Further Mathematics PROGRAMME
Contents
| Further Mathematics | |
|---|---|
| 1- Algebraic methods 1.1 Proof by contradiction 1.2 Algebraic fractions 1.3 Partial fractions 1.4 Repeated factors 1.5 Algebraic division 2- Functions and graphs 2.1 The modulus function 2.2 Functions and mappings 2.3 Composite functions 2.4 Inverse functions 2.5 y = |f(x)| and y = f(|x|) 2.6 Combining transformations 2.7 Solving modulus problems 3- Sequences and series 3.1 Arithmetic sequences 3.2 Arithmetic series 3.3 Geometric sequences 3.4 Geometric series 3.5 Sum to infinity 3.6 Sigma notation 3.7 Recurrence relations 3.8 Modelling with series 4- Binomial expansion 4.1 Expanding (1 + x)n 4.2 Expanding (a + bx)n 4.3 Using partial fractions 5- Radians 5.1 Radian measure 5.2 Arc length 5.3 Areas of sectors and segments 5.4 Solving trigonometric equations 5.5 Small angle approximations 6- Trigonometric functions 6.1 Secant, cosecant and cotangent 6.2 Graphs of sec x, cosec x and cot x 6.3 Using sec x, cosec x and cot x 6.4 Trigonometric identities 7- Trigonometry and modelling 7.1 Addition formulae 7.2 Using the angle addition formulae 7.3 Double-angle formulae 7.4 Solving trigonometric equations 7.5 Simplifying a cos x ± b sin x 7.6 Proving trigonometric identities 7.7 Modelling with trigonometric functions |
8- Parametric equations 8.1 Parametric equations 8.2 Using trigonometric identities 8.3 Curve sketching 8.4 Points of intersection 8.5 Modelling with parametric equations 9- Differentiation 9.1 Differentiating sin x and cos x 9.2 Differentiating exponentials and logarithms 9.3 The chain rule 9.4 The product rule 9.5 The quotient rule 9.6 Differentiating trigonometric functions 9.7 Parametric differentiation 9.8 Implicit differentiation 9.9 Using second derivatives 9.10 Rates of change 10- Numerical methods 10.1 Locating roots 10.2 Iteration 10.3 The Newton–Raphson method 10.4 Applications to modelling 11- Integration 11.1 Integrating standard functions 11.2 Integrating f(ax + b) 11.3 Using trigonometric identities 11.4 Reverse chain rule 11.5 Integration by substitution 11.6 Integration by parts 11.7 Partial fractions 11.8 Finding areas 11.9 The trapezium rule 11.10 Solving differential equations 11.11 Modelling with differential equations 12- Vectors 12.1 3D coordinates 12.2 Vectors in 3D 12.3 Solving geometric problems 12.4 Application to mechanics |
