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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.

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