Quick Revision Guide for A Levels Maths

Here are some quick tips on revising for the summer exams.

>Resources

• Lots of paper and pens.
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• Past exam papers and mark schemes(use your computer instead of printing them out).
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• Another text book or access to worksheets with lots of questions (and their answers, even better with worked solutions).
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• Place to work without distraction.

>Start revising early. 

• After February half term is best.
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• Even better is to revise for a small amount of time, a couple of months after learning the stuff in maths class.

>Know what revision is.

• It is going over the stuff that you have learnt in class, and can do without help. It is about helping you avoid forgetting the topics already covered.
• Being able to recall methods, facts, formulae, and being able to use the techniques perfectly and know which techniques to use for specific questions, after learning it in class.
• During revision sessions you will come across questions and topics that you have not covered in class, now you have to learn this.

>What not to do and what to do instead.

• Do not just read notes or text books, or any of the questions you have done. Instead, do questions without any help, and if you struggle use your notes, but be honest. OR summarise your notes (not worth it with maths but you can make mind maps of topics covered, methods, facts, names etc). OR explain the topic/method and check you notes to see if correct (best to do with a partner)
• Do not read the question, and then look at the answer or working out straight away. Instead, do the questions by yourself, you have to think, it is the thinking that helps you. Then check the solutions and working out (mark scheme).
• Do not  check your notes and go onto the next topic and forget about the last topic,  because you think you have learned it and will remember it. Understanding something or being able to do it correctly does not mean you will remember it when it comes to the exam. Instead, test yourself straight after learning it, and later on over a period of time (next day, week, months etc)
• Don't learn the stuff from the beginning (ie reading the book, starting from scratch on the topics you have covered). Waste of time. Instead start revising a couple of weeks after learning the stuff in class. You will find topics that you have not covered (questions that you could not do) and these topics you will learn and spend time on practising.
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• Don't leave it till the week before to revise. You will not have enough time, and you will feel overwhelmed and stressed. Instead start revising at least 2 months before the first exams.
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• Don't expect your teacher to do much revision with you. The chances are you will still be studying up to the first exam as you have not finished covering all the material. Instead start taking responsibility for revising by yourself. 
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• Don't revise while doing other things (ie watching tv, listening to music, checking face book etc). Instead just focus on your revision and that is it, get it over and done with. You will get more done and it will be more effective.

>Remember stuff

• There is a lot to remember such as  formulae, facts, methods and applying the methods etc.
• The best way to do this is to answer lots of practice questions from memory, doing more questions on the stuff you are not great at (to get perfect with them), and practising the same topics through out the year (to avoid forgetting).
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• Do sets of questions on different topics, use of past exam papers are really useful here, or end of chapter, mixed questions or review questions from the course textbook.
• Another way is to through use of flash cards, to help you memorise stuff.
• Another way is to teach others how to do a question or what the steps are involved in the method or to know you truly understand an idea.
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• Another way is to think about the topic. Think about how it is linked to other topics. This also applies to types of questions, what other methods and ideas are used in this question type. The more you think about it the more you remember it. This is what practice allows you to do.
• You can also do topic maps, for each exam and each individual topic/chapter, and try and reproduce this from scratch. This is a good way of building framework to help link all the topics together, which helps with remembering it.
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• All these methods have one thing in common, thinking about the topic that you are studying (ie the methods, formulae, facts, problem solving, how each topic connects, patterns etc). The more you think the more you remember and understand. 

>Revision through Practising it

• The majority of your time, you will practise in class as you learn new maths.
• Revising the topic should not take long. Do not spend a long time on one topic, or do lots of practice questions on one specific method.
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• When doing questions, especially on new topics or ones that you struggle with, or just to check you can do it, try and explain the method, use names of the methods used and explain why that method was used (ie product rule as differentiating and the function is made of two functions multiplied together).
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• When doing revision practice, you need to focus on doing the questions from memory first. If you continue to struggle, refer back to worked examples (this site is full of them or try your notes, other textbooks, internet) and try the question again. If still stuck, ask someone (your friends or teacher or forum) to help you. 
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• If you have done a question but got it wrong, then you can check the mark scheme or worked solutions and figure what went well or wrong, and see if you can figure out what you should have done (this might be a simple copying or arithmetic error, or something you forgot). If you don't find where you went wrong, or understand the mark scheme (worked solutions) then ask someone or check internet.
• If a topic or type of question you struggle with (not fluent with it), you need to learn it and/or practise on a few more questions. This is where another text book is handy or you can ask teacher for worksheets or the internet may have something.
• Always good to practise on different types of questions (on different topics) at the same time, this is where exam papers are your best friend or you can choose questions at randomly from different topics from you text book.
• Practise with exam papers, helps you get a feel for the type of questions, and the improve timings and exam technique.
• You know you have revised successfully if you can do the question, without any help, perfectly and at a fast pace (it has become automatic, you don’t have to think about it). Due to time constraints, you may not have time to practise certain topics till you are automatic, but best to focus on practising until you can do it from memory.
• If you have finished modules (ie C1) already (during the current year), focus on doing exam papers for these first.
• If you have done your exams already and need to resit, do some exam papers throughout the year.
• If you are still learning a module and the exam is very close, start doing the exam papers and just leave out any questions you have not covered yet.
• Start doing exam papers not timed, reduces the stress, but dont spend forever on them.
• Next do timed exam papers. If you do not have the time do the exam paper in one sitting, break the paper up into 2 or 3 chunks of several questions, and set the times for a minute a mark plus 2 minutes per question.
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• If revising for several exams (ie C1, C2, D1) then do practice questions in mixed order (ie C1 then C2 then D1 then C2 then C1 then D1 etc), either with practice questions on a specific topic or exam papers.
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• If time is running out, focus on questions that cover topics that you are unsure about. Spend more time on these topics, but now and then do questions that you know you can do (you got right previously).
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• If exam is close, and still stuck on certain topics, practise specific questions from exam papers only, instead of doing the whole paper or doing questions you can do. This assumes, you have done those missed questions well with proof (marked solutions). 
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• If really confident and always getting high marks in past papers, try advanced papers or papers from other exam boards. 

>Revision through flash cards

• Make cards (if you have money get small index cards (A6 or A7) or cut up pieces of paper). Put the question on one side, and the answer on the other. On the answer side, can also write out methods as well.
• Read the question, and test yourself, check if right or wrong. If wrong, put in one pile, if right put in another pile. Rest. Repeat with wrong pile. After several repetitions, the wrong pile will get smaller and smaller. When there are no more cards in the wrong pile, repeat the process with the whole set. Repeat the whole pile another day.
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• You can revise these while on the bus to school, or waiting in a line etc. But do not revise while listening to music or watching TV.
• Start with cards for each topic or a couple of topics if there are only a  small amount cards.
• Best to make these cards after learning the topic in class. You can add to them through out the year.  Also revise them after the topic is done.
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• When making them, use your notes. Anything that you constantly forget should be on there. Any question type where you consistently make a mistake should be on there. Steps in a method can be on there. Formulae should be on there. Facts should be on there (ie circle theorems, perpendicular vectors has dot product = 0). How to solve specific type of problem should be on there.
• Near the exam dates, revise the whole pile of cards for the topics covered in that exam.
• When revising using exam papers and textbook questions, you might find new topics or facts or hints that you need to remember. So make a new flash card and place in appropriate pile (ie A problem in a C1 paper, make a card of what to remember and place in C1 flash cards)
• Label your flash cards with the module/exam that it is for, as they can get disorganised.
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• Place together in plastic wallets or envelopes, or punch whole at the top corner put a string through them (those green string with metal bars).
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• You can also use flash cards in the opposite way, by having the answer first, then try and figure you the question (or the definition or name of method or formula or what type of problem this method will solve etc)
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• Doing lots of practice questions, will also help you remember the ideas on the flash cards as well. So you will find that you will breeze through a pile of flash cards, if you have done a lot of practice questions.

>Where to revise

• Anywhere where you will not be disturbed. For example, the library, empty classroom, home etc. It’s up to you, you know your environment best.
• But you need to focus, as you need to think. The more distractions the less time you get to practise and revise, the less you will think about it, the more chance you will confuse topics you have to remember.Which means spending longer doing revision.
• This also means, turn your mobile to silent no vibrating and put it out of sight. It will ruin your concentration.
• Avoid – busy places (6^th form lounges, living room with TV on etc, a busy class, lunch halls) and do not revise on your bed, use a desk (if you don't have one, go to the library or go to another room with a table).
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• If explaining a topic, or method to yourself, and you are in a library, choose an empty aisle and do it there. Or choose somewhere where you can discuss the topic.
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• Choose different places to revise, do not do all you revision in one place. Go to different libraries, use different classrooms or different rooms at home, go out to a park etc.

>Revising with a group

• If revising with a friend or friends, make sure they are not distracting or disturbing you. They should not be depending on you all the time, like asking you lots of questions, as you need to focus on your own work. You can always set a time aside (ie at 8pm we can discuss problems or do 5 questions in next 30 minutes then discuss) to talk about any issues.
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• Obviously you should not be chatting about non study topics (ie football) when you should be studying. This can be done during your breaks.

>When to revise?

• Every one is different, but I believe it is best to revise in the morning. You have more energy, you are more focused, and you get it out of the way before the evening (but not always) and can do other stuff.
• Also use your free periods at school. Don't waste them.
• Aim to do as much revision (and school work) before tea/supper. Afterwards, you will feel tired and less focused.
• As you get closer to the exams you will have to put more time into revising, this means most of the weekends and some late nights during the week and holidays.

>How long to revise for?

• It depends, I believe that doing 2 hours a week (this does not include the time that you are doing homework for class) should be enough. Maybe an additional  2 hours on the weekend. As you get closer to the exams, you will increase the number of hours for revision.
• Only you will know how much you remember, how many topics you have to practise or remember (flash cards), or new stuff you have to learn or correct misconceptions. So you have to plan appropriately for your own needs.The more you practise and learn from your mistakes the better you will become. The more you practise, the more automatic you become at answering the questions (no thinking) and thus finish questions faster.
• Any time you revise, always have a break of 10 minutes after 50 to 60 minutes of work. Get up and walk, stretch, exercise, avoid still sitting down, you need your blood to flow.
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• Don't over do it. Take some time out to rest and relax. Get enough sleep. Go out with friends, play some sports. But do not over do these extra stuff.

>Commitment

• To get good at any subject and do well in the exams you will have to commit to studying it above other activities. This means reducing or stop using Facebook, YouTube, candy crush or other games, messing around with friends, watching TV. If you really want the best grade you can get, it has to be the most important thing in your life, it has to be main priority amongst all your activities that you can choose from.
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• Commit to revising by having consequences. This will help you avoid procrastination and leaving revision to the last minute.
• This is why working with a group of hard working students (your friends) is great. Especially if they will not allow you to slack off.
• One thing to try is to ask your parents to take your PlayStation/TV away for the week and only give it to you on the Sunday only after you have shown you have revised.

What to do when I finish Year 12?

Year 12 Summer Holidays! YAY! What should I do?

Well done on finishing year 12. The past year would have been tough. The extra workload, the more complex information to learn, the exam to take, the revision to do etc. But you are through. BUT...

It will get harder next year! 

Lots of new stuff to learn, and you will have to use what you learnt in Year 12 to be able to do thiis new maths.

But don't worry, with a little extra work during the summer, it will not be as hard, instead you will be ahead.

Main idea to remember from this article is:

• What we don't use or think about, we forget.
• The more time you spend learning, the easy it gets, and the better you become at what you learn.

From these two ideas, it is obvious what you should do:

>Review (revise) the material you learnt in year 12.

Essential, as A2 (year 13) maths, is built on knowing this material. If you forget it, and it will happen, you will struggle at the beginning of the year and lag behind.

It is similar to how you struggled with remembering basic concepts every time you go back to school after your summer holidays. 

As you have already put in the hours of practise in, you only need to do a little practise (active review) during the holidays. 

Again review should be active, so reading your notes and examples is useless.

This means doing EXAM PAPERS or mixed questions from the text book.

>Start learning the material that you will cover in Year 13 during the summer.

The summer is a great time to get ahead of the class and learn the material before it is taught in school. Getting ahead of your class will make the year easier, you will not spend as much time figuring out stuff you don't get during the lesson, you will be able to spend more time practising in class and thus get more help from the teacher, and you will be able to start on practising exam papers earlier. 

In short, it will lighten your course load during the year, and with that extra time, you can use it for improving your learning in weak subjects or topics, or if you are strong do some extra curricular activities.

FAQ

>How long to work?

I suggest to get it out of the way early in the day. Do 1 to 2 hours within an hour of waking, and you are done.

>How should I split up my learning?

For every A Level you are taking, I would suggest you do at least some review of the modules. This means for every module you studied and took an exam for, do at least TWO exam papers, and spread these throughout the summer. Make sure to mark, and understand your mistakes and add to your notes any thing you got wrong and how to clear up (which means checking books and internet for an explanation of how to do that problem if you cant figure it out from the mark scheme).

You can just focus on one subject, and learn the new modules that you will study in Year 13. This could be useful for subjects that you enjoy as you wont get bored and give up. If going down this route, try and aim to finish one or two modules you will do in year 13 during the summer.

You can also do 1 hour learning something new, and another hour doing exam papers.

If you don't have much to do during the holidays, you can do an intense approach of learning a module within a couple of weeks doing 6 hour days and do exam papers  until the holidays are over. This might be useful if you are studying further maths, as you will not have the time to study all the modules in depth during the next year.

There are many ways to split your time. But I would advise you not to do too much. Better to do a little over a longer period. 

I would be best to have a couple of weeks off at the beginning of the holidays, not do any learning. Just rest and relaxation. Maybe organise all your materials, so your notes are not all over the place. 

>How to review?

The best way to do this is to do exam papers. 

Note how many modules (ie lets say you have studied 15 modules). Then every 2, 3 or 4 days you can do an exam paper for each module. When you have finished all the modules, repeat with a different exam paper. Always best to do them in the order that you learnt you modules ie do C1 then C2 then your applied module. 

For every paper, mark it using the mark scheme. For any questions you did not understand, even after checking the mark scheme, search your books, notes, internet for an explanation, then add this explanation to notes (ie write out the example, with the notes of what to do). 

If you have done all the exam papers, choose an exam paper from a different exam board. You can do this for core modules, but the applied modules will be different. Even the core modules will have some differences in the exam papers, but in general everything you learnt in C1 and C2 will be in one of these papers in the other exams board papers.

I would suggest looking at the exam boards in pairs, as they are similar in terms of content and exam questions, but there will always be slight differences: 

AQA and EDEXCEL
OCR and MEI

>How to learn new stuff without a teacher

I will go through this in more depth later on in a separate article.

Here is slim down version, but is basically how you learn at school:

1. Read the material in your textbook, make sure you understand the ideas and examples, and can follow the method. 
2. Can write down a couple of examples, which you can annotate showing how to do the method
3. If stuck on anything, check other textbooks or internet resources
4. After you are clear on how to do the method, do the questions
5. For the first few, check your answers, if you can check that your working out is correct. IF you book does not provide worked solutinos, check other resources for worked examples and do the question without looking at the solution (cover it up with a paper, or copy question down in notes)
6. Once you can do a few questions yourself without mistakes, and can follow the method correctly, do some more questions without looking at your notes
7. Any problems, or slight differences, make a not of what you need to do extra to solve the problem.
8. Write a general method, a step by step guide to doing a general problem.
9. Once you are happy that you can do that type of problem (or section) move on to the next section and repeat.

>I am stuck or I don't understand the material, what resources can use if I have no teacher to ask?

See this list of links here.

>What if I have a part time job or I am on holiday abroad.

You will not be able to get as much learning done, but you can always do something. 

As you wont have much time, I would suggest you stick to doing reviews (exam papers) rather than getting ahead of the class. But this is up to you, if you are very comfortable with the year 12 material, spend more time learning new material.

You can watch less TV, and do some work. Do some work on the weekends. Read your textbook during lunch. There is always a way of doing something. Don't let all your hard work go to waste.

One thing I would not advise, is too quit your job or not go on holiday. These are wonderful experiences that you should take and you will learn something from them. 

>I want to do this, but I find it hard to start and carry on, what to do?

Make it a habit. Once a habit, you wont have to think about it, and it wont be hard to do. 

To get started, start small. Only do 5 minutes, set a timer, and do this for a few days, then increase the time. If you get into it, then just carry on. Just do start with minutes everyday and stick with this, commit to it, and eventually, it will be easier to do. 

Make a commitment which will have undesired consequence if not followed through. 
For example, 

• ask your parents, to only let you play your computer games only after you have done you work, 
• or give you parents your money and if you have not done you work, you don't get it back and every day you do it they give you a bit back, 
• Or make a public commitment on facebook saying you will have finished learning the module before the start of year. 
• Find something that you are loathe to give up, and give it up to your parents or someone who will not givce it back unless you complete what you wanted to do. 

Make it easy. Night before, set up your desk with the equipment and resources you need to start work, and remove all distractions (e.g phone hidden on silent), you can even go to the library or somewhere where you will not be disturb.

Dont over extend. It is good that you lose track of time, but if you do 2 or 3 hours of work without a break, you will be exhausted and not want to carry on the next day. Best to work for a max of 50 minutes and rest for 10 minutes, and repeat. 

>Anything else I can do?

Do some background reading on the topics, especially for arts subjects (history, French  English etc) and even content heavy subjects like (geography, chemistry, biology). You don't even have to read text books, you can read general books on the topics or articles or Wikipedia. 

Remember, the more background knowledge you have of a subject, the more you will learn. 

>Final point

Don't worry if you did not learn every thing that you wanted to over the summer, or revised everything, as long as you made the effort, and did some thing, it is better than nothing. 

Doing these activities does not mean you can slack off during the upcoming year, you will have to still put in the effort. But if you were struggling in year 12, it should help you keep up with the class.