Maths can do some damage to your self-esteem from time to time, as there is nothing quite like it for making you feel a bit challenged in the intelligence department. I can't say I was surprised when scientists announced earlier this month that we humans have only two or three times the number of genes that our friend the fruit fly has. I reckon it is precisely a maths exam that encourages some fly-like genes to express themselves in a way that ends up making you feel (and look) like Jeff Goldblum - and I'm not talking Jurassic Park here.
So, listen. You have no control over your genes. What you do have some influence over is what happens between now and those two days in June when the Leaving Certificate mathematics exams take place. The detailed outline of the mathematics exams which follows here is intended to help you plan your strategy for those two days, and to help you lose that buzzing feeling - and keep it lost.
You should know that, say, Question 1 of Paper 1 will contain questions to do with this or that or the other idea. Practising questions to do with this or that or the other idea is thus likely to do you some good. Do not be surprised to find in the exam that some topics are not there - you should know what is likely to replace them and to have prepared for this possibility. Do not be surprised to find the same topic used in several questions.
The Chief Examiner's report for last year points out that the hallmark of high achieving students was "clear accurate work that portrayed a sound understanding of all aspects of the syllabus. The solutions presented carried evidence of ongoing practice and thorough recent revision." This means that you shouldn't go into the exam with too rigid a view of which questions you are going to attempt. Spend some time reading the questions carefully so that you don't miss a question that might be straightforward for you to do. (The report will be available soon at www.irlgov.ie/educ/exams/exams.htm - follow the link to Chief Examiner's report). This report also gives specific do's and don'ts for your guidance, and most of these are mentioned in the detailed outline of the mathematics exams in this supplement, and in the remainder of this article.
Preparing for the exam
Make sure you understand and know all the proofs on the syllabus.
Make sure you know all the formulae you require - that is, practise writing these down correctly.
Higher-level students should make sure the following points form part of their revision programme:
- handling fractions
- factorising
- handling inequalities
- getting the square root of a complex number
- recognising a recurring decimal as a geometric series
- proving the product rule from first principles
- differentiating inverse trig functions
- applying differentiation to problems involving parallel tangents
- finding the co-ords of the max point of a log function
- applying integration to area problems
- evaluating limits
- reducing surds to simplest form
- squaring algebraic expressions
Higher-level students should not underestimate the question on further calculus and series in Section B of Paper 2. This question requires serious revision in its own right.
Ordinary-level students should make sure that they know all the formulae for:
- co-ordinate geometry
- sequences and series
- roots of a quadratic
- sin, cos, and tan ratios in a triangle
Foundation-level students should practise rounding-off answers to given numbers of decimal places and significant figures.
Setting out your work
Start each new question at the beginning of a new page.
Do not write in pencil.
Show all your work!
Careful with those calculators!
Write down the sum before you do it on the calculator.
If the calculation is very complicated, break it up into steps.
Check your work!
Get someone to explain what the DRG button does.
Use a calculator you are familiar with in the exam.
If you think some of your work is wrong, cross it out with a single line and resume your work.
If you get stuck in a question, do not abandon ship at once! Is there another way to tackle the question?
Double check any formulae you write down.
Where possible, draw diagrams to help you make sense of questions. As you gain extra bits of information, add them to the diagram.
Check your work when you finish a question. Does this answer look correct? Have you answered all the parts of the question?
Put short remarks in your work to explain what you are doing.
One last point. Are you doing the right level of exam? The Chief Examiner reckons that some 4 per cent of the girls and 5.6 per cent of the boys who did the higher-level papers in 2000 got grades of E, F, or NG. At ordinary level, 11.4 per cent of the girls and 14.3 per cent of the boys got grades of E, F, or NG. This is not a time for heroics. Did you hear that, guys?
Good luck and no buzzing!
Dr John Evans has been teaching mathematics and applied maths at Mount Temple school in Dublin for 24 years, and is a former chair of the NCCA senior cycle mathematics syllabus committee. He is a partner in the IT consulting firm Mimesis and may be contacted at evans@mimesis.net
