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Maths Methods - Tips Tricks & Advice
« on: December 19, 2019, 08:43:24 am »
Tips, Tricks & Advice (to help you appreciate this subject just that little bit more)

Hi! I completed Maths Methods in 2019, as a Year 11 student. Iím not someone that was super exceptional at Methods, but I did understand the subject quite well, and did enjoy learning it. Completing it in Year 11 was fairly daunting, and took up a lot of time from my other subjects, but it was a great learning experience, and I learnt so many study strategies that I will be sure to take into Year 12.

Iím going to be breaking up this article in the form of a Ďtimelineí with my tips and tricks that are more relevant to the beginning of the year, and moving through. I wonít go into much detail about each of the topics, and rather give general tips that may be worth looking into. Enjoy!

1.   The Summer Holidays
The summer holidays are the time to relax, and I would definitely not recommend studying the entire time, however, if you feel the need, it is worthwhile doing some extra reading. Hereís a list of what Iíd recommend:
-   For starters, I believe the most valuable thing you can do is to recognise your weakest areas that you found in that subject in Units1&2, and try to work on those areas. Choose some areas that you were never across, and work on them. Itsí worth to fix your mistakes before trying to learn Unit3&4 content.

-   Then, if you received any homework for that subject (usually given if your school does Headstart on something similar) itís worthwhile to work on that. Schools usually give homework that lightly covers Unit1&2 content and then usually a bit of early Year 12 stuff Ė itís worthwhile to complete these to the max, and perhaps go a bit beyond (i.e. some extra reading on the homework topics).

-   Then, if you would like (although doing this is not necessary to doing well throughout the year) go through some of the early topics covered. It will help, as you can really consolidate these topics when they are taught in class. It is a good idea, as you may find the early topics easy, and will be able to start studying for SACs earlier than your peers. Donít go too ahead though, as you may get confused or forget it when the time comes that you actually need to learn it.

-   Itís probably also worthwhile to create a rough outline of what is happening throughout the year, and create a rough schedule - mark in your SACs, figure out which days you want to dedicate to studying Methods.

2.   Term 1, Unit 3
During this term (and some in Term 2, depending on when your application task is), you will probably learn the fundamentals of Methods, and revise some very important topics that you learnt in Year 11. It is important that you get a good idea of these topics, as you will build upon them as the year goes by. Some key ones are:
-   Implied and maximal domains. This biggest tip that helps with this is knowing that the negative root of a positive square (i.e. 2√-number) and the division by 0 doesnít exist.
-   Knowing how to solve systems of simultaneous questions (easy with the matrix way)
-   How to sketch and the features of various types of graphs (quadratics, truncus, square root graphs, etc)
-   Transformations of graphs Ė it is very important that you understand this!! Your teachers should cover this extensively with you, and it should build upon Year 11. Also, make sure you know how to use matrices for transformations as itís come up a lot in the last few exams.
Hereís a common one people tend to misunderstand:
af(x) Ė dilated by a factor of Ďaí from the x-axis
f(ax) Ė dilated by a factor of 1/a from the y-axis

-   Solving logarithmic and exponential equations, the change of base rule, etc.
-   Circular functions, sine, cos and tan graphs and their properties (I personally didnít think that this topic built that much further than Year 11. However, it is really helpful if you can get this topic down pact)
-   The derivative function, and properties of it, how itís used, etc (very important that you know how to use this in application type questions.)

3.   Term 2, Unit 3
This is the term that you will most likely undertake your application task (however, some schools do it at the end of Term 1, just be aware of this.) This task usually runs across 2 weeks, and will test your knowledge on everything youíve learnt so far.
(see above for topics covered in T2)

4.   Term 3, Unit 4
In this Unit, you will cover the new topics of integration, and build upon the probability you have learnt in Year 11. You will most likely have an Analysis task on each of these topics.
-   Make sure you know ALL of the properties of the definite integral. Multiple choice questions usually ask indirect questions about this, so it is very important that you know how to manipulate this integral to suit your needs.
-   The definite integral gives the SIGNED area between two points
-   Make sure you know how to do Ďintegration by recognition,í as itís a very important skill for exams.

Ahhhhh, my FAVORITE!! (I really mean it!) When we first started this topic, my teacher would always tell us that these would be the easiest marks on the exam for us to get, and at first, I thought he was crazy! After delving deeper into this topic, I found out that he was absolutely right!! To do well in probability, you need to be really smooth with your CAS work. The Cambridge textbook has lots of CAS information within the probability chapters, and its worth checking them out, and writing them in your logbook.
When you tackle a probability question, you MUST question it each time. Always ask yourself what type of distribution is this using, is it without replacement or not, what CAS functions is most suitable to this type of question?
HYPERGEOMETRIC DISTRIBUTION: Used for small populations without replacement.
BINOMIAL DISTRIBUTION (CAS, Binomial CDF, using n,p,x) Large populations or scenarios with replacement
NORMAL DISTRIBUTION Ė (CAS, NormCDF) Ė Distributed on the bell curve, has a mean, standard deviation and variance
Normal CDF using E(P^) & SD(P^) Ė Approximating binomial scenarios with large sample sizes Ė Question will ALWAYS state if you need to use this or not!!

Also, donít forget to define the variables at the start of each question, and make sure you change the letter as the distribution changes. It is commonly done like this:
X ~ Bi(n,p) OR Y ~ N(mean, standard deviation2)

5.   Exam preparation
My teacher was one that really exemplified doing practice exams, so I started doing them as soon as I could. I did not spend much time doing textbook questions, as I personally found them repetitive and easy. I only did them to enhance my knowledge on some topics. At the start of the year, when we covered small topics, I found them questions from exams relating to them, and did those questions. After covering about 50% of the course, I was able to do more questions from exams. I would go through as much of an exam as possible, and just write down the questions I couldnít do, so I knew for later. This saved alottttttt of stress closer to exams, as I had theoretically had covered 50% of the exams before I had finished the entire course. (I mainly did exam questions before a SAC)

My class finished the entire course around the end of August, so I was able to do full practise exams from then onwards.

This helped me finish all the VCAA exams from 2006 onwards, and a few company ones. I interwove the company exams around the VCAA ones, but as it got closer to the exams, I mainly stuck with VCAA.

However, do what works best for you! Donít just do exams for the sake of it, make sure you get the uttermost out of every single one! Quality over quantity.

6.   The exam days
Hopefully by the exam days you should be feeling pretty confident and not stressing too much, as this will not help you. Feel confident in your abilities, and just go out there and give it your best shot. Ideally, a light revision in the morning of your exams should be just fine, but otherwise, just get yourself mentally prepared. Make sure you have all your stuff ready, pens pencils, a CHARGED CAS, and a bound reference that fits VCAAs standard. Especially after the first exam, even if you are feeling disappointed in yourself, donít dwell on it as you donít want to ruin the next exam, which is worth double!

And then when the exams are overÖÖCELEBRATE!! Methods will be officially OVER!!

7.   General (but very important) Tips
-   Know your CAS! I cannot stress this factor enough. Learn all the shortcuts, and everything you CAS can do, and learn how to do it fast. It will save you SO much time and careless mistakes in Exam 2. It can do so much, so use it to your advantage. If you are having trouble, Charlie Watson on YouTube has some great advice on using the CAS.
-   Update your CAS! (Not sure how it works for the T-inspire though) The CAS is like a computer, and needs to receive the latest software in order for it to work efficiently. It will also load things faster, which will save a lot of time, come exams.
-   If you are planning to use pen in the exam, (considering its compulsory now, but using a dark pencil will be just fine) practice it earlier! Although it may seem daunting at first, using pen for maths is not too bad, as you really donít have much time in the exam to be erasing all your mistakes. If you use it while you do all your practise exams, you will get used to it. 
-   Do your logbook throughout the year. Most of the time your teachers will make notes and stuff on the whiteboard as they teach a topic, so make sure you write all that information in your logbook that same day. It will help you remember what was taught, and will save time come the exams.
-   Be careful of your notation and handwriting during the exam. If VCAA canít read what youíve written, you will not be awarded the marks.
-   If a question asks you to find the inverse, of say h(x), DO NOT leave your final answer as y = . You need to re write it as h-1(x)
-   Make sure you have enough working out for each question, even in exam 2. I.e. If a probability question states find the probability that X is greater than 3, ideally you should CAS it. If this question is worth 2 marks, you must write Pr(X>3) to obtain the method mark.
-   Donít forget the +c and dx in integrals.
-   Make sure you label each significant point when sketching graphs (and no hair graphs!!) (0,0) is also a coordinate and should be labelled if it crosses your graph.
-   Donít forget that the asymptote in a graph needs to be clearly dotted in, and the graph must NOT touch this dashed line.
-   The VCAA Methods study design is your BEST FRIEND (and can be found here: https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/mathematicalmethods/Pages/Index.aspx) VCAA canít actually test you on anything that doesnít exist in the study design, so itís worth printing this out and checking it off as you learn topics. It will ensure that you donít miss out on any important topics.
-   If a question says something Ďjoins smoothlyí, the gradient is the same at those two points

8.   Extra Resources
-   Cambridge textbook for consolidating learning
-   ATARnotes Methods book for SAC preparation
-   Edrolo (I found it very helpful for probability)
-   VCAA, Heffernam & MAV practice exams (Insight is also good too)
Heffernam can be a little bit on the easier side, but at the same time, closer to VCAA style. MAV was helpful to me too, but sometimes a little bit trickier.

Anyway, I hope this guide wasnít too long (I tried not to bore you all) and I do hope that it will help you in your future studies! (Also, please correct me if I have added any incorrect information to this. Most of this was things that I discovered myself, and sometimes I do maths in really strange ways ha ha). If you have any other questions, feel free to ask!

Good luck in your Methods studies in the future years!! I believe in you!
« Last Edit: January 18, 2020, 07:03:43 pm by ArtyDreams »


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Re: Maths Methods - Tips Tricks & Advice
« Reply #1 on: January 18, 2020, 07:43:00 pm »
Hi everyone!!
I've been asked a few questions lately about keeping a Bound Reference for Methods, so I thought I'd add to this thread with my tips for creating a Methods bound reference. These are the tips that worked for me, but I do think its important that everyone finds the most efficient way to build up their own reference book.

1. Make sure your book itself sits inside VCAAs guidlines. (Can be found on this page, towards the bottom: https://www.vcaa.vic.edu.au/assessment/vce-assessment/materials/Pages/index.aspx)
Make sure your book is A4 sized or less, doesnt have preferorated pages, theres nothing sticking out of it, and everything inside it is firmly glued in)

2. Make sure your book has enough pages, but not toooo many pages that will cause you to be flipping the pages too much in an exam. I personally settled for a 128 page, which was plenty, but even a little less would have done for me.

3. Have a contents page - it will strongly help you in navigating your book, and finding certain topics quicker and easier.

4. Work on your book throughout the year - dont leave it until the last week before your exam!! This time is much better spent working on practice questions. It is also likely you will miss adding important things to your logbook, if you end up doing it all at once.

5.   Learn how to use your Bound Reference. It is important that you do use the book when completing practise exams, so you learn how to find things quickly and easily, and know where everything is located in your book.

6. Don't add unnessecary information. i.e. if you know exactly how to find the x - intercepts of a quadratic, and are sure that you will not forget this in the exam, don't write it in your reference book. It will just be easier to find things that are actually difficult for you this way.

What I did:
Thought I'd add in a section to this with what I personally did with my logbook. This system worked well for me, and ensured that I didn't leave things until the last minute.
My logbook was kept in chronological order, with things that I did at the start of the year all the way to the end. In class, my teacher would write notes on the board, along with examples as he was teaching, so this is what ultimately ended up in my logbook. Usually, he's let us write in in our logbooks then and there, so we wouldn't forget what we learnt, and if we didn't have time, I'd take a photo and write it as soon as I got home. This way, I had at least one example from each topic we did.

As I went through exercises in the chapters, I'd always make sure that I write down questions that I found tricky in my logbook straight away. Iíd also write down hard questions from VCAA exams, and title them carefully so I knew they were from exams, so I could refer to them later. I did exams as I went throughout the year, so it was easy for me to add these in after each topic. My logbook didnít have much theory, mainly worked examples.

I also left a couple of pages aside after each topic so I could add to them when I needed.

Before a SAC, Iíd make summary pages, (and this helped me soooo much.) These summary pages just had brief information on things that I can never seem to get right. I also did this before the exam.

(Oh - I also had a double page spread of probability formulas. It was easy to see as it was all on the one page, and helped me find formulas very quickly and easily. I do recommend doing this if youíre having trouble with the different types of probability. If anyone wants to see this, let me know!!)

By the time the exam rolled around, there were pages in my logbook that I know I didnít need, and ones that I was almost certain I would need to use. To the pages I was certain Iíd need, (transformations Iím looking at you), Iíd cut the corner of the page so I could access it quickly.

Anyway, I do hope this short guide helped!! Let me know if you have any further questions :)

And HAVE FUN creating your reference book!! I know I did, making everything match and using colours was fun ha ha.
« Last Edit: January 18, 2020, 09:55:45 pm by ArtyDreams »