Algebra and Series

Rational expressions

• Simplifying
• Addition and subtraction
• Partial fractions
  • Denominator contains linear factors
  • Denominator contains repeated factors
  • Improper types

Exam Questions

Binomial Expansion

• Rational powers
• Validity

Coordinate Geometry

• Parametric equations
  • Converting to cartesian form
  • Sketching graphs

Exam Questions

Differentiation

• Exponential functions of the form y=a^x
• trig types sin x, cos x, tan x
  • trigonometric types (extended)
• Parametric functions
  • Tangents and normals
  • Stationary points
• Implicit functions
  • Tangents and normals
  • Stationary points

Integration

• (ax+b)^n types
• Integrals leading to a logarithmic function
• Integrals of the form f '(x)e^f(x)

Trigonometric

• sin x, cos x, sec² x
• sin(ax+b), cos(ax+b), sec² (ax+b) types
• using trig identities
• sin² x types
• cos² x types

Partial fraction types

• Partial fraction types

Substitution

• Substitution

By Parts

• By parts

Mixed examples

• Mixed Examples

Differential Equations

• Exponetial growth and decay (still to be completed)

Numerical Methods

• The trapezium rule

Vectors

• What is a vector and a scalar quantity?
• Notation
• Position vectors
• Equal and negative vectors
• Addition and subtraction of vectors
  • example 1
  • example 2
• Magnitude of a 2 dimensional vector
• Unit vectors
• Magnitude of a 3 dimensional vector

Scalar Product (Dot Product)

• Scalar product
  • example
• Perpendicular vectors
  • example

Lines

• Vector equation of a line
  • example 1
  • example 2
• Angle between two lines
• Parallel lines
• Intersecting and skew lines
• Closest point to a line and shortest distance from the origin

Exam Questions

• Exam questions