Pearson Edexcel International GCSE Mathematics · specification 4MA1 · Paper 1F | Whole paper: Number, Algebra, Geometry, Statistics · Free · no account needed
Expressions, linear equations and formulae (4MA1 specification)
Manipulating algebra reliably: expanding, factorising, solving linear equations and rearranging a formula.
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The 6 Incandio pages that teach this — each explained in full, then proved in marked questions, taught back to an AI pupil and defended in a debate. Completely free.
- Direct & Inverse Proportion — Quantities that scale together, quantities that trade off, and the algebraic y = kx² machinery of Higher Tier proportion.
- Expressions & Index Laws — Collecting like terms and running the index laws on letters — the fluency layer every other algebra module assumes.
- Expanding & Factorising — Brackets out, brackets back in — including the double brackets and quadratic factorising that unlock every quadratic equation.
- Linear Equations — Solving any equation with one unknown — both sides, brackets, fractions — by doing the same thing to both sides, every time.
- Formulae & Rearranging — Substituting into formulae and changing the subject — including the Higher-tier case where the new subject appears twice.
- Algebraic Fractions — Simplifying, combining and solving with fractions whose parts are algebra — factorise first, and they behave exactly like number fractions. Higher Tier.
The teaching routes these belong to: Ratio & Proportion · Algebra — the lessons in order, with every gate.
Specification coverage
2 Equations, formulae and identities — statements 2.1–2.5 (Foundation and Higher Tier)
Assessment objectives: AO1. Suggested learning time: 80 minutes.
Required knowledge
- Understand that symbols may be used to represent numbers in equations and formulae
- Understand and use index laws for positive and negative integer powers, including zero
- Expand brackets and collect like terms
- Factorise, including common factors and quadratic expressions
- Solve linear equations, including those with the unknown on both sides
- Change the subject of a formula
Required skills
- Do the same thing to both sides, every time, and show it
- Factorise by inspection quickly
- Rearrange a formula where the subject appears more than once (Higher)
How it is examined
- Structured questions building from a routine start to a multi-step finish
- Problem-solving questions with no method given
- 'Show that' and reasoning questions where the working IS the answer
Common mistakes
- Forgetting to multiply the second term when expanding a bracket.
- Losing the sign when expanding a negative bracket: −2(x + 4) is −2x − 8, not −2x + 8.
- Rearranging by 'moving things across' without doing it to both sides — this works until it doesn't, usually in the hardest question on the paper.
This page maps the specification. The pages above teach it, and the Mathematics modules hold the whole course — completely free.