11 Mathematical Methods
Stage 1 Mathematics is a 10-credit subject or a 20-credit subject.
Mathematics develops an increasingly complex and sophisticated understanding of calculus, statistics, mathematical arguments, and proofs, and using mathematical models. By using functions, their derivatives, and integrals, and by mathematically modelling physical processes, students develop a deep understanding of the physical world through a sound knowledge of relationships involving rates of change. Students use statistics to describe and analyse phenomena that involve uncertainty and variation.
Stage 1 Mathematics provides the foundation for further study in mathematics in Stage 2 Mathematical Methods and Stage 2 Specialist Mathematics.
Stage 2 Mathematical Methods can lead to tertiary studies of economics, computer sciences, and the sciences. It prepares students for courses and careers that may involve the use of statistics, such as health or social sciences.
Stage 2 Specialist Mathematics can be a pathway to mathematical sciences, engineering, space science, and laser physics. Specialist Mathematics is designed to be studied in conjunction with Mathematical Methods.
Stage 1 Mathematics consists of the following twelve topics:
- Topic 1: Functions and graphs
- Topic 2: Polynomials
- Topic 3: Trigonometry
- Topic 4: Counting and statistics
- Topic 5: Growth and decay
- Topic 6: Introduction to differential calculus
- Topic 7: Arithmetic and geometric sequences and series
- Topic 8: Geometry
- Topic 9: Vectors in the plane
- Topic 10: Further trigonometry
- Topic 11: Matrices
- Topic 12: Real and complex numbers.
Available courses
The topics for Stage 2 Physics are:
· Topic 1: Motion and relativity
· Topic 2: Electricity and magnetism
· Topic 3: Light and atoms.
SACE Stage 2 Physics (complete course)
Stage 1 |
Stage 2 |
1.1 Motion under constant acceleration |
1.1 Projectile motion 1.2 Forces and momentum 1.3 Circular motion and gravitation 2.2 Motion of charged particles in electric fields |
1.2 Forces |
1.2 Forces and momentum 1.3 Circular motion and gravitation 2.1 Electric fields 2.2 Motion of charged particles in electric fields 2.4 Motion of charged particles in magnetic fields |
2.1 Potential difference and electric current |
2.1 Electric fields 2.3 Magnetic fields 2.5 Electromagnetic induction |
4.1 Energy |
2.2 Motion of charged particles in electric fields 3.2 Wave–particle duality |
4.2 Momentum |
1.2 Forces and momentum 3.2 Wave–particle duality |
5.1 Wave model |
3.1 Wave behaviour of light 3.2 Wave–particle duality 3.3 Structure of the atom |
5.3 Light |
3.1 Wave behaviour of light 3.2 Wave–particle duality |
6.1 The nucleus |
3.4 Standard Model |
6.2 Radioactive decay |
2.4 Motion of charged particles in magnetic fields 3.4 Standard Model |
This Stage 1 Physics course (complete semester) is intended for students completing the Engineering Pathways Program.
The topics for Stage 1 Physics are:
· Topic 1: Linear motion and forces
· Topic 2: Electric circuits
· Topic 3: Heat
· Topic 4: Energy and momentum
· Topic 5: Waves
· Topic 6: Nuclear models and radioactivity.
Topic 1: Projectile Motion Application: Projectiles in Sport |
Topic 1: Electric Fields Application: Photocopiers and Laser Printers |
Topic 1: Electromagnetic Waves Application: Laser Airborne Depth Sounder (LADS) |
Topic 1: The Structure of the Atom Application: Lasers |
Topic 2: Uniform Circular Motion Application: The Banking of Road Curves |
Topic 2: The Motion of Charged Particles in Electric Fields Application: The Use of Electric Fields in Cyclotrons |
Topic 2: The Interference of Light Application: Compact Discs and DVDs |
Topic 2: The Structure of the Nucleus Application: The Production of Medical Radioisotopes |
Topic 3: Gravitation and Satellites Application: Weather and Communication Satellites |
Topic 3: Magnetic Fields Application: The Moving-coil Loudspeaker |
Topic 3: Photons Application: The Use of X-rays in Medicine |
Topic 3: Radioactivity Application: Positron Emission Tomography (PET) |
Topic 4: Momentum in Two Dimensions Application: Spacecraft Propulsion |
Topic 4: The Motion of Charged Particles in Magnetic Fields Application: The Use of Magnetic Fields in Cyclotrons |
Topic 4: Wave Behaviour of Particles Application: Electron Microscopes |
Topic 4: Nuclear Fission and Fusion Application: Fission Nuclear Power |
Stage 2 Specialist Mathematics consists of the following six topics:
Topic 1: Mathematical Induction
Topic 2: Complex Numbers
Topic 3: Functions and Sketching Graphs
Topic 4: Vectors in Three Dimensions
Topic 5: Integration Techniques and Applications
Topic 6: Rates of Change and Differential Equations.
Stage 2 Mathematical Methods consists of the following six topics:
Topic 1: Further Differentiation and Applications
Topic 2: Discrete Random Variables
Topic 3: Integral Calculus
Topic 4: Logarithmic Functions
Topic 5: Continuous Random Variables and the Normal Distribution
Topic 6: Sampling and Confidence Intervals.
Stage 2 General Mathematics consists of the following six topics:
- Modelling with Linear Relationships
- Modelling with Matrices
- Statistical Models
- Financial Models
- Discrete Models
- Open Topic
Stage 2 Essential Mathematics consists of the following six topics:
Topic 1: Scales, Plans, and Models
Topic 2: Measurement
Topic 3: Business Applications
Topic 4: Statistics
Topic 5: Investments and Loans
Topic 6: Open Topic
Stage 1 S. Mathematics consists of the following twelve topics:
Topic 1: Functions and Graphs
Topic 2: Polynomials
Topic 3: Trigonometry
Topic 4: Counting and Statistics
Topic 5: Growth and Decay
Topic 6: Introduction to Differential Calculus
Topic 7: Arithmetic and Geometric Sequences and Series
Topic 8: Geometry
Topic 9: Vectors in the Plane
Topic 10: Further Trigonometry
Topic 11: Matrices
Topic 12: Real and Complex Numbers.
Stage 1 Mathematics consists of the following twelve topics:
- Topic 1: Functions and Graphs
- Topic 2: Polynomials
- Topic 3: Trigonometry
- Topic 4: Counting and Statistics
- Topic 5: Growth and Decay
- Topic 6: Introduction to Differential Calculus
- Topic 7: Arithmetic and Geometric Sequences and Series
- Topic 8: Geometry
- Topic 9: Vectors in the Plane
- Topic 10: Further Trigonometry
- Topic 11: Matrices
Stage 1 General Mathematics consists of the following seven topics:
Topic 1: Investing and Borrowing
Topic 2: Measurement
Topic 3: Statistical Investigation
Topic 4: Applications of Trigonometry
Topic 5: Linear and Exponential Functions and their Graphs
Topic 6: Matrices and Networks
Topic 7: Open Topic
Stage 1 Essential Mathematics consists of the following seven topics:
Topic 1: Calculations, Time, and Ratio
Topic 2: Earning and Spending
Topic 3: Geometry
Topic 4: Data in Context
Topic 5: Measurement
Topic 6: Investing
Topic 7: Open Topic
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