Maths, maths and more maths.
If you clicked on this article, you probably have an exam to prepare for.
Well, you’re in the right place. We’re here to advise you on how to get the most out of your maths revision, and being as efficient as possible in the process of extracurricular learning.
Whether you’re a GCSE student looking to get the most A*, A and B grades that you can, an A Level student needing to secure a place at your chosen university, or an undergraduate wanting to get the best start in your professional life, we have some great tips for you to examine here on how best to approach your maths revision and where to find the best free teaching resources to add to your student learning toolkit.
Let’s start with the basics. What is mathematics?
According to Merriam-Webster:
Definition of mathematics: the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations
Of course, this lengthy definition may seem confusing, but maths is more abstract than complex. Maths is the result of logical reasoning and almost everything in the world can be described in a mathematical way.
Whether it is with geometry or equations, our world is interwoven with Maths so everyone is much more in touch with the subject than they think. It is easy to think if you aren’t a natural mathematician, that Maths is this intangible and alien thing but, in reality, it is just a language of numbers and anyone can break the code.
To create a better picture of what exactly mathematics is, we can name a few branches of maths. For example, there are triangles, which are analysed by Pythagorean Theorem, trig, algebra, and geometry.
Organisation and a positive mindset are key! ¦ source: Visualhunt
There is also graphing, which uses math concepts such as transformations and translations, as well as linear equations, simultaneous equations, differential and polynomial equations, and integration.
Now we’re clear on what maths includes, let’s have a look at our four recommendations for all learners, which apply to everyone, regardless of age, study level, or learning environment.
If you want to go far in maths, it’s really important to have a good grasp on what we call “toolbox skills“.
These are the kind of math skills that are fundamental to the functioning of all facets of mathematics, such as addition and subtraction, multiplication and division, place value, factorisation, estimation, rounding, graphing and working with fractions.
A useful anecdote to explain this idea is the mechanic, who, without his toolbox, would not be able to make any repairs.
Equip yourself with the basic skills to support more advanced studies ¦ source: Visualhunt – Marcus Rahm
Maths mastery is down to building a strong foundation. The more comfortable you are with using basic concepts, the faster your progress will be further down the line.
However, basic math concepts don’t just mean easy maths. Learning the multiplication table to revise aggregate function doesn’t make a lot of sense since the level of study is so much higher. So be sensible about what you choose to focus your energy on.
Whether you’re revising for your GCSEs, A Levels, or you’re in higher education at the university, the math learning programme will be completely different for each of the education programs.
While there is a whole world of printable math work sheets and exercises, it always helps to revise GCSE maths online with material based on a specific syllabus.
As you know, Maths is a compulsory subject for all students up to the age of sixteen – even children as young as two are taught basic numeracy and literacy skills in nursery through classroom activities and participation. It isn’t, however, until you reach the age of eleven or twelve (i.e. the start of your secondary education in Year 7, or as you take the leap from Prep to Senior School) that revision starts to really have a place in determining your grades.
Whilst teachers encourage you to do pieces of prep at home to go over a lesson you just learned or to get yourself prepared for a new methodology to come, it almost seems like they set work for the sake of it. However, we can assure you that your GCSE and A Level homework has been assigned for a very good reason and is designed to help you go further on your course.
It would be lovely to think that each and every student can survive on a course with the lessons provided and with the resources used by their teachers, but this just isn’t the case. Every student works at a different pace and finds some parts of Maths much harder to grasp than other parts. Furthermore, everyone responds differently to various teaching methods; some are suited to independent learning whilst others advance much faster when participating in a group.
Either way, you should never think that you are beyond homework and revision, as even the best mathematicians need to work hard and reassure themselves that they are doing things correctly!
So, whether you are a whizz at Maths or you always feel like you are one step behind your peers, the work you put in out of hours can be a huge factor in the outcome of your course. It is not uncommon for people with a better fluency and natural ability with numbers to become complacent and not put in the extra effort they should and to wind up with a poorer grade than a student who has struggled through the course but who worked hard on understanding the methodologies and brushing up on useful techniques and tips.
This is because Maths isn’t all about having a gifted flair for numbers, it is as much about using logical thinking to come to the right conclusion.
So, throughout your studies, and especially if you start to face some difficulties, keep in mind that maths and logic go hand in hand. In other words, whatever concept you’re finding had to grasp can be explained in a logical way, so don’t get yourself worked up. Instead, sit back, take a deep breath, and tackle the problem with a fresh, clear mind.
Whether it’s arithmetic, algebra, trigonometry, geometry, multivariable calculus, equivalent fractions, complex numbers, quadratic equations, precalculus or long division of polynomial functions, the likelihood is that you’ll find a way of understanding it. You just need to find your way.
Maths is a wonderfully rich and diverse subject. However, unfortunately, it only takes one tricky homework assignment and many people wrongly think it’s far too complex for them to learn.
The reality is that there is no secret! You just need to put in the work and find a revision method that suits you.
So, we’ve put together the crème de la crème of maths practice resources which you can use to get to grips with how to solve the kind of maths problems you’ll find in your exam.
Don’t underestimate how valuable these tools can be in your learning journey. Go out and get yourself a revision planner and start scheduling in some revision sessions right now! Depending on how you work best, you can make a start on these easy-to-use numeracy resources alone or you can set up a study group with your friends.
First of all, keep in mind that learning the ins and outs of maths takes time.
But what does it mean to be thorough in this context?
Effective learning means exercising self-discipline and making sure you cover every topic in depth.
For example, set a detailed revision timetable and stick to it. Don’t forget to be kind to yourself and schedule enough breaks to keep you refreshed. It is no good following a revision schedule suggested by your teacher if you are just going to sprint through it and not really take anything in. Make that revision count!
Understand also that attending maths lessons or following math courses with a maths tutor is not enough. Revising what you have covered in class helps you to secure that understanding of the lesson and consolidate your knowledge, focusing on points you find slightly more difficult and giving you the confidence to approach similar questions with little or no apprehension.
By spending time over subjects again and again, you can then give your full attention to each subsequent lesson and apply what you learn along the way.
Don’t get us wrong, not everyone is going to become a math genius overnight, and many will still face challenges that will seem too hard to overcome, but as long as you are realistic in your goal then there is absolutely no reason why you can’t succeed in achieving what you’d like to in this subject.
Remember, if you make mistakes – that’s okay! Every mistake is an opportunity to learn so that you don’t get tripped up on exam day. In fact the more mistakes you make, the more determined it can make you to do better and the more effective that lesson can be. Be motivated by your downfalls – pick yourself up again and fight harder instead of staying down and hoping for the best.
It can be hard to digest if you really dislike the subject but studying on a regular basis will fix your newly acquired knowledge into your mind and make it easier to recall this information. And then, who know’s, you might end up actually enjoying maths lessons!
Remind yourself too that, while revision can seem like a tedious task when you could be doing something more fun, there are few times in your life when you have to work this hard but that there are also rarely opportunities like this that crop up again and have such significance.
Just think, each time you apply for a job throughout the rest of your life, your prospective workplace will always want to know your basic qualifications, one of which will be your ability in the fundamentals of maths. Is it really worth throwing away this opportunity to work hard and to open up doors for your future all for a game on your mobile phone or for hanging out in the car park with your friends and having a laugh?
There will be plenty of opportunities for you to relax and spend time with your mates after the exam period is over, and what’s best is that by then you will have done all you can and can truly let your hair down and feel satisfied that you couldn’t have done more. Or could you?
So don’t think you can twiddle your thumbs until the night before. And don’t allow yourself to look back at this time with regrets. If you want to do well, you’ll have to work for it!
Now, as we know, it’s all very good talking about revision, but how do you even approach revising for a subject that has so many modules and that you’ve spent a year or more studying?! Keep reading for some tips on which resources to use, how and where to find them.
Past maths test papers are an invaluable revision resource.
You can find them on the website of every major exam board including AQA, Edexcel, and OCR. Working through exam papers can help you prepare for the real thing, as you get to know what each board is looking for and how they tend to word problems.
Don’t be tripped up by sneaky exam boards – revise with past papers! ¦ source: Visualhunt
Past exam papers will also help you spot the key topics of your maths course, so you can know what to expect before you turn over the first page of your GCSE or A Level exam.
One of the biggest benefits of using past papers is that you can read the examiners’ notes after your attempt to see exactly how an examiner would have responded to your answers. You’ll see the extent of the detail required to get that top answer, and you can take a really valuable lesson away.
Exam boards also have answer booklets for each paper so you can see how you’re improving.
If you’d like to work through any math questions you got wrong, there are many maths teachers who put their working online so you can follow them to the correct solution, rather than going straight to the answers.
Tip: Make sure you focus on the most recent papers. The UK maths curriculum is changing all the time and it’s important that your revision is up-to-date.
Making links between the concepts you’re learning will help you to see the bigger picture of mathematics and therefore potentially use a different approach to a certain type of math problem.
For instance, why not find out how Pythagoras can be explained using polygons or where Pi comes from.
Making these kinds of connections when you learn maths will not only help you in your understanding, but it will build a firm foundation to further your maths education in the future.
You can do this by consulting the web and just doing some general poking about on maths sites. It is recommended that you stick to websites designed for learners your age so that you don’t get caught up in learning things that aren’t necessary to pass your exam. However, if you really have an interest in a subject area, there is no harm in educating yourself further.
Some websites we would suggest taking a look at are BBC Bitesize for GCSE and Revision Maths for A Level, but we will go into further detail below and introduce you to some teaching materials used by real-life learners.
You’re in year 11 and preparing to sit your final GCSE exams this Summer.
For a lot of students, the math exams are the ones that cause them the most worry.
No need to panic. Just like maths, every problem has a solution.
Year 11 maths is all about algebraic equations, number sense, and graphs. Sub-topics include inequalities, linear equations, theorems, indices, square roots, reasoning, ratio, loci, vectors, probability and math problem-solving.
How did these topics become GCSE nightmares?
It’s all down to the way you learn.
If the methodology of your educator doesn’t suit the way you think, it makes you think you’re less capable than you are.
When it comes to learning math, low self-esteem can be incredibly detrimental, so you need to find revision strategies that suit your style of learning.
BC Bitesize Maths is particularly helpful from KS1 maths to GCSE level, providing learner guides with math videos for qualifications all over the UK. The free resource tailors worksheets, lessons and other free resources for each of the four countries’ curriculum.
For GCSE and A Level math help, there’s The Student Room, where students can discuss queries in forums and find teacher-approved resources.
Studymaths.co.uk has revision notes, maths worksheets, key formulae and even a glossary to help you get into the swing of practicing maths and understanding mathematical vocabulary and scientific notation. If you want to move away from textbook maths and learn in a more interactive way, this website has puzzles and free online maths games to help you learn key concepts. Then when you feel ready, you can have a go at some exam-style questions from the question bank to see how you’re getting along.
These days, everyone has a smartphone or tablet – you can use these for revision! Gojimo, the free interactive math app, can help you prepare for upcoming exams with personalised maths quizzes and the ability to track your progress. The app focuses on topics and maths questions from whichever exam board and qualification you select, so you can do effective revision on-the-go!
You’re studying maths and perhaps related subjects such as physics in year 12 or 13.
Of course, you’ll have work a lot harder for your maths A Level qualification than you did for your GCSE. The key to successful revision is keeping it fun and having a maths tutor can also ease the transition.
Even though differentiation and calculation of probability and statistics don’t scream ‘fun learning’, this means finding interesting ways to learn each topic, aside from re-reading class notes. For example, why not work with a classmate and create flashcards to test each other? Or you could both attempt the same exercises and compare answers as a form of peer mentoring.
The internet also has some great maths websites and downloadable online math resources to help you.
Exam Solutions (maths made easy) provides subscription-free maths help for GCSE and A Level students, focussing on specific exam questions from real past papers. The teacher films himself working through maths exam questions step-by-step, so you’re free to pause, rewind and fast-forward the maths videos. So if you’re looking for a solution to question 3 of the Edexcel C1 paper from June 2014, you’ll find it. Another handy feature is the ‘helpful tutorials‘ placed next to each exam question, so you can revise further if needed.
The internet offers lots of help for maths students ¦ source: Visualhunt – Anna Demianenko
You can also use the Gojimo app for A Level maths revision. Just like for GCSE maths revision, you can focus on a specific exam and revise with maths quiz questions with instant explanations on-the-go!
For you, A levels are long gone. You may be aiming for a career in finance, research or engineering, so you’re destined to be a mathematician in some form.
As your level of study is so advanced, revision tools can be hard to come by – but they do exist!
The Mathematical Institute at the University of Oxford has a range of practice math problems aimed at those starting a maths degree. Each worksheet provides an opportunity for foundation year students and even undergrads to familiarise themselves with degree-level maths.
For those studying economics or finance, the University of Warwick has put together a handy page of notes, exercises and quizzes. These are aimed at helping you with the mathematical aspects of your degree course.
When you’re studying for a degree, your lecturers will provide information on the format of the exam and will give you access to past exam papers as well as sample questions.
It’s down to you to get the most our of these somewhat limited resources. Do every question – even the optional (often more difficult) ones. When you make a mistake, try again. See where you went wrong and learn how to avoid being tripped up next time.
Ultimately, academic success is down to the learner.
Of course, having the right resources is key, but the most successful students also know how to get the most out of them.
There is a strong belief amongst students and parents that revision equates to hundreds of hours of revision, but while we agree that the more time you dedicate to the subject, the better, we also can’t convey strongly enough the importance of making every minute of revision count. This way, even if you can’t fit in as many hours one week than another, at least you can feel confident that you made that time really worthwhile. And with all of these amazing teaching tools available to you for free, there’s really no excuse not to use them to your advantage!
The website, GCSE Revision, asks learners and their carers to see from their perspective regarding taking the right approach to learning and using your initiative to strive for excellence. It offers tips on how to encourage pupils of GCSE age to stay committed to their independent studies.
See the table below for some of their suggestions on what to do and what not to do when scheduling revision sessions across the weeks, months and years, but remember that you ideally need to tailor a revision calendar that works for you and keeps you motivated.
|What to do||What not to do|
|Take breaks every 3-45 minutes||No more than 4 hours per day|
|Do chunks of revision regularly (i.e. 2 hours each day of the week)||Don't leave a gap of more than 4 days between revision sessions|
|Create a timetable||Don't be tempted to leave harder subjects until last.|
|Break down the revision sessions into topics||Don't worry on your 'night off'. You need some stress-free time!|
Finally, don’t lose sight of the fact that Maths is a subject based on logic. It’s fascinating and interesting, but by nature, there is a risk of it becoming boring if it starts to become problematic in any way. Good learning happens when the student is interested in the course content, so know how to keep your degree interesting and most of all, enjoy it! Make life easier for yourself by making maths easier for you.
So, see you on Wall Street in a few years time!?