for every value of x?

Example 4

challenge
If n is even, explain why n2 is even using a variable.

Example 5

medium
If p is the price of one pencil in dollars, write an expression for the cost of 12 pencils.

Example 6

easy
Write an expression for 'a number n doubled, then added to 5'.

Example 7

challenge
Distinguish the roles of x in f(x)=x2 versus f(3)=9.

Example 8

easy
If x=4, evaluate x+7.

Example 9

medium
If y=3x and x increases from 2 to 3, how much does y increase?

Example 10

hard
Evaluate x2−2xy+y2 when x=4,y=1.

Example 11

easy
Fill in: a ____ is a symbol that stands for an unknown or changing quantity.

Example 12

medium
Evaluate x+yx−y when x=7,y=3.

Example 13

easy
If a stands for apples and b for bananas, what does a+b count?

Example 14

medium
A taxi charges a $3 flat fee plus $2 per mile. Write an expression for the cost of m miles.

Example 15

medium
A variable p represents a price in dollars. Why can't p=−4 here?

Example 16

hard
A bag has n red marbles and 2n+3 blue marbles. Write an expression for the total marbles.

Example 17

hard
If A=πr2 and r=3, find A in terms of π.

Example 18

easy
If 2n=18, what is the value of n?

Example 19

medium
If T=2πL/g, which symbols are variables and which is a constant?

Example 20

hard
The sum of three consecutive integers is 48. Let the smallest be n. Write and solve an equation for n.
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