Every GCSE Maths Topic You Need to Know (AQA, Edexcel, OCR)

The GCSE Maths specification can feel overwhelming. There are dozens of topics across five main areas, spread across Foundation and Higher tiers. This guide breaks it all down clearly — every topic you need to know, across all three main exam boards.

How the Specification Is Organised

All three major GCSE Maths boards — AQA (8300), Edexcel (1MA1) and OCR (J560) — organise content into the same five topic areas:

1. Number
2. Algebra
3. Ratio, Proportion and Rates of Change
4. Geometry and Measures
5. Statistics and Probability

The proportions differ slightly by board and tier, but the core content is almost identical. Foundation tier covers roughly 60% of the full specification. Higher tier covers everything, including additional topics not tested at Foundation.

Number Topics

Number is fundamental to every other topic in GCSE Maths. Weak number skills slow you down across the whole paper.

Foundation and Higher:

• Ordering and comparing integers, decimals and fractions
• Four operations with integers, fractions and decimals
• Percentage increase, decrease and reverse percentages
• Percentage of an amount, expressing one amount as a percentage of another
• Factors, multiples, prime numbers, prime factorisation (HCF and LCM)
• Powers and roots (square, cube, and higher)
• Standard form (writing and calculating with numbers in standard form)
• Rounding — to significant figures, decimal places, nearest integer
• Bounds and error intervals (upper and lower bounds)
• Order of operations — BODMAS

Higher only:

• Indices — fractional and negative indices
• Surds — simplifying, expanding, rationalising the denominator
• Recurring decimals — converting to fractions (e.g. 0.̄3̄ = 1/3)

Algebra Topics

Algebra is the highest-mark topic area on Higher tier papers. It rewards students who practise regularly.

Foundation and Higher:

• Simplifying algebraic expressions
• Expanding single brackets
• Expanding double brackets (FOIL / grid method)
• Factorising — common factor, quadratics at Foundation
• Solving linear equations (one-step, two-step, with brackets, with unknowns on both sides)
• Forming and solving equations from written problems
• Simultaneous equations — elimination method
• Inequalities — solving and representing on a number line
• Sequences — term-to-term, nth term of arithmetic sequences
• Straight-line graphs — y = mx + c, gradient, y-intercept, equation of a line
• Quadratic graphs — plotting and interpreting
• Real-life graphs — distance-time, speed-time, conversion

Higher only:

• Difference of two squares: x² − y² = (x + y)(x − y)
• Solving quadratic equations by factorising, formula and completing the square
• Simultaneous equations — substitution method, one linear one quadratic
• Geometric sequences — nth term, sum
• Functions — function notation, composite functions, inverse functions
• Transformation of graphs — translations, reflections, stretches
• Iteration — using an iterative formula to find approximate solutions
• Algebraic proof
• Completing the square — expressing in the form a(x + p)² + q

Ratio, Proportion and Rates of Change

Foundation and Higher:

• Simplifying ratios, dividing quantities in a given ratio
• Direct proportion — graphs and algebraic form
• Speed, distance and time
• Density, mass and volume
• Pressure, force and area
• Best-buy problems and currency exchange
• Simple interest
• Percentage problems involving increase and decrease

Higher only:

• Inverse proportion — y ∝ 1/x, algebraic and graphical
• Compound interest and depreciation
• Exponential growth and decay
• Algebraic direct and inverse proportion

Geometry and Measures Topics

Foundation and Higher:

• Angle rules — on a straight line, around a point, in a triangle, in polygons
• Angles in parallel lines — alternate, corresponding, co-interior
• Properties of 2D shapes — triangles, quadrilaterals, regular polygons
• Perimeter and area — rectangles, triangles, parallelograms, trapeziums
• Circle area and circumference
• Volume of prisms and cylinders
• Surface area of prisms, pyramids and cylinders
• Pythagoras' theorem — in 2D
• Trigonometry — SOH-CAH-TOA, finding missing sides and angles
• Transformations — translation (vector notation), reflection, rotation, enlargement
• Constructions — perpendicular bisector, angle bisector, triangle constructions
• Loci — equidistant from a point, from a line, from two points
• Similarity — recognising similar shapes, scale factors
• Bearings — three-figure bearings, reading and drawing
• 3D shapes — identifying nets, visualising cross-sections

Higher only:

• Arc length and sector area
• Volume of pyramids, cones and spheres
• 3D Pythagoras and trigonometry
• Sine rule and cosine rule
• Exact trigonometric values (sin 30°, cos 45° etc.)
• Circle theorems — all eight standard theorems
• Congruence — RHS, SAS, AAS, SSS proofs
• Vectors — adding, subtracting, scalar multiplication, proof using vectors

Statistics and Probability Topics

Foundation and Higher:

• Mean, median, mode and range from a list of data
• Mean from a frequency table
• Bar charts, pictograms, pie charts
• Scatter graphs — plotting, correlation, line of best fit, interpolation and extrapolation
• Basic probability — theoretical probability, sample space diagrams
• Combined events — AND/OR rules, tree diagrams
• Relative frequency — from experiments
• Sampling — random sampling, stratified sampling, identifying bias

Higher only:

• Mean from grouped frequency tables (midpoint method)
• Cumulative frequency — drawing and interpreting cumulative frequency graphs
• Box plots — drawing from data, comparing distributions
• Histograms — frequency density, drawing and interpreting
• Conditional probability — P(A | B), two-way tables
• Venn diagrams — set notation (∪, ∩, ξ, A')

How Topics Differ Between Exam Boards

The topic list above covers the full AQA, Edexcel and OCR specifications. The differences between boards are small but worth knowing:

• AQA tends to use functional context questions (real-world situations) more frequently
• Edexcel often includes multi-step problem-solving questions with more marks per question
• OCR accepts a wider range of alternative valid methods and credits partial working more explicitly

In practice, the best preparation is to practise questions from your specific board's past papers — the topic content is almost identical but question style varies.

Using This List as a Revision Checklist

Print this list and tick off topics as you revise them. For each topic, use this three-stage check:

1. ✅ I can explain the method — I understand how and why it works
2. ✅ I can answer a straightforward question — given 5 minutes, I get it right
3. ✅ I can answer it under pressure — timed, no notes, exam conditions

Only move a topic to "done" when it reaches stage 3.

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