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

SACE Stage 2 Physics (complete course) 

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


 


Subject Outline:
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.


Section 1: Motion in Two Dimensions

Section 2: Electricity and Magnetism

Section 3: Light and Matter

Section 4: Atoms and Nuclei

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:

  1. Modelling with Linear Relationships
  2. Modelling with Matrices
  3. Statistical Models
  4. Financial Models
  5. Discrete Models
  6. 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