VCE Mathematical Methods Units 3 and 4

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1.1 Graphs
1.2 Exponential Graphs
1.3 Logarithmic Graphs
1.4 Trigonometric Graphs
1.5 Transformations

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33 Lessons

2.1 Polynomials
2.2 Inverse Functions
2.3 Inverse Trigonometric Functions
2.4 Functions
2.5 Trigonometric Graphs
2.6 Simultaneous Equations

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36 Lessons

3.1 Rates of Change
3.2 Differentiation
3.3 Application of Differentiation
3.4 Integration
3.5 Application of Integration

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44 Lessons

4.1 Descriptive Statistics
4.2 Discrete Random Variables
4.3 Binomial Distribution
4.4 Statistical Inference

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22 Lessons

Mathematical Methods Units 3 and 4 are completely prescribed and extend the introductory study of simple elementary functions of a single real variable, to include combinations of these functions, algebra, calculus, probability and statistics, and their applications in a variety of practical and theoretical contexts. Units 3 and 4 consists of the areas of study ‘Functions and graphs’, ‘Calculus’, ‘Algebra’ and ‘Probability and statistics’, which must be covered in progression from Unit 3 to Unit 4, with an appropriate selection of content for each of Unit 3 and Unit 4. Assumed knowledge and skills for Mathematical Methods Units 3 and 4 are contained in Mathematical Methods Units 1 and 2, and will be drawn on, as applicable, in the development of related content from the areas of study, and key knowledge and skills for the outcomes of Mathematical Methods Units 3 and 4.

For Unit 3 a selection of content would typically include the areas of study ‘Functions and graphs’ and ‘Algebra’, applications of derivatives and differentiation, and identifying and analysing key features of the functions and their graphs from the ‘Calculus’ area of study. For Unit 4, this selection would typically consist of remaining content from the areas of study: ‘Functions and graphs’, ‘Calculus’ and ‘Algebra’, and the study of random variables and discrete and continuous probability distributions and the distribution of sample proportions. For Unit 4, the content from the ‘Calculus’ area of study would be likely to include the treatment of anti-differentiation, integration, the relation between integration and the area of regions specified by lines or curves described by the rules of functions, and simple applications of this content.

In undertaking these units, students are expected to be able to apply techniques, routines and processes
involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, graphs, differentiation, anti-differentiation, integration and inference with and without the use of technology. They should have the facility with relevant mental and by-hand approaches to estimation and computation. The use of 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