VCE Methods Question Thread!

[Equilibriaas]

What is the difference between mutually exclusive and independent?

Mutually Exclusive events are events that cannot occur at the same time. The venn diagrams representing these events look like this:


Whereas independent Events occurs when one event does not influence the other event from occuring.
Hence P(A and B) = P(A) X P(B)

Hope this makes sense!

[keltingmeith]

Whereas independent Events occurs when one event does not influence the other event from occuring.
Hence P(A and B) = P(A) X P(B)

Note that the formula you've supplied is not definitional - it is a rule that must be derived. The true definition of independence (and something that I feel is a lot more sensical than that formula) is P(A|B)=P(A).

That is, even though B has happened, even though the possibilities of A has become limited, your new guess of A happening is the same as before. Knowledge of B has not changed your best guess of A.

[popo2121]

2013 VCAA methods question 1f
Hey this is probably one of the easier questions to ask but I can't seem to fully understand it could someone please post a solution with supporting explanations?

[Frozone]

Hey could someone please help me with the following question eg worked solutions.

With question 3 how does one solve by hand (1/2)^n=1/32?

[paper-back]

Is there quick method (i.e. by CAS) to do those 'true or false' questions that seem to appear on every paper?
E.g.
For the function y=f(x) which one of the following statements is correct?
a) 2f(x)+2f(x)=4f(x)
b) 2f(x)-f(2x)=7f(x)
... and so forth

Thanks!

[shadows]

Is there quick method (i.e. by CAS) to do those 'true or false' questions that seem to appear on every paper?
E.g.
For the function y=f(x) which one of the following statements is correct?
a) 2f(x)+2f(x)=4f(x)
b) 2f(x)-f(2x)=7f(x)
... and so forth

Thanks!

Guide to Using the Ti-nspire for METHODS - The simple and the overcomplicated
check this out. It's amazing

[myanacondadont]

@Frozone

I'll do Q2. Someone look over it cause I'm not even sure.


Not sure how to do it so it shows but kx below should be evaluated from 0 to 3, whereas we already knew what fx evaluated from 0 to 3 was (k).
   




the answer should be

Again, can someone check over this I might've missed something important

[keltingmeith]

Hey could someone please help me with the following question eg worked solutions.

With question 3 how does one solve by hand (1/2)^n=1/32?

They've worded 10 weirdly just to throw you off. Ignore the wording, just pick up on the fact that y=ax+b is the tangent to the curve. So, find the tangent to the curve:



Now, at . So, we evaluate:



So,


For the part on three, simply go through it, don't let the fact that they're exponentials scare you:

[#J.Procrastinator]

Hi there!

Just a quick question, is there a way to change my settings to get exact solutions when I graph on my CAS?

[keltingmeith]

It's not pretty, but you can do it.

[TrebleClef]

Could someone please help me with this question, I would really appreciate it. Thank you!

[keltingmeith]

Could someone please help me with this question, I would really appreciate it. Thank you!

You can do this by reasoning with transformations and how you expect this to affect the area - personally, I find that annoying, and instead I use a substitution. Note that I'm about to do is an integration technique taught in specialist - it's not hard to do, you won't be frowned upon for using it (particularly in multiple choice), but if you haven't seen it before, that's why.

So, let's start with breaking up the integral they want you to do:



The second integral is pretty trivial, and comes to 30a. The first one is our issue - so, we make a substitution.

If we let , then So, . Note that when we put this into the new integral, we also need to change the bounds (as indicated about, the bounds are in terms of x - we need them in terms of u). Putting this into the original function, we get that when x=0, u=0 and when x=5a, u=a. So, we now have:



Now, the final integral is just like the one they gave you, which is equal to a, so our final answer becomes 10a+30a=40a, so the answer is D.

[TrebleClef]

You can do this by reasoning with transformations and how you expect this to affect the area - personally, I find that annoying, and instead I use a substitution. Note that I'm about to do is an integration technique taught in specialist - it's not hard to do, you won't be frowned upon for using it (particularly in multiple choice), but if you haven't seen it before, that's why.

So, let's start with breaking up the integral they want you to do:



The second integral is pretty trivial, and comes to 30a. The first one is our issue - so, we make a substitution.

If we let , then So, . Note that when we put this into the new integral, we also need to change the bounds (as indicated about, the bounds are in terms of x - we need them in terms of u). Putting this into the original function, we get that when x=0, u=0 and when x=5a, u=a. So, we now have:



Now, the final integral is just like the one they gave you, which is equal to a, so our final answer becomes 10a+30a=40a, so the answer is D.

Thank you! I was wondering, if you were to have to do it the "Methods way", how would that be done?

[lzxnl]

Dilation of factor 5 from the y axis AND stretch the domain appropriately => area goes up by factor 5
Same for the x axis
Translating the graph horizontally won't affect the area
Translating the graph up will affect the area for obvious reasons

[TrebleClef]

Are there any tips for preventing silly mistakes? This has probably been asked before, but the amount I make is disastrous, like the 2012 vcaa Ex 1, I lost 7 marks to silly mistakes.