VCE Methods Question Thread!

[S_R_K]

I have no clue how that works either, I only thought that rule could be used for logs. However, the way I thought about it was by equating coefficients. You can rearrange the equation and then look at both the power and the coefficient.

This is fine in this particular case, because xe^(2x) = y has only one solution for x, when y > 0 (since e^(2x) is always positive, if y > 0 then x > 0; and when x > 0, xe^(2x) is strictly increasing). But in general xe^(2x) = y is not one-to-one, so you would need to consider the existence of multiple solutions if y < 0.

[marauder52]

2017 VCAA Exam 2 Question 2F.
I cannot figure out where they got the second gradient expression from. I understand the first one where they simply sub in u, but not the second.

[S_R_K]

2017 VCAA Exam 2 Question 2F.
I cannot figure out where they got the second gradient expression from. I understand the first one where they simply sub in u, but not the second.

You are finding the gradient of a line segment, hence use rise/run between two points on the segment. One point is (500, 0) (the location of the boat), the other is (u,root(3025-u^2)+65) (a point on the ferris wheel).

[Azim.m]

What is the probability that Clare sells at least one house on each of three consecutive weeks?

I know i could do (Pr(x=1) + Pr(x = 2))^3 = 1/8 which is the answer. But how come when i do 1- (Pr(x = 0))^3 i get 7/8? Should it not give me the same answer?

[Bri MT]

What is the probability that Clare sells at least one house on each of three consecutive weeks?

I know i could do (Pr(x=1) + Pr(x = 2))^3 = 1/8 which is the answer. But how come when i do 1- (Pr(x = 0))^3 i get 7/8? Should it not give me the same answer?

The second method you're finding the probability that she sells at least one house over the the weeks,  but you need to find the probability that each week she sells at least one. 

Ie, you're including answers such as sell, don't sell any,  sell 2 when you shouldn't be.


Be careful where you place your brackets

[Unsplash]

I'm having trouble doing this question from 2013 iTute Methods Exam 1. The solution is also attached but i'm finding it hard to follow and understand the logic behind it, in particular the first step. Thanks in advance!

By the way, my method was to let f(x)=x and try to find a way so that it would only have one solution but I couldn't progress much further.

[peter.g15]

Hi all, I was having trouble understanding the second line of working for the VCAA exam 2 2017 solutions for question 4h. I understand the gradients and such, but I wasn't sure where they got 2k=tan(60) and 2k=tan(30). Could someone clarify please?

Cheers

[minhalgill]

does anyone know how to do this question?

[minhalgill]

does anyone know how to do this question?

[Yertle the Turtle]

does anyone know how to do this question?

To do this question you would find the minimum points of the untranslated equation, and then translate the graph k units up until the entire graph is above the x-axis. This is the minimum k value, which I will call z, so the answer is 'k is an element of (z, infinity)'.

To find those minimum points you would differentiate and solve for 0, and then substitute values into your original equation to find the lowest y values.

Hope this helps!

[minhalgill]

To do this question you would find the minimum points of the untranslated equation, and then translate the graph k units up until the entire graph is above the x-axis. This is the minimum k value, which I will call z, so the answer is 'k is an element of (z, infinity)'.

To find those minimum points you would differentiate and solve for 0, and then substitute values into your original equation to find the lowest y values.

Hope this helps!

what i did was i let 'sin(x)' = a and then the equation became a^2 -2a+k=0 and i did the discrinimant and did b^2 -4ac<0. and subsituted in the values. why is this wrong?

[minhalgill]

does anyone know how to do d(ii) , you may want to refer to the graph of n(t) as theyre asking for a translation of n(t) onto the graph of m(t).

[minhalgill]

does anyone know how to do this ?? pls help??

[MB_]

what i did was i let 'sin(x)' = a and then the equation became a^2 -2a+k=0 and i did the discrinimant and did b^2 -4ac<0. and subsituted in the values. why is this wrong?

That method should work, \(b^2-4ac = 4a^2(1-k)\) as \(a^2\) is positive you only have to worry about \(1-k\). We know that when \(b^2-4ac<0\) there are no real solutions so we have \(1-k<0 \implies k>1\) so there are no real solutions for \(k  \in  (1,\infty)\) 

[S_R_K]

Hi all, I was having trouble understanding the second line of working for the VCAA exam 2 2017 solutions for question 4h. I understand the gradients and such, but I wasn't sure where they got 2k=tan(60) and 2k=tan(30). Could someone clarify please?

Cheers

There are a few ways to do this one. Specialist students were slightly advantaged by this question, by knowing the compound angle formulae for tan(x). I've seen a number of suggested solutions use that method.

I think the answer intended / expected by the examiners was to use the fact that the graphs of a function and its inverse are reflections about the line y = x, which is at angle of 45° from the positive x-axis. Hence, if the tangents to the graphs of a function and its inverse at a point (x, y) have an angle between them of A, then the tangent to the graph of the function will be at an angle of 45° ± (A/2) from the positive x-axis, and the tangent to the graph of the inverse function will be at an angle of 45° ± (A/2) from the positive x-axis. (Draw a diagram to help see this). Since A = 30, we conclude that the tangents are at angles of 30° and 60° respectively from the positive x-axis, and this gives the gradients, and hence the values of k.