Sum Of All Learning

The Age

Monday September 8, 2008

Michael Cody - Michael Cody teaches at Camberwell Grammar School

All that you have studied in maths will be put to the test, writes Michael Cody.

THE FIRST Mathematical Methods exam is where you finally get a chance to show how much of the past six years of maths learning has stuck in your memory bank. Of course the content emphasis is on the last year of learning but Methods draws on a reasonable understanding of fractions, rounding, coordinate geometry, trigonometry, probability and algebra that pre-dates Mathematical Methods Units 1 and 2.

No notes and no calculator! Sounds daunting, but you will be surprised just how much you do remember for Examination 1. The examiners actually try really hard to produce questions that they hope students can get a start in, and that applies to both papers.

The one hour paper is very much knowledge and skills testing and the formula sheet is provided to help trigger memories of the right rules to follow once you have decided what the question is asking.

Quite a few marks are available if you are able to pick the right rule and make a correct substitution.

There are three major items that students need to "memorise" for exam 1. They are: - The quadratic formula is drilled from Year 9 and 10 and always proves useful somewhere across the two exams. [The quadratic formula provides solutions to ax2 + bx + c = 0 which are, x = -b ? b2 - 4ac 2a Exact angle values are often introduced in Year 10 and take more practice if they are to become second nature. [One approach is to remember the angles 0, , 6 4 3 2 , , and the sine values go: , 2 2 2 2 , , 2 , 6 4 3 2 3 ; the cosine values go the other way; and tan values are sine cosine .] - The "z formula" z = x - ? for Normal Distributions We can assume that it is necessary to remember it and how to use it.

Many students lose marks with careless errors through cancelling incorrectly or not noticing that they are asked f `(x) for instead of f -1(x) or vice versa. You also have to remember that f `(x) can have a slightly different domain to f (x) and that f -1(x) entirely swaps domain and range with f (x). If you are asked to draw f -1(x), it is advisable to also draw y = x and use one to one axes scales to get the correct reflection.

In 2006 students were asked to plot a probability distribution graph and it was surprising just how many messed up the vertical scale. Fractions are the nemesis of many Maths Methods students - take extra care with relative size and cancelling down.

It pays to spend time in the holidays before the exams rereading through the Unit 1 & 2 course description. It's worth reading the entire VCAA course description for Methods available online in the VCAA web site (as are past exams and assessment reports).

Examination 2 is a lot longer, has a multiple choice section and much more detailed analysis questions. I am not sure whether students look forward to the now traditional "Tasmania Jones" adventure questions or whether they are hoping that this year he might not quite make it (some students thought they had killed him off last year in pursuit of the Zambeji diamond, but should have realised that they had made a mistake there!).

This examination permits approved technology and a book of notes. Success is most likely to come to the student who is best organised and knows where to find or use his or her tools the most effectively and efficiently.

Time management will play a role in your success. The multiplechoice section tends to be concept or skill based and, with each answer worth one mark, don't be tying yourself up with the harder ones at the expense of getting into the analysis questions. Some multiplechoice questions may take two or three steps to get an answer and this would be the equivalent of two or three marks in exam 1 (or in the analysis section of exam 2). If your answer isn't amongst the 5 choices, mark the question; make a best guess at the answer and come back to it later if you have time.

Mis-reading questions, or just not fully answering the question posed, costs students marks on the extended questions. Read the question in reading time. Read the question again immediately before you try and answer it, but this time underline/highlight key words.

Read the question again after you have finished working on it. Make sure you have answered what was asked - and as they have asked (as a percentage? as an exact answer?

as a decimal correct to two decimal places? as a decreasing rate? in a particular form?).

It is rare for more than 4 marks to be given to any one particular part of a question on either paper.

If one part is reliant on a previous part then the examiners will build that into the question and you will pick up marks for "consequential" working. Functions; calculus and probability can be intertwined into a multi-faceted question that does not necessarily build in difficulty as you work through it. Just because you may not understand how to do the early parts of a question does not mean that you might not be able to get marks for the later bits, so read carefully and you may surprise yourself.

The key to success is practice and preparation. This article scrapes the surface of what is necessary to perform well in these exams, but hopefully it re-enforces what you are already doing and encourages you to have a go and achieve your best.

Michael Cody teaches at Camberwell Grammar School.In mathematical methods, the second of three major items that students needed to "memorise'' for exam 1 should have said:

- Exact angle values are often introduced in Year 10 and take more practice if they are to become second nature. [One approach is to remember the angles and the sine values go:

the cosine values go the other way; and tan values are sine

cosine

Education apologises for the errors.

© 2008 The Age

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