Every topic in AQA GCSE Maths (8300), one short step at a time. Each step has the key ideas, a worked example showing exactly how to set out your working, and quick checks where you type your answer. Each topic ends with an exam-style question and mark scheme. Your progress is saved on your device.
✏️ Before you start
Have paper and a pen ready
Maths is learned by doing, not by reading. Clicking through on screen is not enough. For every step:
- Copy the worked example onto paper, line by line.
- Work out every quick check on paper before you type or pick an answer.
- Write the exam question answer in full, then mark it yourself with the mark scheme.
Keep your working for each topic together. It becomes your revision notes for the exam.
Foundation or Higher? Every step is labelled Foundation and Higher or Higher only, using the AQA specification. On each topic page choose Foundation or Higher at the top: Foundation students can skip the Higher only steps. Steps marked Non-calculator are methods you need for Paper 1.
Number · Algebra · Ratio · Geometry and measures · Probability · Statistics
🔢 Number
1 · Foundation and Higher
Place Value and Calculation
Place value, ordering, negative numbers, BIDMAS, written methods for all four operations, units and estimation.
2 · Foundation and Higher, with some Higher only steps
Factors, Multiples and Primes
Factors, multiples, primes, prime factor trees, index form, HCF and LCM problems, listing outcomes and the product rule for counting.
3 · Foundation and Higher, with some Higher only steps
Fractions and Decimals
Equivalent fractions, mixed numbers, fractions of amounts, the four operations with fractions, decimals, ratio problems and recurring decimals.
4 · Foundation and Higher, with some Higher only steps
Powers, Roots, Indices and Surds
Squares, cubes and roots, the laws of indices, zero and negative powers, then estimating roots, fractional indices and surds for Higher.
5 · Foundation and Higher
Standard Form
Writing big and small numbers in standard form, ordering them, and calculating with and without a calculator.
6 · Foundation and Higher, with some Higher only steps
Rounding, Estimation and Bounds
Rounding to decimal places and significant figures, estimating, error intervals, and upper and lower bounds in calculations for Higher.
🔤 Algebra
7 · Foundation and Higher, with some Higher only steps
Simplifying, Expanding and Factorising
Algebra notation, collecting like terms, index laws, expanding and factorising single and double brackets, quadratics and identities.
8 · Foundation and Higher
Formulae: Substitute and Rearrange
Substituting into expressions and formulae, writing your own formulae, and changing the subject, including powers, roots and the subject appearing twice.
9 · Foundation and Higher
Solving Linear Equations
One-step, two-step, brackets, letters on both sides, fractions, and writing your own equations from words and shapes.
10 · Foundation and Higher, with some Higher only steps
Linear Inequalities
Inequality symbols, number lines, integer solutions, solving linear inequalities, plus set notation, graph regions and quadratic inequalities for Higher.
11 · Foundation and Higher, with some Higher only steps
Sequences
Term-to-term and position-to-term rules, patterns, finding and using the nth term, special sequences, Fibonacci-type, geometric and quadratic sequences.
12 · Foundation and Higher, with some Higher only steps
Straight-Line Graphs
Coordinates, plotting lines, gradient, y = mx + c, parallel lines, the line through two points, real-life graphs and perpendicular lines.
13 · Foundation and Higher, with some Higher only steps
Quadratic Equations and Graphs
Quadratic graphs, roots and turning points, solving by factorising, the quadratic formula and completing the square.
14 · Foundation and Higher, with some Higher only steps
Simultaneous Equations
Solve pairs of equations by elimination, substitution and graphs, write them from words, and (Higher) solve linear and quadratic pairs.
15 · Foundation and Higher, with some Higher only steps
Graphs of Functions
Recognise and plot quadratic, cubic and reciprocal graphs, read real-life and distance–time graphs, and (Higher) exponential and trig graphs, transformations, tangents, areas and circles.
16 · Higher only
Algebraic Fractions, Proof, Functions and Iteration
Simplify and solve with algebraic fractions, write algebraic proofs, use composite and inverse functions, and find roots by iteration.
⚖️ Ratio, proportion and rates of change
17 · Foundation and Higher
Ratio
Simplifying ratios, sharing in a ratio, ratios and fractions, scaling, best buys, mixing problems and combining ratios.
18 · Foundation and Higher, with some Higher only steps
Percentages, Growth and Decay
Percentages of amounts, percentage change, multipliers, reverse percentages, simple and compound interest, depreciation and iterative growth.
19 · Foundation and Higher, with some Higher only steps
Direct and Inverse Proportion
Direct and inverse proportion problems, proportion graphs, gradient as a rate of change, and forming equations like y = kx² and y = k/x.
20 · Foundation and Higher
Units, Compound Measures and Scale
Metric and time units, area and volume conversions, speed, density, pressure, rates of pay, best buys, and scale drawings and maps.
📐 Geometry and measures
21 · Foundation and Higher
Angles and Polygons
Angle facts, parallel lines, triangles and quadrilaterals, interior and exterior angles of polygons, and simple angle proofs.
22 · Foundation and Higher
Constructions, Loci and Bearings
Compass points, three-figure and back bearings, scale drawings, ruler and compass constructions, and loci and regions.
23 · Foundation and Higher, with some Higher only steps
Transformations
Translations with column vectors, reflections, rotations, enlargements with whole, fractional and negative scale factors, and combined transformations.
24 · Foundation and Higher
Perimeter, Area, Circles, Arcs and Sectors
Perimeter and area of rectangles, triangles, parallelograms, trapezia and compound shapes, then circles, semicircles, arcs and sectors, including answers in terms of π.
25 · Foundation and Higher
3D Shapes: Plans, Volume and Surface Area
Faces, edges and vertices, plans and elevations, then volume and surface area of cuboids, prisms, cylinders, spheres, cones, pyramids, frustums and composite solids.
26 · Foundation and Higher, with some Higher only steps
Pythagoras and Trigonometry
Pythagoras’ theorem, SOH CAH TOA for missing sides and angles, exact trig values, elevation and depression, and 3D problems.
27 · Foundation and Higher, with some Higher only steps
Congruence and Similarity
Congruent and similar shapes, the conditions SSS, SAS, ASA and RHS, congruence proofs, missing lengths, and area and volume scale factors.
28 · Higher only
Circle Theorems
Radii and tangents, chords, angle at the centre, semicircles, same segment, cyclic quadrilaterals, alternate segment theorem and proofs.
29 · Higher only
Sine Rule, Cosine Rule and Area of a Triangle
Area = ½ab sin C, the sine rule and cosine rule for sides and angles, the ambiguous case, bearings and 3D trigonometry.
30 · Foundation and Higher, with some Higher only steps
Vectors
Column vectors and translations, adding, subtracting and scaling vectors, vector paths in shapes, and Higher vector proofs.
🎲 Probability
31 · Foundation and Higher
Probability
The probability scale, equally likely outcomes, outcomes adding to 1, listing outcomes, sample spaces, relative frequency, expected outcomes and frequency trees.
32 · Foundation and Higher, with some Higher only steps
Tree Diagrams, Venn Diagrams and Conditional Probability
Sample spaces, Venn diagrams, the AND and OR rules, tree diagrams with and without replacement, set notation and conditional probability.
📊 Statistics
33 · Foundation and Higher, with some Higher only steps
Sampling and Statistical Diagrams
Types of data, sampling, frequency tables, bar charts, pictograms, pie charts, time series, histograms and cumulative frequency graphs.
34 · Foundation and Higher, with some Higher only steps
Averages, Spread and Scatter Graphs
Mean, median, mode and range, averages from tables, comparing data, scatter graphs and correlation, quartiles and box plots.
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