2016 VCE exam guide — Further Mathematics: Tips for dealing with revised study design

Although much of the previous content remains, there are enough changes for you not to rely only on past trial and VCAA exams, and Examiners’ Reports, for your examination preparations.

One of the most significant changes to the course this year is the greater weighting of the compulsory Core component.

With the inclusion of Recursion and financial modelling, the percentage of examination marks allocated to the Core has increased.

Clearly, a good understanding of the Recursion and financial modelling content will be essential to achieve a strong overall study score.

But how new is the Recursion and financial modellingcontent, really?

Although some of the terminology has changed (they are now called recurrence relations rather than difference equations) many of the mathematical ideas can be found in the old Number patterns and Business-related mathematics modules.

Unfortunately, trying to study for this year’s exams using past questions for these previous modules, will not be sufficient given the overall differences in content and emphasis in the revised study design.

Here are a few ideas that can help your study in this topic.

1. The topic is essentially about the relationships between first order linear and geometric recurrence relations and the financial concepts of simple and compound interest.

You must clearly understand how the mathematical process of iteration using the recurrence relations corresponds to the financial situations of loans, investments, and depreciation.

A summary of the relationships, including those involving both linear and geometric growth or decay, are in Table 1.

Consideration of the similarity between the graphs of recurrence relations and the graphs of the financial concepts will also help build understanding.

2. When using recurrence relations to model financial situations you will only be expected to show up to four or five terms (or values) when starting from the initial term.

This applies is situations such as depreciation tables, investment tables and loan (amortisation) tables.

Although it is expected that you develop such tables in a recursive manner (line by line), recognise that you can use the sequence functionality with technology to at least check your answers. An example of a table for the first 5 values of the recurrence relation V_(n+1)= 1.05 V_(n)+300 V_0=10000

is shown in the screen shot on this page.

Your teacher will be able to show you how to use your particular technology to generate tables and graphs.

3. The finance solver (TVM) of technology can be used to solve all of the questions that involve more than a small number of iterations.

Typically it is best used for cases of geometric growth (compound interest) such as reducing balance depreciation, compounding investments, reducing balance loans, and annuities.

Although the technology does all of the work, skilful use is required in correctly entering the values. Remember the adage:

If the money comes into your hand (such as taking a loan, return from an investment) it is entered as a positive value.

If the money leaves your hand (such as making an investment, making a payment) it is entered as a negative value.

Also remember that the TVM always uses the nominal interest rate per annum, which can be different from the interest rate value used in recurrence relations.

4. Unless advised otherwise, always answer questions to the nearest cent.

Although technology may provide an answer of 36.2, remember that if this is a money amount, it is correctly written as $36.20. Similarly, your local shop may round $36.27 to $36.25, but that is not the mathematical practice in Further Mathematics!

5. The VCAA published sample examinations for the revised study design earlier this year.

You can access the sample papers yourself from the VCAA website.

The sample questions are a good indicator of the style and type of questions that will be asked in November, and should be considered essential preparation.

However, the examiners are a creative bunch, and some sort of surprise or twist can always be expected. The more practice and study you can do, the less that surprise will be.

Gary Motteram teacher VCE Further Mathematics at Mentone Girls Grammar

EXAM DETAILS:

Further Mathematics

EXAM 1

When: October 28, 2pm-3.45pm

Reading: 15 minutes

Writing: 1 ½ hours

Worth: 33 per cent of study score

EXAM 2

When: October 31, 9am-10.45am

Reading: 15 minutes

Writing: 1 ½ hours

Worth: 33 per cent of study score