Free worksheet · Australian Curriculum

Substitution worksheets with answers

Substitution means replacing a letter with its value and working out the answer. Learn the steps, including negatives and powers, then practise with fresh questions and worked solutions.

Make a worksheet ↓How to do it and a quick check ↓

Topic guide

Substitution in algebra, explained

Four rules that get substitution right every time, with an example of each.

1. Replace the letter, using brackets

Write each value in brackets in place of its letter. If $x = 5$ :

$3x + 2 = 3(5) + 2 = 15 + 2 = 17$

The brackets remind you that $3x$ means $3 \times x$ .

2. Follow the order of operations

Brackets, then powers, then multiplication and division, then addition and subtraction. If $a = 4$ and $b = 3$ :

$2a + b^2 = 2(4) + (3)^2 = 8 + 9 = 17$

3. Negative values

Brackets matter most with negatives. If $a = 4$ and $b = -3$ :

$2a - b = 2(4) - (-3) = 8 + 3 = 11$

Subtracting a negative is the same as adding.

4. Powers of negatives

If $x = -4$ , then $x^2 = (-4)^2 = 16$ , because a negative times a negative is positive. But $-x^2$ means the negative of $x^2$ , so $-x^2 = -16$ .

5. Formulas from science and everyday life

Formulas work the same way. To convert $25$ degrees Celsius to Fahrenheit with $F = 1.8C + 32$ :

$F = 1.8(25) + 32 = 45 + 32 = 77$

6. Fractions in expressions

Work out the top and bottom separately, then divide. If $a = 7$ and $b = 11$ :

$\frac{a + b}{2} = \frac{7 + 11}{2} = \frac{18}{2} = 9$

Quick check: 10 questions

Try each one, then open the answer.

Find $4x - 1$ when $x = 3$ .
Answer
$11$
Find $5a + 2b$ when $a = 2$ and $b = 6$ .
Answer
$22$
Find $p^2 + 3$ when $p = 4$ .
Answer
$19$
Find $3m - n$ when $m = -2$ and $n = 5$ .
Answer
$-11$
Find $x^2$ when $x = -5$ .
Answer
$25$
Find $2y^2$ when $y = 3$ .
Answer
$18$
Find $\dfrac{a + b}{2}$ when $a = 7$ and $b = 11$ .
Answer
$9$
Using $v = u + at$ , find $v$ when $u = 4$ , $a = 3$ and $t = 5$ .
Answer
$19$
Using $A = \dfrac{1}{2}bh$ , find the area of a triangle with $b = 12$ and $h = 7$ .
Answer
$42$
Using $F = 1.8C + 32$ , convert $-10$ degrees Celsius to Fahrenheit.
Answer
$14$

Generate a free maths worksheet

Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

Want more than a worksheet?

Practice built from mistakes.

A worksheet on substitution is a good start. Tuterly goes further: it turns any question students get wrong into fresh practice, at the right level, on what’s likely to be in the next test or exam.

~90% of Bayside Academics students using it weekly improved their test marks

Of the Bayside Academics students who used Tuterly at least once a week, about 90% improved their school test marks.

Based on the actual school test marks of 100+ Bayside Academics students (in person and online) in Years 7 to 10, before and after using Tuterly at least once a week. How we measured this

Free worksheet Tuterly

The questionsFree worksheetThe same questions for every student on this topic.TuterlyWritten from the questions they got wrong in homework and school tests, at their level.

How manyFree worksheetOne sheet at a time.TuterlyAs many fresh questions as they need, each one different, never just the numbers swapped.*

Before a testFree worksheetPick a topic and hope it’s the right one.TuterlyA practice test covering every part of the topic. Upload the term planner and it focuses on what’s coming up.

MarkingFree worksheetCheck the answer key yourself.TuterlyMarked as they go, with the exact step that went wrong explained.

ProgressFree worksheetNothing is saved.TuterlyEvery question tracked until it’s mastered, and a weekly review for parents.

For Years 7 to 10: $8.99 a week or $29.99 a month at the launch price (from 1 April 2027, $17.99 a week or $59.99 a month), with a 7-day free trial on the monthly plan only. Better marks in 6 months, or your money back.

Or try it free now on one of their questions →

Coming soon on iPhone. Android soon after.

Free to download · 7-day free trial on monthly · Years 7 to 10 maths · On iPhone. Android coming soon

* Fair use applies with subscriptions.

These topic pages cover this skill, with worked examples, common mistakes and a question to try.

Year 7 worksheetAlgebra Year 7 worksheetExpressions and the distributive law Year 8 worksheetAlgebra Year 10 worksheetSubstituting and rearranging formulas

Questions

What does substitution mean in algebra?

It means replacing each letter in an expression or formula with a given number, then working out the value.

Why use brackets when substituting?

Brackets keep negative numbers and powers correct. For example, if x is negative 4, x squared is 16, which you only get by squaring the whole of negative 4.

What year is substitution taught?

Substitution into formulas is introduced in Year 7 in the Australian Curriculum and used in every later year of algebra and science.

More skill worksheets

Skill worksheetFraction Skill worksheetArea of composite shapes Skill worksheetArea of a triangle Skill worksheetAdding fractions Skill worksheetDividing fractions Skill worksheetExpanding brackets Skill worksheetTwo-step equations Skill worksheetAngles on parallel lines

Better maths marks start with the next wrong answer.

Tuterly turns every missed maths question into practice tailored towards the student, not just a generic worksheet.