VCE Specialist Maths cheat sheet

Unit 1 has two areas of study: 'Algebra, number and structure' and 'Calculus and functions' (with a focus on functions, relations and graphs).

Unit 2 areas of study are 'Calculus and functions' (with a focus on calculus) and 'Data analysis, probability and statistics'.

Unit 3 areas of study: 'Discrete mathematics' (matrices) and 'Functions, relations and graphs' (including transformations, inverse functions, and complex numbers).

Unit 4 areas of study: 'Space and measurement' (vectors) and 'Calculus' (differential equations, kinematics, and further integration).

Each unit has specific outcomes that integrate knowledge and skills; for example, Unit 3 Outcome 1 requires the use of matrices to model and solve problems.

Assessment in Units 1 and 2 is school-based and includes at least one task from each area of study; satisfactory completion requires demonstration of all outcomes.

Units 3 and 4 assessment comprises School-assessed Coursework (SACs) and two end-of-year examinations; SACs contribute 40% and examinations 60% to the study score.

The performance descriptors for each SAC describe typical performance on a 5-point scale; teachers use them to make consistent judgements.

A program should sequence the areas of study across the year, allocating time for the introduction of content, practice, and assessment.

When planning, consider the mathematical prerequisites from previous units; for example, Unit 3 functions build on Unit 1 transformations.

The program must include opportunities for students to develop the key skills of problem-solving, modelling, and use of technology.

Include a variety of assessment tasks (e.g., tests, assignments, investigations) that align with the outcomes and performance descriptors.

Plan for the integration of technology, such as CAS calculators, to support learning and assessment, ensuring tasks are designed to assess both with and without technology.

The program should incorporate the cross-curriculum priorities and general capabilities where relevant, such as literacy and numeracy.

Allow for flexibility to address student needs, including revision and extension, while ensuring coverage of all content.

Document the program in a format that shows the sequence, teaching strategies, resources, and assessment timeline.

Sample learning activities should engage students in active inquiry, such as modelling real-world phenomena with functions or matrices.

Use pseudocode to describe algorithms for numerical methods (e.g., Newton's method, Euler's method) without requiring a specific programming language.

Pseudocode conventions: use indentation for blocks, keywords like IF, THEN, ELSE, WHILE, FOR, and assignment with ← or =.

Example pseudocode for Euler's method: INPUT x0, y0, h, n; FOR i FROM 1 TO n: y ← y + h*f(x,y); x ← x + h; OUTPUT x, y.

When teaching calculus, use activities that connect graphical, numerical, and algebraic representations, such as exploring limits with tables and graphs.

For matrices, activities can include using matrix multiplication to model transformations and solving systems of linear equations.

For vectors, use dynamic geometry software to explore vector addition, scalar multiplication, and dot products in 2D and 3D.

For probability, simulate random experiments using technology and compare empirical results with theoretical probabilities.

School-assessed Coursework (SACs) in Units 3 and 4 typically consists of a number of tasks, including at least one test and one application task, as specified by VCAA.

Each SAC is assessed against performance descriptors that describe a range of typical performance, from low to high.

Performance descriptors are generic across the study and are used to allocate a score on a 5-point scale for each outcome.

The end-of-year examinations consist of two papers: Examination 1 (short-answer and multiple-choice, no technology) and Examination 2 (multiple-choice and extended-answer, with technology).

Examination 1 is of 1 hour duration and contributes 20% to the study score; Examination 2 is of 2 hours and contributes 40%.

Both examinations cover the content from Units 3 and 4, with an emphasis on the application of knowledge and skills.

The examination specifications detail the format, number of questions, and the allocation of marks, and are published annually by VCAA.

Assessment tasks should be designed to allow students to demonstrate the outcomes at a high level, including problem-solving and modelling.