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[differential calculus][integration][algebra][trigonometry]

[sequences & series][coordinate geometry][vectors]

 

ALGEBRA

indices

the laws of indices
multiplication
division
powers
roots & reciprocals

laws of logarithms

the six laws of logarithms
proofs
changing the base
simultaneous equations
a variable in the index

surds

rules
some useful expressions
rationalising surds
rationalising - difference of 2 sqrs.
reduction of surds
rational, irrational numbers

inequalities

symbols & rules
inequalities with one variable
inequalities with two variables
the modulus

quadratic equations

introduction
solution by factorising
completing the square
using the Formula

partial fractions

definitions & addition, subtraction
equations & identities
denominator linear factors
denom. repeated linear factors
denominator quadratic factor

polynomials

introduction
algebraic long division
the Remainder Theorem
the Factor Theorem

the Binomial Theorem

Pascal's Triangle
General Binomial Expansion
Particular Binomial Expansion

iteration

direct/fixed point
by bisection
Newton-Raphson Method

number sets

introduction
common sets
Venn Diagrams
subsets

functions

mapping, 1 - 1 and many - 1
inverse function  f -1
composite functions
exponential & logarithmic

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intro. to integration
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differential equations
integration formula
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definite integrals
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