Algebra:-

Algebra basics

• Algebra - terminology
• Algebra 1 A powerpoint presentation for beginners. (815kb)
• Algebra 2 A powerpoint presentation for intermediate algebra. (923 kb)
• Algebra -examples

Algebraic manipulation

• Algebra - Solving Trig equations
• Algebraic fractions
• Partial fractions
• Factorials
• Pascal’s triangle.
• Binomial theorem

Completing the square

• Completing the square - overview
• Completing the square - coefficient method
• Completing the square - general method
• Completing the square - solving quadratic equations
• Completing the square - usefulness for quadratics

Distance, Speed & Time

• Distance, speed & time
• Distance - time graphs

Equations & Inequalities

• Equations
• Inequalities

Factors

• Factors
• HCF
• Multiples
• LCM
• Prime factors
• Factors - removing brackets
• Foil
• Factorising

• Difference of two squares

Formulae

• Formulae in words
• Evaluating formulae
• Order of operations
• Formulae in symbols

• Changing the subject of the formula

Functions (SG & Higher)

• Functions
• Set notation
• Domain, codomain & range
• One to one correspondence
• Inverse function
• Inverse function - algebraic method
• Inverse function - graphical method
• composite functions
• Simple graphs of functions
• Reflections, translations, etc
• Graphs of functions an Excel reminder. (161 kb)

Functions (Ad Higher)

• Modulus function
• Inverse functions
• Polynomials
• Extrema
• Concavity and points of inflexion
• Odd and Even functions
• Asymptotes

Logs & Exponentials (Higher)

• Exponentials
• Growth functions
• Decay functions
• Logarithms
• Logarithms - converting bases
• Logarithmic equations
• logarithm laws
• Log and Ln
• Exponential / log functions - graphs
• Logarithmic scales on graphs
• Exponential / log functions - graphs An Excel reminder. (86 kb)

Indices

• Indices
• Indices a short Excel reminder. (42kb)

Joint variation

• Direct proportion
• Indirect proportion
• Proportion - square

Polynomials (Higher)

• Coefficients etc.
• Nested form.
• Dividing polynomials
• The factor theorem
• The remainder theorem
• Synthetic division
• Dividing by ax+b
• Solving polynomial equations
• Sketching polynomial equations

Quadratics

• Quadratics
• Factorizing quadratics
• Finding roots of quadratics
• Finding roots of quadratics which don't factorise easily
• Quadratic formula
• Finding roots of quadratics - derivation
• Quadratic graphs
• Sketching quadratic functions
• Discriminant
• Quadratic equations
• Quadratic graphs - tangency
• Finding roots of quadratics an Excel document reminder. (50 kb)

• Complex numbers
• Argand diagrams
• Polar form
• De moivre's theorem
• Roots of a complex number

Sequences (SG & Higher)

• Sequences (SG)

• nth term of sequence
• Recurrence relations
• Divergence / convergence
• Linear recurrence relations
• Formula for linear recurrence relations
• Solving recurrence relations
• Special sequences
• Finding limits an Excel document reminder.

• Recurrence relations
• Fixed points
• Arithmetic sequences
• n^th term of arithmetic sequence
• Sum to n terms of an arithmetic sequence
• Geometric sequences
• Sum to n terms of a geometric sequence
• Infinite series
• Sum to infinity - geometric series
• Sum first n natural numbers
• Sigma notation - Rules
• Common series - sigma notation

simultaneous equations

• Simultaneous equations : graphical method
• Simultaneous equations : solving by elimination
• Simultaneous equations : Vedic method
• Simultaneous equations : solving by elimination an interactive Excel solver.

Surds

• Surds
• Surds test