Overall assessment breakdown

Stage 2 Mathematical Methods has three official assessment components:

• five or six Skills and Applications Tasks — 50%
• one mathematical investigation — 20%
• one external examination — 30%

Together, the school assessments contribute 70% of the final result, while the SACE examination contributes the remaining 30%. Although many schools continue to run six SATs, the current outline permits either five or six.

Skills and Applications Tasks — 50%

These are supervised tests assessing mathematical knowledge, technique, modelling, interpretation and communication. Electronic technology and up to one handwritten A4 page of notes on one side may be permitted, although the exact conditions are decided by the teacher.

Where a school uses six SATs, the most natural arrangement is one assessment around each official Stage 2 topic:

1. further differentiation and applications
2. discrete random variables
3. integral calculus
4. logarithmic functions
5. continuous random variables and the normal distribution
6. sampling and confidence intervals

Schools may instead combine closely related areas or assess calculus across several tasks.

High-performing students select methods efficiently, show enough working, use notation accurately and interpret answers in context. This is particularly important in optimisation, kinematics and statistics, where a calculator result is not automatically a complete answer. Markers are looking for knowledge of concepts, appropriate technique selection, valid modelling, effective use of technology, logical conclusions and clear mathematical communication.

For revision, students should first master routine processes and then move into mixed, unfamiliar and contextual questions. Timed practice, an error log and regular calculator drills are far more effective than simply rereading worked examples.

Mathematical investigation — 20%

The investigation is an open-ended mathematical report based on one topic, several subtopics or a connection across the course. It may involve generating data, changing parameters, exploring patterns, applying a model or developing and testing a conjecture.

Possible investigation directions include:

• modelling and optimising a real object or process
• analysing motion using differential or integral calculus
• comparing exponential or logistic models
• simulating binomial or normal distributions
• investigating sampling behaviour or confidence intervals

These are examples rather than prescribed topics.

The report should explain the problem, chosen model or strategy, calculations, results, interpretation, limitations and conclusion. Technology such as graphing software, spreadsheets or a computer algebra system can support the investigation, but students must explain what the outputs show. The current maximum is 12 single-sided A4 pages, excluding permitted bibliography and appendices.

A strong investigation is concise, mathematically purposeful and reflective. It does not just contain more calculations; it explains why those calculations matter.

External examination — 30%

The final examination is 130 minutes and can assess all six topics. It includes routine questions, analysis, interpretation and problems that connect multiple areas of the course. A formula sheet is provided, and students may bring two unfolded A4 sheets containing four handwritten sides of notes. Approved electronic technology is permitted.

Preparation should become increasingly cumulative throughout the year. Students should complete past examinations under timed conditions, practise writing conclusions for statistics questions and learn to check whether calculator answers are reasonable. The students who perform best are usually those who can recognise the structure of an unfamiliar problem rather than those who have memorised the largest number of isolated procedures.