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...