Well, you might think that’s a pretty obvious place to start this list – but it really isn’t!
Almost everybody starts revision by plunging right in with the hardest topics.
But how much are you going to learn if you practise complex proportion problems, for example, without a thorough understanding of how to multiply and divide fractions?
You’re telling me to revise multiplying and dividing fractions? You must be joking!
Ok, maybe not that … But hang on … are you sureyou know it?
You wouldn’t believe how many of the Year 11 people I teach have forgotten their Year 7 skills!
Get the basics right; then build on them. The simplest maths is the most important!
You’ll find lots more about how to do it if you keep moving down this list!
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2 … And keep coming back to them!
Keep a list of the essential skills you had to revise, and check back from time to time to make sure they’re secure.
Simple, right?
If you understand the foundations of GCSE maths really well, you’ll be able to work out a whole lot of more complex things you haven’t specifically studied.
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3 Let yourself forget things sometimes: relax!
Yes, I’m serious:
Don’t obsess about learning each thing perfectly the first time. If you forget something and have to re-learn it, you will end up knowing it really, really well.
There’s more about forgetting, further down the page.
(And please REMEMBER to share this article with your friends!)
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4 … And find different strategies for re-learning, so it really sinks in.
Ok: your first learning method didn’t work perfectly.
So try a different approach!
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Now you know the topic in two different ways.
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5 Don’t time your work too soon! It isn’t a race!
Timed work is very useful exam practice, but it isn’t a great way to learn maths.
Practise slowly and carefully, reviewing your work in detail. Don’t start doing most of your work timed until the exams are a few weeks away.
Ok, maybe that’s obvious!
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6 But when you DO work to a time limit, focus on understanding WHERE IT WENT RIGHT and WHERE IT WENT WRONG.
This is important:
Don’t just churn through each timed paper, then move on to the next one!
Mark your answers carefully and re-do anything you got wrong … Make sure you have learnt all the important lessons from each paper.
As for the timing: work out where you got held up. What kinds of question delayed you, even if you got the answers right?
You will need to go back to the textbook and practise any difficult topics some more.
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7 Do a little bit, often!
The subheading pretty much explains this one!
You know that feeling when you’re fighting to keep your eyes on the page and your head off the desk?
Of course you do! We’ve all been there.
But how much do you actually learn when you feel like that?
Most of your learning will happen in the first 20 minutes of a revision session. For most people, 45 minutes of learning is enough at any one time.
And if you only have five minutes to do some maths, USE IT!
You could learn a couple of formulae really well in that time.
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8 Be a list-making maniac!
.. Even if you lose them the next day!
The very act of writing things down in order is brilliant for learning.
But there are some lists you really don’t want to lose…
… like this one! DON’T LOSE THIS LIST!
But seriously:
There are some very useful lists you can make, and perhaps keep safe in an exercise book.
Here are some incredibly useful lists:
A list of basic maths skills which need firming up (“Converting fractions into decimals”).
A list of facts to memorise (“Area of a triangle is half base times perpendicular height”).
A list of your most common mistakes (“x² is not the same as 2x”) (see Point 26 below).
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I might mention these again further down …
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9 Focus on your weaknesses TILL IT KILLS YOU …
OK, not that much.
But still:
Once you’re pretty confident with the basics, resist the temptation just to study the topics you like!
When I did a lot of exams (yes, this is one moment when I can feel smug about not being a student any more), I used to list all the topics for a subject.
Every time I thought I understood a topic a bit better, I’d put a tick next to it – and I always revised the thing with the fewest ticks.
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If you work like this, in the end the thing which started with the most ticks will have the least, so you get to revise it again.
Simple!
This method doesn’t suit everybody, but I really like it.
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10 … But make sure you are ROCK SOLID on the topics you find easy.
Everything is forgettable, so don’t relax too much!
Just because you like finding volumes of prisms, it doesn’t mean you shouldn’t practise it!
Look at it this way:
In an exam, you want to get 100% for the topics you know well, in case you lose marks in your weaker areas. So make sure those 100% topics are in the bag.
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11 Don’t be afraid to cram sometimes …
Whatever they may say, cramming isn’t bad revision.
It isn’t just for the day before your exam, either!
Sometimes writing a list of facts and walking round the park, repeating it over and over – or sitting at your desk and copying it five times, if that works for you – is incredibly effective.
When you cram lots of information into your mind at once, you often find connections between ideas and new ways of looking at things which you never spotted when you were working topic by topic.
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Not all facts have to be learned ‘in context’.
Besides, any last minute cramming will only really pay off if you’ve crammed (and possibly half-forgotten) the same information before.
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12 … But most of the time, don’t.
Because the most important thing is to understand your knowledge.
You won’t get a Level 9 by repeating memorised information onto the page like a strangely literate parrot.
13 Use the official syllabus as a checklist …
I find it amazing how few (5%?) of my students have ever looked at the exam board syllabus/specification or the official mark schemes (more about them below!).
It’s a list … ___________... an OFFICIAL list … _______________________________… of the things you have to know!
USE IT!
Print a copy, and tick things off as you go.
Your own list of topics (see Point 9 above) will be more useful day to day, but the syllabus is so valuable.
It’s your only 100% certain proof that you've learnt everything you need.
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14 … But make sure you really know the things that actually come up all the time.
There’s a definite method for this, and everybody should do it.
Print out all the specimen papers (and 9-1 past papers, once they exist) you can find online – and you might want to look at the other exam boards too (with care).
(I don’t think it’s a problem if you’re saving some of these papers for timed practice later: you’re not likely to remember any questions clearly after doing this, anyway.)
Go through all the papers. Each time you find a new kind of question, note it down.
For example:
Finding the equation of the tangent to a circle.
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Add a tick or cross next to each entry on your list each time you find it again.
For example:
Finding the equation of the tangent to a circle x x
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Then number the list, from the most common question (most ticks/crosses) downwards.
When you’ve done this for the 9-1 papers, start a separate list for the final few years of the A* A B C D style papers from your exam board. The syllabuses are a bit different, but most of the core topics are similar.
Now you have an incredibly useful list of what the examiners actually like to test. These are the topics to know REALLY, REALLY WELL.
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15 … But but BUT … Don’t rely TOO MUCH on what they set in previous years!
Your list from Point 14 will be an awesome revision aid …
But you have to prepare for the exam board to test any part of the syllabus in any way they like.
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16 Get used to the wording of questions.
Have you noticed some of these phrases that keep coming up?
“Write down …”: This means you don’t need to show any working out if you don’t want to. The answer will either be a fact you are expected to know, or something you can work out directly from the information in the question, without any in-between stages. For example: “Write down the exact value of sin45°.”
“Evaluate …”: This means “Find the value of …”, or just “Work out …”. For example: “Evaluate _____”
“Hence …”: This means you can get to the answer of part (b) by using your answer from (a).
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And so on!
Get used to recognising what all the common ‘key phrases’ mean.
You’ll find they help you a lot.
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17 Get used to re-writing words as maths – because this skill is IMPORTANT!
The infamous WORD QUESTIONS!
... Which shouldn’t really be scary, because they’re just, well, maths questions … with a few more words than usual.
But turning examiner-waffle into maths is a skill that takes some getting used to.
Here are a couple of simple tricks to show you what I mean:
“Of” always means “multiply” (for example, “What is 2/5 of 3/4?” … Or “Kate takes five of the bags” means “Kate takes 5 x a bag”).
“Out of” always means “divide” (“I take three out of the four beads” means I have taken 3 ÷ 4 or 0.75 of the beads).
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18 Get used to the structure of questions, so you don’t get lost.
I’m not talking about the way a question is worded, here.
I’m thinking of how a multi-stage question is put together.
For example, part (c) of a question might require you to know information which is written above part (a), right at the head of a question.
Or it might require you to build on your work in part (b).
Your understanding of the structure of questions can help you get marks, if you also understand the mark scheme (see Points 20 & 21 below):
If you know that part (b) of a question builds on part (a) – and you made a mess of (a) – you can still use your answer from (a).
This won’t usually lose you any extra marks, because of follow-through marking.
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19 Use the internet cunningly: get the most VALUE from it!
Youtube, for example, is full of videos to talk you through the main methods.
Meanwhile, there are plenty of useful websites for GCSE Maths students.
However … however … use the internet carefully.
Watching videos and reading online explanations is less useful than actually practising maths. It’s easy to convince yourself you’re working, when in fact the information is drifting in through your eyes and out of the top of your head! [photo]
It’s natural to stumble from one topic to another on Youtube (for example) and lose track of the topics (and details of topics) you’re missing out. Too much of this, and there will be big gaps in your knowledge.
And of course – When you’re online, Facebook is only ever two clicks away!
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See what I mean?
For all these reasons, it’s best to use the internet to research specific topics from the syllabus or from your own list of topics.
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20 Learn to find your way round the mark scheme …
Some teachers dislike too much focus on mark schemes: you should be learning mathematics during your course, not just learning to write exam answers!
However, I look at it differently:
There isn’t much point knowing maths if you can’t express your knowledge in a way that gets the marks.
What’s more, it’s VERY difficult to do a timed exam if you don’t know how much working is needed and how to set it out – you could, for example, waste time writing too much where it isn’t needed, and end up writing too little where it IS important.
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Incidentally, this is why my own GCSE Maths materials* show full handwritten answers! This way you can learn to set out your answers clearly and effectively.
(OK, that was a shameless plug.)
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21 … And get to know that mark scheme REALLY WELL.
For all the reasons given above, it’s a very good idea to use the official mark schemes carefully when reviewing past papers …
So you learn to write your answers with a clear idea of what the examiner wants to see.
Keep doing this until you know exactly what is needed.
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22 Swap work with a friend for marking: BE THE EXAMINER!
Lots of teachers encourage this because it saves them work …
Well, it might seem that way!
But in fact, it’s an incredibly useful method:
It’s so hard to look at your own work through the eyes of a marker: you can’t help thinking what you thought when you wrote your answers!
When you look at somebody else’s work, you start to see all sorts of things which will help:
Mistakes you also make;
Things which aren’t quite clear;
Better ways of doing things.
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Find someone whose work’s worth a look, and give it a try!
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23 Practise setting out your working effectively – and hoover up a HEAP of marks!
If you’ve tried Point 22, you’ll have started to get a sense of how other people organise their working out.
Ask yourself these questions about each answer of your own:
Is it clear how I got from the question to the first line of my working?
Have I missed out any important steps?
Do I need to add explanations to any lines of my working?
Does everything build up logically?
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On the other hand …
Did I really need all the working I showed?
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To get a sense of how I like to set out my own working, have a look at my handwritten answers towards the end of this*.
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24 Always have a go! Practise making a start.
Or, to put it another way: If you’re stuck, write down what you know!
The worst thing you can do with a horrible, head-scratching question is to stare at it desperately.
Get used to responding positively instead, whenever you feel like this.
Say this to yourself:
“I don’t know how to solve this. But what DO I know?”
Pull out the key information from the question, and write it down.
Just scribbling down the important things can give you ideas you’d never have found otherwise.
Of course, one of the best ways to organise your ideas is to …
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25 Line up your thoughts by drawing simple diagrams.
Let’s say you’ve got a question about changing the amount of beer in a barrel; or about the relationship between the sides of a trapezium.
It might be difficult to imagine in your head, so:
Draw a nice, big, clear picture, and label it with as much information as you can find in the question.
Then see if you can work out anything you don’t know yet.
Often, this will give you the ideas you need to find a solution.
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26 Be ruthless with your common mistakes!
If you go through, say, five papers you’ve done, and work out how you lost marks, I’m pretty certain you’ll discover this:
Most of your marks disappear on the same mistakes, again and again.
At least, that’s what happens to me.
Keep a list of your main mistakes, and really focus on dealing with them: get to the point where you know you won’t mess up in the same way again!
Square root does NOT mean “divide by 2”! … for example.
_ 27 Always write SOMETHING, for the chance to scrape out another mark or two …
A blank space gets no marks!
Even if you have no idea what to do with a question, write down your best guess.
Even just some random thoughts to do with the topic!
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These might get you a mark or two … and those marks might be enough to tip you into a higher grade.
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28 … At least the units!
Yes – if nothing else, write the correct units in the answer box!
Just occasionally, this could sneak you a mark.
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29 Get used to writing units!
Didn’t I just say this?
Not exactly:
You might be brilliant at Point 28: you stick the right units on even the most horribly wrong answer.
But I bet you’ll still forget to do it sometimes, when you’ve written the right answer!
It is so natural to struggle through a question … then … EUREKA! … you get it!
“YES!” you shout, and scribble down the answer – and in your excitement, you flip the page over and move on to the next question.
__________And of course, you forgot to write the correct units!
______________________AGAIN!
Checking the units needs to be a habit for every single question.
Even when you remember to write units, be careful to check whether they should be cm, cm² or cm³, for example. You need the right ones!
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30 Develop an exam timing system …
OK – I can’t find any way to make this heading exciting:
But it’s still really important!
When you look at the clock after half an hour, how do you know whether you’re ahead of time, behind time – or working at exactly the right speed?
Maybe you’ll find your own way of doing this.
One simple approach is to divide the total number of marks in the exam by the total number of minutes, which will give you a ‘marks per minute’ target:
You need (on average) to be ahead of this target:
This way you’ll have a bit of spare time for tricky questions, and for checking through at the end.
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For example:
If an exam is 100 marks long and you have 90 minutes, 100/90 = 1 1/9 marks per minute.
Whenever you check the clock, you should aim to have completed slightly more than one mark for each minute used up.
Let’s say you realise you’ve completed 25 marks’ worth of answers after 30 minutes: this isn’t a disaster, but you know you have to speed up if you are going to complete the exam in time.
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31 … And a set of funky symbols for difficult questions!
This is so simple, but hardly anybody does it.
Dare to be different!
With a good system of symbols, written beside some key questions, you’ll be able to use a spare 5 or 6 minutes at the end in the best possible way.
You’ll find your own code, but here are some suggestions:
Those symbols weren’t that funky. In fact, I came up with them at random.
You can do better!
But the method is awesome, because you end up knowing exactly how to use those vital few minutes after you’ve come to the end of an exam.
_ 32 Focus on quality, not quantity, of revision.
Many of the points above have touched on this – especially Point 7.
Don’t force yourself to work for an hour if you just aren’t in the mood and it isn’t sinking in.
Instead:
Work for 20 minutes, give yourself a 10 minute break, then do another 20.
Or even …
Work on something else, and come back to maths tomorrow!
_ 33 Use a timetable if it works for you …
Some people find it really helpful to have a clear schedule, telling them how long they are going to spend on each subject each day.
To be honest, I’m not one of them.
Schedules hurt me!
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34 … But don’t schedule revision too rigidly if you know it will put you off.
Because for some people (ME!), a three week chart with huge coloured blocks of revision filling in every day is about as encouraging as a gloopy plate of cold stew.
{{ image 82fac151-e931-11e6-9551-9397b75e4f0a }}
(Sorry if you like cold, gloopy stew. But you get the point.)
For some people, it’s best to start each day’s revision with an open mind about what to cover, perhaps using something like the method in Point 9 to decide which topic (or even which subject) to study next.
Just make sure you don’t miss any topic out for TOO long.
_ 35 Value all the time when you aren’t revising.
Perhaps it’s just me …
But the time when my knowledge really sinks in isn’t when I’m working: it’s when I’m doing something totally irrelevant (reading; playing sport; going for a walk; messing around with a computer game).
When I’m doing these things, ideas flash into my mind.
Bits of knowledge jumble around in my head and somehow sort themselves out into something useful!
So:
Don’t feel guilty about doing things which have NOTHING to do with work …
_ But of course, this only works if you’re studying hard the rest of the time, putting those ideas into your brain in the first place!
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36 Build a list of facts to learn, while you work.
I mentioned this one in Point 8 above.
Sure, you can build a list of formulae and facts to memorise from the syllabus and/or your textbook.
But this is REALLY boring – and it’s really difficult to remember things when you write them down without any memory hooks to hang them on.
But there’s a better way:
It’s much more useful to record key facts as they come up in your practice – and even better, to write them down with a short example.
It’s a bit like learning words in a foreign language: the more you learn facts in context, the better they will sink in! (Although, on the other hand, think about Point 11.)
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Make sure you re-memorise your list every few days. This way, you won’t have to start learning it for the first time when it’s already five pages long!
I like memorising lists while I go for a walk; but everybody’s got their own way.
_ 37 And separate revising FACTS from revising SKILLS.
Memorise facts; practise skills.
If you try to memorise skills/techniques mechanically, by repeating them to yourself, copying them out ten times – whatever the method might be – you’ll probably get overwhelmed and bored.
Anyway, it doesn’t work very well.
Save cramming for facts; for the techniques, focus on practice – perhaps by doing a particularly tricky question again the next day.
Also, this way you’ll get lots of opportunities to practise using the facts you’ve learnt by applying them to real situations. _
38 Use the textbook intelligently.
In other words, don’t try to revise by going through it from beginning to end!
Your textbook is a brilliant resource for practising particular topics when you realise you’re stuck.
Having problems with simultaneous equations? There’s a chapter for that!
You’ve forgotten exactly how to make a histogram? That’s me about once a year. Use the textbook!
… But use it wisely. _
39 Develop exam routines to avoid disasters!
All sorts of important routines can help in an exam:
So it’s worth practising them while you revise.
For one thing, you ought to have a routine for each question:
Underline key words/numbers in the question.
Re-read the question.
Write down first ideas.
Write the working and answer.
Write units.
Re-check the question.
Does the answer seem likely, based on the question?
Have I fully answered the question?
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There are other useful exam routines you can develop.
For example:
Get used to scribbling down some facts you’ve revised when you first sit down, before you’re allowed to open the paper.
This way, you tune in your mind to its Maths Channel.
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40 Practise CHECKING your answers …
I mentioned this just now, in Point 39.
But what does it actually mean?
Well: All kinds of things! (And read on for some more tips in Points 41 and 42 .)
For one thing, in algebra questions you can usually check that your answer is exactly right.
For example, if you’ve solved an equation (or a system of equations), put your solution back into the original equation(s) to see whether it works.
_ And … I might have mentioned this already ;) … ALWAYS CHECK YOUR UNITS!
_ 41 … Including by re-checking the question …
After all, the one thing an exam is definitely testing is whether you can answer the questions!
You could write ground-breaking mathematics – a unifying theory of physics, say – in the answer space of a GCSE question, and it still wouldn’t get any marks unless the question had asked for it.
So: you need to get used to breaking the question down into a set of instructions, and making sure that you have followed each one.
_ 42 … And using common sense!
Think about these examples:
The question is asking me to calculate how much liquid is left in a jug. I say 72 litres.
The question is asking about the average speed of a Formula 1 car in a race. I say 34.5 km/h.
I need to calculate 1.7 x 24. I give the answer as 4.08.
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What do these answers have in common?
None of them makes any sense!
Nothing which can hold 72 litres is likely to be called a ‘jug’. A tank, or a trough, maybe!
I suppose 34.5 km/h might be the average speed of an F1 car while it’s being driven into the garage.
How can 1.7 x 24 give an answer which is less than 24?!
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But people make mistakes like this all the time!
There’s an easy solution:
Before you start answering a question, make a sensible guess. If the answer isn’t in the same region as your guess, check it carefully.
For example:
I guess that a jug is unlikely to hold more than 3 litres.
I guess that the average speed of an F1 car (in a race) will be between 200 and 350 km/h.
I guess that 1.7 x 24 will be between 35 and 45.
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Another very useful, common sense tip, while we’re here: Get to know the graphs of sine, cos and tan, so you can predict (for example) that cos165 is going to be close to -1.
You’ll find other useful shortcuts like this while you revise. _
43 Develop your own mnemonics.
Mess around with different memory ideas to help tie down the key facts.
The weirder and wonkier your mnemonics are, the better you’ll remember the information.
You can try absolutely anything:
Have you tried singing the quadratic formula to the tune of Space Oddity?
It doesn’t really work, to be honest! … But you’ll learn the formula, just by trying.
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And all that SOH-CAH-TOA stuff (I apologise, on behalf of maths teachers)?
Well at least put a picture to it!
A grandmother, holding her sewing in one hand, towing a car with the other, perhaps …
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44 Get used to your calculator …
How many people buy a new scientific calculator the week before their exam, then waste about ten minutes in the test working out how to use it?
Too many people!
Get a reliable, new calculator a few months before your exam, and use the same one for all your practice.
Make sure it’s a design that’s permitted by the exam board.
If you lose it or break it soon before the exam, replace it with an identical one! _
45 … But learn to do almost everything WITHOUT A CALCULATOR!
For one thing, you also have to sit non-calculator papers.
For another, people who don’t understand how to do maths without their calculator often believe any nonsense it spits out!
Get right back to basics.
Can you do long division, reliably?
Can you subtract, add and multiply on paper?
Are you comfortable handling decimals with these methods?
Can you move easily between fractions, decimals and percentages?
Can you do any percentage calculation on paper, if you have to?
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Strong, quick times tables are fundamental – if they need practice, do this as a priority!
A useful tip for paper division, while we’re here:
Get used to writing the division as a fraction and simplifying it if possible, before using long division/ the ‘bus shelter’ method.
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46 Re-use papers you’ve done before.
Re-doing old work is often more useful than doing something new.
Come back to a paper you tried a few weeks ago, and try again!
Sometimes you’ll re-do the whole thing; sometimes you might just want to focus on the difficult parts.
This way you get to understand the questions (and associated topics) really thoroughly.
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This approach also taps into the power of forgetting and re-learning, mentioned in Point 3 – expecially if you leave a decent gap before trying again.
_ 47 Get used to ignoring advice!
Well done!
You’ve made it to the end of this list!
Now actual GCSEs will be easy, interesting … downright enjoyable by comparison to all this revision chat.
There’s a lot of advice in this article … and you’ll get lots more from teachers, parents, helpful friends … and lots of their suggestions will be totally contradictory.
So that’s why you need to get used to ignoring advice.
Try out lots of things:
Keep what’s useful;
Ditch the rest!
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At the end of the day it’s your work, and it’s your future.
One last suggestion (to ignore, of course): try the free paper and solutions, taken from GCSE Maths by RSL, which you can download here*.
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Good luck!
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