Turn words into algebra — expressions for costs, ages, perimeters and patterns, and formulae that link quantities. It is a Foundation topic, aimed at grade 2. Free questions with answers are on this page. Worked examples show each line before you try the questions.
An expression is a recipe that still has a letter in it. If Ben is b years old and his sister is 3 years younger, she is b−3, not 3−b (that would make her age go down as Ben gets older, which is nonsense). 'Each', 'lots of' and 'bags of' mean multiply; 'more' and 'total' usually mean add; 'less' and 'younger' mean subtract.
A formula has an equals sign and names the subject: C=8n+2 for the cost of n tickets at £8 plus a £2 fee. The fee is not multiplied by n unless the question says the fee is per ticket.
Read the sentence twice. '3 more than n' is n+3; '3 more than twice n' is 2n+3. Those two are not interchangeable, and they are both regular visitors.
Objectives
n can be the number of tickets.
“4 more than n” is n + 4.
£3 per ticket for n tickets is 3n.
Key points
Write an expression from a description such as 'multiply by 4 then subtract 7'.
Write an expression for a total cost using letters for the prices.
Write and simplify an expression for the perimeter of a shape with algebraic sides.
Write a formula (with an equals sign) linking two quantities, then use it by substituting.
Worked examples
Example 1
Write an expression for 2 more than n.
1 marks
2 more than n means add 2 to n.
Start with n, then add 2.
The expression is n + 2.
Answer: n + 2
Common slips
Slip: 4 more than n means add 2 to n. That changes a number from the question, so it answers a different question.
Slip: Start with n, then add 5. That changes a number in the working, so the step no longer follows from the one before.
Slip: The expression is n + 6. That does not match the working above it.
Example 2
Write an expression for 3 less than n.
1 marks
3 less than n means take 3 away from n.
Start with n, then subtract 3.
The expression is n − 3.
Answer: n − 3
Common slips
Slip: 5 less than n means take 3 away from n. That changes a number from the question, so it answers a different question.
Slip: Start with n, then subtract 6. That changes a number in the working, so the step no longer follows from the one before.
Slip: The expression is n − 7. That does not match the working above it.
Example 3
Pens cost £4 each. Write an expression for the cost, in pounds, of n pens.
1 marks
One pen costs £4, so n pens cost 4 multiplied by n.
Write 4 before the n, with no sign between them.
The expression is 4n.
Answer: 4n
Common slips
Slip: One pen costs £6, so n pens cost 4 multiplied by n. That changes a number from the question, so it answers a different question.
Slip: Write 7 before the n, with no sign between them. That changes a number in the working, so the step no longer follows from the one before.
Slip: The expression is 8n. That does not match the working above it.
Questions and answers
GCSE Maths writing an expression questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Tickets cost £5 each and there is a booking fee of £5. Write an expression for the total cost, in pounds, of n tickets.
Show answer
Answer: 5n + 5
n tickets cost 5n pounds.
The £5 fee is added once, after the tickets.
M1 — n tickets cost 5n pounds.
A1 — Answer 5n + 5
Question 2 Easy2 marks
A number n is 6. Work out 2n + 6.
Show answer
Answer: 18
Replace n with 6: 2n is 2 × 6 = 12.
Add 6: 12 + 6 = 18.
M1 — Replace n with 6: 2n is 2 × 6 = 12.
A1 — Answer 18
Question 3 Medium2 marks
Pens cost £5 each. Write an expression for the cost, in pounds, of n pens.
Show answer
Answer: 5n
One pen costs £5, so n pens cost 5 multiplied by n.
Write 5 before the n, with no sign between them.
M1 — One pen costs £5, so n pens cost 5 multiplied by n.
A1 — Answer 5n
Question 4 Medium2 marks
Tickets cost £2 each and there is a booking fee of £3. Write an expression for the total cost, in pounds, of n tickets.
Show answer
Answer: 2n + 3
n tickets cost 2n pounds.
The £3 fee is added once, after the tickets.
M1 — n tickets cost 2n pounds.
A1 — Answer 2n + 3
Question 5 Hard2 marks
Write an expression for 6 less than n.
Show answer
Answer: n − 6
6 less than n means take 6 away from n.
Start with n, then subtract 6.
M1 — 6 less than n means take 6 away from n.
A1 — Answer n − 6
Question 6 Hard2 marks
Pens cost £2 each. Write an expression for the cost, in pounds, of n pens.
Show answer
Answer: 2n
One pen costs £2, so n pens cost 2 multiplied by n.
Write 2 before the n, with no sign between them.
M1 — One pen costs £2, so n pens cost 2 multiplied by n.
A1 — Answer 2n
Question 7 Exam-style2 marks
Tickets cost £5 each and there is a booking fee of £3. Write an expression for the total cost, in pounds, of n tickets.
Show answer
Answer: 5n + 3
n tickets cost 5n pounds.
The £3 fee is added once, after the tickets.
The expression is 5n + 3.
M1 — n tickets cost 5n pounds.
A1 — Answer 5n + 3
Common mistakes
Most lost marks on this topic are one slip.
Writing “4 more than n” as 4n.
More than means add.
Adding the fee once per item.
A single booking fee is added once, after the product.
Putting in an equals sign when the question asks for an expression.
An expression does not have an answer yet.
Spot the slip
n bags with 4 apples in each bag is written
4n
n + 4
4 + n + 4
Show the slip
4n Equal bags are a product of 4 and n.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Say what your letter stands for if you introduce one (e.g. 'let x be the width in cm').
Simplify your expression fully — an unsimplified perimeter like x+2x+3+x+2x+3 may drop the final mark.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.