I have spent over thirty years teaching mathematics to A level and during this time I have never found any quick fixes or instant recipes for passing A/S and A Level mathematics. It is a subject which can be very demanding and tests ones ability to persevere. Meet these demands and the subject can become very rewarding.
How do you meet the challenge?
Do not rely on reading alone. You must do questions. Even when you think you know how to do a topic, along comes a question which can be phrased in a way that you have never seen before and this may throw you. The more practice you have from different sources the more confident you will become when you face a strange question for the first time.
Often you may read a question and feel that you cannot answer it, but don’t give in. Spend some time looking at the problem, jot down ideas even if you feel they might be wrong, draw diagrams to help bring out the problem and enable you to view it from a different perspective.
Look for similar examples in text books. Learn the methods involved. We all learn by copying so it is important to be able to copy a method and be able to relate it to the question you are attempting. It can often be a change of number or letter that is all that is needed. It maybe that one author may explain a question in a way that suits your way of thinking.
Make sure that you are using all the information given in the question. A solution is very unlikely to be set that does not depend in some way on the parameters given.
It is not usually a good idea to start a paper on the last question and work backwards. Although these questions are generally worth a lot of marks because they are longer it can have a negative effect if things start to go wrong. Most exam papers start with short questions giving you time to settle in and hopefully gain some confidence. As an alternative, select a question that tests a topic in which you are very confident with.
Look at the marks awarded for each stage of a question. The marks are a good indicator of the number of stages in a solution and possibly a rough guide to the amount of time to spend on a question.
One mark questions will often use phrases such as
“Write down ..” or “State the value of .”
Questions like these generally require no working, so if you find yourself attempting a long calculation the chances are that you are missing the point of the question.
“Verify” is often used in a question. When this occurs you will normally be expected to substitute a value in an equation or statement to check that it satisfies a given relationship or condition. For example, verify that the point (2,9) lies on the line y=4x+1. Just substitute x=2 into the equation of the line and check that y comes to 9.
“Show” or “Prove the following. ” is another common statement to look for in a question. Quite often I find students giving up on a question that says show or prove something and not trying to continue the problem. When I say to them “Why did you not continue?” they say “Because I couldn’t prove what they asked” or “I didn’t understand how to do it”. Fair enough, this may be the case but so often the following parts of a question depend on this result and you should be able to continue as if you had proved it.
“Hence or otherwise”. Look out for this phrase in a question. It is a subtle hint that what you have just calculated or proved in the last part of a question will help you solve the next part. Often the or otherwise route is a long winded method that is not related to the previous part. As a guide, look at the marks for an indicator of the number of stages involved.
Look out for the phrase “Find the exact value .” . Expect to leave answers in surd form, or containing pi, logs or exponentials.
Also take care to read the question. The times a question says find the values and a student gives just one answer. For example when a square root is involved and only the plus answer is given rather than the negative value. Hang on every word!
It is important that you learn formulae. Often you will get marks for just quoting a correct formula for a given situation even if you do not know how to correctly use it.
Always try and have a go at a question. Jot down any ideas or statements that come to mind. An attempt at using a formula or method can sometimes get marks as long as it is reasonably clear.
Show working. This is always written on the front cover of the exam paper. This is so important as it gives the examiners the opportunity of seeing how you achieved an answer and it enables them to follow your lines of thought. By showing working and giving clear introductions to your statements is essential so that you can pick up method marks even if the answer turns out to be incorrect.
Accuracy is also an important element. Too many students round up answers at each stage of a solution and compound their errors. If a question says give your answer to 3 significant figures then throughout the question truncate your answers to several figures beyond this. You will see this repeatedly done in my videos.
Make sure you have a good scientific calculator for the calculator papers and that you have time to familiarise yourself with the keys and functions. Calculators are always changing with some being easier to use than others. Below are some of the best sellers from Amazon where you can check out the reviews or you may like to visit our calculator page.
In an exam you may be anxious to move on to the next question but always check that you have answered the question and to the accuracy that is required. You may easily throw away 1 mark for not answering a question to the required degree of accuracy.
If you attempt a question a solution more than once and are not sure which solution is correct (if either!) it is safer not to cross anything out, then both solutions will be marked and you may gain credit for work seen by the examiner.
This is a summary of what I think are essential points in making progress in mathematics and passing exams. If you can add any more comments that would benefit others then please feel contact me.
A good text book is also a valuable resource when it comes to revision. I have grouped together study and revision books for each syllabus and module in our bookshop which hopefully you will find useful. You can even see example pages on some of the books!
Good luck with your A-Level!