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Demosthenes/Notes/A-level Further Maths

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A-level Further Maths notes

Notes for every topic on the A-level Further 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. Further Pure — Complex numbersA-level Mathematics stops at real numbers, so x^2+1=0 has no solution. Allowing a number i with i^2=-1 gives a system in which every…
  2. Further Pure — MatricesA matrix does two jobs in Further Mathematics. It is a compact way of writing a system of linear equations, so that solving the system…
  3. Further Pure — Algebra and seriesThis topic is about getting answers without finding everything first. The coefficients of a polynomial already know the sum and product of…
  4. Further Pure — CalculusFurther calculus extends A-level techniques in four directions. New derivatives — those of the inverse trigonometric functions — supply…
  5. Further Pure — Polar coordinates and hyperbolic functionsTwo new ways of describing curves and functions. Polar coordinates locate a point by its distance and direction from a fixed pole, which…
  6. Further Pure — Vectors and 3D geometryA-level Mathematics uses vectors in two and three dimensions for positions and directions. Further Mathematics uses them to describe lines…
  7. Further Pure — Differential equationsA-level Mathematics solves differential equations by separating the variables. Further Mathematics adds two systematic methods: the…
  8. Further Statistics — Discrete distributionsA-level Mathematics meets one discrete model in depth, the binomial distribution. Further Statistics begins with counting (OCR 5.01):…
  9. Further Statistics — Hypothesis testingA-level Mathematics tests a single parameter: a binomial proportion or a normal mean. Further Statistics adds two kinds of question. The…
  10. Further Statistics — Continuous distributionsA continuous random variable can take any value in an interval, so its probabilities come from areas rather than sums. A-level Mathematics…
  11. Further Mechanics — Momentum and collisionsA-level Mathematics treats forces as acting over a displacement or a time, but rarely studies very short, very large forces. In a…
  12. Further Mechanics — Circular and rotational motionA-level Mathematics treats particles moving in straight lines under constant forces. Further Mechanics drops both restrictions. A particle…