VCE Methods Question Thread!

[koreaboo99]

If you have a limit, you're saying that as you get closer and closer to an x value (eg as x approaches 2), the y value gets closer and closer to a certain value (eg y approaches 4). So, you're saying as x approaches 2, y approaches 4, even if it isn't continuous at x=2 (ie even if the point (2,4) doesn't exist). A limit is approaching that point, not the point itself.
Another example: say you had y=x/x. For any x value except 0, y is 1. But at x=0, y doesn't exist. So we say as x gets closer and closer to 0, y approaches 1 (in this case y is constant) even though (0,1) doesn't exist. So the limit as x approaches 0 for the function x/x is 1.

Hope this helps feel free to ask for further clarification

Thanks for the reply!! so basically limits..they follow the function but don't rely on it?  like..they are independent of the function itself, but just follow the line of the function?

[Shadowxo]

Thanks for the reply!! so basically limits..they follow the function but don't rely on it?  like..they are independent of the function itself, but just follow the line of the function?

Yea, a limit can exist where a function does not. You use the function to find out the limit but the function doesn't need to exist at that point for a limit to exist

[Lavar Big BBB Balls]

Hi,

I need help with part c http://imgur.com/a/s5o6F

I don't understand why my method doesn't not work here? The formula isn't applicable here so I tried doing it intuitively like the answer but I'm not getting the same answer.

Thanks

[VanillaRice]

Hi,

I need help with part c http://imgur.com/a/s5o6F

I don't understand why my method doesn't not work here? The formula isn't applicable here so I tried doing it intuitively like the answer but I'm not getting the same answer.

Thanks

Hi there!
I have repeated your calculations and have produced the correct answer (although I've probably rounded off excessively):

let X = number of tested articles
E(X) = 10*Pr(X<2) + 20*Pr(X=2)*Pr(X=0) + 20*Pr(X=2)*Pr(X>0) + 10*Pr(X>2)
= (10 x 0.914) + (20 x 0.075 x 0.6) + (20 x 0.075 x 0.4) + (10 x 0.012)
= 10.76

Perhaps there was a transcription error somewhere?

Hope this helps 

[codebreaker1_91]

I'm stuck on 8a. I don't know how to approach it or do any part of it. Could someone please help me, will appreciate it very much!

[Shadowxo]

Angle MPN is a right angle
Imagine it now like a big triangle, with the the diameter as the hypotenuse
Length NP = 400cos(theta)
MP=400sin(theta)
Time = NP/2 + MP/5
=40(5cos theta+2sin theta)
Note I used some physics techniques - just the NP=400cos theta etc bits which I'm not sure if you need to use (it's just sinx=O/H so O=H sinx etc), and their answer is different (maybe they used an approximation?)
Also I don't think you're taught how MPN is a right angle

Alternatively, you could use a chord length formula and calculate the length of each chord that way (don't think you're expected to know them though)

To be honest, I don't think you're expected to know how to do questions like that (anyone correct me if I'm wrong), I don't recall having to calculate lengths of chords in methods. May need to know how to use soh cah toa to get lengths though (unsure)

[codebreaker1_91]

Angle MPN is a right angle
Imagine it now like a big triangle, with the the diameter as the hypotenuse
Length NP = 400cos(theta)
MP=400sin(theta)
Time = NP/2 + MP/5
=40(5cos theta+2sin theta)
Note I used some physics techniques - just the NP=400cos theta etc bits which I'm not sure if you need to use (it's just sinx=O/H so O=H sinx etc), and their answer is different (maybe they used an approximation?)
Also I don't think you're taught how MPN is a right angle

Alternatively, you could use a chord length formula and calculate the length of each chord that way (don't think you're expected to know them though)

To be honest, I don't think you're expected to know how to do questions like that (anyone correct me if I'm wrong), I don't recall having to calculate lengths of chords in methods. May need to know how to use soh cah toa to get lengths though (unsure)

Thankyou so so so much!!

[Mattjbr2]

In question 13:
\[Pr(X=15)\cap Pr(X\geq 12) = \frac{6}{169}\]
This, I think, implies \[Pr(X=15)\cap Pr(X\geq 12) = Pr(X=15)\]

and in question 14:
\[Pr(X=1)\cap Pr(X\geq 0) = \frac{1}{9}\]
This, I also think, implies \[Pr(X=1)\cap Pr(X\geq 0) = Pr(X=1)\]

But how/why are these the case? The textbook is useless in explaining. What does that intersection even conceptually mean in terms of each question?

[keltingmeith]

In question 13:
\[Pr(X=15)\cap Pr(X\geq 12) = \frac{6}{169}\]
This, I think, implies \[Pr(X=15)\cap Pr(X\geq 12) = Pr(X=15)\]

and in question 14:
\[Pr(X=1)\cap Pr(X\geq 0) = \frac{1}{9}\]
This, I also think, implies \[Pr(X=1)\cap Pr(X\geq 0) = Pr(X=1)\]

But how/why are these the case? The textbook is useless in explaining. What does that intersection even conceptually mean in terms of each question?

Let's talk ourselves through it. An intersection is an event in common. For example, what do dogs and cats have in common? Both have four legs, tails, fur. Now, when we talk about the intersection of number sets, we instead want to know what numbers are shared between them. Consider on a die, the event of rolling an even number or a prime number - in this case, the intersection is only the number 2.

Now, let's look at the cases given. We have two events - one in which the random variable X takes on the value of 15 (that is, you score exactly 15), and one in which the random variable X takes on the value 12, or higher (that is, you score 12 or more). For what values of X can you score exactly 15 but also more than 12? This sentence might sound weird because it is an odd thing to say, because obviously the only time you can score exactly 15 and more than 12 is when you score 15, that is when X=15. That's why your intersection is equal to X=15. Same logic for your second one.

Let me know if this hasn't properly answered your question.

[KANYEWEST]

can someone please help me solve!!!!!!!!!! please please please!!!!!
----

Lisi is a keen swimmer who trains each morning by swimming laps of 50 meters’ pool. Her coach Don stands 5 meters from the end of the pool at which Lisi commences her laps and Don records her times and velocity. Lisi’s velocity is given by the equation
V(t)= 2(pi)sin(pi * t)
where t is in minutes, t, and v/m minutes is positive as Lisi swims away from Don.
a)   When is Lisi’s velocity zero?






i)   Lisi is swimming laps. What is Lisi doing when her velocity is zero?





b)   Sketch the graph of V against T for 0 (equals to greater sign) t (equals to greater sign) v,   using an appropriate scale for the vertical axis and indicating coordinated of all axial intercepts.







c)   I) show that it takes Lisis four minutes to swim 200 meters.






 ii) Use calculus to confirm that Lisi swims 200 meters during the first four minutes of training.


d)   Find Lisi’s acceleration at the 45 second mark, correct to 1 decimal place.





ii) interpret this result in terms of Lisi’s swimming laps.



e)   Find an equation for Lisi’s position, p(t) from coach Don at any time t.

[Shadowxo]

Hi KW, do you need help with all parts? Some are quite straightforward eg a)i) which just requires finding where 2π*sin(πt)=0. Let me know what parts you're struggling with

[KANYEWEST]

Hi KW, do you need help with all parts? Some are quite straightforward eg a)i) which just requires finding where 2π*sin(πt)=0. Let me know what parts you're struggling with

Hey, I dont own a CAS calculator, as i had it been stolen from me 1 week ago, so i dont know how to answer them without a CAS, if you could help me with all of them, that would be great!

thank you so much (in advance!)

[KANYEWEST]

someone please help with the question above!!

[keltingmeith]

someone please help with the question above!!

Dude, chill - it'd only been a couple of hours since you asked it. Remember that nobody here is paid to help you out - we all choose to do it out of the goodness of our hearts.

Now, as for answering these questions, a lot of them are very basic - this question could easily end up on a non-calc paper. If you're struggling, I recommend going back through your textbook, and trying some of the simpler exercises again.

For part a), you'll need to solve when V(t)=0 using circular function solving methods. This will be a general solution, so if you're unsure about finding these by hand, I recommend checking out this guide that we have.

For part a) (i), remember that velocity is a quantity that determines your speed in a direction. What is she likely to be doing if that speed is 0?

For part b), simple sketching of a graph, check your textbook if you're unsure.

For part c), this can get quite complicated, and there's a few ways to do it. By far, the easiest way to do part (i) is to simply find the area under the curve between t=0 and t=4, but this is definitely beyond methods level (although it sounds like that's what they want you to do in part (ii)). A very easy way, however, is to try and put a rational to it. Figure out conceptually what each period represents physically (hint: is it swimming half a lap, one length of the pool, five laps, etc.), and remember that one lap is 50m. Then, figure out how many periods are covered between t=0 and t=4.

For part d), acceleration is the derivative of velocity, then sub in t=45 seconds (remember to convert this to minutes). You will need a calculator to compute this, but even a scientific will work fine.

For part e), you'll want to find an anti-derivative of the velocity to get a position function, then use the fact that she's going to start near where the coach is (the question mentions 5 metres away from him!) to solve for c.

If you're still struggling after all of this, could you please post up your attempt at the questions so we can point out where you've made a mistake? Good luck!

[KANYEWEST]

Dude, chill - it'd only been a couple of hours since you asked it. Remember that nobody here is paid to help you out - we all choose to do it out of the goodness of our hearts.

Now, as for answering these questions, a lot of them are very basic - this question could easily end up on a non-calc paper. If you're struggling, I recommend going back through your textbook, and trying some of the simpler exercises again.

For part a), you'll need to solve when V(t)=0 using circular function solving methods. This will be a general solution, so if you're unsure about finding these by hand, I recommend checking out this guide that we have.

For part a) (i), remember that velocity is a quantity that determines your speed in a direction. What is she likely to be doing if that speed is 0?

For part b), simple sketching of a graph, check your textbook if you're unsure.

For part c), this can get quite complicated, and there's a few ways to do it. By far, the easiest way to do part (i) is to simply find the area under the curve between t=0 and t=4, but this is definitely beyond methods level (although it sounds like that's what they want you to do in part (ii)). A very easy way, however, is to try and put a rational to it. Figure out conceptually what each period represents physically (hint: is it swimming half a lap, one length of the pool, five laps, etc.), and remember that one lap is 50m. Then, figure out how many periods are covered between t=0 and t=4.

For part d), acceleration is the derivative of velocity, then sub in t=45 seconds (remember to convert this to minutes). You will need a calculator to compute this, but even a scientific will work fine.

For part e), you'll want to find an anti-derivative of the velocity to get a position function, then use the fact that she's going to start near where the coach is (the question mentions 5 metres away from him!) to solve for c.

If you're still struggling after all of this, could you please post up your attempt at the questions so we can point out where you've made a mistake? Good luck!

I am so sorry! i didnt mean to sound rude, i totally understand this is a website for all to use and share - and i completely shouldnt be taking it granted for! i was just panicking because my teacher sent this to us for practise before our actual methods SAC today, and i didnt know how to do it, so i got a little scared!

I had a look at the explanations you did, and it 100% makes sense, and i have completed them, i dont know how to upload a file for you to check, onto here because i did it on paper, but we can assume i (hopefully) did it right!

but, thank you so much!

I am extremely sorry, as i didnt seem to sound rude! I feel really bad!

Thank you for taking your time in helping me, means alot!
Have a good day