natural

integers

rational

irrational

transcendental

algebraic numbers

in other bases

Entering negative numbers

Entering exponents 1.5E4

Inverse trigonometric

Powers of negative numbers (-2)^3

concept of instantaneous rate of change

derivatives of polynomials

use of table look up for sin(ax), cos(ax), exp(ax), log(ax)

stationary values

inflexion points

second derivatives

determine the shape of the curve given the derivatives

determine maxima, minima

simple applications (limited to functions not involving chain rule, product rule or quotient rule)

application of product, quotient andchain rules

opposite of differentiation

constant of integration

Integrals of polynomials y =ax^n + ...

table look up x^n, sin(ax), cos(ax), exp(ax), ln(ax)

algebraic substitutions

trigonometric substitutions

change of limits

using partial fractions

Integration by parts

Applications

Numerical integration

scalar or dot product

cross product

radians

degrees

mills

Pythogorous identity

tangent

sketching appropriate figures

application of sin, cos or tan

angle of elevation and depression

Use of R>P and P>R on calculator

sin(A+B) = ...

cos(A+B) = ...

tan(A+B) = ...

apply rules of indices

square root notation

meaning of a^0

linear equations

simultaneous equations

quadratic equation

polynomial equations

polynomial

trigonometric

exponential

logarithmic

adding or subtracting the same

multiplying both sides

reciprocating both sides

taking square roots both sides

raising both sides to a fractional power

exponentiate both sides

taking logs on both sides

apply a function to both sides

sketch intervals

simple formulae

formulae with mixed units and mixed scales

expand brackets mixed signs

factorization

polynomial division

algebraic fractions

Remainder theorem

Linear factors

Repeated factors

Linear and quadratic factors

Improper fraction requiring long division

linear relationships

polynomials

exponentials

logarithms

trigonometric

Analytical techniques

Initail value problem

Numerical methods

Analytical techniques

Initial Value Problem

Boundary Value Problem

Numerical methods