3.1 Rates of Change3.2 Differentiation3.3 Application of Differentiation3.4 Integration3.5 Application of Integration
4.1 Descriptive Statistics4.2 Discrete Random Variables4.3 Binomial Distribution4.4 Statistical Inference
1.1 Graphs1.2 Exponential Graphs1.3 Logarithmic Graphs1.4 Trigonometric Graphs1.5 Transformations
2.1 Polynomials2.2 Inverse Functions2.3 Inverse Trigonometric Functions2.4 Functions2.5 Trigonometric Graphs2.6 Simultaneous Equations
- VCE Mathematical Methods Units 3 and 4 – All TopicsUS$3.20 / month
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 consist 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 likely 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. 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