THe importance of prime numbers and recurring decimals

Topic: numbers

Transversals will always cut parallel lines in the same ratio

Topics: geometry, transversals

Finding the integral of exponential functions.

Topics: exponentials, integration

Placing imaginary numbers on a graph

Topics: complex numbers, argand diagram

Describing complex numbers as vectors and points

Topic: complex numbers

Looking at lines in the complex plane

Topics: complex numbers, locus

Partial fractions is the reverse of combining algebraic fractions.

Topics: integration, partial fractions

Angular velocity vs linear velocity

Topic: circular motion

INtroducing the conic sections

Topics: conics, ellipse

The parametric form of the hyperbola

Topic: hyperbola

Looking further into the relationship between the roots and coefficients of a polynomial and extending on the Extension 1 style of question

Topics: polynomials, roots & coeffcients

Creating quadraticfactors from complex roots

Topics: complex numbers, factorising

Finding the equation of the chord of contact and other geometric properties of the conic sections.

Topics: conics, chord of contact, geometric properties

investigating the forces involved with a conical pendulum

Topics: dynamics, conical pendulum

Defining trig terms

Topic: trig

De Moivre put the mod arg relations into a theorem

Topics: complex numbers, de moivre

Defining the rectangular hyperbola

Topics: hyperbola, conics, rectangular hyperbola

Finding the volume of solids with circular cross-sections by taking slices parallel to the axis of rotation

Topic: volumes

Some properties of conics

Topic: conics

Testing for multiple roots of a polynomial

Topics: polynomials, roots

moving curves around the number plane

Topic: curve sketching

Looking at some different induction questions

Topic: induction

Newton's laws of motion and their use in solving motion problems.

Topics: motion, acceleration

Taking into account resistance

Topics: motion, resistance

How to operate numbers in polar form

Topics: complex numbers, mod arg

Functions and the Argand Diagram

Topics: complex numbers, locus

Finding the equation of a parabola from its geometrical description

Topics: locus, parabola

Using the patterns of series to solve problems.

Topics: series, geometric series, arithmetic series

Motion that oscillates between two points is known as Simple Harmonic Motion (SHM)

Topic: simple harmonic motion

Standard integrals involving inverse trig

Topics: inverse trig, calculus

Sketching the inverse trig graphs

Topic: inverse trig

Defining the inverse trig functions.

Topic: inverse trig

Integrating functons that result in a lo9garthmic function

Topics: logarithms, integration

Finding solutions to difficult equations

Topic: approximations

Finding the greatest coefficient/term without expanding the binomial

Topic: binomial

Introducing the terms and basic ideas of probabiolity

Topic: probability

How do the arrangements change when arranging in a circle?

Topic: permutation

Finding the relationships & patterns of binomial coefficients

Topics: binomial theorem, coefficients

Generalising the expansion using Pascal's Triangle for the binomial coefficients.

Topic: binomial theorem

Techniques for how to approach factorising

Topics: algebra, factorising

Differentiating a second time

Topics: calculus, second derivative

Mathematical inverse of graphs

Topic: functions

The idea behind solving quadratics

Topics: algebra, quadratic

If the product of factors is zero, then at least one factor must be zero.

Topic: quadratic

Start with the basic curve and transform it to a new curve.

Topic: curve sketching

A key procedure when dealing with surds is making the denominator a rationsl nuber.

Topics: surds, rationalising the denominator

A basic principle of mathematics is used for solving surdic equalities.

Topic: surds

Rationals and irrationals do not mix!!

Topic: surds

Selecting the objects when order is NOT important

Topic: combination

The shortest distance between a point and a line

Topic: cartesian geometry

Finding the shortest distance between a point and a lne.

Topics: linear function, perpendicular distance

Calculating the acute angle between two lines

Topics: linear function, angle between lines

Waht if some of the objects we are arranging look the same?

Topic: permutation

Geometry theorems involving triangles

Topics: geometry, triangle theorems

Using te counting techniques to solve probability problems.

Topics: permutations, combinations, probability

Investigating the linear function (straight line)

Topic: linear function

Dividing intervals in ratios other than 1:1

Topic: coordinate geometry

Putting the different ideas together in order to solve probability problems

Topic: probability

Using the discriminant to investigate the roots of a quadratic

Topics: discriminant, quadratic

Looking at some properties of the parabola

Topics: parabola, parametrics

Using the first derivative to help sketch curves.

Topics: calculus, curve sketching

Describing the locus of points

Topics: locus, parabola

How to use the second derivative to help curve sketching

Topics: concavity, calculus

Solving inequalities vis induction

Topics: induction, inequalities

Polynomial results that assist when factorising

Topic: polynomial

Using the theory to solve the problems

Topic: series

What happens when we can't find an integral?

Topics: integration, approximation

Calculating the mean of different types of wequences.

Topics: mean, series

Using the induction technique for prrof of a sum of series

Topics: series, induction

How to induce a solution

Topics: induction, series

Looking at a couple of past questions

Topic: induction

Using integration to find area.

Topics: integration, area

Using symmetry to sketch graphs

Topic: curve sketching

Using the symmetry of functions to help sketching

Topic: Symmetry

An extension to Pythagoras Theorem

Topics: trigonometry, cosine rule