Topics Grade boundaries Exam dates Yumio GCSE Maths Grade 3 Substitution
Substitution – GCSE Maths Foundation and Higher · Grade 3
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On this page Objectives Key points Examples Questions Mistakes Tips Worksheet Replace letters with numbers, including negatives, and evaluate expressions and formulae using BIDMAS. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Substitution is replacing every letter with a number, then evaluating with BIDMAS. Use a bracket for every replacement, especially negatives: 3 x 2 x = − 2 3 ( − 2 ) 2 = 3 × 4 = 12 − 12 − 2
If two letters are given, substitute both in one pass. If the expression is a formula (v = u + a t
Replace every letter with its number, using brackets around negatives: 5 p − 2 q q = − 3 5 ( 4 ) − 2 ( − 3 ) ( − 4 ) 2 = 16 − 16
Objectives If x = 4, 3x + 2 = 3 × 4 + 2. x means 1x. If x = 3, x² + 1 = 9 + 1 = 10. Key points Replace each letter with its value, using brackets for negatives. Apply BIDMAS: brackets, indices, division/multiplication, addition/subtraction. Understand that 3 x 3 × x x 2 x × x Substitute into real formulae such as v = u + a t s = u t + 2 1 a t 2 Worked examples Example 1 x = 2. Work out 3x + 2.
2 marks
Replace x with 2: 3 × 2 + 2. Multiplication comes first: 3 × 2 = 6, so 6 + 2. The value is 8. Answer: 8
Common slips Slip: Replace x with 2: 32 + 2. 3x means 3 × x. It does not put the digits side by side. Slip: Add first: 2 + 2 = 4, so 3 × 4 = 12. Multiplication comes before addition. Slip: The value is 12. That is the value of 3(x + 2), not 3x + 2. Example 2 x = 2. Work out 2x − 1.
2 marks
Replace x with 2: 2 × 2 − 1. Multiplication comes first: 2 × 2 = 4, so 4 − 1. The value is 3. Answer: 3
Common slips Slip: Replace x with 2: 22 − 1. 2x means 2 × x. It does not put the digits side by side. Slip: Subtract first: 2 − 1 = 1, so 2 × 1 = 2. Multiplication comes before subtraction. Slip: The value is 2. That is the value of 2(x − 1), not 2x − 1. Example 3 x = 3. Work out x² + 1.
3 marks
Replace x with 3: 3² + 1. Indices come first: 3² = 9, so 9 + 1. The value is 10. Answer: 10
Common slips Slip: Replace x with 3: 2 × 3 + 1. x² means x × x. It does not mean 2 × x. Slip: Double first: 2 × 3 = 6, so 6 + 1. That doubles x instead of squaring it. Slip: The value is 7. That is the value of 2x + 1, not x² + 1. Questions and answers GCSE Maths substitution questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy 2 marks x = −2. Work out 3x + 2.
Show answer Answer: -4
Replace x with (−2): 3 × (−2) + 2. Multiplication comes first: 3 × (−2) = −6, so −6 + 2. M1 — Replace x with (−2): 3 × (−2) + 2. A1 — Answer -4 Question 2 Easy 2 marks x = 4. Work out 3x + 2.
Show answer Answer: 14
Replace x with 4: 3 × 4 + 2. Multiplication comes first: 3 × 4 = 12, so 12 + 2. M1 — Replace x with 4: 3 × 4 + 2. A1 — Answer 14 Question 3 Medium 2 marks x = −3. Work out 3x + 2.
Show answer Answer: -7
Replace x with (−3): 3 × (−3) + 2. Multiplication comes first: 3 × (−3) = −9, so −9 + 2. M1 — Replace x with (−3): 3 × (−3) + 2. A1 — Answer -7 Question 4 Medium 2 marks x = 6. Work out 3x + 2.
Show answer Answer: 20
Replace x with 6: 3 × 6 + 2. Multiplication comes first: 3 × 6 = 18, so 18 + 2. M1 — Replace x with 6: 3 × 6 + 2. A1 — Answer 20 Question 5 Hard 2 marks x = −4. Work out 3x + 2.
Show answer Answer: -10
Replace x with (−4): 3 × (−4) + 2. Multiplication comes first: 3 × (−4) = −12, so −12 + 2. M1 — Replace x with (−4): 3 × (−4) + 2. A1 — Answer -10 Question 6 Hard 2 marks x = 8. Work out 3x + 2.
Show answer Answer: 26
Replace x with 8: 3 × 8 + 2. Multiplication comes first: 3 × 8 = 24, so 24 + 2. M1 — Replace x with 8: 3 × 8 + 2. A1 — Answer 26 Question 7 Exam-style 3 marks x = −5. Work out 3x + 2.
Show answer Answer: -13
Replace x with (−5): 3 × (−5) + 2. Multiplication comes first: 3 × (−5) = −15, so −15 + 2. The value is −13. M1 — Replace x with (−5): 3 × (−5) + 2. M1 — Multiplication comes first: 3 × (−5) = −15, so −15 + 2. A1 — Answer -13 Common mistakes Most lost marks on this topic are one slip.
Adding the coefficient to x instead of multiplying.
3x means 3 times x.
Squaring the whole expression when only x is squared.
x² + 1 squares x, then adds 1.
Dropping a negative sign on substitution.
If x is negative, the product keeps that sign.
Spot the slip If x = 4, what is 2x?
8 6 24 Show the slip 8 2x means 2 times x.
Exam tips This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark. 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. Write the substituted line with brackets before you calculate anything — it earns a method mark. On a calculator, type negatives inside brackets: ( − 3 ) 2 − 3 2 Printable worksheet The same questions are in a PDF you can print. Answers start on a later page.
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Questions students ask Is Substitution Foundation or Higher? Substitution is on Foundation and Higher, aimed at grade 3.
What is a common slip on Substitution? Adding the coefficient to x instead of multiplying. 3x means 3 times x.
Where can I get Substitution questions and answers? The questions on this page are free. Open Show answer under each one, or download the worksheet PDF. Start free to practise this topic in the app.
Related topics More on Substitution Previous topic Sequences: rules and special sequences Next topic Solving linear equations AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.
Last updated 9 November 2026.