Linear equations and inequalities

Algebraic fractions

Binomial products

Quadratic equations

Simultaneous equations

Factorisation

Linear equations and inequalities

Algebraic fractions

Binomial products

Quadratic equations

Simultaneous equations

Factorisation

Rational and irrational numbers

Simplifying Surds

Rationalising the denominator

Functions and Relations

Inverse functions and relations

Shifting, reflecting and transforming graphs

Inequalities and absolute values

Linear equations and inequalities

Inequalities with the pronumeral on the denominator

Range and domain

Regions and inequalities

Revision of the trigonometric ratios, using the unit circle

Angles of elevation and depression

Bearings

Four quadrants and angles of any magnitude

Exact ratios

Graphs of trigonometric functions and inverse functions

Trigonometric identities

Solving trigonometric equations

Sine and cosine rules for a triangle

Area of a triangle, given two sides and the included angle

Three dimensional trigonometry

The linear function in gradient-intercept form

*y = mx + b*

Finding the equation of a line given the gradient and a point

Finding the equation of a line passing through two given points

Parallel lines and perpendicular lines

General equation of a line *ax + by + c = 0*

Solving simultaneous equations to find the point of intersection of two or three concurrent lines

Equation of a line passing through the point of intersection of two given lines

Regions determined and inequalities

Distance and midpoint formulas

Perpendicular distance of a point from a line

Angle between two lines

Internal and external division of an interval in a given ratio

Gradient of a curve at a point

Differentiation from first principles

Gradient of a curve at a point

Rates of Change

Tangents and Normals

The limit of a function and continuity

Conditions for differentiability

Product rule, chain rule and quotient rule

Graphing functions by factorisation or completing the square or applying the quadratic formula

Equations reducible to quadratics

Sum and product of roots

The discriminant

Quadratic identities

Defining the locus and finding its equation

The Parabola

Parametric equations

Chords of a parabola and chords of contact

Equations of tangents and normals in parametric and cartesian form

Coordinate geometry

Geometric properties of plane shapes

Angles at a point and of angles

Angles on parallel lines

Angle sums of triangles, quadrilaterals and general polygons

Exterior angle

Congruence and similarity tests for triangles

Area formulae

Properties of circles: chords, arcs and tangents

Angle properties of a circle

Alternate segment

Arithmetic series formulae for the nth term and sum of n terms

Geometric series formulae for the nth term and sum of n terms

Limiting sum of a geometric series

Sigma notation

Applications of arithmetic series and geometric series in compound interest problems and repayment problems

Recurring decimals and geometric series

Significance of the sign of the derivative: increasing or decreasing functions

First derivative and stationary points

Second derivative and concavity

Points of inflection and change of concavity

Sketching functions

Problem solving involving maxima and minima

Primitive function

Mathematical induction proofs