11+ Maths · Topic explained
Expressions and substitution
If a = 4, what is 3a + 2?
The big idea
Substitution means swapping each letter for its number, then working out the answer.
Picture it
Like a recipe with a blank: pop the number in, then follow the steps in order.
Key words
- substitute
- Put a number in place of a letter.
- expression
- Numbers and letters with no equals sign, like 3a + 2.
- formula
- A rule linking amounts, like cost = 3 + 2m.
Worked examples
- 1Warm-up
If a = 4, find 3a + 2
- 3a = 3 × 4 = 12
- 12 + 2 = 14
- 211+ standard
If x = 5 and y = 2, find 4x − 3y
- 4x = 4 × 5 = 20
- 3y = 3 × 2 = 6
- 20 − 6 = 14
- 311+ standard
If n = 3, find n² + 2n
- n² = 3 × 3 = 9
- 2n = 2 × 3 = 6
- 9 + 6 = 15
- 411+ standard
A taxi costs C = 3 + 2m pounds for m miles. What does a 7-mile trip cost?
- m = 7: 2m = 14
- C = 3 + 14 = £17
The common mistake
The mistake
If n = 3, then 2n² = 6² = 36.
Instead
Square first: n² = 9, then 2 × 9 = 18.
Why: Powers come before multiplying (BODMAS): the ² belongs to the n only.
Where it comes up in the 11+
Formula questions like 'cost = 3 + 2m', and finding the value of expressions.
The video
Video coming soon
We're making a short video that explains expressions and substitution step by step. Until then, everything it covers is on this page.
Free printable
Expressions and substitution worksheet
Practice questions on this topic to print and try on paper, at home or on the way to school.
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Quick quiz
Have a go first, then tap to see the answer.
1. If p = 6, find 5p − 8.
- 22
- 48
- 57
- 30
Show the answerHide the answer
22
5 × 6 = 30, and 30 − 8 = 22.
2. If a = 3 and b = 4, find ab + b.
- 11
- 16
- 38
- 28
Show the answerHide the answer
16
ab = 3 × 4 = 12, and 12 + 4 = 16.
3. If t = 10, find t ÷ 2 + 7.
- 12
- 8.5
- 17
- 1
Show the answerHide the answer
12
10 ÷ 2 = 5, and 5 + 7 = 12.