ALevel Further Mathematics

1.1 Roots of polynomial equations

Roots of polynomial equations and their relationships.

1.2 Rational functions and graphs

Rational functions, asymptotes, and sketching.

1.3 Summation of series

Summation of series and method of differences.

1.4 Matrices

Matrices, transformations, and determinants.

1.5 Polar coordinates

Polar coordinates and curves.

1.6 Vectors

Vectors in 2D and 3D, scalar and vector products.

1.7 Proof by induction

Proof by mathematical induction.

2.1 Hyperbolic functions

Hyperbolic functions, identities, and inverses.

2.2 Matrices

Matrices, eigenvalues, and diagonalisation.

2.3 Differentiation

Differentiation and applications.

2.4 Integration

Integration and applications.

2.5 Complex numbers

Complex numbers, loci, and De Moivre's theorem.

2.6 Differential equations

Forming and solving differential equations.

3.1 Motion of a projectile

Projectile motion in two dimensions.

3.2 Equilibrium of a rigid body

Forces, moments, and equilibrium.

3.3 Circular motion

Circular motion and centripetal force.

3.4 Hooke's law

Elastic strings and springs.

3.5 Linear motion under a variable force

Motion with variable force.

3.6 Momentum

Momentum and impulse.

4.1 Continuous random variables

Continuous random variables and probability density.

4.2 Inference using normal and t-distributions

Inference with normal and t-distributions.

4.3 t-tests

Hypothesis testing using t-tests.

4.4 Non-parametric tests

Non-parametric statistical tests.

4.5 Probability generating functions

Probability generating functions and applications.