Further pure math 3 (Edexcel AS and A level modular math)

Hyperbolic functions

The definitions of the hyperbolic functions

Graphs of hyperbolic functions

For hyperbolic functions, finding and using identities that are very similar to trigonometric identities

Defining and using the inverses of the hyperbolic functions, similar to those of the trigonometric functions

Solving equations involving hyperbolic functions

Further coordinate systems

Equations for an ellipse

Using parametric equations to find tangents and normals

Cartesian and parametric equations for a hyperbola

Finding equations of tangents and normals to a hyperbola

Defining the focus and directrix of the ellipse and hyperbola

Finding equations of simple loci

Differentiation

Differentiating hyperbolic functions

Differentiating inverse hyperbolic functions

Differentiating inverse trigonometric functions

Integration

Recognising standard integrals

Integrating expressions involving hyperbolic functions

Using trigonometric and hyperbolic substitutions in integration

Integrating expressions of the form 1/√(x²+qx+r) and 1/√(px²+qx+r)

Integrating inverse trigonometric and hyperbolic functions using integration by parts

Deriving and using reduction formula

Using integration to find the length of an arc of a curve

Using integration to find the area of a surface of revolution

Review Exercise 1

Vectors

The definition of the vector product of two vectors

Interpreting the magnitude of the vector product a × b as an area

Finding the triple scalar product a · (b × c) of three vectors a, b and c, and using it to find the volume of a parallelepiped and of a tetrahedron

Writing the vector equation of a line in the form (r − a) × b = 0

Writing the equation of a plane in the scalar, vector, or Cartesian form

Using vectors in a variety of contexts

Further matrix algebra

Finding the transpose of a matrix

Finding the determinant of a 3 × 3 matrix

Finding the inverse of a 3 × 3 matrix where it exists

Using matrices to represent linear transformations in 3 dimensions

Using inverse matrices to reverse the effects of a linear transformation

Finding the eigenvalues and eigenvectors of 2 × 2 and 3 × 3 matrices

Reducing a symmetrical matrix to diagonal form

Review Exercise 2

Examination style paper

Answers

Index