# Stage 1 Essential Mathematics

## SACE Stage 1 Essential Mathematics – Calculations, Time and Ratio

Calculations Time and Rates Ratio and Scale

## SACE Stage 1 Essential Mathematics – Earning and Spending

Earning Spending Budgeting

## SACE Stage 1 Essential Mathematics – Geometry

Shapes Angle Geometry Geometry and Construction

## SACE Stage 1 Essential Mathematics – Data in Context

Classifying Data Reading and Interpreting Graphs Drawing Graphs Summarising and Interpreting Data Comparing Data Sets

## SACE Stage 1 Essential Mathematics – Measurement

Linear Measure Area Measure Mass Volume and Capacity Power and Energy

## SACE Stage 1 Essential Mathematics – Investing

Simple Interest Compound Interest Investing for Interest

# Stage 1 General Mathematics

## SACE Stage 1 General Mathematics – Investing and Borrowing

Investing for Interest Investing for Shares Return on Investment Costs of Borrowing

## SACE Stage 1 General Mathematics – Measurement

Application of Measuring Devices and Units of Measurement Perimeter and Area of Plane Shapes Volume and Surface Area of Solids…

## SACE Stage 1 General Mathematics – Statistical Investigation

The Statistical Investigation Process Sampling and Collecting Data Classifying and Organising Data The Shape, Location and Spread of Distribution of…

## SACE Stage 1 General Mathematics – Applications of Trigonometry

Similarity Right Triangle Geometry Area of Triangles Solving Problems with Non-Right Triangles

## SACE Stage 1 General Mathematics – Linear and Exponential Functions and Graphs

Linear Functions and Graphs Exponential Functions and Graphs

## SACE Stage 1 General Mathematics – Matrices and Networks

Matrix Arithmetic and Costing Applications Networks

# Stage 1 Mathematics

## SACE Stage 1 Mathematics – Functions, Graphs and Polynomials

Lines and Linear Relationships Inverse Proportion Relations Functions Quadratic Relationships Cubic and Quartic Polynomials

## SACE Stage 1 Mathematics – Trigonometry, Counting and Statistics

2.1 Cosine and sine Rules2.2 Circular Measure and Radian Measure2.3 Trigonometric functions2.4 Counting2.5 Discrete and continuous Random Data2.6 Samples and…

## SACE Stage 1 Mathematics – Differential Calculus, Growth and Decay

3.1 Indices and Index laws3.2 Exponential functions3.3 Logarithmic Functions3.4 Rate of Change3.5 The Concept of a Derivative3.6 Computations of Derivatives3.7…

## SACE Stage 1 Mathematics – Geometry, Sequences and Series

Arithmetic Sequences and Series Geometric Sequences and Series Circle Geometry

## SACE Stage 1 Mathematics – Vectors in the Plane and Further Trigonometry

5.1 Vector Operations5.2 Component and Unit Vector Forms5.3 Projections5.4 Geometric Proofs using Vectors5.5 Further Trigonometric Functions5.6 Trigonometric Identities

## SACE Stage 1 Mathematics – Matrices, Real and Complex Numbers

6.1 Matrix Arithmetic6.2 Transformations in the Plane6.3 The Number Line6.4 Introduction to Mathematical Induction6.5 complex Numbers6.6 The complex (Argand) Plane…

# Stage 2 Essential Mathematics

## SACE Stage 2 Essential Mathematics – Scales, Plans and Models

Perimeter Similarity Bearing

## SACE Stage 2 Essential Mathematics – Measurement

Measurement Pythagoras Theorem Trigonometry Identities Area Surface Area Volume

## SACE Stage 2 Essential Mathematics – Business Applications

Planning a business Premises Costing Calculations Business Structures and Taxation

## SACE Stage 2 Essential Mathematics – Statistics

Sampling from Populations Analysis and Representation of Sets of Data Linear Correlation

## SACE Stage 2 Essential Mathematics – Investments and Loans

Lump-Sum Investments Annuity Investments Loan Annuities

# Stage 2 General Mathematics

## SACE Stage 2 General Mathematics – Modelling with Linear Relationship

Simultaneous Linear Equations Linear Programming

## SACE Stage 2 General Mathematics – Modelling with Matrices

Application of Matrices to Network Problems Application of Matrices to Transition Problems

## SACE Stage 2 General Mathematics – Statistical Models

Bivariate Statistics The Normal Distribution

## SACE Stage 2 General Mathematics – Financial Models

Investment Borrowing Money Critical Path Analysis

## SACE Stage 2 General Mathematics – Discrete Models

Critical Path Analysis Assignment Problems

# Stage 2 Mathematical Methods

## SACE Stage 2 Mathematical Methods – Further Differentiation and Applications

Introductory Differential Calculus Differential Rules Exponential Functions Trigonometric functions The Second Derivative

## SACE Stage 2 Mathematical Methods – Discrete Random Variables

Discrete Random Variables The Bernoulli Distribution Repeated Bernoulli Trials and the Binomial Distribution

## SACE Stage 2 Mathematical Methods – Integral Calculus

Anti-Differentiation The Area under Curves Fundamental Theorem of Calculus Applications of Integration

## SACE Stage 2 Mathematical Methods – Logarithmic Functions

Using Logarithms for Solving Exponential Equations Logarithmic Functions and their Graphs Calculus of Logarithmic Functions

## SACE Stage 2 Mathematical Methods – Continuous Random Variables

Introduction to Continuous Random Variables Normal Distributions Sampling

## SACE Stage 2 Mathematical Methods – Sampling and Confidence Intervals

Confidence Intervals for a Population Mean Population Properteis Confidence Intervals for a Population Proportion

# Stage 2 Specialist Mathematics

## SACE Stage 2 Specialist Mathematics – Mathematical Induction

Proof of Mathematical Induction Divisibility Proof Inequality Proof

## SACE Stage 2 Specialist Mathematics – Complex Numbers

Cartesian and Polar Forms The Complex (Argand) Plane Roots of Complex Numbers Factorisation of Polynomials

## SACE Stage 2 Specialist Mathematics – Functions and Sketching Graphs

Composition of functions One-to-One Functions Sketching Graphs

## SACE Stage 2 Specialist Mathematics – Vectors in Three Dimensions

The Algebra of Vectors in Three Dimensions Vector and Cartesian Equations Systems of Linear Equations

## SACE Stage 2 Specialist Mathematics – Integration Techniques and Applications

Integration Techniques Applications of Integral Calculus

## SACE Stage 2 Specialist Mathematics – Rates of Change and Differential Equations

Implicit Differentiation Differential Equations Pairs of Varying Quantities - Polynomials Related Rates, Velocity and Tangents Trigonometric Parameterisations

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