# Mathematical Methods Units 3 and 4

## Overview

Mathematical Methods covers four broad areas – Functions and graphs, Calculus, Algebra, Probability and statistics. **Unit 3** begins with graphs of different functions, how to sketch them and find their equations. We also explore how to transform the functions graphically and algebraically.

The functions we cover are varied: polynomials (parabolas, cubics and so on); logarithmic, exponential and trig. functions (sine, cos and tan).

In Calculus we look at the rates of change in these functions. We use algebraic skills and graphs to analyse how rates of change affect each function. Calculus continues from Unit 3 into **Unit 4**, where we study integration – how to find the area under the curve of a graphed function.

Many of the functions are applied to practical problems. Things like tide movements, growth in population, or temperature fluctuations, are some of the examples where functions and calculus are applied.

The final topic is Probability and statistics. Describing the outcomes of chance, working out probabilities and analysing statistical data are the main areas of this topic.

Algebra occurs throughout each topic. We use algebra to complete tasks in most weeks. Algebraic skills include simplifying expressions, setting up equations, identifying key information and interpreting answers.

Technology plays a role as well. Students use their CAS calculator to check their answers, graph and interpret information, and to investigate mathematical problems.

## Who is it for?

Mathematical Methods CAS is central to many areas of science and technology. Mathematical Methods CAS provides background in mathematics for students to better understand the world around them and for further study. It provides a foundation for study in various fields, ranging from medical technology and engineering to economic predictions and statistical modelling.

Many students are interested in Mathematical Methods CAS as a prerequisite for their pathway plan. While it is certainly helpful for students to be good at maths, with revision and extra study, an interested student can still achieve in the subject. The key is to allocate regular study time and develop consistent study habits.

## What do you do?

In graphing, students explore the effects of transformations of a graph interactively. They study how the equation of the graph changes when it is transformed.

In calculus, students explore the relationship between a graph and the way its gradient changes interactively. They develop algebraic skills to describe relationships and apply them in practical problems.

Students also use their CAS calculator throughout to check answers and complete calculations.

## What skills do you need?

Mathematical Methods assumes some background skills: knowing how to graph straight lines and parabolas, factorise quadratics and find trig. ratios (sine, cos and tan). Algebraic skills such as substituting values into algebraic expressions and solving equations are an important part of the course.

While we provide revision of many of these skills, a general review of algebra, graphing and trigonometry from Year 10 and Year 11 Maths is recommended.

## What skills do you develop?

Mathematical Methods develops several skills:

- being able to sketch graphs of functions
- applying graph sketching to solve problems
- developing skills in manipulating equations
- solving equations of various functions, including trig. functions
- interpreting answers to practical problems
- using a CAS calculator efficiently to solve problems, check graphs and equations.

## Requirements

The purchase of the following textbook will also be required: *Maths Quest 12, Mathematical Methods*, published by Jacaranda. Students have the option of either purchasing the textbook or the eBook.

The purchase of the following textbook is recommended: Checkpoints 2018, *VCE Mathematical Methods Units 3 and 4.*

**CAS calculator**

For this study, students need access to a VCAA-approved CAS calculator. DECV course notes are written using the TI-Nspire CAS and students are highly recommended to get one, if they are going to buy a new calculator. *The Maths Quest 12* textbook includes instructions for both TI-Nspire CAS and Casio ClassPad calculators. However, any of the VCAA-approved CAS calculators can be used.

Visit the VCAA website for further information on VCAA-approved calculators

## Things to think about

It’s important to be clear about your reasons for wanting to study Mathematical Methods. Is it something you’re interested in, a prerequisite for future study, or some other reason?

If you like maths, Mathematical Methods will be interesting and sometimes challenging. If Maths isn’t your favourite subject you may need to make time to revise topics and to include extra practice.

Think about your commitments. Can you make the time available each week for study and skills practice?

One thing we recommend is contacting your teacher whenever you have questions. You can progress through your studies much more quickly by asking for help when you are stuck.

## Things you can do now

Go to the VCAA website for more information about this subject.

## Things to have a look at

##### PurpleMath

For maths revision in a range of topics the Purplemath site has many free review lessons.

##### Ti-Nspire

This site includes movies on how to use the Ti-Nspire CX calculator.

##### ClassPad Help

The ClassPad Help site includes a series of videos on the how to use the Casio ClassPad calculator.