VCE Methods Question Thread!

[Shadowxo]

Hi, anyone know how to do this question?

lim (as x-->a) {(sin^2(2x)-sin^2(2a))/x-a}

Thank You

I'm not sure if this is for methods, I don't think limits is covered.

This is of the form 0/0 (substitute it in to find this).
From here you can use L'Hopital's rule:

[jazzycab]

I'm not sure if this is for methods, I don't think limits is covered.

This is of the form 0/0 (substitute it in to find this).
From here you can use L'Hopital's rule:

As Shadowxo has mentioned, this can be done using L'Hopital's rule, however, it isn't in the Methods course. The only way of evaluating this in Methods is by using the limit function in the CAS

[lzxnl]

As Shadowxo has mentioned, this can be done using L'Hopital's rule, however, it isn't in the Methods course. The only way of evaluating this in Methods is by using the limit function in the CAS

Not TECHNICALLY true. Let's do some rearranging.


If the student knows the definition of a derivative, they can recognise this as differentiation from first principles of sin^2(2a).

[peachxmh]

Hullo - can someone step me through how to do this question by hand? Thanks

If a < 0 and x is an element of all real numbers, then find the solution(s) to the equation x⁴ + x³ - ax² - 2x² - ax + 2a = 0

[StupidProdigy]

Hullo - can someone step me through how to do this question by hand? Thanks

If a < 0 and x is an element of all real numbers, then find the solution(s) to the equation x⁴ + x³ - ax² - 2x² - ax + 2a = 0

Attached my working in the pic, just note we can't find sqrt(a) because a is less than zero as specified in the question stem. Hope it helps

[peachxmh]

Sorry to post another question but maths really isn't my forte so here goes haha

If Pr(A) = 3/4, Pr (B) = 1/4, and Pr (A|B) = 1/2, then Pr (B|A) is...
the options are (A) 1/2 (B) 1/6 (C) 2/3 (D) 3/8 (E) impossible to determine

I got 1/6 but was marked wrong - what I did was:
1. as Pr(A|B) = 1/2 is given, therefore Pr (A and B) / Pr (B) must = 1/2, so I solved for that and got Pr (A and B) = 1/8
2. as Pr (B|A) = Pr (B and A) / Pr (A), I substituted Pr (A and B) = 1/8 in as well as Pr (A) = 1/2 and got 1/6 as the answer

Could someone explain where I went wrong and how to get to the correct answer? Many thanks!

[RuiAce]

Sorry to post another question but maths really isn't my forte so here goes haha

If Pr(A) = 3/4, Pr (B) = 1/4, and Pr (A|B) = 1/2, then Pr (B|A) is...
the options are (A) 1/2 (B) 1/6 (C) 2/3 (D) 3/8 (E) impossible to determine

I got 1/6 but was marked wrong - what I did was:
1. as Pr(A|B) = 1/2 is given, therefore Pr (A and B) / Pr (B) must = 1/2, so I solved for that and got Pr (A and B) = 1/8
2. as Pr (B|A) = Pr (B and A) / Pr (A), I substituted Pr (A and B) = 1/8 in as well as Pr (A) = 1/2 - is this a typo? and got 1/6 as the answer

Could someone explain where I went wrong and how to get to the correct answer? Many thanks!

1/6 is definitely correct.

[peachxmh]

1/6 is definitely correct.

Ahh yes that was a typo! whoops it was supposed to say 3/4 haha
Thanks for your help - guess my teacher must have marked it wrong

[m2121]

Please help with the following questions
answers for question 3 attached below

[Sine]

Please help with the following questions
answers for question 3 attached below

what particular aspect of the question is troubling you?

[m2121]

I was able to work out question 3a but got stuck on Question 3b and not sure how to do it

[Sine]

I was able to work out question 3a but got stuck on Question 3b and not sure how to do it

Cost to produce the product = C = x^3 + 100x +2000
revenue = sales received = S = 500x

Profit = revenue - cost
Profit = 500x - (x^3 + 100x + 2000)
Profit = 500x - x^3 - 100x - 2000
P = -x^3 + 400x -2000

[m2121]

How about question 7b and 11b?

[Sine]

How about question 7b and 11b?

what working out did you try of those ones?

[Qwerty1234qwerty]

So the length between the two intercepts is 6 since 0,0 and 6,0

Let the two small equal sections next to the rectangle on both sides = a=6-x
Length of rectangle = x-a
x-6+x
2x-6