LEARNING FROM PAST MISTAKES 12 EXAM TIPS FOR HSC GENERAL MATHEMATICS STUDENTS 2006 Based on tips by Robert Yen

1. Show working in your answers Writing a ‘bald answer’ in an exam with no working shown is the most common mistake made by HSC students.

Students who wrote a ‘bald’ wrong answer scored 0 out of 3, while those who gave a wrong answer with some correct working scored 1 or 2.

If using a formula, show the values being substituted as this may earn you that first mark. Before you write the final answer, write the unrounded answer first as this may earn you a mark even if you round it incorrectly.

2. Don’t round your answer too early Rounding a decimal answer should be done only once and at the very end. If you round during the middle of a calculation, then your final answer might be inaccurate. Instead you should either keep partial answers on your calculator’s display and recall them using the ANS key, or write them down on paper with all decimal places shown for use in further calculations

Answer: 1364.219482 = 1364 cm3

3. Check that your answer makes sense Good students check the reasonableness of their answers. When calculating an unknown length or angle, see from the diagram whether or not your answer seems practical and realistic.

4. Read and answer the whole question Sometimes, students don’t read a HSC question completely and answer what they think the question is asking, leave out some important part of the answer or waste time doing more than what was required

3/5x60=36 What some students did instead: Gave the probability of winning $4 (i.e. their answer was 3/5)

A=3600x4.3101 = $15516.36

What some students did instead: Used the future value formula or did repeated calculations, which took much longer

When reading an exam question, identify exactly what needs to be found, highlighting any key words, especially those in CAPITALS or italics Double-check that you have actually answered the question Beware of double-barrelled questions, where two questions are asked in one. e.g. ‘Identify ONE trend in this graph, and suggest a valid reason for this trend.’

4. Really know your work (don’t cram!) The examiners are always impressed by those students who show deep understanding of concepts and who write clear and concise answers Like the judges on Australian Idol, they can spot a phony straight away so don’t try to bluff your way through

Sometimes, it’s not the maths that is difficult, but the concepts and terminology

F.E. =3/5x($4) + 1/5x($0) + 1/5x(-$8) = $0.80 Some students did not know that financial expectation referred to a monetary amount and wrote answers such as ‘not bad’ or ‘she expects to win’

Don’t forget to study the preliminary course because 30% of the exam can be based on it Brush up on basic skills such as percentage calculations, ratios & rates, scientific notation, algebra and solving equations Last year, some students had trouble remembering the difference between the mean, mode and median of a set of data

Mean = 63 divided by 9 = 7 Make sure you know other formulae that aren’t on the formulae sheet

6. Realise when parts of a question are related Most HSC questions have related parts, where the answer in part (i) leads to the solution of part (ii) and so on This is usually the case with the sine or cosine rule question

Students who ignore this often use incorrect or more complicated methods that take longer or ‘re-invent the wheel’ and solve the first part of the problem again

7. Choose the simplest and quickest method Every question in a HSC exam has been designed to be answered within a specific time, with the number of marks allocated suggesting how long it should take Students are often guilty of using a more complicated method when a simple one would do the job effectively

This was a simple trigonometry question that required using sin, cos or tan, but some students used the sine and cosine rules for non-right-angled triangles taking more time and with a greater chance of error

Before answering a question, spend time thinking about the most efficient method Consider drawing a diagram or graph, making a list or table, looking for a number pattern, using logic, common sense, guess-and-check, some theory or formula, or the answer to a previous part of the question If it is taking too long then it is probably wrong or inappropriate Don’t use trigonometry if Pythagoras is easier

8. Highlight the key words of a HSC question Students are often unfamiliar with the terminology found in HSC questions. Here are some examples from last year’s exam: Q24 (d) (i): Show that the total number of people living in Sumcity is 160 000 Q25(a) (ii) and (c) (iii): Justify your answer with suitable calculations Q28 (b) (i): Write the formula for the cost ($C) of running the dance for x people

9. Know how to explain your answers in words Many questions require a worded answer rather than a numerical one

The previous 3 questions requiring worded answers were worth one mark each but some students wrote answers that went for a page!! Stay focussed on answering the question, working with the facts rather than personal opinion

10. Learn the language of General Maths Do you known what each of the following terms from last year’s exam mean: tax deductions ogive dividend yield declining balance method ignore time zones capture-recapture technique compounding annually great circle distance

11. Read and draw graphs accurately Many students fail to bring a ruler to the exam for drawing and measuring purposes As a result, their graphs and diagrams are too small, messy and without scales Successful students draw big, neat graphs that take up half a page, with labels and axes marked accurately

Spend time revising how to draw bearings (in trigonometry) and tree diagrams (in probability) Most measurement diagrams are marked ‘NOT TO SCALE’ meaning that the lengths and angles shown are not an accurate representation – you can’t measure them with a ruler or protractor! Only a scale diagram can be measured using measuring instruments

12. Know your financial calculations Develop a good understanding of the terminology, methods, tables and graphs involved in compound interest, annuities and depreciation Can you use your calculator to evaluate long expressions such as needed for last year’s exam?

Remember that in formulae, r must be entered as a decimal and n may be in months or years depending on the problem

BEWARE OF SIMPLE MISTAKES: In Q25 (a), some students converted a monthly amount to a yearly amount by dividing by 4 and then multiplying by 52 instead of just multiplying by 12 NEVER use 1 month=4 weeks!!! Another common mistake is to use the wrong interest, annuity or depreciation formula. Finally, check that your answers sound reasonable and realistic.

10 Steps For Success: Find out all you can about the format of the exam (review past HSC papers) Be prepared Use the reading time and number of marks to plan your approach to the exam. Note the harder questions – you may need to spend more time on them

Spend the first minute of each question planning, thinking and choosing the best strategy to use. Spread out your work. Draw big diagrams Pace yourself – keep an eye on the time Make sure you have answered the question. Check that it sounds reasonable.

Don’t get bogged down – move on if you’re getting nowhere Don’t get bogged down – move on if you’re getting nowhere. If your working out to a hard question is taking too long, then it’s probably wrong. Retrace your steps, start again, or come back to it later. If you make a mistake draw a neat line through it. Don’t scribble over it or use correction fluid. You may still get marks for it if it is right.

At the end of the exam, check your work and go back and attempt harder or uncertain questions

Good luck …and one last thing