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Leaving Certificate: Higher Level Maths

The Higher Level paper is one which tends to cause a huge amount of unnecessary anxiety amongst students.

I hope that the following advice will provide students with an idea of how best to prepare for the papers in June.

Step 1: Basics

It is essential when a student prepares for the exam that the basic concepts get the majority of the attention. I have seen many students stress about the most difficult calculus problems and pay little or no attention to differentiating simple functions like ‘f(x)=2Sin3x' or other questions of similar difficulty. This leads to a ridiculous loss of marks in an (a) part where 10/10 marks should be always achievable. It is very upsetting to mark an exam or view a script with a student in September to see that they obtained full marks on a difficult part (c) and lost 6-7 marks on an (a) part.

Surprisingly, it is often the more capable students who will lose marks on an (a) part, as they are in such a rush to get to the (c) part that the easy section is skimmed through. Never forget that the (a) part of the question carries at least 20pc of the marks for each question.

Step 2: Derivations (Proofs)

Derivations form an integral part of the Maths curriculum. We should say thank you to the exam for every derivation that appears on the paper in June. We have no excuse for losing marks in such a question. Very often, these derivations form a full (b) or (c) part of a question with the exception of some of the more straightforward proofs. This means we can often obtain up to 15-20 marks for a derivation. That translates as 2-3.5pc of our overall result for each derivation, which is certainly not to be sniffed at.

It is obviously very difficult to predict which derivations will be asked in the exam but suffice to say that if students took it upon themselves to write out all of the main derivations on the course in one place, it wouldn't occupy more than 20-30 pages and it could easily be done over a weekend.

Step 3: No chapter is an island

The main emphasis of the Higher Level exam is not to see what students have learned topics by rote. Its aim is to ascertain which students truly understand the content and their ability to link it with different sections of the curriculum.

A good example of this is Algebra and Differentiation on Paper 1. Most people think of the paper as having two/three Algebra questions as well as two Differentiation questions.

I tend to think of Paper 1 as comprising a mythical topic ,which I call “Differalgebra” (A combination of Algebra and Differentiation in the same question). Many questions requiring a knowledge of both areas have appeared over the last number of years.

Step 4: Never leave out a topic

Repeatedly, students try to second guess the examiner and leave out topics. This is an insane approach to Higher Level Maths. It is frightening how many students think it is feasible to omit Sequences & Series on Paper 1 and Probability & Statistics on Paper 2. This is very careless and will certainly not lead to top grades.

It has been very obvious over the past number of years that the examiner is taking action against people who do this. On many occasions Sequences & Series have appeared in different questions and even on different papers to where they would traditionally be expected to be. For example, a question has appeared on Paper 2 whereby students were asked to find the standard deviation from the mean of the first five terms of an Arithmetic Sequence.

How could you be expected to do this if you have no idea what an Arithmetic Sequence is? Probability & Statistics forms the basis of two questions from Section A on Paper 2. Students are required to complete FIVE questions from section A but there are only seven questions in this section. This means that if you don't revise Probability and Statistics you effectively have no choice on Paper 2. This is most certainly not a comfortable situation to be in and we can be fairly certain one or more of the other five questions in this section will be very difficult to answer.

Step 5: Practise

Maths, like any other language, requires many hours of practice to become proficient. It is important that some revision is done every day to ensure that basic ideas are adequately understood.

Each week, you should allocate a certain amount of time to perfecting your exam technique and timing. My advice is to pick two questions on a topic and see if you can complete them in 45-50 mins, which gives a perfect picture of where we need to be in June. If this task is completed regularly enough, the timing of the exam becomes second nature and is one less thing to think about in June. Obviously, if you continually give yourself too much time for a question you will find it very difficult to cope with exam conditions.

Step 6: Heed the warning

The front page of every Maths exam contains the following warning: Marks will be lost if all necessary work is not clearly shown.

It is critical that everyone heed this warning. It effectively gives the examiner a legal right to take away marks from any student who doesn't adequately show their working. We really need to lose the attitude that “the examiner knows what I mean”. Neither I nor anybody else can mark what's going on in your head. In conclusion, if a student wishes to obtain a high grade in the exam they must take a workmanlike approach to revision and chip away at the topics methodically.

Remember, Maths is a language and, therefore, can't be learned overnight. It needs regular attention over a long period of time to achieve success.