Eight Healthy Habits For Exam Success

Sydney Morning Herald

Monday June 19, 2006

Writer: Robert Yen teaches at Hurlstone Agricultural High School and lectures at HSC study days. He writes and edits for Reflections, the journal of the Mathematical Association of NSW.

The following tips are based on successful strategies used by students who achieved high marks in the General Mathematics HSC exam.

1. Show working in your answers

The number of marks allocated to a question indicates how much working you should show. Give the examiner a reason to award you marks. Writing a "bald answer" in the exam with no working shown doesn't help. Last year's question on calculating the volume of a brick was worth three marks, and students who wrote a bald wrong answer scored nought out of three, while those who gave a wrong answer with some correct working may have been awarded one or two marks. Candidates who showed full working gave themselves the chance to be awarded full or part marks. Marks are awarded for correct steps, so set out your answers clearly and logically.

2. Check that your answer makes sense

Always check the reasonableness of your answers. When calculating an unknown length or angle, see from the diagram whether your answer seems practical. The length of a hypotenuse in a right-angled triangle is obviously wrong if it is shorter than one of the other sides. Last year's question on a fund-raising dance asked students to calculate the new price of a ticket to increase the profit. Those students who gave answers that were below the original price had clearly not checked the reasonableness of their answers.

3. Really know your work (don't cram)

HSC examiners are impressed by answers that show deep understanding of the course and are written clearly and concisely. Like the judges on Australian Idol, examiners can spot a phoney straightaway, so instead of cramming for the exam and trying to bluff your way through, spend time carefully learning the theory. Last year's exam tested financial expectation, normal distribution, skewness, sample standard deviation and changing the subject of a formula. How sharp is your knowledge of these concepts?

Also, don't forget to study the Preliminary course because up to 30 per cent of the exam can be based upon it (not including lead-in questions). Brush up on basic skills such as percentage calculations, ratios and rates, scientific notation, algebra and solving equations, and make sure you understand the difference between the mean, mode and medium.

4. Choose the simplest and quickest method

In last year's exam, instead of using sin, cos or tan to find an unknown angle in a right-angled triangle, some students used the sine or cosine rules, which still worked but took longer and had a greater chance of error. You should always look for the most efficient solution to a question, using the marks allocated as a guide. Consider drawing a diagram or setting up a table, or whether the formulas sheet or the answer to a previous part of the question needs to be used. Don't use trigonometry if Pythagoras' theorem is easier, or the sine and cosine rules on right-angled triangles.

5. Know how to explain your answers in words

Another way HSC exams test deep understanding is to ask students to explain or justify their answers in words. Two examples from last year were:

* Identify ONE trend in this graph and suggest a valid reason for this trend.

* Briefly explain what is meant by the term standard deviation.

The second example was worth only one mark, with a sufficient answer being "a measure of the spread of scores", but some students wrote whole-page essays involving diagrams. Stay focused on answering the question and work with the facts rather than personal opinion. Students who over-interpret a question risk writing long explanations and contradicting themselves. Remember that this is mathematics, not creative writing. Learn to describe, explain, interpret and justify your answers using correct terminology. Practise your writing skills with past HSC questions.

6. Know the language of General Mathematics

As General Mathematics is an applied mathematics course, each topic has its own jargon. Here are some terms from last year's exam: tax deductions, ogive, dividend yield, declining balance method, ignore time zones, capture-recapture technique, compounding annually, great circle distance. Do you know what each one means? Some students even had difficulty interpreting a phrase such as greater than four in a probability question - does this include four? Spend some time learning the language and compile a glossary for your revision notes.

7. Read and draw graphs accurately

Remember to bring a ruler to the exam for drawing and measuring. This will help you to draw graphs and diagrams that are not too small, messy or without scales. Draw big, neat graphs with labels and mark the axes accurately. Spend time revising how to draw bearings (in trigonometry) and tree diagrams (in probability), as these skills are tested frequently. With last year's question on an area graph, some students incorrectly treated it as a line graph or had trouble reading the scale on the vertical axis.

8. Know your financial calculations

Develop a good understanding of the concepts, formulas, tables, calculations and graphs involved in compound interest, annuities and depreciation. The NSW HSC Online website has a graph of a car loan where you can change the values of the principal, interest rate and monthly repayment (hsc.csu.edu.au/maths/general

/hsc/fin_maths/fm4/). Remember that in the formulas, r must be entered as a decimal and n may be in months or years depending upon the problem. Learn to evaluate long expressions such as ? on your calculator.

If using a graphics calculator, show working by listing the substitution values. Finally, check that your answers sound reasonable and realistic.

© 2006 Sydney Morning Herald

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