SACE

SACE Maths

Learn About The Subject

SACE Maths is a group of mathematics subjects under the South Australian Certificate of Education (SACE), an internationally recognized qualification. Similar to other Australian high school programs, SACE Maths is divided into progressively challenging streams: General Mathematics, Mathematical Methods, and Specialist Mathematics.

The program is designed to comprehensively develop mathematical skills, from practical, everyday applications to abstract thinking and solving complex problems. Achieving high results in SACE Maths is crucial for obtaining a competitive ATAR (Australian Tertiary Admission Rank), which opens doors to prestigious universities in Australia and around the world.

Common Challenges When Learning SACE Maths

Choosing the appropriate stream (General, Methods, Specialist) based on future academic and career goals.
Tackling Investigation tasks as part of school-assessed components (Folio).
Understanding complex, abstract mathematical concepts, particularly in Specialist Mathematics.
Mastering the use of a graphics calculator to solve problems efficiently.

Course Content

SACE Mathematical Methods Syllabus

Unit 1: Further Differentiation and Applications

1.1: Introductory Calculus Review (Limits, First Principles, Power Rule)

1.2: Differentiation of Exponential & Logarithmic Functions

1.3: Differentiation of Trigonometric Functions (sin, cos, tan)

1.4: The Product, Quotient & Chain Rules

1.5: The Second Derivative, Concavity & Points of Inflection

1.6: Optimisation Problems in Context

Unit 2: Integrals

2.1: Anti-differentiation & the Indefinite Integral

2.2: The Definite Integral & the Area Under a Curve

2.3: The Fundamental Theorem of Calculus

2.4: Integration of Exponential & Trigonometric Functions

2.5: Applications of Integration (e.g., total change)

Unit 3: Discrete Random Variables

3.1: Probability, Random Variables & Probability Distributions

3.2: The Bernoulli Distribution & Bernoulli Trials

3.3: The Binomial Distribution

3.4: Expected Value, Variance & Standard Deviation of Discrete Distributions

Unit 4: The Normal Distribution & Confidence Intervals

4.1: Continuous Random Variables & Probability Density Functions

4.2: The Normal Distribution & its Properties

4.3: Standardised Scores (z-scores) & Probability Calculation

4.4: Random Sampling & the Distribution of Sample Proportions

4.5: Confidence Intervals for Proportions

SACE Specialist Mathematics Syllabus

Unit 1: Mathematical Induction and Vectors

1.1: The Principle of Mathematical Induction

1.2: Introduction to Vectors in Three Dimensions

1.3: The Scalar (Dot) Product, Angle Between Vectors & Projections

1.4: The Vector (Cross) Product & its Geometric Properties

1.5: Vector & Cartesian Equations of Lines & Planes

Unit 2: Complex Numbers

2.1: Arithmetic of Complex Numbers in Cartesian Form

2.2: Polar Form, Modulus, Argument & Euler's Formula

2.3: De Moivre’s Theorem & its Applications

2.4: Roots of Complex Numbers & Geometric Interpretation

2.5: The Fundamental Theorem of Algebra & Polynomial Factorisation

Unit 3: Integration Techniques and Differential Equations

3.1: Advanced Integration Techniques (Substitution, Parts, Partial Fractions)

3.2: Volumes of Solids of Revolution

3.3: Introduction to Differential Equations

3.4: Solving First-Order Linear Differential Equations

3.5: Applications of Differential Equations (e.g., Growth, Decay, Kinematics)

Unit 4: Kinematics and Dynamics

4.1: Motion in a Straight Line with Variable Acceleration

4.2: Motion in a Plane using Vector Calculus

4.3: Newton's Laws of Motion

4.4: Projectile Motion with Air Resistance

4.5: Simple Harmonic Motion

SACE General Mathematics Syllabus

Unit 1: Bivariate Data Analysis

1.1: Scatterplots, Correlation & Causality

1.2: Pearson's Correlation Coefficient (r)

1.3: Linear Regression & the Least-Squares Line

1.4: The Coefficient of Determination (r2) & Residual Plots

1.5: Time-Series Data Analysis (Moving Averages, Seasonal Indices)

Unit 2: Financial Models

2.1: Simple & Compound Interest

2.2: Annuities, Investments & Perpetuities

2.3: Reducing-Balance Loans & Amortisation

2.4: Analysing Loans & Investments using Technology

Unit 3: Networks and Decision Mathematics

3.1: Introduction to Graphs, Networks & Adjacency Matrices

3.2: Walks, Trails, Paths, Cycles & Euler's Rule

3.3: Weighted Graphs & Shortest Path Problems (Dijkstra's Algorithm)

3.4: Project Management & Critical Path Analysis

Unit 4: Modelling with Matrices

4.1: Matrix Arithmetic (Addition, Subtraction, Multiplication)

4.2: The Determinant & Inverse of a 2x2 Matrix

4.3: Solving Systems of Linear Equations using Matrices

4.4: Transition Matrices & their Applications

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SACE Maths

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Frequently Asked Questions

Frequently Asked Questions About

SACE Maths

What is the difference between SACE Mathematical Methods and Specialist Mathematics?

Mathematical Methods focuses on Calculus and Statistics, serving as a foundation for many university-level courses. Specialist Mathematics builds on Methods with more advanced topics such as vectors and matrices, and is essential for high-level STEM fields like Engineering or Computer Science.

What is the weighting between the final exam and school-assessed tasks (Folio)?

In SACE, your final grade typically comprises 70% from the external final examination and 30% from school-assessed tasks, which include Investigations and Skills & Applications assessments.

What are "Investigations" in SACE Maths?

These are project-based tasks where students independently explore a mathematical concept in depth, apply it to a real-world context, and present their findings in a detailed report.

How does Intertu support students with Investigations?

Our teachers guide students in understanding the task requirements, developing a suitable mathematical approach, structuring reports effectively, and leveraging technology efficiently, all while ensuring academic integrity.

Can I use SACE Maths to apply to universities outside Australia?

Absolutely. SACE is an internationally recognized qualification. ATAR scores are widely accepted by universities in the UK, US, Canada, and many other countries as a reliable measure of academic achievement.

How are tuition fees for SACE Maths at Intertu calculated?

Tuition fees for SACE Maths at Intertu Education depend on the number of study hours and the level of support selected (Standard, Premium, Platinum). This ensures the best fit for each student’s needs and academic goals. For a detailed quotation, please contact Intertu’s advisory team directly.

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SACE

SACE Maths

Learn About The Subject

Common Challenges When Learning SACE Maths

Course Content

SACE Mathematical Methods Syllabus

SACE Specialist Mathematics Syllabus

SACE General Mathematics Syllabus

Register For A Consultation With Our Experts

Personalized Learning Approach

Academic Pathway

Competency Assessment

Set Learning Objectives

Create A Learning Path

Implement And Optimize

MEET THE TEACHING TEAM

Dedicated Team Of Teachers Ready To Support Your Learning Journey

Tuan Nguyen

Duy Nguyen

Thuy Nguyen

Tra Nguyen

Tin Nguyen

Hieu Pham

Uyen Vu

Carolina Rondon

Choosing the right study package

Find The Optimal Academic Support Solution For You

Frequently Asked Questions

Frequently Asked Questions About

SACE Maths

CONTACT INTERTU

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