**Further Mathematics: VN’ers**Hey VN’ers, I’m making this guide for the Further Mathematics students, in the hope that it gives some kind of guidance/aid/tips throughout the year.

Firstly, I want to mention an important note that many VCE students don’t quite understand: You do NOT have to complete Unit 1/2 General Maths in order to take up Further 3/4 .

Ok, so you’ve picked up Further math. For many students, Further is picked up for one of three reasons.

Reason 1. You’ve heard that it’s easy.

Reason 2. You’re not that gifted in math

Reason 3. As a sixth subject, which you want a 35 for.

*On A Side Note:*It is imperative for students understand, that picking up Further because of its ‘easiness’ will not help your ENTER in anyway. As you might already know, Further is a subject that scales down, and has its Mean Study Score at roughly 27. This means that, although it may be ‘easy’ to achieve 35 in Further, the scaling of the subject ensures that it will scale down to ~32 or 33. This 32 can be achieved through many other subjects, and can even be achieved from a 25 in Methods (CAS). So in the end, a 35 in Further, is relative to a 25 in Methods (CAS). Hence, if selecting Further Maths because its assumed ‘easiness’ then I would seriously hope you reconsider.

**~~~~~~~~~~~~~**FURTHER MATHS- 2009

**Adumbrate outline of the Course and assessment:**The Further course for 2009 will be same as it has been since 2007. Keep a close eye on the study design as it might change or be updated in a small way. The study design will show you that there are 3 assessments.

1. Your SAC marks (20% for unit 3, 14% for unit 4)

2. Exam 1 Mark (34%)

3. Exam 2 Mark (34%)

In Further Maths (FM) there is the

**compulsory Core**, as well as 3 further modules, which you select out of the 6 overall modules present.

In layman terms:

You must select the Core. The Core (data analysis) is roughly 7-8 chapters long (in any textbook), but bonds together really well. It is more about the use of statistics and how everyday data (Univariate data, Bivariate data) can be arranged to make results more readable/ understandable (arranged into- Linear graphs and modelling, and Linear relations and equations).

Then, after completing the Core, you must select 3 of 6 modules.

(your school will select the modules for you, but you CAN complete different modules on the exam If you wish)- I completed Modules 1, 2, 3 and 6

Module 1: Number patterns [use of formulas to asses whether number patterns act In any relationship (geometric and arithmetic- as well as formulas to manipulate/calculate a certain relationships]

Module 2: Geometry and trigonometry [Basic geometry/trigonometry, with the rather annoying 3D shapes and contour maps]

Module 3: Graphs and relations [Simultaneous equations, feasible region, basic algebra, straight line analysis]

Module 4: Business-related mathematics [don’t know, someone help me out]

Module 5: Networks and decision mathematics: [1.

*Undirected graphs*:planar graphs, Euler's formula, Euler and Hamilton paths

2.

*Directed graphs*:determining reach-ability, dominance in graphs as well as learning about critical paths and the Hungarian algorithm.]

Module 6: Matrices [Addition/multiplication of matrices, arrangement of matrices, the layout of data In matrices In-order to mathematically manipulate]

**SACs:**The first Further Math's SAC Is no doubt the worst SAC you'll have to complete In year 12. Although all schools do It differently, the most common Core SAC runs for approximately 10 lessons, In which you have to analyze data, and present It In differing formats (box plots, graphs ect). It Is mentally draining, but you must ensure that you stay on top of your game- or else you might not get time to finish.

The rest of the SACs are quite normal, and may compromise of chapter tests, or whole sac papers.

**The SACs In FM are worth 34% of your final study score, so don’t slack off.****EXAM 1:**Exam one Is

**40 MC questions. 13 MC on the Core, with 9 MC** on your three selected modules each. The exam runs for one hour and a half. Also, you are allowed a bound reference In the exam (don’t put too much In It, or else It will waste your time In the exam)

**Exam Is out of 40.****Exam one Is worth 33% of FM study score.****EXAM 2:**Exam two Is short answer questions, with ~ 3 question on every section. Each section Is out of 15 marks, and the exam Is one hour and a half.

**Total marks for exam two Is 60**. Bound reference Is also allowed Into the exam.

**Exam two Is worth 33% of FM study score.****FM SAC 1:** (Description copied from a VCAA guide)

The outcomes for Unit 3 are:

Outcome 1

Define and explain key terms and concepts as specified in the content from the areas of study, and use this knowledge to apply related mathematical procedures to solve routine application problems.

Outcome 2

Use mathematical concepts and skills developed in the ‘Data analysis’ area of study to analyse a practical and extended situation, and interpret and discuss the outcomes of this analysis in relation to key features of that situation.

Outcome 3

Select and appropriately use technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches in the area of study ‘Data analysis’ and the selected module from the ‘Applications’ area of study.

Tasks

In Unit 3 students complete an application task and an analysis task.

Description

A data analysis application task using contexts for investigation from a suitable data set selected by the teacher. The task has three components of increasing complexity:

· display and organisation of univariate and bivariate data

· consideration of general features of the data

· analysis of the data such as regression analysis, the use of transformations to linearity, deseasonalisation, smoothing, or analysis of time series.

and

An analysis task for the first selected module. This may be

· an assignment where students have the opportunity to work on a broader range of problems in a given context; or

· a short and focused investigation, challenging problem or modelling task; or

· a set of application questions requiring extended response analysis in relation to a particular topic or topics; or

· item response analysis for a collection of multiple-choice questions, including analysis of item distractors and their relationship to conceptual, process or reasoning error.

In lay-man terms, this is what’s going to happen in the SAC. You’re going to be presented with THIS data (if anybody wants it, just PM me) and instructed to do various manipulations of it. So what’s going to proceed is, you will se your calculator to RANDOMLY select (I think, but not sure on the number) 20 different countries which you will go on to draw box plots, scatter plots, residual plots, 3median line, line best fit, correlation coefficient..and so on. This will be around 7 lessons worth, and is 20% of your Further Study Score - so take it seriously.

So, on your first SAC you will have this data to:

1. Create a box-plot

2. create a scatter-plot

3. create residual plots

4. Analyse trends in data

5. Analyse the three median line, as well as the line best fit…and make a decsison on which method is more efficient (according to R, and Rsqueared values)

6. write a clear, and cogent piece of analysis that analyses every single aspect of the data (out-liers, Q1, Q3 ect)

7. If necessary, make transformation to the data.

**~~~~~~~~~~~~~****What to do throughout the year:**If you’re not a natural, then it is in your best interests that you work consistently throughout the year. That is, while watching 60% of your classmates slack-off, you have to resist temptation and stay on your game. Buy small exercise books, and gradually plot your difficulties/things you got wrong in it. Slowly but surely, you will have a list, or maybe even a book full of challenging aspects of the course which you know you need to thoroughly revise before exam time. This book is also pertinent to your success at making an exam “cheat book”. Also, ask your teacher, your classmates or even VN’ers about any difficulties that arise. Don’t put it off. If you put off one thing, you will put off other things in other subjects, and all of a sudden you will have a big burden on you (adding pressure to what is already a stressful year). Furthermore, it is an excellent idea to finish the course early and do practice exams whenever you feel like it.. I don’t mean March early, but rather, you should finish the course by mid-july. This is important as it will allow you time to have the ‘year 12 slack off week’ (which normally occurs during July). It also allows you enough time to revise the course thoroughly (if I learnt anything from further, you’re competency wasn’t measured by getting questions right in your room, but rather, how you coped with silly mistakes, and how well you accustomed yourself to all of VCAA’s little tricks). This is only done through practice and clear thinking. Do exams (PM me if you need any exams that aren’t on VN, but there are heaps HERE) Do questions, the you don’t think will be on the exam, do questions that will make you hate further. Those are the questions that will get you the marks, not the ‘halo’ questions.

So, what you have to do:

1. Prepare a book that you can put in difficulties.

2. Actually USE the book!

3. Make the book neat, so you can refer to it whenever.

4. If you have any problems, address them in a rather urgent manner.

5. Do practice exams whenever, and wherever you can.

6.

** DON’T SLACK OFF!****The book you will use in the exam:** As you should know, you’re allowed to bring in a ‘cheat book’ into both exams. There are certain guidelines (which have been set by VCAA and also that I cant find the link to =P) that must be adhered to. But basically, it’s a book (mostly A4) that you take in, and can have whatever you want in it. It can have past exam questions, theories you don’t understand how to do, questions you don’t know how to do, worded answers (randomly distributed residual plot ect..) and hell, it can even have a sudoku in there J

**What I recommend you do to this book is:**1. With the book that has all your problems throughout the year, go through it again, and see what you’re still struggling with.

2. Colour code your book, to make it really user friendly in the exam

3. Make your book in the 3rd school holidays (add a few white, blank pages, incase you want to add anything later) and get used to it. Every time you do a practice exam, use it. Know where things are.

4. Only put important things in there. Don’t put what ITUTE has on its website, or what your teacher has given the whole class, make your own, that is specific to you and your abilities and difficulties. (I put a calendar in there, b/c I knew I’d need it).

5. Remember, you don’t want to be in the exam looking through 400 pages of useless notes b/c you wanted to win the ‘who can have the biggest book on exam day’ contest. When you only have one hour and a half, you don’t have 5 minutes to look for a page.

6. Again, make it user friendly, stress free, easy to handle, accustom yourself to it- and colour code it for use of modules.

**2 Weeks away from exams:**Well it’s two weeks away exam time, and more than likely, you will be stressing about the amount of work you’ve completed throughout the year. These thoughts need to be terminated immediately. What happens from this time on will be more detrimental to your FM study score, than the whole year. If you’re in year 11, then I’d suggest you do as many exams for a week, then relax (fitting in two a day) and get to know you’re bound book and calculator really well for then week leading up. If in year 12, you will be feeling “oh. It’s only further, I’d rather spend the time on other subjects”. Well, to maximize your potential score, all you need to do is practice, and see what the exams are all about. It is at this time, if you have put the right amount of work during the year, you should be enjoying the practice exams you are doing. You will probably be finishing exams in 40 minutes, instead of the required 1.5 hours claiming how easy it is, but I cant tell you with 100% certainty, everything changes in the ACTUAL exam, so don’t become complacent- keep striving for more speed. Furthermore, you should be proud that you are getting most of the questions right. Now, so close to the exam, you must fine-tune these little blunders you are making. (I trust that they will be little blunders, b/c you would have asked for help from others throughout the year, on content that isn’t clear in your mind). Main thing you can do is…PRACTICE PRACTICE PRACTICE! AND MAKE SURE THAT YOU PRACTICE WITH THE VCAA ANSWER SHEET

http://www.vcaa.vic.edu.au/vce/exams/examcovers/Oct_Nov_2008/2008furmath1-cov.pdf**Exam 1:** Exam one is a fast, shifty and adrenalin rushed exam that can be the place where you lose all your marks from silly mistakes. You are to be mentally switched on. Arrive at your venue with time to spare, and take a bottle of water with you. You will have 15 minutes of reading time, and YOU MUST use this time wisely. This 15 minute reading time, although sounds miniature, is equivalent to 17% of your exam- so take it seriously. Many people have different ‘ways’ to go about reading time, but what I personally did was- after I got a feel of the exams content- I went on to answered the ‘easier’ questions. This saved me a lot of time, and also got me ready for the more ‘mind-boggling’ questions. If questions don’t seem clear to you, skip it and complete other ones- and come back to it at the end. (2007 Matrix question 8 was one that didn’t quite make sense the first time I read it. (

http://vcaa.vic.edu.au/vce/studies/mathematics/further/pastexams/2007/2007furmath1.pdf ).

All in all, you must be alert in exam one, read it thoroughly and don’t let anything scare you. Answer questions during reading time. Don’t have a down period, but rather, stay motivated the whole exam, because time FLYS in VCAA exams. AND IMPORTANTLY, NO MATTER HOW MUCH YOU’RE NOT USED TO IT, YOU MUST SHADE IN YOUR ANSWER AS YOU GO ALONG. DON’T LEAVE IT AND SAY; ONCE I FINISH I WILL SHADE IT. GOD FORBID, YOU STUDY FOR 12 MONTHS THEN COME TO THE EXAM, AND DON’T HAVE TIME TO SHADE IN YOUR LAST TEN QUESTIONS. SO PLEASE, MARK IT ON YOUR ANSWER SHEET AS YOU GO ALONG!

Finally the exam is out of 40, so for ever questions you have ~2 minutes. It’s not as long as it seems.

**Exam 2:**Not as tricky as exam 1, but equally important. The important thing in this exam is how you set out your answers. Don’t have numbers all over the place. You must neatly set your steps of working, so that VCAA examiners (who are marking their 50th paper for the night) see all your working clearly and don’t deduct marks b/c they couldn’t see your steps. Highlight words in the stimulus, do anything, just make sure that you understand the questions and what its asking of you. Again, use reading time to your advantage, but rather than answer questions, look at the longer questions and asses which question you are going to tackle first. If you must use your bound notes, pick the question up in reading time, and use your bound notes at that time. Don’t use your bound notes unnecessarily in the exam. You will be shocked to know that to see one page you lose almost 3 minutes off your exam. Finally, the exam is out of 60, so for every mark, you have ~1.5 minutes. DON’T WASTE TIME!

FM Directory 2009:

VCAA STUDY DESIGN

http://www.vcaa.vic.edu.au/vce/studies/mathematics/mathsstd.pdfVCAA EXAMS and ASSESSMENT REPORTS

http://vcaa.vic.edu.au/vce/studies/mathematics/further/exams.htmlBOUND REFERENCE GUIDELINES

http://vcaa.vic.edu.au/correspondence/memorandums/2007/28.htmlASSESSMENT GUIDELINES

http://www.vcaa.vic.edu.au/vce/studies/mathematics/further/furthermathshb.docCALCULATORS (what is permitted, and what isn't)

http://www.vcaa.vic.edu.au/vce/studies/mathematics/calculators.htmlMULTIPLE CHOICE ANSWER SHEET:

http://www.vcaa.vic.edu.au/vce/exams/examcovers/Oct_Nov_2008/2008furmath1-cov.pdf**IF YOU HAVE ANY QUESTIONS, PLEASE JUST ASK. **NOTE: I will be tutoring in 09 if anyone is interested. I will link when it is up.

http://vcenotes.com/forum/index.php/topic,9400.msg120288.html#msg120288A thank you, and mention to

**Gloamglozer** for his description of module 5.

**Moderator Action (laseredd): Removed link to copyrighted materials**