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Demosthenes/Notes/A-level Maths

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A-level Maths notes

Notes for every topic on the A-level Mathematics — OCR route specification, with worked examples and key equations. Free to read; create an account to practise each topic with exam questions and timed papers.

  1. Algebra and functionsEverything else in this course rests on fluent algebra: manipulating surds and indices correctly, knowing exactly what the discriminant…
  2. Coordinate geometryCoordinate geometry translates geometric facts — lengths, angles, tangency, parallel and perpendicular relationships — into algebra that…
  3. Sequences, series and the binomial expansionArithmetic and geometric sequences model the two most fundamental patterns of change — constant difference and constant ratio — while the…
  4. TrigonometryA-level trigonometry moves beyond right-angled triangles into radians, identities and equations with multiple solutions across a specified…
  5. Exponentials and logarithmsExponentials describe quantities that grow or decay at a rate proportional to their current size — population, radioactive decay, compound…
  6. DifferentiationDifferentiation formalises the idea of an instantaneous rate of change — the gradient of a curve at a single point rather than the average…
  7. IntegrationIntegration reverses differentiation, and its two roles — finding a function from its gradient, and finding the exact area under a curve —…
  8. Numerical methodsNot every equation can be solved exactly, and not every integral has a closed-form antiderivative — numerical methods find increasingly…
  9. VectorsVectors describe quantities with both magnitude and direction, and in coordinate geometry they give an efficient, coordinate-based way to…
  10. ProofProof is the discipline of establishing that a mathematical statement is true for every case it claims to cover, not merely for the…
  11. Statistics — sampling and dataBefore any statistical claim can be trusted, the data behind it must be gathered and summarised honestly — sampling without bias, and…
  12. Probability and distributionsProbability quantifies uncertainty precisely, and the binomial and normal distributions are the two standard models this course uses to…
  13. Hypothesis testingA hypothesis test formalises how much evidence a data set gives against an assumed value — it does not prove that assumed value false,…
  14. Kinematics and forcesMechanics applies algebra, calculus and vectors to real physical motion and force. The suvat equations describe motion under constant…
  15. Further mechanicsThis topic extends mechanics beyond straight-line motion and simple equilibrium: projectiles combine horizontal and vertical suvat motion,…