Exam technique and tips

Taking the exam

This is what is known as exam technique. There are many different techniques, but here is one that is probably the best and uses some  actual scientific research. N.B.This plan is suggested for the exams relating to UK A Levels, which have around 7 to 11 questions, I would not suggest this method of an exam with a larger number of questions (ie GCSE exams)

·         First thing – review the questions

o   When you hear the examiner say start, do not begin answering the questions.

o   Start by skimming the questions for 2 to 5 minutes, figuring out which is the easiest and which is the hardest.

§  Write the hardest question down first, all the way to easiest one. Do not worry about exact easiness or hardness, just a rough estimate.

§  You know which question is easiest, if you know what method or steps to get to the solution, straight away.

§  A question is hardest when the solution is not obvious, or is on a topic you are not that confident with.

o   Write this at the top of the first page (usually where the first question is or a blank page is). After answering each question you will refer to this page each time to find out which question to attempt next.

o   The aim of this method is to get the brain thinking in the background, priming the brain, this allows your brain to come up with the relevant knowledge to solve the problem unconsciously

·         (Second thing – Time budget)

o   I would advise against this  for individual questions, as this can be very tricky and time consuming to work out how long to spend per mark and having the pressure on you to check the timings.

o   I would only suggest a time budget for the beginning, to read the questions and mark down the hardest to easiest (around 5 minutes), and at the end, for checking your solutions (5 to 10 minutes). But these are just guides to remind you to get going.

o   Best write down on the paper the actual clock time you need to stop attempting the questions and checking the solutions. Or if have digital watch or timer, use a countdown feature.

·         Strategy: Hardest then easiest question, then next hardest then next easiest and so on, until all questions are attempted.

o   Now start on the hardest question (for you). If can answer the question, go for it.

o   If after 1 or 2 minutes (Check stop watch or clock) or you have read the question two or three times and you are stuck (can’t begin, stuck with finishing the method or a sub question etc) stop and go to the easiest question on the paper (should be at the end of the list)

o   When the easier question is done or as much of it is done, go back to the next hardest question and repeat. Check the list of ordered questions, cross off or circle (not done) the question you just completed and attempt the next question (should be near the top of your list, if list of question difficulty was ordered hardest to easiest).

o   Eventually you will go back and forth throughout the paper, until you have attempted every single question.

o   If an easier question was harder than anticipated, don't stick with it (especially at the beginning of the exam), instead move on after 1 or 2 minutes. Just as above for the hardest questions.

o   Sometimes, the perceived hardest question is actually easier than first thought. This will give you lots of confidence if you complete it.

o   This goes against the idea of doing the easiest first to build confidence, but what this method does is allow your brain as much time to think about the solution when you start the exam. So you could give your brain 80 minutes out of 90, to think about this problem unconsciously, while answering other questions, much better than spending 15 minutes on it and being stuck writing nothing down. As the next question is easiest (as you feel you are strong in that topic) you will still get confidence from doing it very early in the exam.

·         Never waste time on problems that you cannot do

o   If starting with the hardest question, you will likely be stuck (at the beginning or during answering) but as long as you thought hard about the question for 1 or 2 minutes, you can move on to another question.

o   There is no point being stuck on a question at the beginning of an exam, if you cannot answer a question skip it and move on. But give  it a good go (read the question a 2 or 3 times, apply some methods etc)

o   The only time to stay with a question, and try some problem solving techniques is when you have answered all the questions that you can do. Which occurs when you have attempted all the questions.

·         Answering the questions

o   You must realise that an exam paper is just a set of similar questions that you have answered during your classes, homework, and revision sessions. You have covered the majority of different types of questions, and all the topics in the syllabus throughout the course. 

o   Write fast, but keep your writing neat and readable. If you do a lot of working out for each question, you will have less time, so write quickly.

o   Make sure you copy the question and previous lines of working out correctly. Focus. 

o   There are different types of questions, asking for different types of solutions (see here) but you should know this after practising with past exam papers.

o   Use plenty of space, don't worry if you run out, ask the examiner for extra paper. Better to have clear writing and easy to check, then messy writing making it hard for you to spot any errors.

o   Use an empty line between each stage of working out, especially if you have big writing.

o   Always write out the specific question number before writing your solutions, ie “2)a) i)”

o   When finished, make sure you mark on the paper the question done (or the parts of the question done ie “2)a) i)” )

o   Mark down what questions or sub questions that you have left undone or incomplete. Circle the question number or put a question mark next to it. So when you go through the paper you know what to complete.

o   Always underline the final answer. Make it easy for the exam marker to give you the marks.

o   If you cannot do part “a” of question, maybe you can do part “b” and “c” without part “a” needing to be answered. So do not skip the whole question, if you cannot do a part of it, attempt the next one part within the question.

·         Handle anxiety

o   Make sure to stretch your legs and arms through out the exams. Even shake you hand and arms out to avoid them cramping, especially if you feel your hand is tired.

o   Drink regularly through out the exam, drink mainly water.

o   Eat some sweets through out.

o   Do some breathing exercises.

o   Avoid looking at your friends for their reactions. Can lead to anxiety and nerves, or over confidence and not being fully focused.

·         Go back to unanswered questions or sub questions when attempted every question.

o   This should be done only when you have attempted answering all the questions and all that is left are completely unanswered or unfinished questions. OR if you have an idea for the solution for a previous question while answering another question.

o   If going back to a question midway through another question, you can either stop answering the current question and answer the previous question, or make a note on what to do next to the previous question and come back to it after finishing the current question.

o   Start with the hardest question or the question with least amount of solution written down. Leave if after 1 or 2 minutes have passed and go to the next unanswered question.

o   Use the marks on your paper to show you what you have to answer.

o   Make sure you have attempted all questions, there should be no blank spaces for any question or sub question.

o   If stuck write out method or reasoning or your approach to solving in words.

o   Only start to guess near the end of the exam, after all your thinking has come up with nothing.

o   If no progress on finding a solution after a couple of run throughs, then spend a bit longer on the questions and use some problem solving strategies (See Here).

o   After each run through the paper, the number of questions not finished should reduce. If not, then spend a bit of time on each unfinished question.

o   The exam paper is a test and it will have questions that you have never seen before. This might make you panic, but if you have revised well (and covered lots of different types of questions)  you will notice that these questions will be similar to what you have already done in the past.

·         Check your work

o   With 5 to 10 minutes left, hopefully you should have answered every question, you should go back over your work and check that all your solutions are free from errors (see here for types of errors).

o   Always go through your paper as many times as possible, to check everything is clear, the questions are answered, no mistakes in working out and errors are fixed.

o   Remember you can always add to your solution by using arrows to show new working out.

o   Don’t cross out everything if wrong, only the parts that are wrong.

o   If you have not answered all the questions and only 10 minutes left, then leave this question and check the solutions. You can always go back to the unanswered question if you have an idea as you check your work.

·         Leave when the time is up

o   Never leave before the time is up, no matter if you believe you have answered all the questions correctly, need to keep checking work again and again.

o   There is always a mistake that you have made that can be corrected if you just keep checking your work when you have finished answering all the questions.

o   If time is still left after checking all your questions, make sure to keep checking your solutions and make sure all questions are answered.

Test taking - Types of questions

Test taking - Types of questions

In the exams, you will be faced with a series of problems to solve. Some will be straightforward, some you will need to think about. So you need to know what the problem/question is asking you for, before you can answer it. Below is a list of clues (question words) of what a problem is asking you to do.

• One mark questions – don’t spend long, it should be obvious form the graph or equations what the solution is. It could also be a recall question of an identity, definition, curve etc. Here a couple of examples
• “Verify ...” - check that it is correct, so mainly doing a substitution of a value into an equation. State what you are doing when answering.
• “Write down ... “ or “State the value...”  - The answers are there, you need to find them, there is no working out needed (or very little). It is on the diagram or part of an equation.
• “Show ...” or “Prove ...” - Generally show that one side of an equation is the same as the other, or two statements are the same, use algebra or whatever. They will give the mathematical statement to prove, or they will expect you to prove it with something you should already know.
•  If you get this as part of a question, don’t worry if you can’t do it, just carry on with the questions. As the solution is given in the question, and you just use the solution in the next part of the question.
• You can start with the solution given, and work backwards to the answer.
• This occurs a lot with trigonometry questions.
• “Hence or otherwise...” - This means use your answer from the previous part of the question to help you in finding the solution
• In some multi-part questions, they will not use the word "hence", but you may be expected to use a previous answer.
• Always assume in all multi-part questions that you may have to use some of your solutions that you have found in later parts of a question.
• The “otherwise” part means you could use a different method and thus not need to use the previous solution.This is unwise, as using your prior answers will save you time.
• “Find the exact value...” - Leave in surd, logs, exponentials, pi, or fractions form
• They will generally tell you which form you should leave your answer in.
• No writing in decimals to rounded number of decimal or significant places.
• “Find...” or “Solve...” – Using a method/technique to come up with an answer. Generally straight forward. Depending on amount of working out could be between 2 to 5 marks.
• "Use ..." - Here the exam question is asking you to use a specific method to answer the question. If you use another method, you will lose marks.
• Can use another method to check that the solution is correct, but only if you have lots of time to spare and checking your solutions.
• “Express...” and “Simplify...”– turn something (a formula/equation etc) into something else that is the same thing (e.g. put a quadratic in to completing the square form). Just applying a technique, probably a solution in terms of algebra or surds.
• “Sketch...” – means give hand drawn sketch, with key points and their positions (coordinates) or amounts marked on it i.e. x and y intercepts, turning points. Make sure the shape is correct.  Sometimes they will state what is required in the question.
• Always use a pencil
• Make it big enough and clear to be able to be understood clearly first time you look at it.
• If sketching a graph, use a ruler to draw the axes.
• “Plot...” and “Draw...” – Use a ruler, find several points, via subbing in numbers into an equation (make a table). Should be accurate as possible, no straight lines if it is a curve.
• “Factorise ...” – sometimes they will tell you what to do and what technique to do, you just got to remember it and apply it correctly.
• “Find the values...” - If you don’t read the question properly, you might miss this. Don’t just give one answer, as “values” is plural, there are several answers.
• You will also get follow through marks, if use you answer from "part a" in "part b", even if you got "part a" wrong, as long as the method is correct.
• This means never give up on the other parts of a question if you cant do the first part or think you got it wrong.
• If asking for more than one thing in the sentence, split up sentence into parts using a pencil, and as you finish each part, tick it off.

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.