Properties of quadrilaterals

Topics: geometry, quadrilaterals

A couple of questions that have appeared in the past years

Topic: induction

Finally a look at the inequality type of induction problem

Topics: induction, inequality

Deriving formulae for use with geometric aeries.

Topics: series, geometric

The alternate segment

Topic: alternate segment

Finding the means of numbers

Topics: series, means

A quick look at the generalistion of the sum & difference formulae

Topic: sum & difference formulae

Calculating a series

Topic: series

Solving problems using calculus

Topic: calculus

Introducing the useful theorem

Topic: integration

Key features to look for when sketching polynomials

Topics: polynomials, curve sketching

Calculating areas if irregular shapes

Topics: integration, areas

How to find areas for functions too difficult to integrate

Topic: integration

Inequalities involving two variablss

Topic: regions

Finding sides and angles in non-right angled triangles

Topic: trigonometry

Expanding on the idea of transforming the basic curves.

Topic: curve sketching

The first of the angle theorems

Topic: circle geometry

Deriving the double angle formulae

Topics: trigonometry, double angles

The chord joing the points of contcat of the tangents drawn from an external point.

Topics: chord, parametrics

Solving optimisation problems using calculus.

Topics: calculus, maxima, minima

Circles and tangents

Topic: geometry

Introducing sigma notation

Topics: series, sum

Defining the quadratic and how to find its important features.

Topics: quadratic, curve sketching

Some alternative ways of finding the features of quadratics

Topic: quadratic

When two quadrtics are "congruent", the coefficients an be matched.

Topics: quadratic, identities

Classifying quadratics

Topics: quadratics, definite

Results concerning polynomials

Topic: polynomials

Finding the valueof integrals for curves that can't be integrated!!

Topics: integration, approximations

Deriving the inverse trig derivatives!!!

Topic: inverse trig

Applying the general term of a binomial to probability problems

Topics: binomial, probability

Introducing the binomail theorem

Topic: binomial

Looking at the pattewrn of the coefficients in a binomial expansion

Topic: binomial

Equating two quadratics

Topic: quadratic

Raising complex numbers to powers

Topics: complex numbers, de moivres

Defining the parametric coordinates of the ellipse and finding the tangent and normal.

Topics: conics, parmeters, ellipse

Defining the family of conics and more specifically, te ellipse.

Topics: conics, ellipse

Finding the volume of solids with non circular cross sections

Topics: volumes, parallel cross sections

Expanding on the idea from Extension 1

Topics: polynomials, roots, coefficients

A hyperbola whose asymptotes are perpendicular

Topics: conics, hyperbola

Working with surds

Topic: surds

Techniques for solving basic equations/

Topics: algebra, equations

Defining te sine rule for use in non-right angled triangles, as well as a formuls for finding the area of a triangle without having to know the perpendicular height.

Topics: trigonometry, sine rule, area

Three diferent levels of inequality questions

Topic: inequations

solving trig equations

Topic: trigonometry

Making the use of the symmetry of odd and even functions to make integration simpler.

Topics: integration, odd & even functions

Solving inequality problems using graphs

Topic: inequalities

Manipulating the roots of unity

Topics: complex numbers, roots of unity

A rule which allows us to differentiate without expanding out

Topic: calculus

Using the derivative to solve rates of change problems

Topics: calculus, rates of change

The basic algebraic operations

Topics: algebra, indices

Finding the area under a curve

Topics: integration, area

Looking at divisibility types of induction problems

Topics: induction, divisibility

Finding the equation of a line that pase through the intersection of two given lines and another point.

Topics: linear function, lamda formula

Looking at the specific case of the locus as a parabola

Topics: parabola, locus

Introducing the logarithmic function

Topics: logarithms, log laws

Solving trig equations

Topics: trigonometry, trig equations

Polynomial results that assist when factorising

Topic: polynomial

Differentiating a function divided by a function

Topics: calculus, quotient rule

An alternative way of solving simultaneous equations.

Topics: algebra, matrices

Deriving the sine rule

Topic: trigonometry

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

How to operate numbers in polar form

Topics: complex numbers, mod arg

Functions and the Argand Diagram

Topics: complex numbers, locus

When te order is unimportamt....

Topic: combination

What happens when some of the objects being arranged are the same?

Topics: probability, permutations

How do we differentiate inverse trig functions?

Topics: inverse trig, calculus

Standard integrals involving inverse trig

Topics: inverse trig, calculus

Finding the greatest coefficient/term without expanding the binomial

Topic: binomial

Introducing the terms and basic ideas of probabiolity

Topic: probability

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

Topic: simple harmonic motion

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