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OCR GCSE Mathematics topic questions

Practice questions per spec point, written in board paper style with mark-scheme answers.

  1. A1Use and interpret algebraic notation3 questions →
  2. A10Identify and interpret gradients and intercepts of linear functions3 questions →
  3. A11Identify roots, intercepts, turning points of quadratics; complete the square3 questions →
  4. A12Recognise and sketch linear, quadratic, cubic, reciprocal, exponential and trig graphs3 questions →
  5. A13Sketch translations and reflections of a given function3 questions →
  6. A14Plot and interpret real-context graphs; kinematic problems3 questions →
  7. A15Calculate or estimate gradients and areas under graphs; interpret in context3 questions →
  8. A16Recognise circle equations centred at origin; find tangent equations3 questions →
  9. A18Solve quadratics by factorising; completing the square; quadratic formula4 questions →
  10. A2Substitute numerical values into formulae and expressions3 questions →
  11. A22Solve linear inequalities; represent solutions on number lines and graphs4 questions →
  12. A25Deduce nth term for linear and quadratic sequences4 questions →
  13. A3Vocabulary of expressions, equations, formulae, inequalities, terms, factors3 questions →
  14. A4Simplify expressions: collect like terms, multiply over brackets, factorise; expand binomials; factor quadratics3 questions →
  15. A5Use standard mathematical formulae; rearrange to change the subject3 questions →
  16. A6Distinguish equations, identities, formulae; argue with algebraic equivalence3 questions →
  17. A7Interpret expressions as functions; inverse and composite functions3 questions →
  18. A8Work with coordinates in all four quadrants3 questions →
  19. A9Plot linear graphs; y = mx + c; parallel and perpendicular lines3 questions →
  20. G1Conventional terms and notations: points, lines, vertices, planes3 questions →
  21. G10Apply and prove standard circle theorems3 questions →
  22. G11Solve geometric problems on coordinate axes3 questions →
  23. G12Properties of faces, surfaces, edges and vertices of 3D solids3 questions →
  24. G13Interpret and construct plans and elevations of 3D shapes3 questions →
  25. G14Standard units of measure: length, area, volume, capacity, mass, time, money3 questions →
  26. G15Measure line segments and angles; interpret maps and scale drawings3 questions →
  27. G16Formulae for area of triangles, parallelograms, trapezia3 questions →
  28. G17Circumference and area of a circle; surface area / volume of spheres, pyramids, cones5 questions →
  29. G2Standard ruler-and-compass constructions3 questions →
  30. G20Pythagoras and trigonometric ratios; extension to general triangles in 3D4 questions →
  31. G22Sine rule and cosine rule for unknown lengths and angles4 questions →
  32. G3Properties of angles at a point; angles on a straight line; in parallel lines5 questions →
  33. G4Properties of special quadrilaterals3 questions →
  34. G5Triangle congruence: SSS, SAS, ASA, RHS3 questions →
  35. G6Apply angle facts, congruence, similarity and quadrilateral properties3 questions →
  36. G7Identify and construct congruent and similar shapes; fractional and negative scale factors3 questions →
  37. G8Changes and invariance under rotation, reflection, translation, enlargement combinations3 questions →
  38. G9Circle definitions and properties; tangent, arc, sector, segment3 questions →
  39. N1Order positive and negative integers, decimals and fractions3 questions →
  40. N10Convert terminating decimals to fractions; recurring decimals to fractions3 questions →
  41. N11Identify and work with fractions in ratio problems3 questions →
  42. N12Interpret fractions and percentages as operators3 questions →
  43. N13Use standard units of mass, length, time, money and other measures3 questions →
  44. N14Estimate answers; check using approximation and estimation3 questions →
  45. N15Round numbers and measures to an appropriate degree of accuracy4 questions →
  46. N16Apply and interpret limits of accuracy including upper and lower bounds5 questions →
  47. N2Apply the four operations to integers, decimals and simple fractions3 questions →
  48. N3Recognise and use inverse operations and relationships between operations3 questions →
  49. N4Use vocabulary of primes, factors, multiples; HCF and LCM5 questions →
  50. N5Apply systematic listing strategies and the product rule for counting3 questions →
  51. N6Use positive integer powers and associated real roots (square, cube, higher)5 questions →
  52. N7Calculate with roots and integer indices; fractional indices3 questions →
  53. N8Calculate exactly with fractions, multiples of π, and surds5 questions →
  54. N9Calculate with and interpret standard form A × 10ⁿ5 questions →
  55. P1Record, describe and analyse outcome frequencies; tables and frequency trees3 questions →
  56. P2Apply randomness, fairness and equally likely events to expected outcomes3 questions →
  57. P3Relative expected frequencies vs theoretical probability; 0–1 scale3 questions →
  58. P4Probabilities of an exhaustive set of outcomes sum to 13 questions →
  59. P5Empirical samples tend to theoretical distributions with sample size3 questions →
  60. P6Enumerate sets and combinations: tables, grids, Venn diagrams3 questions →
  61. P7Construct possibility spaces for single and combined experiments3 questions →
  62. P8Probability of independent and dependent combined events; tree diagrams4 questions →
  63. P9Conditional probabilities via two-way tables, trees, Venn diagrams4 questions →
  64. R1Convert between related standard units and compound units3 questions →
  65. R10Solve problems involving direct and inverse proportion4 questions →
  66. R11Compound units including speed, density, pressure4 questions →
  67. R12Compare dimensions using ratio; similarity links3 questions →
  68. R13Inverse proportionality; construct equations describing proportion3 questions →
  69. R14Interpret gradient as rate of change; proportion graphs3 questions →
  70. R15Interpret gradient at a point on a curve as instantaneous rate of change3 questions →
  71. R16Growth and decay; compound interest; iterative processes4 questions →
  72. R2Use scale factors, scale diagrams and maps3 questions →
  73. R3Express one quantity as a fraction of another3 questions →
  74. R4Use ratio notation including reduction to simplest form3 questions →
  75. R5Divide quantities into ratio parts; apply ratio to real contexts3 questions →
  76. R6Express a multiplicative relationship as ratio or fraction3 questions →
  77. R7Understand and use proportion as equality of ratios3 questions →
  78. R8Relate ratios to fractions and to linear functions3 questions →
  79. R9Percentage change, reverse percentages, problem-solving5 questions →
  80. S1Infer properties of populations from samples; sampling limitations3 questions →
  81. S2Tables, charts and diagrams: frequency tables, bar charts, pie charts, pictograms3 questions →
  82. S3Diagrams for grouped data: histograms (equal/unequal class widths) and cumulative frequency graphs4 questions →
  83. S4Compare distributions; measures of central tendency and spread4 questions →
  84. S5Apply statistics to describe a population3 questions →
  85. S6Interpret scatter graphs; correlation and causation4 questions →