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Graphs and polynomials

The binomial theorem

Polynomials

Division of polynomials

Linear graphs

Quadratic graphs

Cubic graphs

Quartic graphs

Functions and transformations

Transformations and the parabola

The cubic function in power form

The power function (the hyperbola)

The power function (the truncus)

The square root function in power form

The absolute value function

Transformations with matrices

Sum, difference and product functions

Composite functions and functional

equations

Modelling

Exponential and logarithmic

equations

The index laws

Logarithm laws

Exponential equations

Logarithmic equations using any base

Exponential equations (base e)

Equations with natural (base e)

logarithms

Inverses

Literal equations

Exponential and logarithmic modelling

Exponential and logarithmic graphs

Graphs of exponential functions

with any base

Logarithmic graphs to any base

Graphs of exponential functions

with base e

Logarithmic graphs to base e

Finding equations for graphs of exponential

and logarithmic functions

Addition of ordinates

Exponential and logarithmic functions

with absolute values

Exponential and logarithmic modelling

using graphs

Inverse functions

Relations and their inverses

Functions and their inverses

Inverse functions

Restricting functions

Circular (trigonometric) functions

Revision of radians and the unit circle

Symmetry and exact values

Trigonometric equations

Trigonometric graphs

Graphs of the tangent function

Finding equations of trigonometric

graphs

Trigonometric modelling

Further graphs

Trigonometric functions with

an increasing trend

Differentiation

Review — gradient and rates of change

Limits and differentiation from

first principles

The derivative of xn

The chain rule

The derivative of ex

The derivative of loge (x)

The derivatives of sin (x), cos (x)

and tan (x)

The product rule

The quotient rule

Applications of differentiation

Equations of tangents and normals

Sketching curves

Maximum and minimum problems

when the function is known

Maximum and minimum problems

when the function is unknown

Rates of change

Related rates

Linear approximation

Integration

Antidifferentiation

Integration of e x, sin (x) and cos (x)

Integration by recognition

Approximating areas enclosed by

functions

The fundamental theorem of integral

calculus

Signed areas

Areas between two curves

Average value of a function

Discrete random variables

Probability revision

Discrete random variables

Measures of centre of discrete random

distributions

Measures of variability of discrete random

distributions

The binomial distribution

Problems involving the binomial distribution

for multiple probabilities

Markov chains and transition matrices

Expected value, variance and standard

deviation of the binomial distribution

Continuous distributions

Continuous random variables

Using a probability density function to

find probabilities of continuous random

variables

Measures of central tendency and

spread

Coordinate geometry

Sketch graphs of y = ax m + bx−n + c

where m = 1 or 2 and n = 1 or 2

Reciprocal graphs

Graphs of circles and ellipses

Graphs of hyperbolas

Partial fractions

Sketch graphs using partial fractions

Circular functions

Reciprocal trigonometric functions

Graphs of reciprocal trigonometric

functions

Trigonometric identities

Compound- and double-angle formulas

Inverse circular functions and their

graphs

Complex numbers

Introduction to complex numbers

Basic operations using complex

numbers

Conjugates and division of complex

numbers

Complex numbers in polar form

Basic operations on complex numbers in

polar form

Factorisation of polynomials in C

Solving equations in C

Relations and regions of the

complex plane

Rays and lines

Circles and ellipses

Combination graphs and regions

Graphs of other simple curves

Differential calculus

The derivative of tan (kx)

Second derivatives

Analysing the behaviour of functions using

the second derivative

Derivatives of inverse circular

functions

Antidifferentiation involving inverse circular

functions

Implicit differentiation

Integral calculus

Integration techniques and applications

Technique 1: Substitution where the

derivative is present in the integrand

Technique 2: Linear substitution

Technique 3: Antiderivatives involving

trigonometric identities

Technique 4: Antidifferentiation using

partial fractions

Definite integrals

Applications of integration

Volumes of solids of revolution

Graphs of the antiderivatives of

functions

Differential equations

Related rates

Setting up and solving differential

equations

Numerical solutions of differential

equations

Direction field for a differential

equation

Kinematics

Differentiation and displacement, velocity

and acceleration

Using antidifferentiation

Motion under constant acceleration

Velocity–time graphs

Applying differential equations to

rectilinear motion

Vectors

Vectors and scalars

Position vectors in two and three

dimensions

Multiplying two vectors — the dot

product

Using vectors in geometry

Resolving vectors — scalar and vector

resolutes

Time-varying vectors

Vector calculus

Position, velocity and acceleration

Cartesian equations and antidifferentiation

of vectors

Applications of vector calculus

Projectile motion

Mechanics

Force diagrams and the triangle of

forces

Newton’s First Law of Motion

Newton’s Second Law of Motion

Applications of Newton’s First and Second

Laws of Motion

Applications of Newton’s First and Second

Laws to connected masses

Variable forces

Momentum and Newton’s Third Law of

Motion

Maths: secondary year 7 to year 10
Maths: VCE - General, Foundation, Methods, Specialist
Thermodynamics
Physics
Statics
Dynamics

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