Chapters

Maths, maths and more maths.

If you clicked on this article, **you are probably a Maths candidate with coursework and examinations to prepare for**.

Well, you're in the right place. We're here to advise each Maths pupil 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 or iGCSE 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 further education establishment or university, or an undergraduate wanting to get the best start in your professional life, we have some **great guidance tips for you** to examine here on how best to approach your tuition and maths revision as well as where to find the best free teaching resources to add to your student learning toolkit.

First, let's take a look at the various Maths courses from secondary school through to degree level.

### An Introduction To Maths Courses

No matter if you are studying Maths aged fourteen or twenty-one, the subject holds so much weight professionally. Even if you have no intention of continuing with Maths after school, enrollment on any college course or higher education degree will still depend on your displayed mathematical abilities (thanks to proof of qualifications and your CV), along with any job application. Not to mention how much Maths will come into play in your everyday life!

To give you an idea of what you can expect to study and learn on all of the general Maths courses from school to university, here's a brief overview provided in the most part by the government.

**GCSE Maths**

According to **the specifications set out by the government**, a GCSE in mathematics should enable students to:

1. develop fluent knowledge, skills and understanding of mathematical methods and

concepts

2. acquire, select and apply mathematical techniques to solve problems

3. reason mathematically, make deductions and inferences and draw conclusions

4. comprehend, interpret and communicate mathematical information in a variety of

forms appropriate to the information and context.

During a GCSE course, **the primary topics** that you will encounter in your maths studies are:

- Number
- Algebra
- Ratio, proportion and rates of change
- Geometry and measures
- Probability
- Statistics

Surely there's some room to have fun among these modules? Of course, much of it **depends on your teacher, their teaching style and the time you have to cover the content in lessons** so don't go giving your tutor a hard time of it when they have a class that won't settle quickly.

That said, there's no harm in asking if your teacher has heard of these cool math games and if you might be able to try some similar puzzles and games during class!

**A Level Maths**

As for **A Level and AS students**, the government thinks it's important for them to:

- understand mathematics and mathematical processes in a way that promotes confidence fosters enjoyment and provides a strong foundation for progress to further study
- extend their range of mathematical skills and techniques
- understand coherence and progression in mathematics and how different areas of mathematics are connected
- apply mathematics in other fields of study and be aware of the relevance of mathematics to the world of work and to situations in society in general
- use their mathematical knowledge to make logical and reasoned decisions in solving problems both within pure mathematics and in a variety of contexts, and communicate the mathematical rationale for these decisions clearly
- reason logically and recognise incorrect reasoning
- generalise mathematically
- construct mathematical proofs
- use their mathematical skills and techniques to solve challenging problems which require them to decide on the solution strategy
- recognise when mathematics can be used to analyse and solve a problem in context
- represent situations mathematically and understand the relationship between problems in context and mathematical models that may be applied to solve them
- draw diagrams and sketch graphs to help explore mathematical situations and interpret solutions
- make deductions and inferences and draw conclusions by using mathematical reasoning
- interpret solutions and communicate their interpretation effectively in the context of the problem
- read and comprehend mathematical arguments, including justifications of methods and formulae, and communicate their understanding
- read and comprehend articles concerning applications of mathematics and communicate their understanding
- use technology such as calculators and computers effectively and recognise when such use may be inappropriate
- take increasing responsibility for their own learning and the evaluation of their own mathematical development

The **overarching themes** of an A-Level math course in sixth form are, therefore, the following, with numerous sub-topics making up each section.

- mathematical argument, language and proof
- mathematical problem solving
- mathematical modelling

**Degree-level Math**

At degree level, you can choose to study towards **a basic Maths qualification** (no less demanding than a more specialised course, we'll add!) but you can also choose to **focus on a specialism** like mathematical finance, mathematical physics, mathematical biology, actuarial maths, history of maths, special relativity, quantum theory or medical statistics, though many of these are available as modules in later years of a Maths bachelor of science degree.

The** topics you'll study** during your introductory year on a Maths degree include:

- calculus
- algebra
- analysis
- mechanics
- probability
- statistics
- geometry
- vectors
- computational maths

Of course, the list doesn't end there. Once you've completed a Maths degree, you can either go straight into your desired line of work or you can apply for another qualification in the form of a diploma, Masters or PhD. To see how these advanced courses can help you down a specific career path, see the case study below.

Get yourself a math tutor on Superprof.

**Louise Smith, Technical Business Analyst**

Speaking through Prospects, Louise Smith, of J.P. Morgan, offers her advice for women considering a career in STEM after taking the MSci Astronomy and Physics degree at the University of Glasgow.

A member of the first intake for the Tech Connect programme, a graduate scheme for students from a STEM background, Smith was first given an apprenticeship type role as Software Engineer before expanding her responsibilities, completing her graduate programme and applying the skills gained to become an Associate.

Having received a large amount of support since joining the company, including lots of training and being closely helped by mentors, Smith recommends finding a company that will provide you with the right level of support and development. It is also a good idea to speak to relevant companies, their employers and your careers advisor at university or school. You should also be thinking about acquiring key skills so go to recruitment agencies to ask what employers are looking for.

But to be recognised for your talents and passion, you first need to prove that you are worthy of support! The best way to do this is to be on top of your studies and revision.

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## Essential Learning Tips for Maths Revision GCSE

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.

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.

### Why Do We Need To Study Maths?

Things that you wouldn't expect to bear any relation to Maths do in fact come down to an underlying need for mathematics and** the structure it brings to our everyday lives**.

Take shopping, cooking, buying a property, doing DIY, traveling, gambling, playing video games, driving and telling the time, for instance... none of these would be possible without the existence of Mathematics.

Furthermore, Maths everywhere when you consider **the educational and professional worlds**.

Maths is relevant to a wide variety of academic subjects on the GCSE course and A Level curriculum, which not only means that a poor understanding of maths can cause students to struggle in many other subjects but also that it could limit their further studies options as well as their employability when they come to think about career options.

Whether you aspire to study sociology, psychology, physics, biology or even economics, **maths is held in high regard**, and you will be called on solve various maths problems, as part of your work.

### Be Well-Acquainted with the Basics

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.

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 worksheets and exercises, it always helps to revise GCSE maths online with material based on a **specific syllabus**.

Otherwise you could find yourself an online maths tutor to help you with revision.

### Make Good use of Maths Resources

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.yourway

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.

### Success is in the Details - So Be Thorough!

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 going 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.

### Use Maths Resources Like Past Papers to Revise

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.

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.**

### Work Out How Topics are Related

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.

## More Primary Maths Resources For GCSE

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.

### Where to Find the Best GCSE Maths Revision Materials

BBC 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.

BBC Bitesize Maths is an ideal website for those who want to supplement their formal education as well as GCSE maths students looking for **free math revision material **in the run-up to their exams.

The website includes resources sorted by school year and topic, so learners can access step-by-step guides as well as video tutorials for their specific maths curriculum. The topics are also linked to the different curricula from the different regions of the UK, so all learners from England, Scotland, Wales and Ireland are catered for.

What's great about this website is how easy to use it is. Its name, Bitesize, is a true indication of how easy it is to learn morcels of information, and how you can schedule revision sessions based on **easily-digested, bitesize chunks of knowledge.**

For GCSE and A Level math help, there's The Student Room, where students can discuss queries in forums and find **teacher-approved resources**.

The Student Room is an online forum for students which counts over 1.8m members worldwide, allowing you to discuss a range of topics with other pupils from countries around the world. Whether it's **revision, lifestyle, university or relationships** - there's an opportunity to chat about them all!

What's more is that this website, which caters for students from GCSE level (and it's international equivalents) upwards, offers **free revision help **to students via a range of easy to use tools. There are revision guides and past papers and there is information on exam reforms and what you should be prepared for on results day.

If it's one particular subject you want help with, like Maths and its sub-topics, you can **browse the materials and tools by subject**.

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**!

## Maths Worksheets For A Level

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.

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!

## Maths Resources For University Degrees

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.

#### Maths Revision Tips

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!?