Bazza's 3/4 Question Thread

[WhoTookMyUsername]

Thanks for the nice explanation
Do you think this on is more dodgy than usual, in that there's more than one way to measure something? Like any applicant shorter than 174.46 isnt accepted, but any applicant over 174.46 is, so if you are 174-175 centremetres, its actually more likely you're more than the requird height?

Usually these rounding ones i find pretty straightfoward... Is this one dodgy?

[BubbleWrapMan]

Idk, I imagine they're usually integer limits, though I haven't had that much experience. =P I don't think they'd ask something that picky but it's good to be prepared.

[WhoTookMyUsername]

For the attached question, i thought the answer was d, becaue the y value peak of X1 is greater, so doesn't that mean it's less spread out?
Thanks!



Also for the second attachment... Is it just me or is this question worded really badly? I thought it meant effectively pr(x=9)/ pr (x<10) ( conditional prob)
But the answers meant, probability from 9 to  11 is 0.25, then you'll get an e(x) of under 10...

[BubbleWrapMan]

That first one is screwed up since one of the curves clearly bounds more area than the other, which shouldn't be the case. But the right-most graph looks thinner so I would have said it had the lower standard deviation.

For the second attachment, I agree it's worded badly, I interpreted it the same way as you did.

[WhoTookMyUsername]

Thanks for clearing that up

Bit of a dodgy question but anyway: does a SPOI account for x^3 of some sort?

I.e. if there's a quartic with a SPOI, do we automatically know there can be at most one more TP that is not a SPOI?

Ie.2 a cubic will never have a SPOI and another turning point as cubics are x^3 and the x^3 degree  accounts for the POI?


2) this is a question that has been bugging me for ages lol ( was on a sac)
A customer can order a  regular 500 ml cup drink or a double 1000 ml cup drink from a vending machine. T make a double cup drink, the vending machine dispenses twice. To make a regular drink, the vending machine dispenses once. Drinks which dispense from the vending machine follow a normal distribution with mean 470 ml and sd 20 ml. The amounts that are sucessively dispensed are indipendent.

- what  is the probabiliyt that for a double cup, no overflow occurs?
I wasnt sure on the day, and i was running out of time so i took a stab in the dark


I  did  pr(2X<1000) = pr (x<500) = 1-0.66807 = 0.9332
Which was correct.
But i lost a mark because i didn't examine the standard deviation - my teacher said it was a 'fluke' that i got it with my worker and with 3X and 4X it wouldn't have worked... I'm not so sure?

I.e. if it was 3X and a 1500 cup
VAR(3X) = =9VAR(X) and SD(3X) = 3SD(X)
Therfore it's the exact same probability dist except each corresponding x value should be tripled?

Do you guys agree with me?


Thanks

[BubbleWrapMan]

Yes to both of the polynomial questions.

I see where you're coming from, but it's better to be on the safe side and show all that stuff.

e.g. let Y = 2X, then E(Y) = 2E(X) and Var(Y) = 4Var(X), so Y ~ N(940, 1600), then use the new distribution.

It would work for other multiples of X but it's better to justify it like you just did, so VCAA knows that you know. I'm not sure why your teacher thought it was wrong, maybe I'm missing something haha.

[WhoTookMyUsername]

thanks once again (you've been a great help for maths )

Got a few last minute questions (mostly technicalities)

1) are we allowed to use sin^2(x) + cos^2(x) = 1 in methods? It's not on the formula sheet but i remember solving one VCAA question utilising it (tech active)
2) Is it 'wrong' to say that dx=2du? (this may be more of a spesh question)
ie. i've basically treated dx/du as a fraction which it's not?
3) I'm always confused about the wording of 'by how much does sally overestimate the area using right hand rectangles?' If area of with rectangles is 2, but integrating is 1, is this a 100% overestimation, or a 50% overestimation?
4) Does |  ... | mean +... OR -... ?

Ie. lets say we have S 1/(x-2) dx and we are asked to solve for y when y(0) = ln(2)

So y = ln|x-2| + c

BUT initial cond x =0
Does this mean that y = ln (2-x)+c or y = ln|x-2| + c?

5) Should we always restrict time for probability to be >0?
What if there's a significant amount of time under 0 for a certain probability distribution, do we just assume this would be rounded up to 0 or ... ?

e.g. on Heff 12 there was a significant amount of time under 0 for a normal dist, and it asked for time < 2 minutes, I restricted to 0, but i was unsure what to do for the following questions as the area above 0 wasn't = to 1. If it was 3<y<4 shoudl i just have integrated from 3 to 4? Or do i have to do something else... or am i overthinking it... or would VCAA always make it quite clear that time is rounded up to 0?

Thanks very much!

[BubbleWrapMan]

1) Don't see why not
2) Yeah it's best to keep it as a fraction. From experience, the easiest way is to solve for g'(x) in terms of du/dx, e.g.:

If we were integrating sin(2x)/cos(2x), you'd let u = cos(2x), so du/dx = -2sin(2x). The integral has sin(2x) rather than -2sin(2x) so we rearrange it to get what's already in the integral: sin(2x) = (-1/2)du/dx. Sub the right hand side into the integral. I find it's the quickest method, and easiest to keep track of.

3) It's the percentage of the actual value, minus 100. So in that case it would be 100, yes.
4) Good question. In short, solutions to initial value problems will have to be continuous, so yes, it would be ln(x-2), since there'd be a break at x = 2 if it could be negative as well.
5) It depends on the context I would say, could you post the actual question? Or describe the situation?

[WhoTookMyUsername]

thanks very much


Marking or 'tightness question'
ON VCAA exam 1 there was a question that said 'find OTHER solutions' (apart from pi/3)

I wrote x = pi/3,4pi/3
Wil I lose a mark?

Also for the question with the modulus graph,
was the domain requred for the translated graph??

Also (29/64? XD? For the days received calls one?)

'thanks!

[BubbleWrapMan]

Not sure on the 4π/3, personally I wouldn't mark you down for it

Domain wasn't required since it asked for the equation

And 29/64 is what I got...

Sounds like you did well

[WhoTookMyUsername]

hopefully haha (in part due to you )

I think it's probably more likely i lost the 4pi/3 one than not.
I nice marker will probably go - there's nothing /wrong/ there (1)
a harsher marker/more standard marker will go - technically didn't explicitly answer question (0)

However if they award .29 and 29/64, 39/40 does mean i'll be pulled into the pack because it was such an easy exam apart from that question.
I guess all i can do is try and full mark this exam 2!

[BubbleWrapMan]

They really shouldn't award 3 marks for 0.29, trust me

[Phy124]

If the answer is deemed to be 0.29 (doubtful, IMO), I'd think they would change the amount of marks the question is worth.

One line of working doesn't really seem reasonable for 3 marks when more difficult questions were worth the same/less.

[WhoTookMyUsername]

Last minute question D:

Does the 'area bound by two curves over xE[2,11]

Mean the area 'enclosed' / 'enveloped' by the two curves (e.i. enclosed  intercepts, lets say an intercept is at 3 and 11 and no others, is it referring to integral (11,3) ? or simply the area between the curves over that x region?


Thanks!

[BubbleWrapMan]

The latter, but hopefully they wouldn't make it too ambiguous.