Differentiation is the process of finding the gradient of a curve. Recall that the gradient is a measure of steepness. The gradient on a straight line is constant but on a curve is always changing. Differentiation and Integration form a branch of mathematics known as Calculus.

## Differentiation in AS-Level Maths (from Sep 2017):

During the year that students study for an AS-Level in Maths, they will be required to cover the following topic areas in DIFFERENTIATION:

- Find and use the derivative of a function at a given point.
- Sketch a gradient function.
- Find and use second derivatives.
- Differentiate from first principles.
- Differentiate linear combinations of polynomials.
- Find equations of tangents and normals.
- Find and classify stationary points.
- Identify increasing and decreasing functions.
- Differentiating e to the power of kx

These topic areas will be tested in the Pure Mathematics paper – Paper 1.

## Differentiation in A-Level Maths (from Sep 2017):

In addition to the above, students studying for an A-Level in Maths will also be required to study the following areas in DIFFERENTIATION:

- Differentiate trigonometric functions from first principles. Understand the connection between the second derivative and convex/concave functions.
- Differentiate trigonometric and exponential functions.
- Use the product rule, quotient rule and chain rule.
- Implicit and parametric differentiation.
- Construct simple differential equations.

This is done over 2 years and these additional topic areas will be tested in Pure Mathematics Paper 2.