An A Level/AS Maths exam typically has 9-10 questions, with a total of 75 marks. That’s an average of 8-9 marks per question. There are between 8-11 topics in each module, meaning there is going to be roughly one question on each topic. So, there may only be one opportunity to get all that knowledge you have, say on logarithms out there. What if you can’t do the question?
- Firstly, don’t panic. Easier said than done of course, but staying calm and confident is really important.
- There are only so many ways the topics are examined. If you have done plenty of past papers you will have seen the type of question before. It may be that the language used is confusing.
- Re-read the question, taking notes. Think about how you might make a start. Often, if you can’t see how to do it, writing some maths down and manipulating it a bit helps.
- Write down any rules which go with the topic. They are useful to refer to, and may help you see how to start the question.
- All the information provided in the question will probably need to be used. Make sure you have taken everything in.
- If it is a multi-part question though, just concentrate on the first part.
- Some multi-part questions ask you to prove something in the first part and then go onto use it in the second part. If you can’t do the proof, you can still attempt the second part.
- Remember there are marks available for working.
- If you are really stuck, leave it. Do the other questions on the paper and come back to it at the end with an open mind.
Lets look at an example. This is Q6 from the Edexcel C2 May 2012 paper:
The first part of the question is a ‘Show that’ and the second part invites you to use the first part, ‘Hence solve’. So, if you can’t do the first part, you can still do the second part and pick up 5 of the 7 marks.
Concentrate on the first part to begin with. The question asks you to show that the equation can be written in the form given. You should write down the first equation and manipulate it until it is in the form required. Firstly, compare the two expressions. What is the main difference between the two? Both expressions have a sin 2x term, so you are unlikely to have to manipulate this. However, the tan 2x term has gone. How else could the tan 2x term be written? This should prompt you to remember that tan a = sin a/cos a. This is the way in, replace tan 2x with sin 2x / cos 2x. Here is my solution:
The second part invites you to use the first part to solve for x. So write down the second expression. How can it be solved for x? Note that you must provide answers for x in the range 0 to 180º. There are expression in both sin 2x and cos 2x, so you are probably going to need to use the cos-1 and sin-1 function on your calculator in conjunction with drawings of the cosine and sin function or the CAST method. The key to starting the question is to realise that as there are 2 parts to the expression, (1-cos 2x) and sin 2x, if either of these parts are zero, then the whole expression will be zero. Work on each part separately and make sure you consider all possible value for x, there are 5 of them, hence the 5 marks. Here is my solution:
Note the question asks you to give your answers to 1 d.p. where appropriate. As the 0, 90 and 180º are exact, don’t include any precision.