Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Substitution — replacing letters with numbers and evaluating expressions — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise Substitution in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Substitution revision-guide angle, while Tutopiya’s Substitution subtopic page owns the learning resource and the free Substitution quiz owns the practice.

Substitution is one of the most straightforward Algebra skills in Cambridge IGCSE Mathematics (0580/0607) — and one of the easiest places to drop marks through sign errors or wrong order of operations. Examiners give you values for letters and ask you to evaluate an expression or formula. The method is simple: replace, then calculate carefully. This guide explains what Substitution covers, how examiners phrase the questions, and where to practise.

Key takeaways

• Substitution means replacing each letter with its given numerical value, then evaluating.
• Use brackets when substituting negative numbers — e.g. replace x with (−3), not −3 without care.
• Follow BIDMAS after substitution: brackets, indices, division/multiplication, addition/subtraction.
• Substitution follows Changing the Subject of the Formula and supports Simplifying Algebraic Expressions.

What is Substitution in Cambridge IGCSE Maths?

Substitution is the process of replacing variables in an algebraic expression or formula with specific numbers and calculating the result. If y = 2x + 1 and x = 4, then y = 2(4) + 1 = 9. In Cambridge IGCSE Mathematics, questions may involve two or more variables, negative values, fractions or powers. It is a foundation skill tested on its own and embedded inside geometry and science formulas.

Read the full explanation on Tutopiya’s Substitution subtopic page before you attempt questions.

The core steps you must master

Step	Action	Why it matters
1	Write the expression	Keeps the question visible
2	Replace each letter with its value in brackets	Prevents sign errors
3	Apply BIDMAS	Correct order of operations
4	Simplify to the required form	May need fraction or decimal format

How to substitute — step by step

1. Copy the expression exactly as given.
2. Replace every instance of each letter with the given number, using brackets: x = −2 in 3x² means 3(−2)².
3. Evaluate powers before multiplication — (−2)² = 4, then 3 × 4 = 12.
4. Complete addition and subtraction last.
5. Check the required accuracy — decimal places or significant figures if stated.

Test yourself with the free Substitution quiz once the bracket habit is in place.

Positive vs negative substitution: common trap

Given value	Expression	Wrong	Correct
x = −3	2x²	2 × −3² = −18	2(−3)² = 2 × 9 = 18
a = −2, b = 5	a − b	−2 − 5 = 3 (sign error)	−2 − 5 = −7
x = ½	4x + 1	4½ + 1 (ambiguous)	4(½) + 1 = 3

Substitution in past-paper wording: command words that matter

Command word / phrase	What the question wants	Typical stem
Find the value of	Evaluate after substituting	”Find the value of 3a − 2b when a = 5 and b = 2.”
Work out	Same as evaluate	”Work out y when x = −1 and y = 2x² + 3.”
Calculate	Numeric answer, often with accuracy note	”Calculate T correct to 1 decimal place.”
Show that	Substitute given values to verify	”Show that A = 50 when r = 5.”
Hence	Use a previous result then substitute	”Hence find the value when n = 4.”

Worked exam-style stems (how to answer the wording)

1. “Find the value of 2x² − 3y when x = −2 and y = 4.” 2(−2)² − 3(4) = 2(4) − 12 = 8 − 12 = −4. Reward: brackets around −2 before squaring.
2. “Given A = πr², work out A when r = 3. Give your answer correct to 3 significant figures.” A = π × 3² = 9π ≈ 28.3 (3 s.f.). Reward: correct use of π; correct rounding.
3. “Show that s = 20 when u = 0, v = 10 and t = 4 in s = (u + v)t/2.” s = (0 + 10) × 4 / 2 = 40/2 = 20. Reward: full substitution shown; arithmetic correct.

Work similar stems on the Algebra topical past paper questions and the Substitution quiz.

How Substitution connects to the rest of Algebra

Rearranged formulas from Changing the Subject of the Formula are evaluated by substitution. Simplifying before substituting can save effort — see Simplifying Algebraic Expressions. Use the Cambridge IGCSE Maths resource hub for the full Algebra unit.

Common mistakes students make

• Substituting −3 into x² as −3² = −9 instead of (−3)² = 9.
• Forgetting to substitute every occurrence of a letter in the expression.
• Ignoring BIDMAS after substitution — multiplying before squaring.
• Rounding too early when the question specifies accuracy at the end.

When you need more support

If sign or order-of-operations errors persist, work through the Simplifying Algebraic Expressions quiz and the Algebra topical past paper questions, then get help from a Cambridge IGCSE Maths tutor.

Frequently asked questions

Is Substitution hard in Cambridge IGCSE Maths? It is one of the more accessible Algebra topics. Marks are lost through carelessness with negatives and BIDMAS, not through complex theory.

Should I simplify before substituting? If the expression is long, simplifying first can help. If values are given directly, substituting then calculating is usually fine.

Can substitution appear inside other topics? Yes — area formulas, speed-distance-time and trigonometry all require substituting into given formulas.

How do I revise Substitution effectively? Practise ten questions with at least three negative values, always using brackets, then take the Substitution quiz.

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