Methods (CAS) 2009 exam 2 Suggested Solutions.

[homghomg1]

So TT do you agree about the interpretation of 3cii?

Well itute solutions are up and they did it my way:
so yeah I'm not not sure myself now...

yeah, was just gonna say that itute got same answer as you

I have to say I agree with NE2000 though, because there are two requirements. The balls had to fit in the tin and be outside the desired range, not JUST the latter. So you had to use the conditional probability calculated in part c) i), which was the probability that the balls are within the desired range given they can fit in the tin. 1 -[Answer to part i] is the probability that the balls are outside the desired range given they can fit in the tin.

True, but it still comes down to interpretation, the question never said given that they fit, it just said a tin of 4 balls.

So the balls are in the tin yes?  It specifies the size they need to be to fit in a tin so we can presume that they are less than or equal to that size.

Thats stupid, what if they squashed the shit out of the balls and put them in the tin, they sed they had 4 balls in a tin. They never sed 4 balls that fit in a tin.

lol i think for the purposes of vce methods 3/4, when they say a ball with a diameter larger than 68.5 mm doesn't fit in a tin, it doesn't fit in the tin whatever you do.

[jimmy999]

The answer to 3cii comes down to personal interpretation. 3ci says 'a' ball is selected but 3cii says 'one of these balls' so you would have to use the answer found in b. the desired range already accounts for 'fitting' in the tin since it is lower than 68.5. I don't know if my reasoning is entirely correct.

Yes the desired range does account for a ball fitting in. However you have to take 1 - Pr(Ball in range) which includes sizes below 65.6 and sizes ABOVE 68.4. Which means that balls above 68.5 are included, but if a ball is in the tin, then it must be below 68.5, therefore you need to use the answer from 3ci


Also on a personal note, I know for sure that I lost more marks on both methods exams than I did with my Specialist exams. Lost 1 mark on exam 1, potentially 3 marks on exam 2, whilst on spesh I lost less than 2 marks all up

[Lighties]

For question 3eii; why must you state that the derivative it's undefined when x=0? If you didn't write it, wouldn't it be assumed that x=0 isn't part of the domain, and thus wouldn't matter?

[Over9000]

For question 3eii; why must you state that the derivative it's undefined when x=0? If you didn't write it, wouldn't it be assumed that x=0 isn't part of the domain, and thus wouldn't matter?

No derivatives in probability that I know of.

[anti]

"Note: Thanks to aw for pointing out that in Q3cii, p = 1- 0.8985 = 0.1015, answer is 0.3483."

From the Itute website.

[TrueTears]

For question 3eii; why must you state that the derivative it's undefined when x=0? If you didn't write it, wouldn't it be assumed that x=0 isn't part of the domain, and thus wouldn't matter?

Consider continuous probability if you don't write f(x) = 0 ELSEWHERE do you assume it to be 0?


And yeah looks like c ii) is wrong, you minus the c i) probability from 1.

[Lighties]

For question 3eii; why must you state that the derivative it's undefined when x=0? If you didn't write it, wouldn't it be assumed that x=0 isn't part of the domain, and thus wouldn't matter?

No derivatives in probability that I know of.

*My bad, I actually mean question 1eii @.@

For question 3eii; why must you state that the derivative it's undefined when x=0? If you didn't write it, wouldn't it be assumed that x=0 isn't part of the domain, and thus wouldn't matter?

Consider continuous probability if you don't write f(x) = 0 ELSEWHERE do you assume it to be 0?

But this isn't a continuous probability? Also, say when you state a function as f:(0,infinite]>R, f(x)=ln(x), do you state that the function is undefined for 0 especially?

[homghomg1]

"Note: Thanks to aw for pointing out that in Q3cii, p = 1- 0.8985 = 0.1015, answer is 0.3483."

From the Itute website.

yep, and if you use a value of p which is correct to more than 4 decimal places (more accurate than your rounded answer) you get 0.3482, don't know if examiners will care about that or not.

[TrueTears]

For question 3eii; why must you state that the derivative it's undefined when x=0? If you didn't write it, wouldn't it be assumed that x=0 isn't part of the domain, and thus wouldn't matter?

No derivatives in probability that I know of.

*My bad, I actually mean question 1eii @.@

For question 3eii; why must you state that the derivative it's undefined when x=0? If you didn't write it, wouldn't it be assumed that x=0 isn't part of the domain, and thus wouldn't matter?

Consider continuous probability if you don't write f(x) = 0 ELSEWHERE do you assume it to be 0?

But this isn't a continuous probability? Also, say when you state a function as f:(0,infinite]>R, f(x)=ln(x), do you state that the function is undefined for 0 especially?

No I was making an analogous example, when you have ln(x) you consider all values of x already. That is why it is called implied domain.

But stating the derivative is not implied. You must consider all values of . You considered x>0 and you look at x<0 what about x = 0? You can not dismiss that.

And no, not stating x = 0 is undefined in this case does not imply it is undefined.

[hyperblade01]

So.. if 3c)ii in TT's solutions is incorrect, would the method mark be lost as well?

Curious as to what VCAA will say about this question...

EDIT: And the reason I wanna know is because it could affect me - I also used the 'wrong' 0.8385 value

[anti]

So.. if 3c)ii in TT's solutions is incorrect, would the method mark be lost as well?

Curious as to what VCAA will say about this question...

EDIT: And the reason I wanna know is because it could affect me - I also used the 'wrong' 0.8385 value

I think you'll get a method mark for recognising binomial distribution.

[THem]

So.. if 3c)ii in TT's solutions is incorrect, would the method mark be lost as well?

Curious as to what VCAA will say about this question...

EDIT: And the reason I wanna know is because it could affect me - I also used the 'wrong' 0.8385 value

depends what working u showed and how vcaa mark this q.
:/ ( i did the same thing)

[hyperblade01]

Showed what n equalled, p equalled, wrote the whole binomial notation - about 4 lines of working

Fingers crossed that they do give me the mark as I'm looking to score as high as possible now that 80/80 is definitely out 

[NE2000]

For question 3eii; why must you state that the derivative it's undefined when x=0? If you didn't write it, wouldn't it be assumed that x=0 isn't part of the domain, and thus wouldn't matter?

No derivatives in probability that I know of.

*My bad, I actually mean question 1eii @.@

For question 3eii; why must you state that the derivative it's undefined when x=0? If you didn't write it, wouldn't it be assumed that x=0 isn't part of the domain, and thus wouldn't matter?

Consider continuous probability if you don't write f(x) = 0 ELSEWHERE do you assume it to be 0?

But this isn't a continuous probability? Also, say when you state a function as f:(0,infinite]>R, f(x)=ln(x), do you state that the function is undefined for 0 especially?

No I was making an analogous example, when you have ln(x) you consider all values of x already. That is why it is called implied domain.

But stating the derivative is not implied. You must consider all values of . You considered x>0 and you look at x<0 what about x = 0? You can not dismiss that.

And no, not stating x = 0 is undefined in this case does not imply it is undefined.

Just note that in the non-CAS the question stated so I don't think it would be necessary to explicitly consider it there.

Just trying to clear things up. In the CAS, because it didn't say that I would've probably stated that derivative does not exist at x = 0. Because one of the important things in methods is letting the marker know what you're doing.

[Ball Lightning]

Well iTute have changed their answer for 3cii to have it use the answer from 3ci not 3b