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How a calculated approach can help you hit high figures in Maths

Maths teacher at Yeats College Dr Aisling Kenny-Naughton highlights the key things to be aware of in the Higher Level Maths exam in this very different year

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Challenge accepted: The Higher Level Maths exam will contain difficult and challenging questions, so expect the unexpected

Challenge accepted: The Higher Level Maths exam will contain difficult and challenging questions, so expect the unexpected

Area & Volume is a topic required for Paper 2. However, it can appear on Paper 1 in the form of a max/min question or an area question

Area & Volume is a topic required for Paper 2. However, it can appear on Paper 1 in the form of a max/min question or an area question

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Challenge accepted: The Higher Level Maths exam will contain difficult and challenging questions, so expect the unexpected

Below I have listed my top tips on how to approach the Leaving Cert Maths exam. These tips are used by my students every year and have proven very effective. Different techniques work for different students. It’s important to develop and practise your approach to the exams in advance of the Leaving Cert.

1 Keep calm

If you feel that a question is not going well, make sure to get as many attempt marks as possible. It is also important not to allow a bad question to have an effect on the rest of the paper. Move on and approach your next question with as much enthusiasm and confidence as your first.

2 Before answering a question, read it several times and pick out the important information

When you’ve completed the solution, re-read the question to ensure you have answered the question asked and given the answer in the correct format. For example, if you’re asked for the coordinates of a point, make sure to find both x and y.

3 Be familiar with the marking scheme of past exam papers

Although attempt marks change from year to year and from paper to paper, it is helpful to have looked at marking schemes in advance. Students won’t know how many marks a question is worth on the day. Do not assume a difficult question is worth a lot of marks.

4 Be very familiar with your calculator and the Formulae and Tables Booklet

In particular, you need to know how to reset your calculator, how to switch between degrees and radians and how to use table form. Be aware of what formulae are available in the booklet and where to find them. When studying, use your tables to find formulae so that you become more familiar with them.

5 There are a lot of good websites that can help you study

For example, www.projectmaths.ie contains a lot of resources, student activities, interactive files and quizzes. Also the website www.scoilnet.ie has resources organised by topic and is a very useful study aid.

6 Do not erase anything during the exam

If you make a mistake, simply put a line through your work. The examiner will look at all your attempts and give you the marks for the best attempt.

7 Show your workings

Present your work in a logical and neat way. Draw a diagram, sketch or graph where necessary.

8 Attempt every question

Do not leave any blanks in the exam. There are no marks awarded for a blank space so it’s always worth your while to make an attempt.

9 Check your progress

If you struggle with a particular question while studying, look through the solution, then come back to it at a later date and try it again.

10 Expect the unexpected and prepare to be challenged

The Higher Level Maths exam will certainly contain difficult and challenging questions.

Staying motivated

Maths at higher level is a very long and difficult course. It can be hard to stay motivated while studying and revising. Work and revision must be consistent. Maths must be done every single day.

Here are a few techniques to remember:

▶ Be patient with your progress.

▶ Make sure you’re making progress!

▶ Break the course into topics and create a study plan to cover all topics before the exam.

▶ Create a checklist of your topics and tick off items as you understand them.

▶ Practise, practise, practise!!

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Area & Volume is a topic required for Paper 2. However, it can appear on Paper 1 in the form of a max/min question or an area question

Area & Volume is a topic required for Paper 2. However, it can appear on Paper 1 in the form of a max/min question or an area question

Area & Volume is a topic required for Paper 2. However, it can appear on Paper 1 in the form of a max/min question or an area question

Exam technique

▶ Prepare and practise your exam techniques in advance. Find out what works for you. Do you prefer to answer Section A or Section B first? Most of my students prefer to find a question based on their favourite topic and answer that first. Others like to read through the entire paper first. Some just start at the first question and answer each question in order. In particular, for Leaving Cert 2021, it is important to think about your strategy in advance. With a choice on the paper and more time, students have more flexibility in how they approach the paper.

▶ Remember the questions are going to challenge everyone. If you’re finding a question difficult, chances are every other student is finding it difficult too. Don’t let a difficult question overwhelm you.

▶ Confidence is key!

Exam structure

There are two Maths papers. Each paper lasts 2 hours, 30 minutes and, for this year, each paper will be worth 220 marks.

Each paper has two sections.

Section A: Concepts and Skills will consist of six questions worth 30 marks each. The student will be required to answer four of these. This section examines your basic maths skills.

Section B: Contexts and Applications will consist of four questions worth 50 marks in total. The student will be required to answer two of these. In this section, students have the extra challenge of dealing with a word problem.

The timing for the exam is usually very straightforward. In previous years, the student would simply divide the marks by 2 to find the time allowed for it. A 50-mark question should take 25 minutes. However, this year is different. If you intend to answer the minimum amount of questions required, you should spend 32 minutes on a Section A question and 55 minutes on a Section B question. This would leave you with 12 minutes to look over your paper. However, my advice is to stick to the time limits from previous years. Spend 15 minutes on each Section A question and 25 minutes on each Section B question. This now leaves you with 40 minutes extra to answer additional questions. This ensures you get the most out of the exam.

Be aware that some topics can appear on either paper. For example, Area & Volume is a topic required for Paper 2. However, it can appear on Paper 1 in the form of a max/min question or an area question. You need to be prepared for it to appear on either paper. Similarly, trigonometric functions can appear on either paper. Finding the slope of a tangent to a circle has never been examined and this topic could appear on either paper. Also, you may be asked to do a construction in Paper 1 (construct √2 or √3 ) so have the necessary tools with you.

Marking scheme

Each marking scheme is based on a table of scales. This table changes from year to year and, at times, it even changes from Paper 1 to Paper 2. Although students know that a Section A question will be worth 30 marks, they don’t know in advance how many marks are going for each part of the question. They also don’t know how many attempt marks will be given. It is vital that students attempt everything. Attempt marks vary but at times they are quite generous.

Past paper analysis

The Project Maths syllabus was examined fully for the first time in 2015. Some topics still have not appeared on the exam.

Throughout the article, I will refer to topics that have never been examined before. It is important to pay attention to these topics and to prepare them for this year’s exam.

Preparing for Section B

Students tend to struggle more with questions in Section B. The questions challenge even the strongest students, so be prepared for that. They also tend to combine several topics into one question. Students need to practise questions that involve many topics. For example, solving a question on the circle could involve a mixture of coordinate geometry, trigonometry and geometry.

Read the questions very carefully and several times. It is very important always to first figure out what the question being asked is. Then, look at the keywords in the question and try to pick out the important points. Write the points using Maths terms. For example, if the question asks for a maximum, you should know that you will need to differentiate. Or if you are given the rate of change of a volume, you should know to write this as .

It is very important to prepare for this section by practising questions. Practise using past papers and your textbook. These questions require problem-solving skills that take time to develop. Start now and be patient with your progress.

Advice for Fifth Years

Fifth-Year students need to be very aware that this is a very long and difficult course. Students need to work hard across the two-year programme in order to be successful.

▶ Revise any topics covered in school by completing the relevant past exam paper questions.

▶ Work hard now to perfect your basic algebraic skills. Make sure you know how to factorise, deal with fractions and solve equations. It is important that you don’t leave it until Sixth Year to develop these skills. You will be using algebra to solve problems on a regular basis and you need to be able to do this easily.

▶ Trigonometry is a massive topic for Paper 2. If you have covered Trigonometry in school, spend time revising it. The skills used will be built upon next year so they need to be perfect.

▶ Test yourself! Review any class tests from throughout Fifth Year. Retry questions that you did not answer correctly in the exam and mark yourself. Make sure you are improving!

▶ Consistency is as important in Fifth Year as in Sixth Year. Do not wait until Sixth Year to start revision. Do a little bit every day throughout the two-year cycle.


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