Cambridge · A Level · Syllabus 9231
Further Mathematics
6 topics6 with notes
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Form 5 · Lower 6 2 topics
- Further Pure 1: roots, rational functions, series and induction Sums and products of roots (Σα, Σαβ, αβγ); symmetric functions; Sₙ = αⁿ + βⁿ + γⁿ using recurrence from the equation; transformations (y = 2x, y = x + 1, y = x²).
- Further Pure 1: matrices and polar coordinates 2×2 and 3×3 matrices; determinants and inverses; transformations in 2D (rotations, reflections, enlargements, stretches, shears) and their compositions; invariant points and invariant lines; area scale factor |det|.
Form 6 · Upper 6 2 topicsExam year
- Further Pure 2: hyperbolic functions, further calculus and differential equations Definitions of sinh, cosh, tanh; identities (cosh²x − sinh²x = 1); inverses in logarithmic form; derivatives and integrals including ∫1/√(x² ± a²) dx.
- Further Pure 2: complex numbers and matrices (eigenvalues) (cos θ + i sin θ)ⁿ = cos nθ + i sin nθ; expressing cos nθ and sin nθ in powers of cos θ and sin θ; expressing powers (e.g. sin⁵θ) in multiple angles using z ± 1/z; summing series with complex exponentials.
Form 5 · Lower 6 2 topics
- Further Mechanics Equation of trajectory y = x tan θ − gx²/(2u²cos²θ); range on a horizontal plane; maximum heights and two possible angles to hit a target.
- Further Probability and Statistics Probability density functions; E(X) = ∫xf(x) dx; Var(X) = ∫x²f(x) dx − μ²; cumulative distribution functions; median and percentiles; distribution of functions of a random variable.