Expressions, equations, formulae and identities

Algebra is a language. Learn its key words, then practise turning sentences into expressions and formulae.

Practise this lesson free (7 questions)

The key words

A term is a single part, such as 3x or 5.
An expression is terms joined by + or โˆ’, with no equals sign: 3x + 5.
An equation is true only for certain values: 3x + 5 = 20 (only x = 5).
A formula links quantities: A = lw.
An identity is true for every value, written with โ‰ก: 2(x + 3) โ‰ก 2x + 6.

From words to algebra

5 more than n: n + 5
n less than 5: 5 โˆ’ n (order matters)
Double n, then subtract 3: 2n โˆ’ 3
n shared equally between 4: n4
Three times the sum of p and 2: 3(p + 2)

Writing formulae

Decide what each letter stands for, then write the rule.
A taxi charges ยฃ4 plus ยฃ2 for each km. Cost in pounds: C = 4 + 2k.
Perimeter of a rectangle with length l and width w: P = 2l + 2w.
Worked example

Jo has x sweets. Ali has 3 more than twice as many as Jo. Write an expression for the total number of sweets.

  1. Twice Jo's: 2x. Three more: 2x + 3
  2. Total: x + 2x + 3
  3. Collect like terms

Answer: 3x + 3

Key idea

Expressions have no equals sign, equations are true for some values, formulae link quantities, identities are always true. Read word problems carefully: order matters for โˆ’ and รท.

Key words
Term
One part of an expression or sequence. In 3x + 5, the terms are 3x and 5.
Expression
A collection of terms with no equals sign, such as 4a + 3b.
Equation
A statement with an equals sign that is true only for some values of the letter, such as 2x + 1 = 9.
Formula
A rule linking two or more variables, such as A = lw for the area of a rectangle.
Identity
A statement that is true for every value of the letter, such as 2(x + 1) โ‰ก 2x + 2.
Perimeter
The total distance around the outside of a 2-D shape.

All KS3 Mathematics key terms and definitions โ†’

Common mistakes
Quick check

Try two quick questions

See if it has sunk in. Answers are marked straight away.

Extra practice

2 more questions

Try each one, then tap to check.

  1. Which of these is a formula?

    1. 2l + 2 = 10
    2. 2l + 2w
    3. 2(l + 1) โ‰ก 2l + 2
    4. P = 2l + 2w
    Show the answer

    Answer: P = 2l + 2w

    A formula links different quantities, such as perimeter, length and width.

  2. Which of these is true for every value of a?

    1. 5a โˆ’ 1 = 9
    2. 5(a โˆ’ 1) โ‰ก 5a โˆ’ 5
    3. y = 5a โˆ’ 5
    4. 5a โˆ’ 5
    Show the answer

    Answer: 5(a โˆ’ 1) โ‰ก 5a โˆ’ 5

    5(a โˆ’ 1) expands to 5a โˆ’ 5 for all a, so it is an identity.

Check you have got it

Answer 7 quick questions with instant marking. If you get one wrong, GCSE-ready shows you why and gives you another go. It is free, and you do not need an account.

Practise this lesson free (7 questions)All KS3 Mathematics lessons

Video for this lesson coming soon. Subscribe on YouTube

Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.

Related lessons