Mathematical Methods @ Lyndale

A compilation of tips and general advice, that may assist you in your studies for Mathematical Methods CAS Units 3 and 4, Exams 1&2 2014

PREPARING FOR THE EXAM:
Mark down questions you were unable to do or had difficulty doing, and then add these to your bound reference post doing a few questions which are similar to the one you got stuck on - Tip by "Nightseeker"

DURING THE EXAM:
NOTE: THIS PAGE HAS BEEN EDITED BY EULERFAN101 (ATARNOTES). THANK YOU TO EULERFAN101 FOR EDITING THIS POST
Profile of EulerFan101

1) Read and re-read the question (especially in the Extended response section of Exam to make sure you are not missing anything

2) Pay attention to the marking scheme. E.g. a 1 mark question will only usually require ~~calculator syntax alongside~~ the answer to gain the mark, whereas a 2-3 mark question would need some working out ~~in addition with calculator syntax out~~ to obtain full marks

EDIT: NEVER WRITE DOWN CALCULATOR SYNTAX

3)
In the extended response section pay close attention to the question number and letter, sometimes* you would use different values for unknowns though they are in the same question
Example:
(My comments will be italics)

1) A function is as following; $f(x)=ax^3+bx^2+3x+5$

a) Find a and b, if the graph passes through (x,y) and (x,y)I have found a=2, and b=4
a ii) Find the minimum and maximum

b) Find the derivative of this function
Now it is important that I don't use the values a=2, and b=4 here, as though it's in the same question, this segment is under the letter (b) whereas we were told a=2 and b=4 in segment (a)
Instead I would find the derivative as; $f(x)=3ax^2+2bx+3$

If segment (b) said "Find the derivative of this function with the answers gained in Part (a)" or if it had said at the start of the question "A function is as following... where a =2, and b=4" THEN I would use a=2, and b=4 for part B, and in the latter scenario, for the entirety of the question

- End example-

This is especially important when doing Probability questions

*Comment by EulerFan101"Let's say you have a function f(x)=ax^2 + bx. If we know that a=2b will ALWAYS be true based on some logic (such as geometry rules), it is assumed you will use this in any future part. BUT, if they say for a single part that a point is (x, y), and from this you find a=2b, you shouldn't use this in future parts. Hope that made sense. "

4) When finding the inverse of a function, make sure to write the domain of the inverse especially if the original function is expressed as;
$f:\text{domain}\rightarrow R, f(x)=...$

5) Pay attention to the part of the question which tells you to either
a) Express to (x) decimal places
b) Leave your answer in exact form

You do lose marks for not rounding up to the required amount of decimal places
If it doesn't specify, leave your answer in exact form

6)
$\sqrt{x^2}=\mid x\mid \\\text{it does not equal} \ x!!$

7) Some questions may require you to find the range of a function, whilst giving you a domain
E.g. Find the range for the following function $f:0\leq x\leq \frac{5\pi}{4}\rightarrow R, f(x)=2\cos(3(x-\frac{\pi}{2}))$
You may instinctively substitute the values of the domain into the function to gain the range as;
$1\leq y\leq \sqrt{2}+1$
However this is not correct!!
The correct range would be
$-1\leq y\leq \3$

The best thing to do if you encounter a question like this is to sketch the graph on a graphics calculator for the given domain and work out the minimum and maximum values from there
This will give you the correct range

8) $\\\text{(Only!) If events are independent then;} \\Pr(A|B)=Pr(A)$

9) Do NOT write down calculator syntax when doing Probability questions, or in any question for that matter, you will not get the method marks, Write binomial and normal distribution notation instead
Example Q:
Find probability where x>2, where n=10, p=0.53
Correct notation;
X~Bi(10,0.53), Pr(X>2)=
NOT
binomCDF(10,0.53,3,10)

10) $(\left | x-1 \right |)^{2}=( x-1 \right |)^{2}$

11) $\\(x-1)^{2}\geq 0= \\x \ \epsilon \ R \\\text{not} \\x\geq 1 \ !!!$

12) Alternative way to find Area of a triangle:
$A=\frac{1}{2}\cdot b\cdot c\cdot \sin(\theta)$ ,
Where 'b' and 'c' are side lengths

13) You can find the intersection points of a function and it's inverse, by making the function equal to x.

14) You can quickly find what the inverse of a function looks like by sketching the function on the right-bottom hand corner of the page and then folding it in

15) Spend only a maximum of 30 minutes on the Multiple choice section of Exam 2. You should aim to utilize a full 1 hour and 20 minutes on the Extended response and then spend the last 5-10 minutes checking over the paper.
Practice this sort of time management on all of your practice papers

Exam checklist: Maths Methods exam checklist
Get a print out of these tips:

"Paul's Mathematical Methods - Pre-Exam 2 Advice for 2012"
ATARnotes: Mathematical Methods Guides and Tips

Mathematical Methods @ Lyndale

Pages

Thursday, 12 March 2015

Notes @ Lyndale

Sunday, 26 October 2014

A very short final post for 2014

Sunday, 21 September 2014

Mathematical Methods - 15 Exam Tips and General advice

Monday, 8 September 2014

Free trial exams

Saturday, 30 August 2014

VCAA Past Exam Probability questions

Sunday, 24 August 2014

The Continuous and Normal distributions

Sunday, 17 August 2014

Binomial distribution and Markov chains