# Resources for Sixth-form mathematics

This is a growing section of the site. The resources here are not designed to substitute for a good textbook—which most sixth-formers tend to have access to anyway. The content here instead centres around dynamic interactive applets with three main purposes in mind:

- conveying concepts more clearly than is possible with static diagrams on a page or a slide;
- offering several question generators that can be used in class to develop fluency e.g. through use of guidance fading, material for mini-whiteboard or oral questioning; and
- providing step-by-step procedural guides for students.

# Pure Mathematics resources

### Differentiation

- Gradient of a line passing through two points
- Limits
- Differentiation from first principles
- Differentiating expressions of the form \(kx^n\) with respect to \(x\)
- The gradient at a point on a curve
- Tangents and normals

### Matrices

- Introduction to matrices
- Adding and subtracting matrices
- Multiplying matrices
- 2 × 2 Matrices and linear transformations
- Determinants of 2 × 2 matrices
- Inverses of 2 × 2 matrices
- Invariant points and lines in 2 dimensions
- 3 × 3 Matrices and linear transformations
- Determinants of 3 × 3 matrices
- Inverses of 3 × 3 matrices
- Matrices and simultaneous equations

### Binomial expansion

# Mechanics resources

### Newton’s Laws

### Projectiles

- Recap of constant acceleration formulae and splitting a velocity into perpendicular components
- Projecting a particle directly upwards
- Projecting a particle at any angle
- Projectile motion formulae