VCE Specialist 3/4 Question Thread!

[Syndicate]

Hi,
Do we have to know the formulas for circle geometry (ie. area of major segment, chord, arc length etc..)

Thanks

[LifeisaConstantStruggle]

Hi,
Do we have to know the formulas for circle geometry (ie. area of major segment, chord, arc length etc..)

Thanks

Absolutely yes!! (stressing on this because there are a lot of questions involving the area of segments+sector questions in complex loci questions, which aren't done very well by a lot of students (some students try to use calculus), this means that it's gonna come out again and again)
- knowing the formulas for the area of segments (eg: minor segment: 0.5r^2[angle-sin(angle)]) can save you a lot of time in doing these questions, and maximise your marks

[Sine]

Hi,
Do we have to know the formulas for circle geometry (ie. area of major segment, chord, arc length etc..)

Thanks

Not too sure about "formulas" but you should be familiar with those terms and some questions have needed that knowledge. Also some questions have referred to semi major/semi minor axis for ellipses. Although ellipses is out of the course it may come up via complex numbers (graphing).

Also it wouldn't hurt to know some circle theorems (these are quite formula based).

[Rieko Ioane]

I'm not sure how you are getting sqrt(2206)/10. The standard deviation should be sqrt(4.4²+2.7²) which is sqrt(2665)/10

Thanks again and RuiAce, I'm an idiot lmao..
----

Can someone check my working for this question https://imgur.com/a/KTlqR
The answer had z = 3cis(-alpha) and -3cis(alpha). Their 2nd solution seems sus, they factored out -3 and simplified the inside to cis(alpha). But an magnitude of -3 doesn't really make sense.

[Eric11267]

Thanks again and RuiAce, I'm an idiot lmao..
----

Can someone check my working for this question https://imgur.com/a/KTlqR
The answer had z = 3cis(-alpha) and -3cis(alpha). Their 2nd solution seems sus, they factored out -3 and simplified the inside to cis(alpha). But an magnitude of -3 doesn't really make sense.

Yeah in general you don't want the magnitude to be a negative number, though its not technically wrong. However you did make a mistake simplifying -3isin(α)-3cos(α)
It should go along the lines of this
-3isin(α)-3cos(α)=
-3cis(α)=
3cis(π)cis(α)=
3cis(α+π) rather than the π-α you had
But since polar form requires the principle argument it would actually be
3cis(α-π)


Also I'd like to point out that in your first line of working you forgot to include the i, so under the root it should have been -36sin²(α). But you corrected for this by incorrectly subbing in cos²(α)=sin²(α)+1

[Shadowxo]

Thanks again and RuiAce, I'm an idiot lmao..
----

Can someone check my working for this question https://imgur.com/a/KTlqR
The answer had z = 3cis(-alpha) and -3cis(alpha). Their 2nd solution seems sus, they factored out -3 and simplified the inside to cis(alpha). But an magnitude of -3 doesn't really make sense.

Just adding to what Eric said,
Under the square root sign it should be (note I'll use x for simplicity)
(6isinx)²-4*(-9)
= -1*6²sin²x + 36
= -36sin²x + 36
= 36(1-sin²x)
= 36(cos²x)
Which results in the answer you got. You should also know sin²x + cos²x = 1 so cos²x = 1 - sin²x, and same for sin

Also for -3cis(x), imagine drawing 3cis(x) on the argand diagram. -3cis(x) is just the negative of that (you should be able to imagine this, but the y values goes to the negative of itself, same for the x value; just imagine the line extended in the opposite direction or rotated 180°). This means the magnitude (3) stays the same but the angle is increased by 180°, so the angle becomes x+pi= x+Pi-2pi = x-Pi.

Also note cos(x) = cos(-x) and -sin(x) = sin(-x)

Let us know if you're still confused about anything

[Rieko Ioane]

Thanks Eric and Shadowxo, I appreciate the help a lot!!!

[Rieko Ioane]

Me again soz for being dumb 

For this https://imgur.com/a/ylV9t

Part a) this was quite unclear in the Cambridge text book as well, but even though we are summing iid random variables, we can't express the sum as an integer multiple of that random variable right? This is why I did not square the 4s when calculating the variance, whereas the answers did?

Can someone clarify this?

b) What tells you that this is a one-tail test? Is seems to be the "it finds..." statement but this doesn't imply it's a one-tail does it, since they aren't claiming it is less than 8.6?

Thanks

[LifeisaConstantStruggle]

Wassup ma dude Rieko

a) Normally we would be instructed to calculate the variables separately as independent variables instead of clumping it together, (correct me if I'm wrong) for example, if you look at the exercises in 15B in the cambridge textbook (specifically question 7, where we are told that "only one battery is working at one time" and "the batteries operate independently"), there are different examples of combining variables to form Var(nX) or treating variables independently to form Var(X1+X2)
b) If the question states that they are testing "whether the mean weight of the tyre is less than that being claimed by the manufacturer", you'll know that it's a one-tailed test. If the question states that they are testing whether the "mean weight of the tyre has changed" then it will be a two-tailed test.
Hope that helps, correct me if I'm wrong tho.

[manishmao]

Can we write answers in terms of g in tech free vcaa exams i.e. 24 + 20g Newtons instead of 120 newtons?

[LifeisaConstantStruggle]

Can we write answers in terms of g in tech free vcaa exams i.e. 24 + 20g Newtons instead of 120 newtons?

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2016/SM1_examrep16.pdf

Might be spoilers for practice exams but for question 1) c) 245N is the answer instead of 25g, so it's probably safer to write it as 220N instead of 24+20g.

[MightyBeh]

Can we write answers in terms of g in tech free vcaa exams i.e. 24 + 20g Newtons instead of 120 newtons?

Seconding the above, I'd advise against it - especially for the example you gave. A quick scroll through the last couple of years' exam 1 reports shows g in working out but not in the answers. In addition to that, in the instructions of each exam there's a part that says 'Take the acceleration due to gravity to have magnitude g ms–2, where g = 9.8' which is a pretty strong indication that they want you to use the numerical value where possible.

[peanut]

VCAA Sample exam, exam 2 question 6e(ii):
I got the correct answer for e(i) = 0.196, however, according to itute, the answer to e(ii) is a type II error. I know what a type II error is, however, how did they come to that conclusion? Nowhere in the question did it say that the H0 was rejected or not rejected (we only calculated the p-value??)

[Sine]

VCAA Sample exam, exam 2 question 6e(ii):
I got the correct answer for e(i) = 0.196, however, according to itute, the answer to e(ii) is a type II error. I know what a type II error is, however, how did they come to that conclusion? Nowhere in the question did it say that the H0 was rejected or not rejected (we only calculated the p-value??)

is this the last page of sample exam 2?

because I'm pretty sure that question is flawed and I wouldn't be too worried

[Eric11267]

VCAA Sample exam, exam 2 question 6e(ii):
I got the correct answer for e(i) = 0.196, however, according to itute, the answer to e(ii) is a type II error. I know what a type II error is, however, how did they come to that conclusion? Nowhere in the question did it say that the H0 was rejected or not rejected (we only calculated the p-value??)

The question could have been better with the wording, but its a type 2 error in part d you were calculating the value of C such that the results were statistically significant, so for that value of C, the null hypothesis would have been rejected. Then the same value of C is used in part e)i), with a different mean however. Since 0.196>0.05, in that case, the null hypothesis would not be rejected. So if the mean was actually 9.5 rather than 10, the null hypothesis would have been wrongfully rejected, leading to a type two error