VCE Methods Question Thread!

[lzxnl]

To find the mean? OK. Let's think about this from a common sense perspective. If we conducted this experiment 16 times, we would expect x to equal -2 4 times, to equal -1 once, to equal 0 3 times, to equal 1 twice, to equal 2 twice, to equal 3 once, and to equal 4 3 times.
What's the average of this? -2*4 + -1 + 0*3 + 1*2 + 2*2 + 3*1 + 4*3
= -8-1+2+4+3+12
= 12
So average is 12/16 = 0.75

I don't think the answer should be 0.5. It doesn't look like it.

[Alwin]

Can someone help me with part b) of this question? Thanks!

Original Questions

We have So,


For a tangent that passes through the origin, it must be in the form

The equation of any tangent to at is given by:


I think I wayyy overcomplicated it, but thats one method haha

So average is 12/16 = 0.75

I get 0.75 too hmm

EDIT: Didn't read the question haha, added in the co-ordinate part

[Jaswinder]

whoops sorry guys i meant median.
whats a good way of finding the median of that table

[b^3]

Add up the probabilities until you hit or exceed 0.5 (halfway probability wise through the distribution)
If you exceed 0.5 then the value of for which you exceed it on is the median.
If you hit 0.5 exactly, then average the two values of what you hit it with and the next value.

So in this case , so we 'hit' . We hit it with , so taking and the next value, .
So the median is

[arush002]

Would be very grateful if someone could give me a hand with Chapter Review 12, Short Answer, Question 7. Usually pretty good with these types of questions but the f(3x) throws me off a little...

[zvezda]

Would be very grateful if someone could give me a hand with Chapter Review 12, Short Answer, Question 7. Usually pretty good with these types of questions but the f(3x) throws me off a little...

Take an equation of the form y=mx and graph it. Now, obviously theres a triangle thats formed between the line and the x-axis. Take this triangle and plot the coordinate (9, 9m). From here, 0.5 x base x height in order to find m. So then you have your equation. Apply dilation of 1/3 from y and find the image equation. The rest should be ok.

[zvezda]

Hey,
Just have a question with q3 from exercise 15D of essentials.
Not sure how to go about it.
Help is appreciated

[abcdqd]

Hey,
Just have a question with q3 from exercise 15D of essentials.
Not sure how to go about it.
Help is appreciated

you can just use cas, i didnt even know that it would work lol. we want pr(x=5)>0.25, so the minimum number of trials is given by pr(x=5)=0.25
should give the answer

[zvezda]

you can just use cas, i didnt even know that it would work lol. we want pr(x=5)>0.25, so the minimum number of trials is given by pr(x=5)=0.25
should give the answer

Yeah i tried that before and it didnt work hahah. Thanks anyway

[Alwin]

you can just use cas, i didnt even know that it would work lol. we want pr(x=5)>0.25, so the minimum number of trials is given by pr(x=5)=0.25
should give the answer

Yeah i tried that before and it didnt work hahah. Thanks anyway

Hey, stankovic123! I dunno what CAS you're using, but I have the classpad
Last year, for some qs like that I had to graph the function and use Graph-solve to find x when y=0.25
Or, had to whip up a spread sheet, depending on whether my CAS felt like graphing it or not lol

I guess you have to use other numerical methods to solve it, if "solve" cas function doesn't work . . .

[Stick]

Would be very grateful if someone could give me a hand with Chapter Review 12, Short Answer, Question 7. Usually pretty good with these types of questions but the f(3x) throws me off a little...

Take an equation of the form y=mx and graph it. Now, obviously theres a triangle thats formed between the line and the x-axis. Take this triangle and plot the coordinate (9, 9m). From here, 0.5 x base x height in order to find m. So then you have your equation. Apply dilation of 1/3 from y and find the image equation. The rest should be ok.

Is there an algebraic way of doing these sorts of problems? I thought applying transformations might work, but it didn't. Here's the question for anyone who doesn't have access to the textbook at this instant:

[clıppy]

Just a quick question because I think i've forgotten how powers work.
Lets say I need to find the inverse of the equation:

I swap x and y, start moving things around and then get to this point:

Which is equal to:


Here is where I am lost on how it works. How do i make into
I just can't remember how moving powers across equal signs work.

[Jaswinder]

Is there an algebraic way of doing these sorts of problems? I thought applying transformations might work, but it didn't. Here's the question for anyone who doesn't have access to the textbook at this instant:

(Image removed from quote.)

I get 5/3 as an answer for both of them. pree sure thats wrong :/ anyways

Christopher has five pairs of identical purple socks and three pairs of identical green socks. His socks are randomly mixed in his drawer. He takes two identical socks at random from the drawer in the dark. The probability that he obtains a matching pair is?

I keep getting 13/28, however the answer is 1/2 :s

[lzxnl]

Is there an algebraic way of doing these sorts of problems? I thought applying transformations might work, but it didn't. Here's the question for anyone who doesn't have access to the textbook at this instant:

(Image removed from quote.)

I would look at it this way. What have you done to get from f(x) to f(3x)? The integration bounds are equivalent as they have been dilated too. To get from f(x) to f(3x), you have to dilate from the y axis by a factor of 1/3. This means that your area is going to be shrunk. Draw it out if you need to. Translations don't affect the area, for obvious reasons.

I get 5/3 as an answer for both of them. pree sure thats wrong :/ anyways

Christopher has five pairs of identical purple socks and three pairs of identical green socks. His socks are randomly mixed in his drawer. He takes two identical socks at random from the drawer in the dark. The probability that he obtains a matching pair is?

I keep getting 13/28, however the answer is 1/2 :s

I'm happy with 5/3 for both of them.
OK, so how can he get a matching pair? Either he takes two green or two purple.
He has TEN purple socks as it says five pairs, and he has SIX green socks.
How does he take two green socks? 16 socks in total, 6 socks, so 6/16*5/15 = 6/16*1/3 = 1/8
How can he take two purple socks? 16 socks in total, 10 socks, so 10/16*9/15 = 5/8*3/5 = 3/8
Sum the probabilities to get 1/2

I think you might have done this:
Five purple socks, three green socks
Probability is 5/8*4/7 + 3/8*2/7 = (20+6)/56 = 13/28.
The question says pairs of socks, not socks.

Just a quick question because I think i've forgotten how powers work.
Lets say I need to find the inverse of the equation:

I swap x and y, start moving things around and then get to this point:

Which is equal to:


Here is where I am lost on how it works. How do i make into
I just can't remember how moving powers across equal signs work.

Ok. (x+3) = y^-1/2
Square both sides
(x+3)^2 = y^(-1/2*2) = y^-1
Reciprocal
(x+3)^-2 = y

Just remember what the domain and range of this thing is.

[Alwin]

Is there an algebraic way of doing these sorts of problems? I thought applying transformations might work, but it didn't. Here's the question for anyone who doesn't have access to the textbook at this instant:

Original Question

I see in your signature that you do spesh Stick, so a hint for the algebraic way is substitution
for a, let u=3x, then you have to change the terminal

for b, i'll also show a non spesh way of doing it for those of you not doing spesh


and nliu's gone and answered the rest while I was LaTexing

The only think I would add is:

Translations don't affect the area, for obvious reasons.

Consider f(x) + 1 nliu