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Easymaths Coursework Help When you are finally handed your maths GCSE coursework, it's never quite what you expected, even if you've been able to practice with a specimen coursework paper beforehand. You think to yourself "How
on earth am I going to do THIS!!!!". Don't panic just yet! |
There's no way to prepare for coursework in the way that you can revise for your maths exams. There are lots of different coursework topics suggested by the exam boards each year, and some schools and colleges may even provide you with a coursework paper which has been designed by one of the teachers for use in your school or college only.
So, if you can't do lots of practice questions to improve your mark, what can you do?
It obviously helps if you have managed to understand the maths topics you've been presented with so far as you may be able to use this experience in answering your coursework questions. You are not expected to do any special maths for your coursework.
Coursework is an investigation. Think of it in the same way as a detective investigating a murder, so at the end of the coursework you can prove beyond all reasonable doubt that your theory holds true.
In a nutshell, coursework requires you to look at a maths problem, describe the problem and examples of solutions in a way that people unfamiliar with it can still follow your reasoning and logic. You will then normally be expected to use your examples (also called results) and try to find a pattern which links them together. Once you have a pattern you then need to generalise this pattern and ideally create a mathematical formula which will enable you to make predictions of future results. Higher level students will be also expected to prove their formula.
You should try to follow a plan all the way through doing your coursework, this will help you know what to do next, it will help you present your thoughts clearly on paper and it will make sure that you don't miss out any crucial bits
Here's the plan for higher level GCSE maths students (foundation and intermediate students' plans should be similar but don't need normally need to go beyond point 8):
1) Read the problem very carefully, then read it again. Think about how you might be able to solve the problem and then read it another time. This is important as you can waste loads of time if you spend weeks answering a different question to the one which is actually asked.
2) Think hard. Have you seen a similar problem before? Can part of the solution come from some maths which you already know?
3) Start by doing easy things. For example, if the problem can apply to any number see what happens with the simplest number first i.e. 1. Try out tests with specific cases - sometimes the coursework will help you and suggest specific cases to try out first.
4) Make sure you write down an explanation of what you are doing, why you are doing it and what you hope to achieve.
5) Write down all of your results and accompanying diagrams. Diagrams, graphs and tables are very important as they show your results very clearly. Be sure to label everything clearly also.
6) Try to see a pattern in your results - if you can't then try some more test cases this may help. If you see any patterns then write them down and test them to see if they are true. These patterns are called conjectures (they are guesses or proposals of why things are happening mathematically in your results in the way they do).
7) If you have a great conjecture and then find some test cases which don't stick to your rules, then be sure to write them down as counter-examples. This is important as it shows the examiners that you are doing a "proper" investigation. Now that the counter-examples have spoilt your conjecture, think of other ways of looking at the problem and come up with another conjecture.
8) When you are happy that your conjecture should work for all test cases, then you should try to generalise your conjecture by creating an appropriate formula be sure to explain clearly what all the symbols mean in your formula - no matter how obvious it may seem to you at the time! Be sure to comment on your generalisations. Also write down a couple of new test cases and show that the generalisation can be used to predict these accurately.
9) If you can, you should now try to justify the generalisation. This can be done in several ways, though justification using differences is very popular (see first link below). This is a partial proof that shows you are on the right track - but does not stand up to the same sort of criticism as a full proof can. This step can be missed out if you have a convincing proof.
10) Finally, you need to prove the general result (i.e. your formula). This is never easy. What you need to do is use logic to prove that your general result is correct. The proof should use logic in the sense that either something is true or it is false - nothing else will do. Your teachers should be able to point you in the right direction when it comes to proof time.
Here is a link which gives general coursework tips and shows the justification by differences technique.
Here's another link which has helpful tips and suggestions.
This site is currently building a library of GCSE coursework and may be able to help you with tricky areas.
Here you can find help with the classics "Emma's Dilemma" and "The Payphone Problem".