VCE Methods Question Thread!

[TrueTears]

if , then what would

Replace x with (x+6)/2

so that f(x) = ((x+6)/2)^2 -5((x+6)/2)+2

[captainamy]

Thanks Rangaaaa, I needed question 10 b though, "Explain why this approximate value is greater than the exact value of cubed root 8.06." Sorry!

Oh my mistake,

have a look at this diagram I've made:

(Image removed from quote.)

As you can see, it is merely or in this case rearranged



As the slope of the curve decreases as x increases at the estimated value will be above that of the real.

Additionally, for graphs such as the gradient will be increasing as increases, therefore the approximated value will be lower than the actual.

I'm pretty sure all VCAA would be looking for is that that the approximation for is reliant on the gradient of , what the gradient type is (increasing/decreasing) and hence whether the value is higher or lower than the actual.

Thankyou, it's a lot clearer now. I appreciate your help!

[soccerboi]

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007mmCAS2.pdf

Section 2 Q1,d)
Why did they sub in the minimum value of r to get the maximum possible surface area?

Section 2 Q3c)ii)
i got y=A(x+3)(x+1)(x-1)
and subbed x=(6-2root3)/3     and      y= (32root3/9), but why is this wrong? <--Those values are the coordinates of the  max of g(x).

Thanks

[BubbleWrapMan]

There is only one stationary point and it is a minimum, so the global maximum has to be at one of the endpoints. It's just a matter of deciding which of them gives the larger area.

3c is asking for the maximum vertical distance between the two curves

[soccerboi]

There is only one stationary point and it is a minimum, so the global maximum has to be at one of the endpoints. It's just a matter of deciding which of them gives the larger area.

3c is asking for the maximum vertical distance between the two curves

With that first question, by logic wouldn't the volume be at its largest when the radius is at its largest? And how would you determine which endpoint it is, i can't graph it to see as there are two unknown variables.

[KevinooBz]

Can someone help me out with this question?
Jane has three bags of lollies. In bag 1 there are three mints and three toffees, bag 2 there are three mints and two toffees and in bag 3 there are two mints and one toffee. Jane selects a bag at random, and then selects a lolly at random. Find:
a)The probability she chooses a mint from bag 1: Pr is 1/6 as I have done this part.
b)the probability she chooses a mint: ans was 53/90
c)the probability that Jane chose bag 1, given that she selects a mint: ans was 15/53

[kensan]

Tree diagram will help, first 3 branches being the bags, then the 2 branches from each bag will be the probability of T or M, from that bag. Shout out if you need it drawn

[KevinooBz]

Tree diagram will help, first 3 branches being the bags, then the 2 branches from each bag will be the probability of T or M, from that bag.

Ty, I just worked it out a couple of seconds before you posted. Tree diagram did help.

[bonappler]

I have a small question the answer given for 4a is (-infinity,0)\{-5/2} why is that?

[BubbleWrapMan]

It's wrong, the domain of g shouldn't change

There is only one stationary point and it is a minimum, so the global maximum has to be at one of the endpoints. It's just a matter of deciding which of them gives the larger area.

3c is asking for the maximum vertical distance between the two curves

With that first question, by logic wouldn't the volume be at its largest when the radius is at its largest? And how would you determine which endpoint it is, i can't graph it to see as there are two unknown variables.

If you find both endpoints, you should be able to factor out V^(2/3), which is positive, and show that one is greater than the other.

[supermanflyaway]

How do we tell if a question asks for the signed area, not the magnitude?

[BubbleWrapMan]

Pretty much if they ask for area they mean the magnitude. I don't think there'd be a geometric situation where they'd want the signed area.

[Special At Specialist]

Someone please show me how to do this question. There is no way that I can transpose the equation when dealing with inverse normal and the solve function on my calculator doesn't seem to understand this either.

Find the standard deviation if:
Mean = 51.2
Pr(X > 55. = 0.2

[BubbleWrapMan]

Pr(X > 55.8 ) = 1 - Pr(X < 55.8 )

Therefore Pr(X < 55.8 ) = 1 - 0.2 = 0.8

When X = 55.8, Z =

So , you should be able to find it from that

[Mr. Study]

Pr(X>55.08)=0.2

Hence Pr(Z>X)=0.2

To find x, we can do invNorm(0.8,0,1) = 0.84162

So Pr(Z>0.84162)=0.2

Z=x-median/deviation => deviation = x-median/z = 55.08-51.2/0.84162

Therefore Deviation is 4.61

EDIT: Sorry for not latexing ... I am not too good at divisions/notations on latex .... Also too tired . XD