VCE Methods Question Thread!

[radiant roses]

Hi! I have a question from 2017 VCAA Exam 2 Question 4(h)

I was able to find the equations of L1 and L2.
But I don't understand why the solutions make 2k equal to tan 30 and tan 60. And why do they not make 1/2k equal to anything?

Only 2% of people got full marks for this question, so if you can help that would be great 

[EmadMo]

If possible could I get help with this trig question:

State the smallest value of k such that x=3pi/4 is a solution of tan (x) = cos (kx)

[sk2000]

If possible could I get help with this trig question:

State the smallest value of k such that x=3pi/4 is a solution of tan (x) = cos (kx)

simply just plug 3pi/4 into each equation:
tan(3pi/4) = cos(3k*pi/4)
As tan(3pi/4) = -1, this gives
cos(3k*pi/4)=-1
Now looking at the unit circle we know that cos(x) first equals -1 when x=pi (first rotation), so
k*3/4 = pi
Solve for k
k=4/3

[persistent_insomniac]

For vcaa 2016 exam 1 qs 5a iv) when it says to find the nature of the stationary point I always use a sign test. But on the examiners report (attatched) it has a few other ways - can someone briefly explain how you would determine the nature using the other ways listed below?
Thanks

[randomnobody69420]

My teacher told me that VCAA examiners don’t care about units at all in spesh. Is it the same for methods? If the question is like “express your answer in metres” do I have to include the unit after my answer?

[colline]

My teacher told me that VCAA examiners don’t care about units at all in spesh. Is it the same for methods? If the question is like “express your answer in metres” do I have to include the unit after my answer?

I think your teacher made a mistake there, or maybe you misunderstood them? IDK how it works in spesh, but in methods, if you forget units (or leave it in the wrong units), you lose a mark overall. It's just that it doesn't matter whether you make one mistake or ten, you'd only lose one mark. Same goes for rounding errors.

[MaiSakurajima]

Not sure if anyone has this question but from 2017 NHT Exam 1 question 8, c. ii

I understand how to get c=1 but how did they get c>2 for g(x) = inverse of g(x) to have one real solution?

[MB_]

Not sure if anyone has this question but from 2017 NHT Exam 1 question 8, c. ii

I understand how to get c=1 but how did they get c>2 for g(x) = inverse of g(x) to have one real solution?

\(x=\pm\sqrt{c-1}\), when \(c\in{(1,2]},\) there are two real solutions for \(x\) (as \(x\geq-1\)). So \(c=1\) or \(c>2\) gives one real solution.

This may help to visualize.

[ArtyDreams]

Just a general question - not even sure if this makes sense,

but when do two graphs share the same gradient at the same point?

like, if they 'join smoothly' they share the same gradient at the point they join smoothly

Are there any other conditions?

thank you!

[KiNSKi01]

Just a general question - not even sure if this makes sense,

but when do two graphs share the same gradient at the same point?

like, if they 'join smoothly' they share the same gradient at the point they join smoothly

Are there any other conditions?


thank you!

Are you referring to tangents?

[studyingg]

Just a general question - not even sure if this makes sense,

but when do two graphs share the same gradient at the same point?

like, if they 'join smoothly' they share the same gradient at the point they join smoothly

Are there any other conditions?

thank you!

If you are referring to piecewise functions, the place where the 'pieces' of the graph join is considered smoothly continuous if:
-the functions both join at the same x and y coordinate
-they have the same gradient at this point
-if they have the same left and right limits -- if they are differentiable at that point, it means they have the same left and right limits.
... I think these are the conditions but I may have missed some.
You'll probably need this in questions which ask for the domain of the derivative of a piecewise function -- points that aren't smoothly continuous can't be differentiated

[tigerclouds]

Just to confirm, is it 100% ok to write with pencil on both the exams?

[pugs]

could someone please help me with question 8c of the 2019 NHT methods exam 1?

i don't understand how you use information from previous questions to obtain the answer (nor do i know how to obtain the answer lol)

many thanks!!

edit: sorry the screenshot is pretty much useless if you don't have the question lol. i was going to link the pdf to the exam but i'm not sure if that's allowed

[AnonymooseUser]

could someone please help me with question 8c of the 2019 NHT methods exam 1?

i don't understand how you use information from previous questions to obtain the answer (nor do i know how to obtain the answer lol)

many thanks!!

I solved it by visualising a binomial distribution. The highest probability in a binomial occurs at the expected value - np. So for W, np = 50*1/6 = 8.3333. So k could be 8 or 9.

So using the formula from b. sub in k=8 and k=9 and see which one is higher --> k=8.

Not sure if that's the correct way but its what I did...

[pugs]

I solved it by visualising a binomial distribution. The highest probability in a binomial occurs at the expected value - np. So for W, np = 50*1/6 = 8.3333. So k could be 8 or 9.

So using the formula from b. sub in k=8 and k=9 and see which one is higher --> k=8.

Not sure if that's the correct way but its what I did...

ooh so you'd sub k=8 or 9 into the whole formula from part b? i thought it was just the bottom part whoops

thank you!