Mathematics 0580 · syllabus C2.1, E2.1
Cambridge IGCSE Mathematics 0580 — Formulae and substitution topical past papers
Using letters for numbers, writing expressions and formulas from words, and substituting values, including negatives and fractions, into them.
- Questions
- 115
- Years
- 2009–2026
- With mark scheme
- 99%
- Questions 2022–2026
- 54
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What Formulae and substitution covers
Algebra starts with letters standing for numbers. You write expressions from descriptions, such as 2n + 7 for the cost in dollars of n pens at $2 each and a bag at $7, and formulas that link quantities, such as P = 2l + 2w for the perimeter of a rectangle. You also need the conventions: 3ab means 3 × a × b, n² means n × n, and x/4 means x ÷ 4.
Substitution means replacing each letter with its value and working out the result in the correct order. The values can be negative or fractional, and formulas can come from science or everyday life, such as v = u + at or the cost of hiring a car for a number of days. Without a calculator, a negative value needs care: with x = −2, 3x² = 3 × 4 = 12, because the square of −2 is 4.
This is Core content, so it can be set on all four papers, and much of algebra builds on it: constructing and solving equations, changing the subject, sequences, where a formula gives the nth term, and functions, where substitution is evaluating f(x). Substituting into the formulas on the list provided in every paper, such as the volume of a cone, is part of mensuration too.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- C2.1 Introduction to algebra
- E2.1 Introduction to algebra
What you should be able to do
- Write an expression or formula from a description in words
- Use algebraic conventions, such as 3ab, n² and x/4, correctly
- Substitute positive, negative and fractional values for the letters in an expression or formula
- Evaluate formulas from contexts, such as v = u + at or P = 2l + 2w, with the right units
- Follow the order of operations when substituting, especially with powers and brackets
Key ideas
- A term such as 4x² means 4 × x × x: the power applies to x only, not to the 4
- (−3)² = 9 but −3² = −9, so put a negative value in brackets when substituting
- An expression has no equals sign; a formula links two or more quantities, such as A = πr²
How Formulae and substitution has been examined
From 2022 to 2026, Formulae and substitution was on Paper 3 · Calculator (Core) in 6 of 14 exam series, worth about 3% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Non-calculator (Core) | 18 | 2% | 11 of 14 |
| Paper 2 · Non-calculator (Extended) | 15 | 2% | 7 of 14 |
| Paper 3 · Calculator (Core) | 15 | 3% | 6 of 14 |
| Paper 4 · Calculator (Extended) | 6 | 1% | 3 of 14 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 3.
Filed in Momentum under: Formulae.
A worked example
Find the value of s = ut + ½at² when u = 12, t = 5 and a = −2, and the value of 2x² − 3xy when x = −3 and y = 4.
- Substitute with brackets: s = (12)(5) + ½(−2)(5)².
- Work out the power first: 5² = 25, so s = 60 + ½ × (−2) × 25 = 60 − 25 = 35.
- For the second expression: 2(−3)² − 3(−3)(4).
- (−3)² = 9, so the first term is 18; −3 × −3 × 4 = +36, so the value is 18 + 36 = 54.
Answer: s = 35; 2x² − 3xy = 54
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Squaring the number in front as well as the letter: with x = 5, 2x² is 2 × 25 = 50, not 10² = 100.
- Dropping the sign of a negative value: with a = −4, a² − 3a = 16 + 12 = 28, because −3 × −4 is +12.
- Writing 4 − n for '4 less than n': the phrase means n − 4, as testing with a number such as n = 10 shows.
- Leaving out the units, or giving the wrong ones, when a formula produces a length, an area or a speed.
Exam technique
- Write the formula, then write it again with each value in brackets in place of its letter, then calculate; that line usually earns the method mark.
- Check an expression you have written by trying a simple value for the letter.
- Work out powers before multiplying and dividing, and those before adding and subtracting.
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.