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Edexcel GCSE Mathematics revision notes

Concise notes per spec point, written in plain English with worked examples. AI-generated, admin-verified.

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