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