Practice Symbolic Abstraction in Math

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

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Quick Recap

Using letter symbols to represent mathematical concepts in a form that holds independent of any specific numerical values.

Instead of $2+3=3+2$ and $5+7=7+5$ , write $a+b=b+a$ for ALL numbers.

Showing a random 20 of 50 problems.

Example 1

challenge

Disprove the claim '

\sqrt{a^2+b^2}=a+b

for all

a,b

' using symbols.

Example 2

medium

Sarah has

\$x

and Tom has

\$10

more. Write Tom's amount.

Example 3

medium

Write 'a number

n

is between

0

and

10

, exclusive' as an inequality.

Example 4

easy

Write an odd integer using integer

k

Example 5

medium

Express 'the average of

a

b

, and

c

' symbolically.

Example 6

medium

Write 'the square of the sum of

a

and

b

Example 7

medium

Write the perimeter of a rectangle with length

\ell

and width

w

Example 8

hard

The volume of a cylinder is

V=\pi r^2 h

. What happens to

V

r

is doubled and

h

is halved?

Example 9

challenge

Show that

n^2-n

is always even for integer

n

, symbolically.

Example 10

medium

Write the sum of three consecutive even integers starting with

2k

Example 11

easy

Write 'four more than twice a number

x

Example 12

medium

The area of a square is

A=s^2

. If the side length is tripled, by what factor does

A

change?

Example 13

medium

g(x)=x^2-1

, find

g(a+1)

in simplified form.

Example 14

easy

Write 'the sum of a number and its square' for variable

x

Example 15

medium

Write 'a two-digit number with tens digit

t

and units digit

u

' symbolically.

Example 16

easy

Write a multiple of

7

using integer

k

Example 17

easy

Write an even number symbolically using integer

k

Example 18

easy

Express 'three less than a number

y

' symbolically.

Example 19

hard

f(x)=x^2

and

g(x)=x+1

, write

f(g(x))

in simplified form.

Example 20

easy

Write the commutative law of addition for all numbers

a

and

b

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Related Concepts

Variables Proofs Generalization