VCE Methods Question Thread!

[HopefulLawStudent]

Can someone please help me with part d? (MAV, 2013: Exam 2)

NB: I haven't supplied any of the answers for a-c but only because I don't think you really need them for d and the answer that you need, from c, is given in the question for part d anyway. But I can totally supply them if you need them.

[wombat123]

Can anyone help me with Question 2.d) of the short answer section of 2012 Methods (CAS) Exam 2?
I understand the first part where I have to substitute the coordinates into the function, but I don't understand what to do with the two p values that I have found?
The solutions say you sub in p into f, but I don't know what values to use and what I'm looking for??

Dumbed-down answers are much appreciated lol

[CQcumber]

can someone explain how to get the answer to this question?
it is vcaa 2009 methods exam 2 question 3d

[StupidProdigy]

How would you do this question attached with info.

Find the value of c, correct to 3 decimal places, for which the two probabilities of misclassification are equal.

By CAS. You're solving the antiderivative of f(x) from the lower limit of 0 to the upper limit of c and equating this to normcdf(0,c,22,2) which gives approx 22.950...Are you after a more in depth explanation haha?

[knightrider]

How would you do this question attached?

[zsteve]

How would you do this question attached?

I'll do this the long way, explicitly using chain rule. Be aware, however, that you *should* be able to do it by eyeballing and using the rule 'diff the inside' * 'diff the outside' repeatedly.

Let's set up and
Thus - you should be able to do this
And
Therefore

Hence your answer is E

[knightrider]

I'll do this the long way, explicitly using chain rule. Be aware, however, that you *should* be able to do it by eyeballing and using the rule 'diff the inside' * 'diff the outside' repeatedly.

Let's set up and
Thus - you should be able to do this
And
Therefore

Hence your answer is E

Thanks so much zsteve 

[Mc47]

I'll do this the long way, explicitly using chain rule. Be aware, however, that you *should* be able to do it by eyeballing and using the rule 'diff the inside' * 'diff the outside' repeatedly.

Let's set up and
Thus - you should be able to do this
And
Therefore

Hence your answer is E

How is this part true?

[warya]

For part ii, why is area b/w two curves method incorrect? I got 35/12 which was the common incorrect answer, it's meant to be 11/6, but I'm struggling to see what I've done wrong

[cosine]

For part ii, why is area b/w two curves method incorrect? I got 35/12 which was the common incorrect answer, it's meant to be 11/6, but I'm struggling to see what I've done wrong

Area =

where f(x) = linear graph (the tangent)
where g(x) = parabola
where x1 = intersection of the x-axis of the linear
where x2 = intersection of the x-axis of the parabola

Show us your working out - this method should work.

[Mc47]

For part ii, why is area b/w two curves method incorrect? I got 35/12 which was the common incorrect answer, it's meant to be 11/6, but I'm struggling to see what I've done wrong

You can't use an integral to find the area (between the curves) from x=0 to x=5. This is because between x=4 and x=5 the parabola goes below the x axis, but you only want to find the area above the x-axis. Instead, use the integral to find the area from x=0 to x=4, and then use A=(1/2)bh to find the remaining area. So it should be the integral as cosine posted (where x=4) + 1/2 x 1 x 1, which should equal 11/6

[warya]

Area =

where f(x) = linear graph (the tangent)
where g(x) = parabola
where x = intersection of the x-axis

Show us your working out - this method should work.

I see where I'm going wrong, can you pick it up cosine? Haha

Edit: Thanks mc47, got it

[cosine]

I see where I'm going wrong, can you pick it up cosine? Haha

Edit: Thanks mc47, got it

does not equal the area required as you are adding an extra region (negative parabola and putting minus sign means adding the negative area, hence your answer being extra).

Also if you wish not to lose an easy mark on the exam, if you have a polynomial in the integrand, you have to put brackets as I did above. Or else you would be saying the 'dx' part is only applicable for the last term, which would lose marks.

[knightrider]

How would you do this question attached?

[knightrider]

For this question and solution (attached)

The Roosters and the Swans are rival handball teams. When they play against each other the probability of winning is dependent upon the result of their previous match. If the Roosters have won the previous match, then the probability that they will win the next match is 0.6. If the Swans have won the previous match, then the probability that they will win the next match is 0.7.

These two teams are about to start a “best of three” finals series which is played until either team has won 2 matches. The probability that the Roosters win the first match is 0.6.

In the solution for the tree diagram why haven't they drawed all of the final branches ? Like why do they only draw the S and R branches for the last ones?