Written by Steve
So here you are with your end of year Mathematics exams fast approaching and whether they are Core 1 and 2 or Core 3 and 4 or even further pure exams the revision techniques should be roughly the same.
The exams will be an hour and a half long and will test you on each of the topics from the relevant module. So expect one question from each broad topic of the course. This can vary between 7 and 9 questions, worth up to 15 marks per question. Remember that the first few questions tend to be entirely skills based with the later questions requiring a higher level of thought and application, as we will discuss.
For Core 1 and 2 you should expect questions on: indices and surds, differentiation, integration, sequences and series, coordinate geometry and graphs, algebra and functions, exponentials and logarithms, and trigonometry.
For Core 3 and 4 you should be splitting the courses into sections such as Algebra and Functions, Trigonometry, Numerical Methods, Differentiation and Integration, Differential Equations and Vectors.
The Further Pure modules will vary depending on your exam board and whether you are studying all or just one or two of the modules. Make a list of the topics that you will need by using the chapter headings from your textbook or by looking at the specification provided by your exam board. For AQA you will find it here, for Edexcel you will find it here and for OCR you will find it here.
Hopefully at this point you have a good idea of what your strengths are and the areas needed for improvement. You can help determine this by taking a practice examination under timed conditions and ask your teacher to mark it or use a mark scheme and analyze it yourself. Decide which of the questions from your practice exam relates to which topic, perhaps ranking them from strongest to weakest.
Of course these will change as you do your revision, so return to this step of reviewing your knowledge against the specification (see links above) or topic lists that you made from your textbook on a regular basis. It will help you to recognize progress and provide renewed encouragement as you approach the exams.
So now you know which are your weakest areas, what is the best way to revise?
Knowing your weaknesses and focusing mainly on these will prove less time consuming and will get you improvements more quickly than just plugging your way systematically through the textbook. Once you have identified the topic causing most concern, you can break it down further using the chapter headings from your textbook or by using the detail from the specification.
For example, Differentiation can be split into several parts such as: differentiating a polynomial, exponential, logarithmic or trigonometric function, using the product rule, quotient rule or chain rule, or applying differentiation to connected rates of change and differentiating implicitly.
As you will realize, it is unlikely that every area will need improvement. You should find this reassuring! Having identified your specific area of weakness, you now need to spend time reading over your notes on the concept and then attempting problems on this specific topic. Most texts have worked examples that allow you to look at how others have tackled them. So cover over the solution, attempt the question and then compare your solution with the suggested one from the text, remembering that there are a variety of methods to complete each question.
You may also find a study group useful. Sharing ideas with other students and explaining your reasoning to others is a valuable and very legitimate way of learning. You can see other methods and figure out how to present your solution in a coherent manner; after all, you will need the examiner to be able to understand what you have done! Chances are that if you can explain why a particular method works then you will understand how to apply it to an exam question. Seeing other people’s solutions can also be very eye opening and allow you to see links between topics in ways that you haven’t before. Other people will also have a variety of different strengths and weaknesses relative to you, and you will be able to help each other immensely.
But the most important resource for improving your grade is the ‘past paper’. Past papers were written by the same group of people who write your exam and so the style will be similar to the paper that you will sit. This means that completing these will give you practice on similar questions, will show you the way questions have been set in the past and hence allow you to predict the future. Past papers for AQA can be found here, for Edexcel can be found here and for OCR can be found here.
As the questions are becoming more ‘problem solving’ and less structured in nature, it is a good idea to focus on the last five years, and if you have international papers or exemplar questions from your exam board, you will find them particularly useful as they will show the areas of particular importance to the examiners (ask your teacher or look at the ‘Past Paper’ lists on the exam board websites for these). Some exam boards will suggest the grades for particular questions. For example Edexcel provides graded papers: Gold, Silver and Bronze, which allow you to focus on questions around the grade you are expecting and boost your chances. It is important that you are realistic about your current level and build from there. Starting with entry level questions where you just need to apply a technique such as “differentiate ” and then moving towards questions where topics have been merged together like “find the equation of the tangent to the curve at the point with -coordinate 3” will allow you to ensure a good base knowledge when you enter the exam room.
As with all subjects, it is important to make sure that you revise for each of the modules of your course and do so in a variety of ways to ensure that whatever your paper looks like you have the best chances of success. So you will also need to spend time completing a similar process for each of your applied options as well, whether they are Probability and Statistics, Mechanics or Decision. Remember that each of the papers is equally weighted and you should be preparing for all of them simultaneously.
Be sure to give us a shout if you have any questions!