Factorising (Factoring)
difference of two squares
grouping
quadratics
Factor theorem
Fractions
partial
simplifying algebraic
Functions
composite
domain
increasing, decreasing
inverse
modulus
notation
range
Geometric Progression (series)
Gradient of
curve
parallel lines
perpendicular lines
straight lines (line segment)
Graphs
cubic
quadratic
reciprocal
transformations
Half-angle formulae
Harmonic identities
Identity
identity or equation – what’s the difference?
Imaginary numbers
Implicit functions
differentiation
Indices
Inequalities
double
linear
modulus
quadratic
Integral
definite
Integrals of the form
axn
(ax + b)n
exponential: ex, eax and e(ax+b)
f ‘(x) / f(x)
f ‘(x) ef(x)
f [g(x)] g ‘(x)
reciprocal: 1/x and 1/(ax + b)
trigonometric functions
Integration
by parts
change of variable
definite
equation of a curve given dy/dx
general methods
partial fractions type
substitution
Integration – applications
area bounded by a curve and x-axis
area between a curve and the y-axis
area between a parametric curve
Inverse
function
trigonometric functions
Iteration
iteration – fixed point
Newton-Raphson
Linear transformations, matrices
Line
equation of
gradient of
mid-point
Locus – complex plane
Logarithms
change of base
differential – see differentiation of
rules
simplifying and expanding
simultaneous equations
Long Division
algebraic
Matrices
addition and subtraction
cofactor
determinant 3×3
inverse
linear transformations
minors
multiplication
transpose
Maximum and minimum – see stationary points
Mid-point of a line
Modelling curves
Modulus Functions
Newton-Raphson
Normal
to a curve
to parametric curves
Numerical methods for equations
change of sign
graphical
iteration
Newton-Raphson
Numerical methods for integration
trapezium rule
Parametric
differentiation
equations
tangents and normals
Polynomials
roots and coefficients
Product rule
Proof
counter example
exhaustion
identities
Pythagorean identities / equations
Pythagoras’ theorem

Check out the following indexes for further topics