# Online Courses

47 Lessons

## VCE Specialist Mathematics Units 3 and 4 – Calculus

3.1 Inverse Trigonometric Functions3.2 Differentiation3.3 Integration3.4 Area by Integration3.5 Volume by Integration3.6 Differential Equations3.7 Kinematics3.8 Related Rates of Change

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19 Lessons

## VCE Specialist Mathematics Units 3 and 4 – Vectors

4.1 Vectors4.2 Vector Applications

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24 Lessons

## VCE Specialist Mathematics Units 3 and 4 – Mechanics

5.1 Mechanics5.2 Motions in Straight Lines

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0 Lessons

## VCE Specialist Mathematics Units 3 and 4 – Probability and Statistics

6.1 Expectation6.2 Sample Mean6.3 Discrete Random Variables6.4 Continuous Random Variables6.5 Hypothesis Testing

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27 Lessons

## VCE Specialist Mathematics Units 3 and 4 – Functions and Graphs

1.1 Rational Functions1.2 Absolute Value Functions1.3 Reciprocal Trigonometric Functions1.4 Trigonometric Identities1.5 Inverse Trigonometric Functions

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26 Lessons

## VCE Specialist Mathematics Units 3 and 4 – Algebra

2.1 Rational Functions2.2 Complex Numbers

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Specialist Mathematics Units 3 and 4 consist of the areas of study: ‘Functions and graphs’, ‘Algebra’, ‘Calculus’, ‘Vectors’, ‘Mechanics’ and ‘Probability and statistics’. The course content development should highlight mathematical structure, reasoning and applications across a range of modelling contexts with an appropriate selection of content for each of Unit 3 and Unit 4. The selection of content for Unit 3 and Unit 4 should be constructed so that there is a balanced and progressive development of knowledge and skills with connections among the areas of study being developed as appropriate across Unit 3 and Unit 4.

Specialist Mathematics Units 3 and 4 assume familiarity with the key knowledge and skills from Mathematical Methods Units 1 and 2, the key knowledge and skills from Specialist Mathematics Units 1 and 2 topics ‘Number systems and recursion’ and ‘Geometry in the plane and proof’, and concurrent or previous study of Mathematical Methods Units 3 and 4. Together these cover the assumed knowledge and skills for Specialist Mathematics, which are drawn on as applicable in the development of content from the areas of study and key knowledge and skills for the outcomes.

In Unit 3, a study of Specialist Mathematics would typically include content from ‘Functions and graphs’ and a selection of material from the ‘Algebra’, ‘Calculus’ and ‘Vectors’ areas of study. In Unit 4, this selection would typically consist of the remaining content from the ‘Algebra’, ‘Calculus’, and ‘Vectors’ areas of study and the content from the ‘Mechanics’ and ‘Probability and statistics’ areas of study.

In undertaking these units, students are expected to be able to apply techniques, routines and processes
involving rational, real and complex arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, graphs, differentiation, anti-differentiation and integration and inference with and without technology. They should have the facility with relevant mental and by-hand approaches to estimation and computation. Using numerical, graphical, geometric, symbolic and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment is to be incorporated throughout each unit as applicable.

source – VCE Mathematics Study Design