Year 7 - Algebra - Free practice

Year 7 Algebra Worksheets & Practice Tests

Variables, substitution, formulas - fresh questions every click, with worked solutions.

Quick answer

How do you use variables and substitute values into formulas in Year 7 algebra?

A variable (pronumeral) is a letter that stands for an unknown number. To use a formula, replace each variable with its given value and calculate. For example, the perimeter of a rectangle is P = 2l + 2w, so when l = 5 and w = 3, P = 2(5) + 2(3) = 16.

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

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Worked examples

Year 7 algebra: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Substituting into a formula
The perimeter of a rectangle is given by the formula $P = 2l + 2w$ . Find $P$ when $l = 9$ and $w = 4$ .
Show worked solution
Key idea: Replace each pronumeral with its given value, then evaluate.
1. Write the formula: $P = 2l + 2w$
2. Substitute $l = 9$ and $w = 4$ : $P = 2 \times 9 + 2 \times 4$
3. Multiply: $P = 18 + 8$
4. Add: $P = 26$
Answer: $P = 26$
Example 2 · Writing and evaluating an algebraic expression
A shop charges a flat booking fee of $5 plus $12 per ticket. Write an expression for the total cost $C$ in dollars for $n$ tickets, then find the cost of buying 7 tickets.
Show worked solution
Key idea: Identify the fixed part and the part that changes with $n$ , then substitute.
1. The cost is a flat $5 plus $12 for each of the $n$ tickets, so $C = 12n + 5$ .
2. Substitute $n = 7$ : $C = 12 \times 7 + 5$
3. Multiply: $C = 84 + 5$
4. Add: $C = 89$
Answer: $C = 12n + 5$ ; the cost for 7 tickets is $89.
Example 3 · Real-life formula problem
A community garden has a rectangular section with a length of $12$ m and a width of $7$ m. Fertiliser costs $3 per square metre. Using the formula for the area of a rectangle $A = l \times w$ , find the area of the section, then calculate the total cost of fertilising it.
Show worked solution
Key idea: First use the area formula to find $A$ , then multiply by the cost per square metre.
1. Write the area formula: $A = l \times w$
2. Substitute $l = 12$ and $w = 7$ : $A = 12 \times 7 = 84$ square metres
3. Write the cost expression: $\text{Cost} = 3 \times A$
4. Substitute $A = 84$ : $\text{Cost} = 3 \times 84 = 252$
Answer: The area is $84$ m² and the total fertiliser cost is $252.

Common mistakes

Where students usually lose marks

Multiplying before adding the constant

$C = 12n + 5$ with $n = 7$ worked as $C = 12 \times (7 + 5) = 144$

Only substitute the value for the pronumeral, then follow the order of operations. The constant $5$ is added after the multiplication: $12 \times 7 + 5 = 89$ .

Confusing the formula for perimeter with area

Finding the perimeter of a rectangle by calculating $P = l \times w$ instead of $P = 2l + 2w$

Perimeter is the total distance around the shape (add all sides), while area is the space inside (multiply length by width). Always check which formula the question is asking you to use.

Forgetting to multiply both terms when using the distributive law

$3(x + 4) = 3x + 4$

Every term inside the brackets must be multiplied by the number outside. The correct expansion is $3(x + 4) = 3x + 12$ .

Writing the expression in the wrong order from a word problem

"5 more than three times a number" written as $5n + 3$ instead of $3n + 5$

Read the problem carefully and match each part to its role: the multiplier goes with the pronumeral and the extra amount is added separately. "Three times a number" means $3n$ , and "5 more than" means add 5, giving $3n + 5$ .

Try one yourself

Your turn

A plumber charges a call-out fee of $80 plus $35 for each hour worked. The total cost in dollars is given by the formula $C = 80 + 35h$ , where $h$ is the number of hours worked. Find the value of $C$ when $h = 4$ .

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About this worksheet

Why we built it

Year 7 is when algebra stops being arithmetic with letters and starts feeling like a language. These worksheets give your student practice writing formulas, substituting values, and rearranging simple expressions - exactly the moves the curriculum expects them to be fluent in by the end of the year.

What's covered

Sub-skills your student will practise

✓Use a pronumeral to represent an unknown
✓Substitute values into formulas (perimeter, area, simple cost equations)
✓Apply the distributive, associative and commutative laws
✓Write algebraic expressions from word problems
✓Tables of values from a rule, plot on the Cartesian plane

From our families

Parents on the practice questions.

“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”

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Year 8 · Maths

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Year 9 · Maths

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Year 10 · Maths

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Frequently asked

Questions parents ask about algebra

What does Year 7 algebra cover in the Australian Curriculum?

Year 7 introduces variables, algebraic expressions, and simple linear equations. Students learn to substitute values into formulas, apply the distributive law, and translate worded problems into algebraic expressions. It's the foundational year before linear equations get harder in Year 8.

What's the most common mistake students make with Year 7 algebra?

Treating variables like labels instead of numbers. When students see 3x + 2 = 14, they often guess instead of working backwards. The fix is lots of practice substituting values and verifying solutions - which is exactly what these worksheets drill.

How long should a Year 7 student spend on algebra each week?

About 30-45 minutes of focused practice per week is enough to keep algebra fluent through the year. Two 15-minute worksheet sessions twice a week works better than one long session.

Do these worksheets follow the Australian Curriculum?

Yes - every question is written to the Year 7 number and algebra content of the Australian Curriculum (Version 9), which every state teaches in some form. Victoria, NSW and WA use their own versions, but the maths at this level is the same.

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