Video tutorials, diagnostics, text and interactive exercises covering over 80 maths topics.

Arithmetic

  • Fractions Basic Ideas
  • Fractions Adding And Subtracting
  • Fractions Multiplying And Dividing
  • Decimals
  • Percentages
  • Ratios
  • Rules Of Arithmetic
  • Surds

    • Algebra

  • Mathematical Language
  • Powers or indices
  • Logarithms
  • Substitution And Formulae
  • Expanding And Removing Brackets
  • Pascal's triangle and the binomial theorem
  • Factorising Quadratics
  • Transposition of Formulae
  • Linear Equations in one variable
  • Completing The Square
  • Completing The Square Maxima And Minima
  • Quadratic Equations
  • Simultaneous Linear Equations
  • Solving Inequalities
  • Cubic Equations
  • Simplifying Algebraic Fractions
  • Polynomial Division
  • Partial Fractions

    • Functions, Graphs, Sequences & Series

  • Introduction to functions
  • Linear functions
  • Polynomial functions
  • Exponential and logarithm functions
  • Trigonometric functions
  • Hyperbolic functions
  • Composition of functions
  • Inverse functions
  • Sigma notation
  • Arithmetic and geometric progressions
  • Limits of sequences
  • The sum of an infinite series
  • Limits of functions

    • Geometry & Vectors

  • Properties of straight line segments
  • The gradient of a straight line segment
  • Equations of straight lines
  • The geometry of a circle
  • Conic sections
  • Polar co-ordinates
  • Introduction to vectors
  • Cartesian components of vectors
  • The scalar product
  • The vector product

    • Trigonometry

  • Pythagoras' Theorem
  • Trig ratios in a right-angled triangle
  • Trig ratios of an angle of any size
  • Radian measure
  • Trig equations
  • Trig identities
  • Triangle formulae
  • Cosec, sec and cot
  • The addition formulae
  • The double-angle formulae
  • a cos x + b sin x = R cos (x - a)

    • Differentiation

  • Differentiation from first principles
  • Differentiating powers of x
  • Differentiating sines and cosines
  • Differentiating logs and exponentials
  • Using a table of derivatives
  • The quotient rule
  • The product rule
  • The chain rule
  • Parametric differentiation
  • Differentiation by taking logarithms
  • Implicit differentiation
  • Extending the table of derivatives
  • Tangents and normals
  • Maxima and minima

    • Integration

  • Integration as summation
  • Integration as the reverse of differentiation
  • Integration using a table of anti-derivatives
  • Integration by parts
  • Integration by substitution
  • Integrating algebraic fractions (1)
  • Integrating algebraic fractions (2)
  • Integration using trigonometric formulae
  • Finding areas by integration
  • Volumes of solids of revolution
  • Integration leading to log functions