Hi everyone! If you are reading this, then chances are you are a current or soon-to-be VCE Methods student. You might have already heard of methods’s infamous reputation, but fear not! While methods can definitely seem like a daunting subject, it’s unprecedented reputation is a bit uncalled for.
I did 3/4 methods last year and received a raw 50 despite being far from a STEM-oriented person. In fact, during year 10 subject selections, methods wasn't even on my list. It ended up being one of my most enjoyable subjects and I hope this guide might also make the subject a little less painful for anyone reading
(I remember reading so many posts on how to do well in methods (and many other VCE subjects) last year as I was preparing for 3/4. After getting back my results last year, I promised I'd write one too. I didn't expect it to take me so long so I'm sorry to all the people to who I promised would be done by December.)____________________
I. Some General ThingsTextbook QuestionsDo not underestimate the power of basic and repetitive textbook exercises - make the most of them as they will ensure you have the foundation to tackle harder application problems. I suggest starting by writing up just a list of the topics in methods 3/4 and
mark out the topics which you struggled with in 1/2 or you think will be challenging this year. This helps you get a sense of the big picture and ensures you’re not blindly diving into the textbook for the sake of completing questions.
I know some people say you should take it slow and steady and you shouldn't rush through the textbook - but I would
highly recommend getting through the textbook questions ASAP so that you can make a start on harder exam-style questions early. This doesn't mean you should
rush through it, but it's unnecessary to do every single little exercise and
you should ABSOLUTELY be aiming to do the textbook questions at a quicker pace to your school's.
And finally... Cambridge vs Jacaranda: I know many say Cambridge is miles better, but frankly I don't think there was a noticeable difference - at least, none in the sense that using the Jacaranda book will somehow jeopardise your chances at a higher study score. So don't fret if your school is using MathsQuest!
Note-takingYou should *not* be taking a lot of notes for methods throughout the year, because
it is simply not necessary. VCAA wants to know how well you can apply textbook concepts to application style questions. They are not interested in seeing how well you can recite the process of differentiating by the chain rule, they want you to SHOW them that you understand the concept. For some it may be beneficial to jot down some brief reminders every now and then, but
please don't overdo it because it will be such a waste of time.
Most importantly, if you do want to take notes, then please
always handwrite, never type! It's also helpful to
take notes using pen to prepare yourself for the end of year exam, as naturally students would be more comfortable with doing their exam in pencil.
Commercial Resources - what type of resources should I get?NOTES & CONDENSED SUMMARIES:
Don't buy them. Seriously - do not purchase notes/summaries from ANY company. I know various tutoring companies will sell highly detailed and condensed notes of the entire VCE methods course which may seem enticing, but in most if not all cases, they are nothing more than a waste of money. The reason is because, like I said above with regards to note-taking, they're simply unnecessary for VCE Methods, a subject which focuses on practical application. Your textbook should be more than enough to get you through the theory side of things, and even if it's not, there are plenty of free online resources at your disposal.
(*ahem* Khan Academy *ahem*)PRACTICE QUESTIONS / TOPIC TESTS: These are definitely much more worth buying than summaries and notes, but to be absolutely honest, they aren't 100% necessary either. The good thing about buying a book full of practice questions is since they're generally separated into topics, you can do targeted practice regarding specific areas you aren't confident in. I'd say in general topic tests are a hit or miss. If you're really struggling in a particular topic it may be worth getting one - but buying
multiple topic tests from various companies is definitely overkill.
FULL PRACTICE EXAMS: I know I've been quite cynical about commercial resources for the above two categories, but this sentiment does not extend to practice exams. They are so incredibly useful and if you must fork out some money buying resources from companies, spend it on this! While company exams are
not as good as VCAA's, they still offer great revision throughout the year and even leading up to the exam. I know some say you should just focus your time and energy on VCAA/NHT exams, but I advise starting with companies and leaving anything from VCAA until late September/early October. The reason is because there are only a limited amount of official past exams available on the VCAA website, and they may not be enough to fully prepare you for the final exam. Instead, spend some time doing company exams under non-exam conditions, just to accustom yourself to the formatting and structure of what you'll get in November.
Commercial Resources - which companies should I buy from?(Note: Below are my own thoughts regarding various companies, their resources, and how helpful they were, and are in no way objective)
Second only to VCAA: MAV, Heffernan
Worth your money: Kilbaha, Insight, iTute
Hit or miss: QATS, TSSM, Neap
I wouldn't say there are any companies whose exams you should absolutely avoid at all cost because any practice is good, and doing one exam from a "subpar" company definitely won't sabotage your final result in anyway.
Official VCAA ResourcesSTUDY DESIGN / EXAMINER'S REPORTS: It goes without saying that you should
treat these as gospel. While I wouldn't say it's an absolute necessity to print out the study design and pour over it word-for-word, you should definitely aim to make the most out of anything on the VCAA website. I would say past examiners reports are the most important piece of resource you can possibly get for methods, and any VCE subject in general.
PAST VCAA AND NHT EXAMS: Do NOT touch them until after you've finished most - if not all - of the content!
Always aim to do them under full exam conditions to ensure you're getting an accurate reflection of your skills and capabilities. Save all VCAA and NHT exam papers from the current study design till last. As for the rest of the ones that are available on the VCAA website, even if they aren't relevant to the current study design you should still treat them with equal importance and take each practice seriously.
Getting the most out of practice examsWhether it's a VCAA exam or just a paper from a tutoring company, you should never waste the practice opportunity. Different people have different approaches, but what I did was to set up a spreadsheet for me to record the details of each exam: one column for my results, one column with a list of questions I lost marks on, one with the topics my mistakes fell under, and one for things I did well in, but didn't realise until I checked the reports (i.e. flukes). I also colour-coded the spreadsheet - orange for any mistake I made a second time round, and red if I've made the same mistake three or more times.
Now, obviously you don't have to create an entire excel spreadsheet to get the most out of each exam (I'm Asian and making spreadsheets is just in my blood) - but it is absolutely vital that you don't just rush through an exam, mark it, and move on. First off,
mark harshly (duh!); next, try to
attempt whatever you got wrong again YOURSELF before consulting any worked solutions. Finally, make sure you
note down the mistake somewhere, be it in your notebook or your mind palace, to avoid making the same mistake twice in the future.
II. Some practical tips which you can use RIGHT NOWNote: Two of my tips refer to the CAS. I used the TI-Nspire, which was the one everybody at my school used, so I do not know whether these tips can be carried over to other calculators like the Classpad.
1. Know your CAS inside outI struggled a lot with working my CAS at the start of the year, and only noticed significant improvements after I started training myself to use it properly. First of all, make sure your CAS is on the right settings (eg. Radians instead of degrees. I would also suggest putting it on automatic instead of exact or approximate, though I know some may prefer exact). Next, make sure to scope out ALL the possible relevant commands which could help you on the exam. Aside from the obvious ones like 'solve' (which you should already know), there are some slightly more obscure commands out there which could make your life significantly easier if you became comfortable with using them - for example, check out the
slider on the graphing page when you're working with an unknown factor of dilation, or the
nSolve function on the calculator page if you need a quick approximation.
Time is absolutely crucial, particularly in exam 2. You are allowed a CAS, so make sure to use it to the fullest, as it will boost your speed significantly. On that note, make sure to also train yourself in quickly identifying which questions are meant to be solved with technology, and which are better off solved by hand.
Not every single question on Exam 2 is meant for the CAS, and if you try to apply the CAS to every single problem, you will slow down significantly.
There are some CAS workshops available at tutoring companies, mostly incredibly overpriced. If you think they are within your budget and are potentially helpful, go for it. In my honest opinion, YouTube tutorials are generally sufficient. I suggest a good place to start would be by checking out videos from
TI Australia which has videos specifically targeted towards the usage of the CAS in VCE Methods.
2. Try writing your own CAS commands I know many don’t exactly approve of this method. Nevertheless, I believe in taking full advantage of whatever you’re given, so if you’re given the opportunity to take a CAS into the exam room, then you should use it to the best of your ability.
For those who don’t know, aside from the CAS commands already programmed into the calculator, you can also write UDFs. They could be something as simple as finding the distance between two points, to giving you all the relevant descriptive statistics of a probability distribution function without ANY working out on your part.
To write your own commands, simply open a new document and define all your commands on the first page. Then, you can open new pages for calculations and the defined commands carry over. They will
NOT carry over if you opened a new document or a new problem, and of course won't work either if you delete that page, so make sure you save it to a folder you can easily access.
If you choose to do this though, there are some really important things to keep in mind:
1) Write the commands yourself. It would be tempting to simply copy off someone else, but you would’ve just wasted a perfectly sound learning opportunity. Writing your own commands is a good test of whether or not you understand the formulas and concepts, so please don’t skip this crucial step.
2) Working out is so much more important than whatever answer you get. On the final exam, most of the marks will come from your working out, so please don’t just write down whatever answer your CAS gives you and move on. I would suggest only using this short-cut for multiple choice, since you only get answer marks for them, and to check over answers you've already found for short-answer questions as a way of making sure you didn't make any silly mistakes with calculations.
3. For revision, try creating your own questions.I will be forever grateful to my methods teacher who challenged me to write my own exam 1 paper, and I think I owe a major part of my study score to that one piece of advice alone.
Writing your own questions is honestly one of
the most effective ways to solidify your understanding of maths concepts. As you are approaching content you learnt throughout the year from a completely different angle, it really challenges you to think outside the box and approach problems from new perspectives. For one, you’ll be putting yourself in the examiner’s shoes as you think about things such as: what are the concepts most students struggle with? What tricks could be put into the question? What common mistakes are made with the topic? Naturally, you will also be more aware of these things when you sit the exam too. As you keep creating your own questions, you will eventually realise that there are only so many ways for VCAA to test you, and that all long application problems are all really just built upon a couple of simple functions, obscured by wordy paragraphs and seemingly complicated diagrams - and with time, you would start noticing for yourself common patterns and traps hidden within the problems.
Not to mention, writing your own questions is a much more interesting way to study revise. If you’re feeling unmotivated or tired of doing practice exam after practice exam, day after day, give this a go instead! This is also a good way to revise with your peers. Gather your friends and get everybody to make up a question or two (preferably
application-style problems as opposed to simple calculation questions like 'find the derivative of this'), then swap what you’ve written and do the questions. It’s a great way to get everybody on board with revision, and remember, the better your own cohort does, the better off you’ll be too!
It might be a bit weird or difficult when you first start - so don't be too ambitious - just start with short, straightforward questions like "solve" or "differentiate" instead of long application problems with several parts. Once you become comfortable, you can start building it by applying scenarios to extend the question in some way.
4. Have not one but two (or more!) logbooks to keep track of your mistakesAt the suggestion of a previous student, I got myself an empty scrapbook and made it my personal “booklet of mistakes” in January. I used it as a logbook to keep track of every single mistake I made while working through my Maths Quest Jacaranda textbook - after completing each exercise in the textbook, I would correct my work and copy the questions I got wrong into this scrapbook (with the exception of careless mistakes). If I got a question right, but I had used a long-winded and complicated process of working out when there was a much more straightforward method I could have used, I also copied it down. Throughout the year, all my mistakes from my school SACs were also copied in; and once I finished the textbook and got started on practice SACs and exams, I would also cut out all my mistakes and glue them in. By the time I finished the textbook, I had collected more questions in that scrapbook than you’d find in three copies of Cambridge Checkpoints (i.e., I made a lot of mistakes).
I found that many students did something similar, but please don’t just stop there - having one logbook is only the beginning! Whenever you have time, work through all those stacks of questions you’ve compiled. If you get it right, great, move on to the next one. If you get it wrong, get yourself a bright highlighter or red pen or something and make it REALLY obvious that you tripped up on the same concept or made the exact same mistake for a
second time. Then, get yourself a second scrapbook and copy the question in. Keep going until you have re-attempted ALL questions you collected in your first logbook and all the questions you got wrong again have been copied over to your second one. If you're doing it right, then your second logbook should be significantly shorter than the first. Finally, work through all the questions in Logbook #2. Ideally, by now you would've mastered all the areas you used to trip up on, but if it's not enough, then get a third one!
The booklet isn't just for questions. It’s also helpful for you to identify exactly what areas you are weaker in. For instance, whenever I glued a new question into my scrapbook, I also made a note of what concepts the question related to (and be specific - don't just say "calculus" or "probability"). For example, in my case, I found that most of my mistakes related to identifying the correct factor of dilation in matrix transformations — so I knew exactly which areas I needed to specifically work on as exams drew near.
Also, it may act as an excellent bound reference, which leads on to my final tip:
5. Never EVER use someone else’s bound reference. Make your own. I cannot stress this enough. One thing in common I've noticed with students who have scored above 45 in methods, is that ALL of them made their own bound reference
from scratch. So do NOT be lazy and do any of the following:
- Printing a PDF of someone else's methods notes off the internet
- Buying a bound reference from a past student (no matter how well they did)
- Using your textbook or commercial course notes
You can buy a top quality and comprehensive set of notes from some maths genius with a premier's award in methods and it still won't be as helpful as simply writing one brief page of notes yourself. What you must realise is that the purpose of the bound reference is NOT for you to read and check over concepts during the exam.
To be frank, you should
not need to bring in ANY notes at all, because all of the concepts that could possibly pop up on the exam should already be ingrained deep into your mind. Just to illustrate my point further, my methods teacher once told the class, "If you have the need to refer to your bound reference even just ONCE during your exam, then kiss 40 goodbye". Sounds harsh, but the point she was making is clear: Do not rely on your bound reference to save you on the exam.
So what exactly is the point of your bound reference?
- To give you an extra opportunity of revision before the exam
- To remind you of mistakes you're prone to making
- To placebo your brain into feeling slightly less nervous on the day
The most important thing is the PROCESS of making your bound reference, which allows you to remind yourself of what mistakes you're prone to making and what to watch out for on the day of the exam.
And finally, while the process of making your bound ref is important, try not to spend too much time on this. Don't try to condense the entire unit 3 and 4 course into a 128-page notebook because your time would be much better spent doing a practice exam or even just giving yourself a break. While it's ultimately up to you, I suggest having no more than 5 pages.
(Just for funsies:
here is my entire "bound" reference)
Some more bonus tips - It's useful to get SACs and worksheets from other schools because you don't want to get used to just the questions the teachers at your school writes.
- Teaching others a concept is a great way to learn it yourself.
- It is absolutely vital to have a solid understanding of the basics of functions and calculus because the entirety of the VCE Methods course is built upon this, even later topics such as probability and statistics.
- Learn to do questions in the
most efficient way possible. This is especially important for calculus - for example, learn not to rely on the time consuming method of writing "let
u = ____, let
v = ____" every time you differentiate, as it wouldn't give you any extra marks anyway.
- Make sure you're actually answering the question every time, especially in longer application problems - always ask yourself: can I leave my answer as it is or is the question asking for something else?
- The wording of the question can give clues to how to approach the problem. For example, if the question starts with
"hence", then you should use your answer/working out from previous parts to solve the new problem.
III. Some FAQsDid you do methods tutoring? / Do you think it helped? / Do you recommend it?Yes, yes, and maybe.
I started tutoring midway through year 12 - 1.5 hours a week, every week (except school holidays) until the week before the exam. I definitely found it to be helpful and I wish I had started it at the very beginning of the year, as it would've probably made revision less painful (my foundation of unit 3 was a lot shakier).
My tutor was a uni student doing private tutoring, and it was a small group with me and four other students. I think the fact that it was such a small group definitely helped me improve, though I do not have experience with doing tutoring in a large class or 1-on-1 so I can't really make a comparison. This was also the first and only time I've done any type of maths tutoring, so there's not much comparison I can make.
I also do not think that tutoring is
always helpful or necessary - please see
this post.
How many hours a day did you study? / how many practice exams did you do? Hours: I really can't tell you as I never kept count myself. I studied whenever I knew there was something I needed to work on, so I never had set study hours as I found them to be mostly counterproductive. On some days I could be studying methods for up to five hours straight, on other days I didn't touch it at all (however, from term 4 onwards, I made sure to do even just one short methods problem a day to keep my brain working).
Practice exams: I did all the past VCAA exams from 2006 onwards (though I skipped quite a number of questions not relevant to the current study design), as well as all NHT exams. All of them were done under full exam conditions. As for non-VCAA exams, I did about 20 from various companies (MAV, Heffernan, Insight, Kilbaha, Neap, iTute, QATS, TSSM), most were not done under exam conditions or even completed in one go - generally I'd do multiple choice together, and do two or three short answer questions at a time.
What's a good score to aim for on the exam?This generally changes depending on the difficulty of the paper. I received 80/80 on exam 1 and 157/160 on exam 2. That said, it's important to keep in mind that there is definitely an element of luck at play which could influence your score. When I did practice exams, I usually scored around 37/40 on exam 1 and 70-75/80 on exam 2 in November.
What was your plan for studying methods? / When did you finish the textbook? / When did you start practice exams?My school used the textbook by Jacaranda and I started working through textbook questions by myself in during the January holidays, finishing it at the end of term 1. During the holidays between term 1 and term 2, I worked through my mistakes booklet for revision, and also did some worded problems from the Cambridge methods textbook which I thought wasn't too different to Jacaranda. In term 2, I started tackling harder, exam-style questions from companies and started doing practice exam questions. I began VCAA exams during the holidays between term 3 and 4, and they were ALL completed under full exam conditions. In the first week of term 4, I re-did all three SACs that we did at school under timed conditions. From then on, it's just a continuous cycle of practice exams, VCAA exams, correction, and then re-doing them. I left the 2018 VCAA and 2019 NHT papers to a week before the legitimate end-of-year-exam.
If I wrote it out as a timeline it would look roughly like this;
Jan: began textbook questions
Apr: finished textbook questions, began working through my first mistakes booklet
May: began company practice exams
Sep: began VCAA practice exams
Oct: re-attempted all SAC questions
Nov: VCAA 2018, NHT 2019
IV. Some Free Resources mainly YouTube videosThe Study DesignYour Holy Bible. This is a great place to start just so you have an idea of all the topics you'll be covering and a great tool to refer to throughout the year.
https://www.vcaa.vic.edu.au/Documents/vce/mathematics/2016MathematicsSD.pdfKhan AcademyDoes this even need an introduction? If you find your textbook to be inadequate in explaining some concepts, or if you want to solidify your understanding, then check this out.
https://www.khanacademy.org/mathMathWorldFun fact: this site is actually on VCAA's official list of recommended resources for VCE Methods. Once you get past the horribly dated website formatting, it's a great complement for your textbook and Khan Academy.
http://mathworld.wolfram.com/ScrewMathsMethodsI absolutely love this channel. There are only 7 videos on there, 3 of which are no longer relevant to the study design (the videos are all from 2013), but they're still quite informative, not to mention highly entertaining.
https://www.youtube.com/channel/UCpVpXpGBsglUkF4q9VlkLMAWorm's Maths AcademyThis channel has really detailed step-by-step solutions for past VCAA (and more recently NHT) exams. There are also Khan-Academy-style instructional videos on certain topics.
https://www.youtube.com/channel/UCGtWtg8CZhDL77cBdk1M23gTI AustraliaAs mentioned above, this is a great channel to check out if you are using the TI-Nspire CAS Calculator.
https://www.youtube.com/user/TIAustralia[More to be added!]
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I hope this is at least somewhat helpful and gives you some confidence in tackling methods! And I hope that, no matter how daunting it may seem right now, you'll learn to love this subject as I did. Good luck to you all for VCE!