VCE Specialist 3/4 Question Thread!

[Carolinemai]

Can someone help me out this question.

[LifeisaConstantStruggle]

Hey guys could I please get some help with two questions from the 2017 NHT Spesh Exam 2:

Exam: http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/nht/2017SM2-nht-w.pdf

Answers: http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/nht/sm2nht_examrep17.pdf

I'm having trouble with Qs 2 part D and Qs 3 Part D, I have no idea how to approach these two 

Thanks in advance!

Oooo q2 part d is a hard one, doesn't mean it's not doable tho. From this, you can change the complex equation into a cartesian equation:

So

|z-a|=B becomes (x-a)²+y²=B²

You can now use the cartesian equation and do all sorts of fun stuff with it, like, using the values of the complex coordinates to find a and B via simultaneous equations with your CAS, ie: substitute (0,0) (root3,1) and (root3,-1) into x and y, and find a and B.

Q 3) d) is the standard Euler's method question, basically you are just predicting (very inaccurately), what the next number is gonna be (P when t=3.5)
So I know that P is 0.75 when t=3, and I have a step size of 0.5
and for the Euler's method to work you gotta use the formula:

P_new=P_old+(step size)(P'(t))

[LifeisaConstantStruggle]

Can someone help me out this question.

Wow alright I see
You can try to visualise this in your head for this one, and because this is a cube (a square box), the path it takes resembles a section of a circle (or an arc), moving clockwise at exactly 90 degrees, so the distance would be the length of the arc, and that's simply a quarter of the circumference.

Part c and d is way harder, but still alright if you know that the pathway it moves resemble a section of an ellipse, with c being the semi major axis, and b being the semi minor axis, and you can sort of do it from there. (the arc length of the pathway of an ellipse is WAAAAY too hard for specialist plebs like us so I'd just suggest that you google "perimeter of an ellipse" and something will come out that will help you calculate). (correct me if I'm wrong for this one).

The questions in the exam would not be too complex I reckon, but it's still good practice.

[Ahmad_A_1999]

Oooo q2 part d is a hard one, doesn't mean it's not doable tho. From this, you can change the complex equation into a cartesian equation:

So

|z-a|=B becomes (x-a)²+y²=B²

You can now use the cartesian equation and do all sorts of fun stuff with it, like, using the values of the complex coordinates to find a and B via simultaneous equations with your CAS, ie: substitute (0,0) (root3,1) and (root3,-1) into x and y, and find a and B.

Q 3) d) is the standard Euler's method question, basically you are just predicting (very inaccurately), what the next number is gonna be (P when t=3.5)
So I know that P is 0.75 when t=3, and I have a step size of 0.5
and for the Euler's method to work you gotta use the formula:

P_new=P_old+(step size)(P'(t))

Thank you! I think I can manage to do 2 D now I'll let you know how it goes, with Qs 3 D I'm an absolute idiot I'm sorry

[shiba woof woof]

Hey guys can someone plz help me out with some questions from the northern hemisphere specialists exam 2. Don't understand how to do them... 
 Questions 1d,3b and 3c please!

Thanks so much

Exam paper http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/nht/2017SM2-nht-w.pdf

[atar.notes.user]

Hi guys
i havent done anything for spec so far bc i focussed on my other subjects!! what do u think i should do in these days until exam?? really wanna use this time to study 'smartly'

[Sine]

Hi guys
i havent done anything for spec so far bc i focussed on my other subjects!! what do u think i should do in these days until exam?? really wanna use this time to study 'smartly'

go over ssessors reports from the past 2-3 years and see what they said are "areas of concern" or places where "students perormed poorly" more than likely those type of questions will be incoporated into this years exam in some form. (not always explicitly)

[LifeisaConstantStruggle]

Hey guys can someone plz help me out with some questions from the northern hemisphere specialists exam 2. Don't understand how to do them... 
 Questions 1d,3b and 3c please!

Thanks so much

Exam paper http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/nht/2017SM2-nht-w.pdf

1)d) it is a related rates question so you ought to think about dh/dt=(dh/dV)*(dV/dt)
So from the equation V=? you can differentiate it in terms of h (dV/dh), and flip it over so it becomes dh/dV, and you multiply it by dV/dt, which is stated in the question (0.03), after that you can sub in the depth you want (h=0.6) and you're set!
3)b) this is a fairly difficult one but dP/dt=0
c) from here you are supposed to fill in the integrals, that's basically it, but how do you do it?
You'd know that the question wants the time for the bacteria to cover 80% of the Petri dish, so one endpoint should be 0.8 (which is r, in this case)
And the time starts at t=1 second after the bacteria is spread over the Petri dish (though the question states that it starts from time 0, which is the time in which the toxin is added). s would be 1 in this case.
For q you have to check 3)a)iii) to find out the proportion of P when t=1.

[shiba woof woof]

1)d) it is a related rates question so you ought to think about dh/dt=(dh/dV)*(dV/dt)
So from the equation V=? you can differentiate it in terms of h (dV/dh), and flip it over so it becomes dh/dV, and you multiply it by dV/dt, which is stated in the question (0.03), after that you can sub in the depth you want (h=0.6) and you're set!
3)b) this is a fairly difficult one but dP/dt=0
c) from here you are supposed to fill in the integrals, that's basically it, but how do you do it?
You'd know that the question wants the time for the bacteria to cover 80% of the Petri dish, so one endpoint should be 0.8 (which is r, in this case)
And the time starts at t=1 second after the bacteria is spread over the Petri dish (though the question states that it starts from time 0, which is the time in which the toxin is added). s would be 1 in this case.
For q you have to check 3)a)iii) to find out the proportion of P when t=1.

Thanks a lot! I understand the first two but then for 3c) I'm still a bit confused to why i'm using t=1 rather than t=0... is it because the domain of the equation says that T must be equal or greater than 1?

[LifeisaConstantStruggle]

Thanks a lot! I understand the first two but then for 3c) I'm still a bit confused to why i'm using t=1 rather than t=0... is it because the domain of the equation says that T must be equal or greater than 1?

You have to relate it to 3)a), and yes it is also stated in the question that t>=1 (sorry I didn't see that my bad).

[Denzel Ncube]

Whats the easiest way to do question 3 on the 2016 trial exam(hypothesis testing)? Also, what sort of questions CAN they ask on hypothesis testing in exam 1?

[LifeisaConstantStruggle]

Whats the easiest way to do question 3 on the 2016 trial exam(hypothesis testing)? Also, what sort of questions CAN they ask on hypothesis testing in exam 1?

There really isn't a lot of ways you can do hypothesis testing for the mean(?) It's always just that one way and that one way throughout (null and alternate hypothesis-->p-value).
What you might need to know is the value for your different z-scores, though this can be done by the CAS, doing it by hand can be very tricky.
It's better if you know the z-values for 0.90, 0.95, 0.99, with tail setting left, right, or centre (I mean that's what I did anyway), so for left tail setting at 0.05 my z-score would be -1.64... if my z-score is smaller than that, there will be sufficient evidence to reject the null hypothesis (as p-value<0.05).
What they haven't asked in the exam tho, are type 1 and type 2 errors (false positive and false negative respectively), you might wanna brush that up just in case.
Idk if I explained it okay? but tl;dr, try to memorise a few z-scores just in case! and remember your types of errors!

[Denzel Ncube]

There really isn't a lot of ways you can do hypothesis testing for the mean(?) It's always just that one way and that one way throughout (null and alternate hypothesis-->p-value).
What you might need to know is the value for your different z-scores, though this can be done by the CAS, doing it by hand can be very tricky.
It's better if you know the z-values for 0.90, 0.95, 0.99, with tail setting left, right, or centre (I mean that's what I did anyway), so for left tail setting at 0.05 my z-score would be -1.64... if my z-score is smaller than that, there will be sufficient evidence to reject the null hypothesis (as p-value<0.05).
What they haven't asked in the exam tho, are type 1 and type 2 errors (false positive and false negative respectively), you might wanna brush that up just in case.
Idk if I explained it okay? but tl;dr, try to memorise a few z-scores just in case! and remember your types of errors!

Nah I get what you mean! Cheers!!

[justsomerandom]

Hey guys, I'm having trouble with Q11 of the NHT Specialist Exam 1 (question below). Can someone please help me 

Find the length of the curve specified parametrically by x = aθ – asin(θ), y = a – acos(θ) from θ = 2π/3 to θ = 2π, where a ∈ R+. Give your answer in terms of a.

Thanks in advance

[Rieko Ioane]

Just posting here to get out of my methods nightmare, fuck that shit lmao.