GCSE Maths Topic Checklist

Every topic in GCSE maths, for AQA (8300) and Edexcel (1MA1). Both boards teach the same content from the Department for Education's subject content list, and use the same topic codes.

Number

• N1Order integers, decimals and fractions; use =, ≠, <, >, ≤, ≥
• N2Add, subtract, multiply and divide integers, decimals, fractions and mixed numbers (positive and negative); place value
• N3Order of operations, including brackets, powers and roots; inverse operations
• N4Primes, factors, multiples, HCF, LCM and prime factorisation (product notation)
• N5Systematic listing of outcomes
• N5The product rule for counting Higher
• N6Powers and roots (square, cube and higher); recognise powers of 2, 3, 4 and 5
• N6Estimate powers and roots of any positive number Higher
• N7Calculate with roots and integer indices
• N7Fractional indices Higher
• N8Calculate exactly with fractions and multiples of π
• N8Surds: calculate exactly, simplify (e.g. √12 = 2√3) and rationalise denominators Higher
• N9Standard form
• N10Convert between terminating decimals and fractions
• N10Convert recurring decimals to fractions and back Higher
• N11Fractions in ratio problems
• N12Fractions and percentages as operators
• N13Standard units, including compound measures
• N14Estimate answers and check calculations by approximation
• N15Round to decimal places or significant figures; error intervals from rounding and truncation
• N16Limits of accuracy
• N16Upper and lower bounds in calculations Higher

Algebra

• A1Algebraic notation (ab, 3y, a², a/b, brackets)
• A2Substitute numbers into formulae and expressions
• A3Vocabulary: expression, equation, formula, identity, inequality, term, factor
• A4Simplify: collect like terms, expand brackets, take out common factors, expand two binomials, factorise x² + bx + c and the difference of two squares, laws of indices
• A4Algebraic fractions; expand three or more binomials; factorise ax² + bx + c Higher
• A5Use formulae; rearrange to change the subject
• A6Equation vs identity; show two expressions are equivalent
• A6Algebraic proof Higher
• A7Functions as inputs and outputs
• A7Inverse and composite functions Higher
• A8Coordinates in all four quadrants
• A9Straight-line graphs: y = mx + c, parallel lines, the line through two points
• A9Perpendicular lines Higher
• A10Gradients and intercepts of straight lines
• A11Quadratic graphs: roots, intercepts and turning points; find roots algebraically
• A11Turning points by completing the square Higher
• A12Recognise and sketch linear, quadratic, simple cubic and reciprocal (y = 1/x) graphs
• A12Exponential graphs (y = kˣ) and trig graphs (sin, cos, tan) for any angle Higher
• A13Translations and reflections of a graph Higher
• A14Real-life graphs, including reciprocal graphs and distance, speed and acceleration
• A14Exponential graphs in real contexts Higher
• A15Gradients and areas under graphs, including curves (distance-time, velocity-time) Higher
• A16Equation of a circle centred at the origin; tangent to a circle at a point Higher
• A17Linear equations, including the unknown on both sides
• A18Quadratic equations by factorising; approximate solutions from a graph
• A18Quadratics by completing the square and the quadratic formula, including ones that need rearranging Higher
• A19Simultaneous equations (linear and linear)
• A19Simultaneous equations (linear and quadratic) Higher
• A20Approximate solutions by iteration Higher
• A21Form and solve equations from a situation, and interpret the answer
• A22Linear inequalities in one variable, shown on a number line
• A22Inequalities in two variables, quadratic inequalities, set notation, regions on a graph Higher
• A23Term-to-term and position-to-term rules
• A24Special sequences: triangular, square, cube, arithmetic, Fibonacci-type, quadratic, simple geometric
• A24Geometric sequences with a surd ratio, and other sequences Higher
• A25nth term of linear sequences
• A25nth term of quadratic sequences Higher

Ratio, proportion and rates of change

• R1Convert between units, including compound units
• R2Scale factors, scale diagrams and maps
• R3One quantity as a fraction of another
• R4Ratio notation; simplest form
• R5Share in a ratio; ratio problems
• R6A relationship between two quantities as a ratio or fraction
• R7Proportion as equality of ratios
• R8Ratios linked to fractions and linear functions
• R9Percentages: change, reverse (original value), simple interest
• R10Direct and inverse proportion problems, including graphs and algebra
• R11Compound units: speed, rates of pay, unit pricing, density, pressure
• R12Compare lengths, areas and volumes using ratio; similarity and scale factors
• R13Inverse proportion as proportional to 1/x; interpret proportion equations
• R13Construct equations for direct and inverse proportion Higher
• R14Gradient as a rate of change; graphs of direct and inverse proportion
• R15Gradient at a point on a curve; average and instantaneous rates of change Higher
• R16Growth and decay, compound interest
• R16General iterative processes Higher

Geometry and measures

• G1Geometric terms and notation, symmetry; draw diagrams from descriptions
• G2Ruler-and-compass constructions and loci
• G3Angle facts: at a point, on a line, vertically opposite, parallel lines, triangles, polygons
• G4Properties of quadrilaterals and triangles
• G5Congruence criteria: SSS, SAS, ASA, RHS
• G6Simple geometric proofs using angle facts, congruence and similarity; Pythagoras
• G7Transformations: rotation, reflection, translation, enlargement (including fractional scale factors)
• G7Enlargement with negative scale factors Higher
• G8Combined transformations and invariance Higher
• G9Circle vocabulary: radius, chord, tangent, arc, sector, segment
• G10Circle theorems, and proofs using them Higher
• G11Geometry problems on coordinate axes
• G12Faces, edges and vertices of 3D shapes
• G13Plans and elevations
• G14Standard units of measure
• G15Measure lines and angles; maps, scale drawings and bearings
• G16Area of triangles, parallelograms and trapezia; volume of prisms, including cylinders
• G17Circumference and area of circles; composite shapes; surface area and volume of spheres, pyramids and cones
• G18Arc length and sector area
• G19Congruence and similarity; lengths in similar shapes
• G19Areas and volumes in similar shapes Higher
• G20Pythagoras and SOHCAHTOA in right-angled triangles
• G20Trigonometry in general triangles and in 3D Higher
• G21Exact values of sin, cos and tan for 0°, 30°, 45°, 60° and 90°
• G22Sine rule and cosine rule Higher
• G23Area = ½ab sin C Higher
• G24Translations as vectors
• G25Add, subtract and scale vectors
• G25Vector proofs Higher

Probability

• P1Outcomes of experiments: frequency tables and frequency trees
• P2Randomness, fairness and expected outcomes
• P3Relative frequency and the 0 to 1 probability scale
• P4Probabilities of all outcomes sum to 1
• P5Bigger samples get closer to the theoretical probability
• P6List outcomes with tables, grids, Venn diagrams and tree diagrams
• P7Sample spaces for combined events
• P8Independent and dependent combined events; tree diagrams
• P9Conditional probability (two-way tables, tree diagrams, Venn diagrams) Higher

Statistics

• S1Samples and their limitations
• S2Tables and charts: bar, pie, pictogram, vertical line, time series
• S3Histograms (equal and unequal widths) and cumulative frequency graphs Higher
• S4Compare distributions: mean, median, mode, modal class, range, outliers
• S4Box plots, quartiles and interquartile range Higher
• S5Describe a population using statistics
• S6Scatter graphs, correlation vs causation, line of best fit