Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Algebra

Expressions, equations, quadratics, simultaneous equations, inequalities and algebraic fractions. Number and algebra together carry about 60% of the qualification.

Every lesson here ends the same way: learn it, teach it to an AI pupil who asks the awkward question, then defend it against the thinker with the strongest claim on it — free · no account needed.

8 modules of Pearson Edexcel International GCSE Mathematics (1 Higher Tier), each explained in full — what it is, why it works, when a question is asking for it, the mistakes that cost marks and worked examples — with five graded questions marked on your own device. Completely free.

The modules in Algebra

Expressions & Index Laws

Collecting like terms and running the index laws on letters — the fluency layer every other algebra module assumes. A letter stands for a number we haven't chosen yet.

When a question is asking for it: Simplifying is never the whole question — it's the opening move of almost every algebra question. Learn Expressions & Index Laws →

Expanding & Factorising

Brackets out, brackets back in — including the double brackets and quadratic factorising that unlock every quadratic equation. Expanding multiplies brackets out: 3(2x − 5) = 6x − 15; (x + 5)(x − 3) needs every term in the first bracket times every term in the second.

When a question is asking for it: Expand when brackets block you from collecting terms or solving; factorise when you want to SOLVE (a product equal to zero splits into cases) or simplify a fraction. Learn Expanding & Factorising →

Linear Equations

Solving any equation with one unknown — both sides, brackets, fractions — by doing the same thing to both sides, every time. An equation is a balance: whatever the left side weighs, the right side weighs the same.

When a question is asking for it: Directly, in 'solve…' questions. Learn Linear Equations →

Formulae & Rearranging

Substituting into formulae and changing the subject — including the Higher-tier case where the new subject appears twice. A formula is a machine relating quantities: V = πr²h turns radius and height into volume.

When a question is asking for it: Physics-style substitution questions; every 'make … the subject' question; and inside real problems, where the formula you have outputs the wrong thing (you know the volume, you want the radius). Learn Formulae & Rearranging →

Quadratic Equations

Four ways to solve a quadratic — factorising, the formula, completing the square, and reading a graph — why each one works, how to choose between them, and how to reason about how many solutions there are. A quadratic equation can be written ax² + bx + c = 0 (a ≠ 0).

When a question is asking for it: Factorise when integer roots are likely (try it for about thirty seconds). Learn Quadratic Equations →

Simultaneous Equations

Two unknowns, two equations — elimination, substitution, and the Higher-tier pairing of a line with a curve. Two equations that share the same x and y pin down a single pair of values.

When a question is asking for it: Worded price problems ('3 coffees and 2 teas cost…') are elimination in disguise. Learn Simultaneous Equations →

Inequalities

Solving inequalities like equations — with the one extra rule about negatives — and reading off the integers they allow. An inequality states a range rather than a value: 3x + 5 < 17 is solved exactly like an equation, giving x < 4 — every number below 4 works.

When a question is asking for it: 'Solve the inequality' (keep the symbol, not an equals sign), 'find the integers satisfying…' (solve, then LIST), and 'the largest/smallest integer such that…' (solve, then step to the nearest allowed whole number). Learn Inequalities →

Algebraic Fractions (Higher Tier)

Simplifying, combining and solving with fractions whose parts are algebra — factorise first, and they behave exactly like number fractions. Higher Tier. Algebraic fractions follow the same laws as number fractions: cancel common FACTORS, use common denominators to add, cross-multiply to solve.

When a question is asking for it: 'Simplify fully' with quadratics upstairs and down; 'write as a single fraction'; and equations with x in the denominator — multiply through by the denominators and a polynomial equation appears. Learn Algebraic Fractions →

The mistakes that cost marks in Algebra

One from each module — the error examiners see most, with the module that puts it right.

• Collecting unlike terms: 3x + 2y ≠ 5xy. No shared letter part, no collecting. (Expressions & Index Laws)
• Forgetting the second term: 3(2x − 5) = 6x − 5 ✗. The 3 multiplies EVERYTHING inside: 6x − 15. (Expanding & Factorising)
• Doing an operation to one side only. Every operation, both sides, no exceptions. (Linear Equations)
• Substituting into ut + ½at² by squaring at instead of just t. Powers bind to what they touch: ½a(t²). (Formulae & Rearranging)
• Solving x² + 2x − 48 = 45 by factorising the left side as it stands. The zero-product rule needs ZERO on one side — move the 45 first. (Quadratic Equations)
• Subtracting when the matched coefficients have opposite signs. +3y and −3y cancel by ADDING; same signs cancel by subtracting. (Simultaneous Equations)
• Replacing the inequality with '=' and answering x = 4. The symbol IS the answer's shape: x < 4. (Inequalities)
• Cancelling terms instead of factors: crossing off the x²'s in (x² + 5x + 6)/(x² − 4) ✗. Factorise first; cancel brackets, not letters. (Algebraic Fractions)

Where Algebra sits in the specification

Content area 2 of 4MA1, sub-topics 2.1, 2.2, 2.4, 2.3, 2.7, 2.6, 2.8. Incandio is aligned to the specification and is not published by Pearson; the numbers are given so you can check every module against your own copy.

• 2.1 — Use of symbols
• 2.2 — Algebraic manipulation — algebraic fractions (Higher)
• 2.4 — Linear equations
• 2.3 — Expressions and formulae
• 2.7 — Quadratic equations (formula and completing the square: Higher)
• 2.6 — Simultaneous equations (linear/quadratic pairs: Higher)
• 2.8 — Inequalities

How Algebra is mastered on Incandio

Every module above ends the same way: five questions that climb Grade 6 → 9+, then you teach the method back to Ember, an AI pupil who asks the awkward question, and defend it against the mathematician with the strongest claim on it. Exam Ready carries 85 authored exam-style questions across this strand, marked on Incandio.

All of Incandio Mathematics · The 4MA1 specification · Exam Ready