Chapters

- 01. Why is GCSE Maths Useful for your Future?
- 02. AQA GCSE Maths Specification In More Detail
- 03. Skills Developed By AQA Maths GCSE
- 04. Choosing the Right Maths GCSE Tier
- 05. Year 10 And Year 11 Maths Topics Across Both Tiers
- 06. Expanding Further On The GCSE Syllabus
- 07. Secrets of Getting a Top Maths GCSE Grade
- 08. Mastering the GCSE Maths Syllabus with GCSE Past Papers

The course for GCSE Maths is specifically designed to help fourteen to sixteen-year olds (but is not limited to that age range with some older students taking GCSE education courses!) **pass the national GCSE Exam**, based on the most up to date curriculum.

The initial part of the **course that you are to study focuses on covering** the basics of mathematics and core math skills, with multiplication and division, addition and subtraction, counting, fractions, and basic algebra specifications all having a part in the timetable.

After developing a strong base in these topics, the GCSE Maths course will then transition slowly towards more advanced concepts and topics. It eases you in gently, so to speak, before turning it up a notch! So if you started your course and thought to yourself: "My maths lessons are pretty easy", then don't get yourself too comfortable just yet! And, definitely, don't think it's okay to just skip lessons or homework assignments.

But, regardless of **your natural ability in math**, the main thing is to stay focused and keep your eye on the prize - that elatement gained when you get the grade you wanted or, even better, the highest grade achievable. Don't let yourself fall behind at any point, because this will only cause you to struggle for the remainder of the course. And this course is **highly important** for a number of reasons, as you will see below.

If you pass GCSE Maths, you are considered proficient in numerous mathematical skills such as arithmetical skills, problem-solving skills and adept in** common core standards of maths,** which is desired by secondary education or higher education institutions, universities , apprenticeship organisers, and a wide range of recruitment professionals working for an employer and/or organisation.

The GCSE Maths exam focuses on the practical side of mathematics. It tests the ability of a candidate to apply core mathematical concepts to solve mathematical problems** derived from everyday lives**.

Use of formulae, theorem, and techniques are also required to be able to come up with a cost-effective, optimum and feasible solution to the problems. As a mathematician, you will sure to have strengths and weaknesses but that doesn't mean you won't be able to excel with progression; a private maths educator can be the answer to reaching your potential in your GCSEs and further education.

## Why is GCSE Maths Useful for your Future?

Your school doesn't just make you study Maths for the sake of it. In England, there are three main subjects that **schools, colleges and employers all want to hear about**: English, Maths, and Science. But why is it that these subjects are so important and are seen as the sole means of assessing your fundamental competencies in academia?

It is not expected that all students will get top marks in all of these areas, far from it. With a focus on these quite rigid competencies, prospective colleges and employers can **use the grade boundaries as benchmarks** to see how you measure up against other pupils in attendance at interviews in the key areas.

You don't necessarily have to excel in all three to get a good job, either, but if you **dream of working in a bank or accountancy firm** then they will be looking primarily for your skillset in Maths and expecting a pretty decent grade to show that you're up to a job working with numbers. Having said that, you must still display a certain level of academic ability in the other two areas as well if you want even **more opportunities in life**.

English, Maths, and Science are currently taught to pupils as young as 5 in the UK and Northern Ireland, with some nurseries and pre-schools even introducing numeracy and literacy to toddlers that attend classroom activities, through interaction and participation. It is at this age that the mind is like a sponge so, with any luck, you will already have a reasonable understanding and practice of **the basic skills** required of you as you head into your Maths GCSE!

### Key Skills Developed By the Maths GCSE Syllabus

Remember that, by studying Maths, you can develop a range of skills that are not only sought after by employers but that will also help you **throughout your day to day life**. For example, Maths encourages logical thinking, decision-making and problem-solving. If you want to learn how to budget with your money then maths is a vital skill!

You’ll soon see that, on any professional application form for any type of role, you will be asked to confirm your qualifications to date, with a particular focus on the three aforementioned subjects. This is so that establishments can get a feel for **your overall academic competencies**, which reflect a number of key skills in business such as effective communication, adequate numeracy, and logical thinking.

To add to that, Maths is a key area of study for those seeking a career in the Finance, Engineering and Information Technology industries. Just some jobs that are directly related to a Maths qualification are **Chartered Accountant, Investment Analyst, Systems Developer and Secondary School Teacher of Maths**.

### Is Maths GCSE Useful Even if Not Continuing to Study Maths?

Maths is a highly useful subject to have, even if your anticipated degree path isn’t directly related to the area of study. Maths lends itself to **a range of transferable skills** which could benefit you in your chosen subject, even if only to help you to apply a rational thought process or make logical well-thought-out decisions.

It is quite fascinating to think that Maths is the only language that is exactly the same for students of all nationalities, regardless of their first or second language, culture, religion or gender. Just like Pi is always going to be roughly 3.14 no matter who or where you are, the principal Maths tools and functions are **exactly the same for everyone**. In some ways, therefore, this makes Math easier than English Literature for a non-British learner, for example.

In fact, as a subject that is purely logical and objective, Maths is one of the few subjects whereby you can really measure yourself against the rest on the programme.

If you know a Maths answer, you know it - there are no two ways around the situation. The only place that students could fall short of getting the same top mark that a fellow pupil got is if they failed to show all of their working out which can be equivalent to getting awarded more marks than just answering right. It's important that students realise this going into the exam.

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### How Non Calculator Topics Are Linked To Other Subjects

Maths and the skills that emerge from understanding its tools and functions are directly linked to a number of other subjects in the education sector and beyond.

For instance, Maths and Physics are interrelated while some of the methods applied to solve questions in Maths also **apply to Chemistry, Information Technology, and the Sciences.**

Maths additionally makes a great joint subject, because it is so neutral and can offer a nice balance in your student life. It is easily combined with courses like History, English, Music as well as languages to provide you with a varied and all-round learning experience.

Add to that the fact that you will have the opportunity to meet very different crowds of pupils, and you can benefit from a very rich experience as you embark on a university course or other degree-level qualification.

Moreover, if you do decide to throw yourself into your Maths studies and take it as a joint or individual degree at university alongside another subject, this could lead you to receive a better financial reward further down the line than some of your peers.

**The prospects for Maths graduates** are pretty high, especially if you study at an establishment that is highly-rated for its Maths department.

### Yet Another Reason to take your Maths Studies Seriously

If the above isn't enough to sway you to quickly sign up to a Maths course, then take a look at these** real-life success stories** who can put much of their celebrity status down to having a pretty good level of education in Mathematics. Not only do they prove that Maths is a 'cool' subject to know about, but they also confirm that being good with numbers can really **enhance your ability to build something great and become an influencer of your time**.

That said, not all of them were maths geniuses, so don't feel under pressure to soar to the top of the class! A little bit of maths knowledge can go a long way...

*Mark Zuckerberg, Technology Entrepreneur and Co-Founder of Facebook*

Educated at Harvard, by the same professor as Bill Gates only 26 years later, Mark Zuckerberg may not have been top of his class in Maths but there is absolutely no doubt that **a certain ability in the subject will have helped him to gain the knowledge he needed to think up the technology behind his social networking sites**. Not only that but to have become the billionaire he is today will have required a good understanding of finances, even if he is advised by a financial professional. That amount of money doesn't just come to people who don't have the brain for business!

Mark Zuckerberg and Yuri Milner have also announced a $3 million prize for mathematics known as the Breakthrough Prize in Mathematics, which once again highlights **the emphasis they place on Maths on their success journey**. This is the third such prize that the Valley's elite have created and its intention is to portray scientists as the heroes that they are.

*Bill Gates, Principal Founder of Microsoft Corporation*

Bill Gates, the genius behind Microsoft, was also a Harvard pupil, **graduating in computer science and math**. His professor, Harry Lewis, said of Gates to Forbes Magazine: “He could have been a mathematics professor [...]He was a determined student who liked puzzles, liked challenges, liked showing people things he could do that they couldn’t do.”

Even though Gates took a different path, it is one that stemmed from his interest in computers and mathematics. Thanks to the huge success of Microsoft, Gates is now worth an estimated $89 billion, making him both the richest person in the U.S. and around the world.

Proof that **Bill Gates' Mathematical brilliance was exceptional from the start** is that "his insights were published in the journal Discrete Mathematics in 1979, in a paper co-bylined with then-Harvard professor Christos Papadimitriou." According to the Business Insider, Papadimitriou was once reported saying that Gates was 'the most intelligent man that he'd ever met', despite just being a junior.

*Steve Jobs, Founder of Apple*

While Steve Jobs veered more towards the creative side of technology than the mathematical side, however, he **took maths and his different way of thinking to create a new market**.

In fact, he gave a great explanation for why math and humanities need each other, as reported by Venture Beat: "Thinking back on the calligraphy classes he audited in college, Jobs recalls that typography 'was beautiful, historical, artistically subtle in a way that science can’t capture, and I found it fascinating. None of this had even a hope of any practical application in my life. But ten years later, when we were designing the first Macintosh computer, it all came back to me. And we designed it all into the Mac. It was the first computer with beautiful typography.”'

Therefore, as the online magazine touches upon, it is** imperative to combine both maths and humanities subjects** to reflect a new business world that demands math and social science skills.

While you, personally, may not have the desire to find success in our fast-growing technology sector, we hope that these examples will still serve as some** inspiration of what clever thinking can do for you professionally**.

As you can see, it's not just maths you need to focus your attention on but all of your key subjects and how they combine to help you make **powerful decisions and choices**.

With that in mind, let's take a look at the GCSE course in a bit more detail so that you know what to expect from your Maths GCSE lessons.

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## AQA GCSE Maths Specification In More Detail

AQA is one of the principal exam boards for GCSE Maths in Britain and is taken by thousands of students across the United Kingdom.

Most of the course content of GCSE Maths is structured in such a way to enable students to develop a thorough understanding of core **mathematical concepts** and methods which usually include the following core topics:

- Statistics
- Algebra
- Geometry
- Measures
- Probability
- Number

Keep in mind that the **syllabus content discussed here is according to the GCSE in Mathematics A**, Pearson but the course content is usually the same for all the boards with the difference only in the way they hold their tests.

## Skills Developed By AQA Maths GCSE

By following the syllabus of GCSE Maths, students learn and polish their skills in:

- The ability to solve math problems using various
**mathematical strategies** - Acquiring the right Mathematical concepts, methods, and strategies
- Choosing the
**right math concepts**and techniques to deal with real-world problems - Applying the common core mathematical concepts and theorems to solve the everyday problems
- Mathematical reasoning, mathematical deductions, inferences and drawing conclusions
- Communicate mathematical facts, data and information after
**interpreting it correctly**

## Choosing the Right Maths GCSE Tier

There are basically two tiers in GCSE Maths i.e :

- Foundation
- Higher

Sadly, it is not as simple as that, though.

The **numerical grade has been assigned to each tier in a particular range**. The Higher tiers are assigned the numerical grade of 9 to 4 with the grade 3 as the minimum safe zone. The foundation tier has the numerical grade range of 5 to 1.

For advanced mathematicians, and likewise those who struggle to scrape a good grade, this poses no problem. However, it is those who are in the middle range that have a dilemma on their hands. Do they **play it safe** and only enter for the Foundation tier, confident in the knowledge that they can achieve the top '5' grade? Or do they **take a chance** on the Higher exam, knowing that if they don't make the minimum '3' grade for whatever reason on the day, they could get an unmarked question paper and thus bring their overall grade right down?

Your Maths teacher will, of course, make recommendations of how you should proceed and provide an explanation of the system to ensure that you understand the situation you are in, but it may be that they leave it up to you to make this** all-important decision about your program of study. **You may also wish to speak to your local or online maths tutor who can offer you instructional advice on what they think is right for you in relation to how you learn and what they deem is a realistic outcome for you.

In my eyes, if there's an **opportunity to exceed the mid-range bracket** and feel proud of achieving an excellent grade in Maths, then it's worth the shot, even if you have to pay for some **extra tuition or homework support** to acquire and secure that additional knowledge and skill you most definitely want to have going into the exam.

Both these tiers include such questions which are the same in both.

A reform was introduced in GCSE Maths syllabus and the new GCSE Maths course includes content which is not only more challenging but also more demanding, with a considerable focus on the questions related to problem solving.

This introduction of new content material has made achieving the bottom grade in higher tier more demanding as well as the top grade on the foundation tier.

#### The Importance Of Entering The Right Maths GCSE Exam

Here is a quick reminder of the grades you can achieve from one tier to the next.

Foundation | Higher |
---|---|

Grades 1-5 | Grades 3-9 |

## Year 10 And Year 11 Maths Topics Across Both Tiers

The topics included in the foundation tier of the GCSE Maths are same as mentioned above, the only difference being the level of difficulty.

Here is the subject content in both tiers:

- Statistics
- Algebra
- Geometry
- Measures
- Probability
- Number

## Expanding Further On The GCSE Syllabus

**Numbers**

The main topics included in the topics related to number manipulation are addition, subtraction, multiplication, dividing, ordering of rational numbers, using of **the concepts and vocabulary of** multiple, highest, least common factor, divisor, prime numbers and prime factor decomposition.

**Algebra**

The content of algebra includes differentiating between the different symbols and notations used in algebra and interpreting their correct meaning. **Identifying correctly an equation, a formula, an identity, and an expression.**

Manipulating algebraic expressions using the basic and most common laws such as collection the like terms, multiplying of the term outside the bracket with the term inside the bracket and taking out common factors.

It also focuses on the **multiplication of two linear expressions**, factorization of quadratic expressions and simplification of rational expressions. Apart from that, setting up and solving simple equations such as two simultaneous equations to find any unknown variable is also extremely crucial skills to learn.

The preparation of algebra is incomplete without becoming **adept in understanding the gradient of parallel lines** and the equations of the form **y=mx+c **which is the equation of straight line. Solving these equations in one variable **x** to obtain another variable **y** allows us to plot a graph corresponding the straight-line equations.

Other key topics in algebra include:

- Transformation of functions using the transformations of reflection, enlargement, rotation etc.
- Indirect and direct proportions
- Graphs of simple loci
- Graphs of simple cubic functions

**Geometry**

**Geometry in GCSE maths consists** of topics of angles at a point and on a straight line, right angles and other types of angles. Perpendicular lines, properties of angles of parallel lines, quadrilaterals, triangles. Calculating and using the sums of exterior and interior angles of polygons along with the properties of special quadrilaterals such as squares, rectangles, parallelogram, trapezium, rhombus and kite.

2-D shapes and their reflection and rotation properties along with understanding the concepts of congruence and similarly is also core geometry topics in GCSE Maths.

**The famous Pythagoras theorem both in 2-D and 3-D is included too.** Planes, diagonals of a cuboid, trigonometric ratios of sine, cosine, theta, to find the angles between lines and a plane, angles of elevations, angle of depression and to solve 2D and 3D problems are all very important part of geometry.

Vectors are the basic topics in geometry and the geometry portion teaches students to understand and also use vectors to solve various problems and to calculate various operation on vectors such as the sum of vectors, the difference of vectors, scalar multiplication of vectors. Learning how to apply vector methods can also help in solving simple yet tricky geometrical proofs.

**Measures**

This part of the course develops the skills of the students to interpret scale drawing and maps and it helps them understand the effect of enlargement of area, volume, and perimeter of **solids and other shapes**.

Under this subject content, students master the skills of interpreting scales and finding the inaccuracy in certain measurements. Conversion of measurements from one unit to another unit also falls into this category.

**Statistics**

Statistics are used to solve statistical problems with the help of statistical analysis and collection of data from several sources. Students need to learn the following in order to master the** statistics portion of GCSE Maths:**

- Identifying the sources of bias and understanding how data relates to a certain problem and how the size of samples affect the conclusions
- They should be able to design a survey or an experiment and they should also be able to identify the type of data that is needed to be collected and the format of the data. Their concepts of population and sample should be crystal clear and they should also consider fairness and be able to either design or
**criticize a questionnaire** - Their understanding should include
**the know-how of designing data-collection sheets**which enable them to distinguish between different kinds of data - Extracting data from lists and tables, using and designing two-way tables for both grouped data and discrete data, producing charts, diagrams, histograms, graphs etc for all kinds of data types and learning to find mean, median, mode, range, modal class is all part of very crucial topics in statistics.

**Probability **

Learning the use and meaning of vocabulary of probability sets the basis of other key concepts in the subject. Students should learn to distinguish between unlikely, equally likely, even chance and impossible events and should be able to mark probabilities as well as events on **a probability scale of either 0 or 1.**

The key skills to learn probability are :

- Using estimates, measure of probability, relative frequency, theoretical models
- Finding the probability of successive events for examples toss of a coin or several throws of a dice.

The GCSE Maths course mentioned above is for both foundation and higher tier but the higher tier includes slightly advance topics in addition to the ones mentioned above.

## Secrets of Getting a Top Maths GCSE Grade

While it is mainly down to what you know and what you can do, your chances of passing a maths exam can be significantly improved by **using skills and techniques** taught to you by your class teacher or your home tutor.

For example, in order to maximize your chances of getting a good grade, always write down and **display every step of your working out** and the solution to a question, no matter how straightforward it may seem. Even if you get the answer wrong, you might get some marks for providing a partially-correct solution.

Make sure to revise your maths GCSE syllabus effectively by scheduling in either independent and group study sessions (or a mixture of the two) and by breaking the topics down and using textbooks, worksheets and past papers to your advantage.

If you want some help dividing the syllabus up into easy to digest sections, why not try visiting BBC Bitesize which has done all of the hard work for you. Not only can the website help you to plan your revision time, it can also be a useful resource in itself too, offering revision notes and activities based on your actual curriculum.

If you feel like you are weak in some topics more than in others, make it your mission to turn that weakness into your strength.

**Do not let those topics intimidate you** and practice until they become a piece of cake for you. Following the right learning style along with planned preparation will surely ensure you a good grade, if not a prestigious 9!

Don't wait any longer, **get stuck into maths right now**! Find a maths tutor for A-level maths revision & GCSE Maths revision and see how your confidence grows by leaps and bounds.

## Mastering the GCSE Maths Syllabus with GCSE Past Papers

Your teacher will no doubt have already told you, but past papers are one of **the best forms of revision that you can do in the run up to your exam**, whether we are talking about Maths or any other subject for that matter!

Doing past papers is especially useful if you are new to exams, which could well be the case as a GCSE entrant. By using past papers properly, you can work on **improving your technique and growing in confidence**. However, it is no good simply reading past paper questions or just jotting down answers haphazardly.

You must train yourself to cope with the pressure of exams so make sure that you put yourself under the same conditions as you would in a real-life exam. If you are not sure what to expect from an examination centre, ask your teacher to provide you with some details.

While your teacher may organise a mock exam for you during your two-year course (most likely to be at the end of each academic year when you have learned a sufficient amount of information to take an exam), or set a classroom task which simulates an exam. Either way, the key is to **stay focused** and to take away the maximum from this very valuable experience.

If you are **practicing at home using past papers**, don't shy away from doing them properly. Ask your family not to disturb you for the duration of the trial exam (if you consult your exam board's website, you can find out exactly how long your exam will be, although this should be clear enough on the paper you have downloaded and printed out too).

Be sure to get yourself in the zone beforehand - make sure you have revised thoroughly, have been to the toilet and only have the essentials with you like a bottle of water and some stationery.

Most importantly, make sure you have **switched your mobile phone off** so that you are not distracted.

**Further Facts About Exams**

GCSE exams are not all about perfect answers given under pressure though. A very important aspect of being assessed is** the way you respond and offer your working out**.

Consulting past papers can enhance your ability to respond well and gain extra marks by helping you to realise what it is the examiner is looking for and how you **grab a few extra marks** where you really don't know the answer to something. Even some minor points could all add up when it comes to your final achievement, and some of your notes could even be the equivalent to getting half a question right, just because you showed you knew how to approach the problem.

Edexcel and AQA tutors may have

different marking schemes to work from when marking and grading.

Familiarise yourself with the types of questions that are commonly set and ask yourself what it is they are trying to get out of you. Furthermore, find out what can add or lose you points in the exam, as **mastering this technique** could be the difference in you getting one grade or another when the results are published.

You can do all of this by checking out the **mark scheme and examiners' notes**, two very important documents that should not be ignored if you are serious about doing well in your Maths specification.

If you are not sure what tier you are sitting - **foundation or higher** - check with your teacher so you can be explained the grading system.

Since you may not have sat in an exam hall before, you should know that there are many rules in place to ensure that every student has a fair assessment.

Pupils must **arrive on time**, and can only take a small number of items (including refreshments, stationery and, at times, books) into the hall with them. But, most importantly, there is **strictly no talking**, passing notes or any other form of communication allowed. This can be quite hard to get used to but it really is very important to **respect the conditions set out by the assessor **and ensure you don't get asked to leave as this could result in an unmarked exam and bring your overall grade right down because of one silly mistake.

And nobody wants to resit an exam unnecessarily!

Nearer the time of your exams, you can also **find timetables for your exams** on your exam board's website to help you with preparing your revision sessions.

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