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