GCSE Maths
Algebra
revision.
Play this section Linear equations, quadratics, simultaneous equations and graphs, built on the balance method rather than shortcuts.
Algebra guides
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Students type: quadratic graphs GCSE
Open guide Revision guideIteration and trial and improvementStudents type: trial and improvement GCSE
Open guide Revision guideHCF and LCMStudents type: HCF and LCM GCSE
Open guide Revision guideQuadratic sequencesStudents type: quadratic sequences nth term GCSE
Open guide Revision guideFactorising quadraticsStudents type: factorising quadratics GCSE
Open guide Revision guideChanging the subject of a formulaStudents type: changing the subject of a formula GCSE
Open guide Revision guideNth term of linear sequencesStudents type: nth term linear sequence GCSE
Open guide Revision guideInequalities on a lineStudents type: inequalities on a number line GCSE
Open guide Revision guideCompleting the squareStudents type: completing the square GCSE
Open guide Revision guideThe quadratic formulaStudents type: quadratic formula GCSE
Open guide Revision guideSimultaneous equationsStudents type: simultaneous equations elimination GCSE
Open guide Revision guideGraphsStudents type: y = mx + c gradient intercept
Open guideAlgebra
Collect like terms, expand and factorise, and solve linear equations with the balance method: whatever you do to one side, do to the other.
Quadratic equations
Solve ax² + bx + c = 0 by factorising, completing the square, or the quadratic formula, and know how many roots to expect.
Graphs
Plot and interpret y = mx + c, read gradient and intercept, and recognise linear, quadratic and other standard GCSE graphs.
Simultaneous equations
Solve two linear equations together by elimination or substitution, and read the solution as the intersection of two lines.
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.
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.
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.
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.
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.
Factorising quadratics
GCSE Maths factorising quadratics: highest common factor first, then two brackets for x² + bx + c, and grouping when a ≠ 1 — expand every time as a check.
Quadratic sequences
GCSE Maths quadratic sequences: constant second difference, nth term an² + bn + c — find a from half the second difference, then b and c from the first two terms.
HCF and LCM
GCSE Maths HCF and LCM: prime factor trees, index form, the Venn method for two numbers, and HCF × LCM = product for a pair.
Iteration and trial and improvement
GCSE Maths iteration: trial and improvement to find roots of equations, iterative formulas xₙ₊₁ = f(xₙ), and when a solution converges or diverges.
Quadratic graphs
GCSE Maths quadratic graphs: parabola shape, roots, y-intercept, turning point from completing the square, and sketching y = ax² + bx + c.
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