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AQA GCSE Mathematics revision notes
Concise notes per spec point, written in plain English with worked examples. AI-generated, admin-verified.
- AAlgebra
- A1Use and interpret algebraic notation
- A10Identify and interpret gradients and intercepts of linear functions
- A11Identify roots, intercepts, turning points of quadratics; complete the square
- A12Recognise and sketch linear, quadratic, cubic, reciprocal, exponential and trig graphs
- A13Sketch translations and reflections of a given functionHigher
- A14Plot and interpret real-context graphs; kinematic problems
- A15Calculate or estimate gradients and areas under graphs; interpret in context
- A16Recognise circle equations centred at origin; find tangent equationsHigher
- A17Solve linear equations algebraically and graphically
- A18Solve quadratics by factorising; completing the square; quadratic formula
- A19Solve simultaneous equations: linear/linear; linear/quadraticHigher
- A2Substitute numerical values into formulae and expressions
- A20Find approximate solutions to equations using iterationHigher
- A21Translate situations into algebraic expressions; derive and solve in context
- A22Solve linear inequalities; represent solutions on number lines and graphs
- A23Generate sequences from term-to-term and position-to-term rules
- A24Recognise sequences: triangular, square, cube, Fibonacci, arithmetic, geometric, quadratic
- A25Deduce nth term for linear and quadratic sequencesHigher
- A3Vocabulary of expressions, equations, formulae, inequalities, terms, factors
- A4Simplify expressions: collect like terms, multiply over brackets, factorise; expand binomials; factor quadratics
- A5Use standard mathematical formulae; rearrange to change the subject
- A6Distinguish equations, identities, formulae; argue with algebraic equivalence
- A7Interpret expressions as functions; inverse and composite functionsHigher
- A8Work with coordinates in all four quadrants
- A9Plot linear graphs; y = mx + c; parallel and perpendicular lines
- GGeometry and measures
- G1Conventional terms and notations: points, lines, vertices, planes
- G10Apply and prove standard circle theoremsHigher
- G11Solve geometric problems on coordinate axes
- G12Properties of faces, surfaces, edges and vertices of 3D solids
- G13Interpret and construct plans and elevations of 3D shapes
- G14Standard units of measure: length, area, volume, capacity, mass, time, money
- G15Measure line segments and angles; interpret maps and scale drawings
- G16Formulae for area of triangles, parallelograms, trapezia
- G17Circumference and area of a circle; surface area / volume of spheres, pyramids, conesHigher
- G18Arc lengths, angles and areas of sectors of circlesHigher
- G19Congruence and similarity; areas and volumes in similar figuresHigher
- G2Standard ruler-and-compass constructions
- G20Pythagoras and trigonometric ratios; extension to general triangles in 3DHigher
- G21Exact values of sin θ and cos θ for 0°, 30°, 45°, 60°, 90°Higher
- G22Sine rule and cosine rule for unknown lengths and anglesHigher
- G23Area = ½ab sin C for area, sides or angles of a triangleHigher
- G24Describe translations as 2D vectors
- G25Vector addition, subtraction, scalar multiplication; geometric arguments and proofsHigher
- G3Properties of angles at a point; angles on a straight line; in parallel lines
- G4Properties of special quadrilaterals
- G5Triangle congruence: SSS, SAS, ASA, RHS
- G6Apply angle facts, congruence, similarity and quadrilateral properties
- G7Identify and construct congruent and similar shapes; fractional and negative scale factorsHigher
- G8Changes and invariance under rotation, reflection, translation, enlargement combinations
- G9Circle definitions and properties; tangent, arc, sector, segmentHigher
- NNumber
- N1Order positive and negative integers, decimals and fractions
- N10Convert terminating decimals to fractions; recurring decimals to fractionsHigher
- N11Identify and work with fractions in ratio problems
- N12Interpret fractions and percentages as operators
- N13Use standard units of mass, length, time, money and other measures
- N14Estimate answers; check using approximation and estimation
- N15Round numbers and measures to an appropriate degree of accuracy
- N16Apply and interpret limits of accuracy including upper and lower boundsHigher
- N2Apply the four operations to integers, decimals and simple fractions
- N3Recognise and use inverse operations and relationships between operations
- N4Use vocabulary of primes, factors, multiples; HCF and LCM
- N5Apply systematic listing strategies and the product rule for counting
- N6Use positive integer powers and associated real roots (square, cube, higher)
- N7Calculate with roots and integer indices; fractional indicesHigher
- N8Calculate exactly with fractions, multiples of π, and surdsHigher
- N9Calculate with and interpret standard form A × 10ⁿ
- PProbability
- P1Record, describe and analyse outcome frequencies; tables and frequency trees
- P2Apply randomness, fairness and equally likely events to expected outcomes
- P3Relative expected frequencies vs theoretical probability; 0–1 scale
- P4Probabilities of an exhaustive set of outcomes sum to 1
- P5Empirical samples tend to theoretical distributions with sample size
- P6Enumerate sets and combinations: tables, grids, Venn diagrams
- P7Construct possibility spaces for single and combined experiments
- P8Probability of independent and dependent combined events; tree diagrams
- P9Conditional probabilities via two-way tables, trees, Venn diagramsHigher
- RRatio, proportion and rates of change
- R1Convert between related standard units and compound units
- R10Solve problems involving direct and inverse proportion
- R11Compound units including speed, density, pressure
- R12Compare dimensions using ratio; similarity links
- R13Inverse proportionality; construct equations describing proportionHigher
- R14Interpret gradient as rate of change; proportion graphs
- R15Interpret gradient at a point on a curve as instantaneous rate of changeHigher
- R16Growth and decay; compound interest; iterative processesHigher
- R2Use scale factors, scale diagrams and maps
- R3Express one quantity as a fraction of another
- R4Use ratio notation including reduction to simplest form
- R5Divide quantities into ratio parts; apply ratio to real contexts
- R6Express a multiplicative relationship as ratio or fraction
- R7Understand and use proportion as equality of ratios
- R8Relate ratios to fractions and to linear functions
- R9Percentage change, reverse percentages, problem-solving
- SStatistics
- S1Infer properties of populations from samples; sampling limitations
- S2Tables, charts and diagrams: frequency tables, bar charts, pie charts, pictograms
- S3Diagrams for grouped data: histograms (equal/unequal class widths) and cumulative frequency graphs
- S4Compare distributions; measures of central tendency and spread
- S5Apply statistics to describe a population
- S6Interpret scatter graphs; correlation and causation