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 Year 10 or 11 student student looking to get the most A and B grades that you can, a Year 12 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.
Year 10 Maths
According to VCAA, here are the requirements for pupils completing year 10 Mathematics in Victoria:
- Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems
- Apply index laws to numerical expressions with integer indices
- Express numbers in scientific notation
Money and financial mathematics
- Solve problems involving simple interest
Patterns and algebra
- Extend and apply the index laws to variables, using positive integer indices and the zero index
- Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
- Apply set structures to solve real-world problems
Linear and non-linear relationships
- Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software
- Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software
- Sketch linear graphs using the coordinates of two points and solve linear equations
- Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations
During a Year 10 Maths Methods course, the primary topics that you will encounter are:
- Patterns and algebra
- Linear and non-linear relationships
- Pythagoras and trigonometry
- Geometric reasoning
- Data representation and interpretation
- Real numbers
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!
Year 11 Foundations Maths
As for Year 11 Foundations Maths pupils, VCAA outlines the necessary areas of knowledge as:
- application of integers, decimals, fractions, ratios, proportions, percentages and rates to solve practical problems
- geometric conventions and properties of shapes and objects
- interpretation and use of plans, elevations, maps, models and diagrams
- application and use of similarity and symmetry
- enlargement and reduction of diagrams and models
- interpretation and use of location, distance, direction and scale on diagrams, maps and plans
- application of Pythagoras’ theorem in practical situations.estimation, approximation and reasonableness of results
- use and interpretation of formulas and algebraic expressions to describe relationships between variables and to model patterns
- manipulation and solution of expressions and equations to solve problems including predicting a required quantity or finding a break-even point.
- features, conventions and terminology used when representing information in diagrammatic, graphical and tabular forms
- collection and representation of data in diagrammatic, tabular and graphical forms
- interpretation of diagrams, charts, tables and graphs
- use of measures of central tendency (averages) and spread to summarise and interpret data
- comparison and interpretation of data sets.
- application and use of metric units and measures, including derived measures
- interpretation of scales on digital and analogue instruments
- solution of personal, societal and workplace problems involving metric measurement with consideration of error, required accuracy and tolerances
- estimation and approximation strategies
- interpretation and use of time and duration including time and date specifications, conventions, schedules, timetables and time zones.
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:
- 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 pupils with 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.
Check for a good Maths tutor Sydney.
Primary School Maths Worksheets
Allow me to provide a word or two about some fun worksheet resources for primary school aged pupils to complete.
Twinkl has some fun worksheet style activities for primary school pupils to complete online for free. They cover each major area of primary school maths such as subtractions, multiplication, division, money, decimals, the times table, graph analysis as well as number patterns.
If you are looking for a printable worksheet, they have you covered. They also have online activities for students to complete.
If your child needs additional help with subtraction, multiplication, division or decimals, then consider this great resource.
Essential Learning Tips for High School Level Maths Revision
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 university degree options, which not only means that a poor understanding of maths can limit a student's further studies options as well as their employability when they come to think about career options.
Whether you aspire to study 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.
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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 Year 10, 11 or 12 studies, or you're in higher education at 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 maths online with material based on a specific syllabus.
Otherwise you could find yourself an online maths tutor to help you with revision.
Utilise Good Maths Resources
As you know, Maths is a compulsory subject for all pupils up to the age of fifteen or sixteen (depending which state you live in) - 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 Year 10, 11 and 12 homework is assigned for a very good reason and is designed to help you go further in 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.
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You Will Find Success 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.
Check out available online Maths tutor on Superprof.
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 Year 12 end of year 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.
If you'd like to work through any math questions you got wrong, talk to your teacher about what mistakes you made in your working out. This will help you identify where exactly you are going wrong, not just on what topic you are making mistakes.
Tip: Make sure you focus on the most recent papers. The VCE (and other states') Maths curriculum is changing all the time and it's important that your revision is up-to-date.
Find 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.
More Primary Maths Resources For VCE (Year 11 and 12) Students
You're in year 12 and preparing to sit your final Maths Methods exam in November.
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.
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 Year 12 Maths Revision Materials
Mathsmethods.com.au has some fantastic 'cheat sheets' which you can copy in preparation for your Year 12 Maths Methods exams.
Their materials cover all topics you can encounter in the world of Maths Methods and they are completely free to download from their website.
This is great for students who want to complete practice exams with supplementary material. Occasionally, students will be able to bring in a cheat sheet for the SAC assessments throughout the school year. Using cheat sheets from this website ensures that you have all the relevant information for you to ace that assessment!
What's great about this website is how easy to use it is. Instead of having to become a kind of artist and prepare you own neat and concise cheat sheets, they've done it for you in easily-digested, bitesize chunks of relevant knowledge.
The Mathematical Association of Victoria also has some great resources available to VCE maths students completely free of cost.
They have trial exam papers as well as extended solutions to exam questions in order to ensure student can prepare themselves fully for both SAC assessments and exams using their websites tools.
They also have many resources for teachers such as SACs for teachers to give to their classes. These can either be used as 'mock' or 'practice SACs' or they can be used as the real thing. These will require a school subscription to access, however it takes a lot of the hassle out of preparing assessment materials for the STEM teachers who are teaching VCE subjects.
This website is a great resource for teachers and students for different reasons!
Maths Resources For University Degrees
If you're aiming for a career in finance, research or engineering, 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!
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.
Wherever your mathematic journey takes you, good luck and always show your working!