GCSE Maths

Algebra
revision.

Linear equations, quadratics, simultaneous equations and graphs, built on the balance method rather than shortcuts.

Algebra guides

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Each box is a full revision page. The smaller line is the search students type — not the name of the guide.

Revision guideChanging the subject of a formula

Students type: changing the subject of a formula GCSE

Open guide Revision guideNth term of linear sequences

Students type: nth term linear sequence GCSE

Open guide Revision guideInequalities on a line

Students type: inequalities on a number line GCSE

Open guide Revision guideCompleting the square

Students type: completing the square GCSE

Open guide Revision guideThe quadratic formula

Students type: quadratic formula GCSE

Open guide Revision guideSimultaneous equations

Students type: simultaneous equations elimination GCSE

Open guide Revision guideGraphs

Students type: y = mx + c gradient intercept

Open guide Revision guideQuadratic equations

Students type: quadratic formula GCSE

Open guide Revision guideAlgebra

Students type: how to solve equations GCSE balance method

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01

Algebra

Collect like terms, expand and factorise, and solve linear equations with the balance method: whatever you do to one side, do to the other.

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Quadratic equations

Solve ax² + bx + c = 0 by factorising, completing the square, or the quadratic formula, and know how many roots to expect.

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Graphs

Plot and interpret y = mx + c, read gradient and intercept, and recognise linear, quadratic and other standard GCSE graphs.

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Simultaneous equations

Solve two linear equations together by elimination or substitution, and read the solution as the intersection of two lines.

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05

The quadratic formula

GCSE Maths quadratic formula: write a, b and c including signs, compute the discriminant, keep the ± until the last line, and round only when the question asks.

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Completing the square

GCSE Maths completing the square: rewrite x² + bx + c as (x + p)² + q, read the turning point, and handle a ≠ 1 by factoring a out first.

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Inequalities on a line

GCSE Maths inequalities: solve linear inequalities with the balance method, reverse the sign when multiplying or dividing by a negative, and show the answer on a number line.

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Nth term of linear sequences

GCSE Maths linear sequences: find the common difference, write the nth term as an + b, and use it to generate terms or to decide whether a number is in the sequence.

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Changing the subject of a formula

GCSE Maths changing the subject: use inverse operations in reverse order, including squares, fractions and brackets, and factorise when the new subject appears twice.

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Keep going

More GCSE Maths
in the same style.

GCSE Maths revision that treats method as the mark scheme: reverse percentages, compound interest, quadratic formula, completing the square, SOHCAHTOA, sine and cosine rules, vectors, tree diagrams and histograms, with working shown line by line.

All Maths revision