I know that a lot of people wanted me to give advice as to how I got a 50 in this subject and now that I have a bit of time on my hands I guess I'll write something up. I hope you find this guide helpful.

I completed Geometry and Trigonometry, Graphs and Relations and Business-related Mathematics as my three modules. Therefore, I unfortunately cannot pass on any words of wisdom regarding the other three modules. I apologise for this inconvenience.

As you all know, my Further Mathematics journey last year was not an easy one for me. This was because my teacher had awfully high expectations of us and he encouraged us to compete against each other. He'd surprise us with tests (not SACs) almost every week and in most cases he publicly ranked us to get us motivated. He could also be incredibly lazy and this added to the stress because at times he did not cover some aspects of the course adequately or even at all. I just would like to note that you don't need to go to the lengths that I did in order to succeed, and that your experience taking this subject will most likely be much more positive compared to mine.

This guide assumes that you are aware of and understand the technical details of the course outline because I'm not going to cover it. I'm going to focus on how I tackled the subject as well as how I advise you to tackle it.

I know it's very long (in excess of 5000 words) but I feel some of the advice I've provided is invaluable, so please do allow time to read this guide properly. Feel free to ask me any questions you have regarding the course. I'll try to make an effort to stick around this forum throughout the year, as I know it tends to get a bit neglected. I'll keep adding to this thread as I think of more useful information.

**Why should I take up this subject?**In my opinion, these are the students who would most likely benefit from taking Further Mathematics in VCE:

- Year 11 students with a strong foundation in Mathematics

- Students also undertaking Methods as part of their VCE

Since VCAA has allowed students to enrol in all three VCE Maths courses, Further Maths has become arguably the most competitive VCE subject there is. Sure, the content is generally quite easy to grasp, but you can't afford to lose too many marks from silly errors if you want a 40. This is a bit of a controversial point, but if you're not a very strong Maths student, I'm not entirely sure if you should be taking Further Maths, only because the Methods/Specialist students also enrolled in this subject (such as myself) have really stuffed things up in terms of rankings. You'll also find that this subject is not a prerequisite for many courses so there's no point forcing yourself to do Maths if it's really not your thing. By all means, if you think you'd benefit from having a basic understanding of Mathematics, you should definitely take this course.

Going off on a bit of a tangent here, but if there are any Year 11s considering accelerating in a Maths subject, I personally would advise Further Mathematics over Mathematical Methods (CAS), despite the fact the latter seems more appealing. This is because Methods is a far more demanding course and you cannot afford to neglect your Year 11 studies. I felt Further Maths was very flexible and I was able to give all of my subjects equal attention throughout the course of the year. I know that there are a lot success stories out there in regards to accelerating in Methods, but I've also heard a lot of negative ones as well; whereas for Further Maths there are generally a lot more positive outcomes due to the more manageable workload and content. My school trialled Methods acceleration one year and the result wasn't very favourable and hence they don't allow it anymore. Stronger students may also want to consider enrolling in both Methods and Specialist Mathematics at the same time - anecdotally I have heard taking this combination at once to also be quite beneficial.

**Are Units 1 & 2 necessary for Units 3 & 4?**In short, no. This is because many students come into Further after dropping out of higher Maths courses, or others change their mind and would like to enrol in a Maths subject after not taking any in Year 11. I didn't take Units 1 & 2 either, but from what I was able to see from the notes on the whiteboard of the Further Maths Units 1 & 2 classroom, the content is basically identical to what you learn in Units 3 & 4.

**Should I complete the entire Further Mathematics course in the summer holidays?**As a both keen and stressed student after my first week of headstart, I decided to do this, so I spent approximately an hour each day working through the textbook doing a handful of questions and taking notes. This took me about three weeks in total, but I have heard that some people who worked at a more brisk pace have managed to finish the course in just a few days. All I can say is that I do not recommend this. I guess this demonstrates that the Further Mathematics course is really quite small and you will manage perfectly fine if you stay at the pace of your class. I personally found that by the time we started the last topic that I had forgotten it all and at the very most I was able to say "Oh yeah, I've seen this before" throughout the year. It is unreasonable to think that you can revise this subject for ten months. I don't think it'd even be possible to find enough content to do this for such a long period of time and repeating the same content is not advisable. If you're aiming high, Further Mathematics is all about exposing yourself to as many different types of questions as possible so that come exam time you can tackle any tasks they throw at you.

Instead, I encourage you to thoroughly research the course outline and understand the details and mechanics of how the course works. It's really important you know what you're getting yourself into so that you can gauge what you need to do to get results.

**What resources do you recommend?**My school's textbook was Maths Quest and I found it to be quite good, with the exception of Business-related Mathematics because it didn't address the study design very well. Luckily for the Maths Quest users this year, a new edition has been released so hopefully you won't have any problems. I also had a pdf of the Essentials textbook and found it useful as well. If we're going to compare these two books, I'd say that the Essentials textbook explains the theory a lot better and provides questions which allow you to build your skills, whereas the Maths Quest textbook has better and more difficult questions to test your skills. You can do well with either textbook and you do not need to consider purchasing both of them. Your textbook has some review chapters that you can use as well. I personally didn't do mine for SAC revision, but don't forget they are there just in case you run out of questions.

I also bought Checkpoints and A+ Notes for SAC revision. I found Checkpoints to be a complete waste of money because the formatting in my book was stuffed up and I was able to access the same questions for free through previous VCAA exams. It also turned out to be a bit detrimental as it meant I remembered the questions when it came to sitting trial exams. That being said, I cannot recommend A+ Notes highly enough. The book only provides questions at a level that would distinguish A/A+ students on the assessments and also has some helpful preliminary notes (I didn't use these, however). There are many more study guides however (including an ATARNotes one!) so do shop around and find yourself a good book.

In terms of lectures and other external tuition services, you probably won't find them to be absolutely necessary. If you're really struggling, they might be of benefit, but otherwise the course is simple enough that you should have no problems learning it in class. In the highly unlikely event that you'll need a tutor, I'd personally go for someone who did the Further Maths course over strong Methods/Specialist students. Sure, the latter will be able to pick up the content quite easily and help you out, but I think the personal experiences and tailored advice from a previous Further Maths student would be invaluable in comparison.

http://www.vcefurthermaths.com is also a very helpful website if you're having trouble with Data Analysis.

**What do you advise in regards to bound references?**Some more detailed advice can be found here:

Constructing a bound reference for Further MathematicsIn short, I highly encourage you to make the effort to construct one. Start from the very first lesson and spend a little bit of time each night writing some theory notes and adding some tricky questions (with solutions and explanations) and continue adding to it as other tricky questions pop up. I found that my biggest problem in previous years was that I'd have a mental blank as a result of the nerves, so this format would help me jog my memory. A bound reference also helps to consolidate your knowledge and remember things throughout the year. Don't leave this until SAC time or the end of the year because you want to be spending time exposing yourself to practice questions instead of making notes.

**Do you have any general studying and revision tips?**It is really easy to become complacent and neglect Further Maths, especially if you're a strong Mathematics student. However, you need to ensure that you allocate ample time for it each night or else you won't get the adequate comprehension of the theory or get the practice you need to break 45. It's really important you use your bound reference while studying throughout the year so that you're familiar with its structure come exam time. Luckily, you're allowed a calculator into all assessments so you don't have to worry about practicing problems by hand - in fact, you need to get to know your calculator inside-out! Not only are you far less likely to make a mistake, but much of the course actually revolves around calculator input and output. For SACs and exams, make sure you complete a lot of practice questions to help minimise silly errors whilst working under pressure, as well as to expose yourself to as many types of tricks that can be thrown your way.

I lost count of the number of trial exams I did in the end, but I can probably suggest that you don't need to go as crazy as I did. Our class finished the course in July so our teacher started giving us papers from the Term 2 holidays. I think starting sometime in late Term 3 would suffice, but I advise you to do as many as you possibly can so you feel you can accomplish all styles of questions. If you're not studying Matrices, past papers from the old study design will also be fine (if you're doing Geometry and Trigonometry and come across a traverse survey question, leave it out - otherwise, all the other questions are OK). You'll find that certain exam companies range in difficulty, but it's important you do both easier and harder trial papers so you get accustomed to the ranging difficulty of the real exams. Make sure you roughly do the same number of Exam 1 and Exam 2 trial exams - many students get lazy and only practice Exam 1, causing them to struggle when it's time to do the real second examination.

When I was doing trial exams at home, I found that I was fairly calm and hence was getting 40/40 and 60/60 with ease. The best practice you can get is if you can sit all your trial papers in an appropriate setting, but this obviously isn't very practical. What I did to add an element of pressure at home was to reduce the amount of time I was able to complete the exam. By term 3, I had to finish the entire exam paper in one hour compared to 90 minutes and once I had attempted a question I was not allowed to go back and check it. This also helped me to get the right answers the first time, rather than find errors later on. When it comes to the real exams, however, make sure you use the entire allocated time effectively.

The exams have been getting progressively more difficult over the years and even written theory questions are not off limits. They are becoming increasingly common, and really are free, easy and quick marks if you understand how the concepts work. A good example is last year's Exam 1 Business-related Mathematics Question 9 - a theory question with absolutely no arithmetic whatsoever. It was something I got in a few seconds during reading time, yet only 20% of students answered the question correctly. Having some copy/paste answers in your bound reference are alright, but you should not become too reliant upon them in case they do not fit the answer appropriately.

Reading the assessment reports is also really key. For Further Mathematics, the assessors seem to be bringing up the same issues every year: rounding off, accidentally missing/misreading a question, filling out the wrong module and inserting an inappropriate copy/paste answer to a theory question are among the most common, along with more module-specific problems. Since these issues have been persistent and the cohort is competitive, there is no doubt that examiners will continue to exploit these, so keeping yourself informed on how to beat the pack come exam time is essential.

Without meaning to sound repetitive, I think making sure that I was accustomed to anticipate almost any type of question and taking the time to truly understand the theory were the keys to my success.

**Do I need to get perfect scores in order to get a 50?**A lot of people tend to get 100/100 for their SACs, but I can assure you with confidence that this is not required for a 50 as I got 99/100 for my SACs before scaling. Instead, it's your ranking that you should be aware of. Of course, rank 1 is what you'll want if you're aiming for a 50 but you can still rest easy and achieve 45+ if the people above you are strong and are likely to perform well on the exams. Remember that if you lose a few marks that it is not the end of the world - you will still have opportunities to climb your way back up the rankings. If it makes you feel any better, after I lost a mark on my first SAC, my ranking fell to about 12th. However, I was the only one in my cohort to get 40/40 for the core SAC, which skyrocketed me to rank 1 for the rest of the year. Since this SAC is worth double compared to the others, it is a great opportunity to climb the ranks as it is long and many students lose focus.

For exams, however, it has been reported that you can only lose one mark over both exams if you want a 50. From there onwards, any mark lost is approximately a study score lost until about 45, where things become slightly more relaxed. Unfortunately, Further Mathematics has become a subject where people are separated based on the amount of mistakes they make, rather than how much they know. I believe this is a major reason as to why VCAA has been turning towards theory questions in the more recent exams.

**How should I tackle the SACs and exams?**You should be able to complete the assessments in this subject quite comfortably in the time provided, so I cannot urge you enough to take your time and work meticulously. Do it once and do it right, rather than get it done quickly and then try to find mistakes later on. Nerves was something I was battling throughout the entire year and it's something that just gets better with practice. At times there were questions which I couldn't tackle initially and I'd feel the nerves start to overwhelm me. If you get this feeling you must stop, close your eyes, take in a few deep breaths and clear your mind of unhelpful thoughts. Once you feel better, move onto a different question altogether and come back and have another go later on. Believe me, I had about six panic attacks during Exam 1 after seeing different styles of questions and this was how I overcame them. In the end, I got 40/40 for this exam, so I guess it works.

If you find your mind is full of negativity, here's a little something that should help you out: "If Stick was able to do it, then so should I."

You all know what an anxious wreck I was during the year, so I hope that gives you some confidence.

Your wording needs to be very careful and your arithmetic must be well set out. You will receive consequential marks in Further Mathematics only if the source of the error is clear, so put down as many steps as you can. Rounding off is a major part of the course and learning to work with very large decimals instead of fractions is imperative. Do not use rounded answers in your workings unless told otherwise. You will only be penalised one mark in the assessments if you make a rounding error, but you will only be awarded full marks for other rounding errors if the examiner is able to see how you made the error. Write down as many decimal places as you can during your working out and round off only at the last step to avoid losing more marks than necessary.

It's also really important that you are able to know deep down that you tried your absolute best come exam time. Not only is it a confidence boost, but it helps to validate your feelings in case things don't quite go to plan. In the weeks leading up to the exams my parents were actually screaming at me to stop doing trial exams in my free time and were considering unplugging the printer so I couldn't do any more. While you don't have to go to such lengths, if you can say that you have done the best you possibly can, then there should be no concerns whatsoever. Taking another perspective on that - don't let yourself have concerns by not trying hard enough. One major motivating factor I have is simply the fear of the anxiety I get in an assessment if I don't know how to answer something. Address that anxiety by ensuring you can answer as much as you can when it's finally time to sit the exams.

Before each assessment you need to allow yourself some time to take a breather. I generally left 3 revision-free days prior to each SAC and no revision in the week leading up to the exams. It's important you don't go into the assessments with an overworked and fatigued mind. Instead, you can ensure you're ready for the task by having a little warm-up - I generally did this by carefully reading the notes I made in my bound reference. Before sitting each exam, I made sure I had a long, relaxing shower and arrived at school fairly close to the start of reading time. Waiting in a nice, quiet place not too far from the exam room is key and make sure you tell all your friends and peers that you'd like for them to avoid asking you questions if possible. Remember, they will be a bit nervous too and they aren't intentionally trying to make you more worried.

If you're a Year 11 student, ask to take the day before your exams off so that you can unwind before the big day. If they don't allow you at first, explain that you're feeling quite nervous and that you think taking the day off will really help. I don't think many schools would say no to this because they are concerned about your welfare and your results. They'd much rather have you catch up on a day's work than have a poor exam performance. Of course, don't use this day to do some last minute revision - this is a day where you should be having fun and relaxing.

**I don't like one of the topics I'm studying. Should I learn another one on my own?**This is not something I recommend lightly. No matter how much you dislike a particular topic, you're going to have to sit a SAC on it anyway and you're going to want to do fairly well in it to maintain a good ranking. You must also take into account that when it comes to exam revision, schools like to save paper and only distribute the required modules, so you'll have a bit of a tough time gaining some adequate resources to prepare for the exams. Some find that they feel somewhat uncomfortable doing something different to everyone else, or doing something without the support of their teacher and peers and that also may affect your overall performance. The time that you take to learn a new module could be used to perfect any module you are having trouble with.

Some people also learn an extra topic throughout the year in case they do not like the questions for one particular module on the exam. This is something I also do not recommend. There is no benefit in answering more sections on the examination papers as required since examiners will only mark the first three modules you completed - not to mention that you probably won't get enough time to ensure your answers are as correct as possible. Again, I'd rather concentrate on perfecting the modules you have already learnt rather than waste extra time and effort learning a completely new topic.

The only instance I ever recommend learning a new topic on your own is if you've sat the SAC for the topic you don't like and you didn't do well in it. If that is the case, you need to do whatever you have to in order to try and save your exam scores. Make sure you communicate with your teacher so that they can do the best they can to help you out.

**Specific advice for Core: Data Analysis**It's super important you understand the theory for this topic because arithmetic alone won't get you over the line since in both the SAC and the exams, the majority of the questions require a written answer. You'll find that there will be some appropriate copy/paste answers that you can use, but ensure that your wording is specific to the question being asked. To give you a specific example, one year the assessors reported that many students referred to sales in their answer to a theoretical seasonal indices question when it actually was talking about rainfall. Remember that you must always talk in terms of the specific variables and that it is not enough to state a mathematical answer to a theory question.

As I have said, the Data Analysis SAC is worth double compared to the other SACs and is a great opportunity to improve or secure your ranking. It is usually a very long assessment and it's very easy for the nerves to get the better of you, or for you to become fatigued and lose focus. Make sure that you give yourself ample down time throughout the duration of your assessment as it generally progresses in difficulty. If you are using Excel for your SAC, it's a good idea to make sure you practice the skills you'll be using beforehand (your teacher should give you some time to practice in class) by completing Section A of trial exams using Excel instead of your calculator.

This topic heavily relies on you using your calculator to enter information and manipulate the results in a meaningful way. Learn to use your calculator effectively and quickly and ensure you are competent at inputting the information correctly. A lot of the questions cannot be done by hand and take a while to do on the calculator, so you cannot afford to make a mistake whilst entering in your data. Unlike the other Mathematics courses, you are allowed your calculator into all assessments so practice using it each night while doing your homework.

**Specific advice for Module 2: Geometry and Trigonometry**This topic basically has no theoretical questions whatsoever and the arithmetic is often quite involved and tricky. This was the only topic where I lost a mark on the SAC and it is very easy to make a mistake if you are not careful. You will be dealing with incredibly large decimals and you must learn to work with them effectively. While stronger students may be tempted to work out these questions by hand, using your calculator effectively will help reduce the amount of errors you make. If you are also a Maths Methods or Specialist Maths student, you must ensure your calculator is in degree mode as no marks are awarded for answers provided in radians. You may spend a lot of time trying to work out some Geometry and Trigonometry questions, especially if there is something specific you need to identify in a diagram. To ensure you answer the right question, you may find it helpful to write out some worded workings or draw some extra diagrams to make things more clear. An example where this is a good idea is total surface area, where it is common for students to accidentally leave out one of the surfaces.

Geometry and Trigonometry is a very popular topic in Victorian schools and every year approximately 70% of the state fills out this section on the exams. It is rumoured VCAA has been trying to level out the topics and this module has been one of the most difficult for several years as a result. You must really take the time to practice or else you will fall victim to a number of traps that are thrown at you in the assessments.

**Specific advice for Module 3: Graphs and Relations**This module is less tricky compared to some of the others, but it is by no means an easier topic. Many stronger students enrolled in other Mathematics subjects assume that their previous knowledge will get them by and that they will only have to do very little work to do well. I can tell you that this is not true as much of the module has been simplified and watered down and some aspects have not been covered in depth in other Maths courses. Regardless of the matter, many students continue to believe that they can fall back on Graphs and Relations if they are having trouble in the exams only to realise too late that they are in a lot of strife. I believe complacency was the reason why only 3% of the state managed to correctly answer 2011 Exam 2 Question 2 correctly. I have never seen a more poorly answered question in my studies.

Graphs and Relations is not too difficult to learn, especially if you're a strong Maths student, and it does have a relation with Data Analysis. There is a little bit of theoretical knowledge tested, but most of the questions require a mathematical answer. One issue which seems to trouble a lot of students is linear programming, especially deciphering the information to determine the equations of the constraints. This is something that you will improve on with a lot of practice and a few problem-solving skills. One thing to note about this module in Further Mathematics is that you will only ever be dealing with two variables in the questions, so keep that in mind if things start to look a bit complicated.

**Specific advice for Module 4: Business-related Mathematics**This module has proven to be very difficult, even for stronger Maths students. If you are enrolled in a higher Maths subject, any advantage you've had over the other students throughout the year is completely lost in this topic. Anecdotally, I've heard students who have completed Accounting Units 1 & 2 have found this topic a bit easier, but their knowledge is still not enough to let them fill out the module with no extra work. Schools have really backed away from teaching this module and only approximately 30% of the state does this topic on the exams. However, as they are supposedly aiming to even up each module, VCAA has really backed off on this topic and the majority of the questions are only at a mid-level difficulty compared to some of the questions found elsewhere.

Business-related Mathematics heavily relies on your calculator's financial solver and understanding how to use it is essential, as VCAA considers drawing out a table of values as adequate working out. That being said, certain styles of questions can be posed to render the calculator useless, so you must also learn how to do the calculations by hand. I encourage you to draw out a table of values where possible, as consequential marks cannot be awarded if the source of the error is unclear.

Whilst only a few theoretical questions tend to pop up each year, you will fail miserably at this module if you do not take the time to properly understand the financial system taught in Further Mathematics. All the questions you do have a practical element to them and it is not always clear which processes you need to do in order to solve the problem if you don't comprehend how things work. Last year's Exam 1 Question 9 is a great example as it was only testing students' knowledge of how reducing balance loans work. As I said, I managed to get this in a few seconds during reading time, whereas many students seemed to have spent a lot of time trying to figure it out and 80% of the state got it incorrect. Others were forced to guess.

Examiners express their concern for Business-related Mathematics almost every year as it is poorly completed without fail. I urge you to read both the study design and the assessment reports for each year as the same issues seem to be arising. If you can understand the theory in this module, you will honestly find the exams a piece of cake, as the questions are not taken to an overly difficult level, for the benefit of the majority of the clueless state.