The Australian Science and Mathematics School has a history of outstanding engagement and success in the Mathematics learning area in Stage 2. With the reframing of mathematics subjects within the SACE the ASMS now only offers Stage 2 Mathematical Methods and Stage 2 Specialist Mathematics.
Mathematical Methods develops an increasingly complex and sophisticated understanding of calculus and statistics. By using functions and 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.
Specialist Mathematics draws on and deepens students’ mathematical knowledge, skills, and understanding, and provides opportunities for students to develop their skills in using rigorous mathematical arguments and proofs and using mathematical models. It includes the study of more advanced calculus and multidimensional approaches to vectors and complex numbers.
Students choosing to study Stage 2 Specialist Mathematics are enrolled in a combined Specialist and Methods hybrid course that re-sequences the curriculum to enhance the significant conceptual overlap between the two subjects. Students are still allocated the same course contact time, 200 minutes per subject totalling 400 minutes in the combined Specialist and Methods course. They also have the benefit of accessing up to four specialist mathematics teachers due to the collaborative approaches used in the teaching and learning program.
Stage 2 Mathematical Methods focuses on the development of mathematical skills and techniques that enable students to explore, describe, and explain aspects of the world around them in a mathematical way. It places mathematics in relevant contexts and deals with relevant phenomena from the students’ common experiences, as well as from scientific, professional, and social contexts.
The coherence of the subject comes from its focus on the use of mathematics to model practical situations, and on its usefulness in such situations. Modelling, which links the two mathematical areas to be studied, calculus and statistics, is made more practicable by the use of electronic technology.
Stage 2 Mathematical Methods consists of the following six topics:
- Further Differentiation and Applications
- Discrete Random Variables
- Integral Calculus
- Logarithmic Functions
- Continuous Random Variables and the Normal Distribution
- Sampling and Confidence Intervals.
Stage 2 Specialist Mathematics extends students’ mathematical experience and their mathematical flexibility and versatility, in particular, in the areas of complex numbers and vectors. The general theory of functions, differential equations, and dynamic systems provide opportunities to analyse the consequences of more complex laws of interaction.
Specialist Mathematics topics provide different scenarios for incorporating mathematical arguments, proofs, and problem-solving.
Stage 2 Specialist Mathematics consists of the following six topics:
- Mathematical Induction
- Complex Numbers
- Functions and Sketching Graphs
- Vectors in Three Dimensions
- Integration Techniques and Applications
- Rates of Change and Differential Equations.
Mathematical Methods provides the foundation for further study in mathematics, 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.
Specialist Mathematics leads to study in a range of tertiary courses such as mathematical sciences, engineering, computer science, and physical sciences. Students envisaging careers in related fields will benefit from studying this subject.
Both Mathematical Methods and Specialist Mathematics follow the same assessment structures
School Assessment (70%)
- Skills and Applications Tasks (50%)
- Mathematical Investigation (20%)
External Assessment (30%)
Students provide evidence of their learning through eight assessments for each subject, including the external assessment component. Students complete:
- six skills and applications tasks
- one mathematical investigation
- one examination.
Students enrolling in the two Mathematics subjects will complete a total of 16 assessments to fulfil the SACE requirements.
Students studying Stage 2 Mathematics are required to have a SACE approved graphics calculator. These can be purchased through the ASMS bulk order at the start of each year. A limited number are available on short term loan from the library collection. Students are also required to have access to a computer to support engagement with learning activities and online resources. A laptop is desirable but school desktop computers are available in the learning spaces. Students also have access to a textbook throughout the year to support their learning.