Algebra:-
The branch of maths which uses letters or symbols to represent numbers.
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- Operations
- Associativity
- Commutativity
- Distibrutivity
- Identity
- Number bases
- base 10 : hundreds, tens, units
- Algebra - terminology
- Algebra 1 A video presentation for beginners.
- Algebra 2 A video presentation for intermediate algebra.
- Algebra -examples
- Algebra - Solving Trig equations
- Algebraic fractions
- Partial fractions
- Factorials
- Pascal’s triangle.
- Binomial theorem
- 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
- Calculating Distance travelled
- Calculating Average speed
- Calculating Time taken
- Distance - time graphs
- Unitary conversions
- 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
- Modulus function
- Inverse functions
- Polynomials
- Extrema
- Concavity and points of inflexion
- Odd and Even functions
- Asymptotes
- 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.
- 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
- Factorizing quadratics
- Factorizing quadratics- alternative
- 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
- nth term of sequence
- Recurrence relations
- Divergence / convergence
- Linear recurrence relations
- Formula for linear recurrence relations
- Solving recurrence relations
- Special sequences
- Recurrence relations
- Fixed points
- Arithmetic sequences
- nth 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
© Alexander Forrest