# GCSE Further Maths

## Properties of Circle

## Geometry

Mensuration Plane geometry Properties of polygons Properties of triangles Properties of circles Pythagoras’ theorem Trigonometric ratio Sine and cosine rules in scalene triangles Cosine rule Sine rule Areas of triangles Sine, cosine, tangent graphs...

## Matrices

Multiplying matrices Identity matrix When used as a transformation matrix No movement occurs Transformations Reflections Reflection in x-axis Reflection in y-axis Reflection in y=x Reflection in y=-x Reflection about origin - Rotation (Rotation is anticlockwise if not...

## Calculus

Differentiation Tangents Normal Stationary point A stationary point is a turning point that occurs when the gradient, , of the graph is zero Determining the nature of stationary points Applications of maxima and minima

## Coordinate Geometry

Straight line graphs The distance between two points can be calculated by constructing a right-angled triangle between the coordinates and applying Pythagoras’ Theorem: The coordinate of the midpoint of the line between the points (????1, ????1) and (????2, ????2) is...

## Number & Algebra

Binomial expansion Manipulation of surds Rationalise denominators Quadratic formula Complete the square Factor theorem Factor theorem solves cubic equation (ax3+bx2+cx+d=0) Given that (x - 5) is a factor of x3 - 8x2 + 17x - 10, work out the quadratic factor. Domain...