VCE General & Further Maths Question Thread!

[LiquidPaperz]

attached it sorry - forgot about it.

and anyone want to explain the last graphs and relations question, http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf

i dont know why they minused the two equations and made it equal 3?

[Splash-Tackle-Flail]

Both these questions are from the VCAA 2013 E1 (Module 3)

Q8) Don't understand it at all...
(Image removed from quote.)

First of all I have no idea how you guys do that cool looking math font, but hopefully I can show my working clear enough!

Personally I did this one by first finding the points, "M" and "N" which were (45,25) and (20,50). Then, I took out A and E because they had negatives.

Then, I moved down the list of options: B,C,D and subbed in their given values for "a" and "b", (so for example for B, I wrote Z=15x +15y) Then, I subbed in the points M, into that equation, to get an answer for Z, which ended up to equal 1050. Then I subbed in the points for N, into the equation to get 1050. Since both give the same answer, I concluded B is correct.

FOr safety I did the same process for C and D, just in case they also gave the same answer when the points were subbed in, but they didn't.
Let me know if I was clear or not, cause theres a high% chance it wasn't!

[myanacondadont]

attached it sorry - forgot about it.

and anyone want to explain the last graphs and relations question, http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011furmath2-w.pdf

i dont know why they minused the two equations and made it equal 3?

Okay so this question. They're asking you to find WHEN they're 3km apart. To do this we can create an equation to find the distance between them. We can do this by subtracting the equation of Michael's Journey from Katie's journey. It's kinda hard to really articulate without printing this out and doing it via hand but I chucked them into CAS and found I have to use Michael's first journey equation.

We can conclude that if we subtract the distance of Michael's first journey from Katie's journey we will have an equation for the distance apart.

So dissecting this you can see we are subtracting the distance of Michael's first journey from Katie's journey and then equating it to 3 (Trying to find when the distance between is equal to 3)


BUT All we have found is when they are first 3km apart - now we need to find when they are last 3km apart. Now if you were to draw Katie's journey onto the graph given you'd see it is approximately 3km away at t=3. So we know it is approximately at t=3. To confirm we are going to have to subtract Katie's journey from the journey of Michael (This time it is rather easy as he's not moving so d=10 is the equation).
 
Dissecting this you can see we subtracted Katie's journey from the journey of Michael at t=3. Solving this:


So we can conclude they were first 3km away at 1.625km, They continued to get closer and closer and finally were 3km seperated again at 3km. So for 3-1.625 their radio transmitters would work.



Not gonna lie - this was a wierd question, first time I've seen something like this in a further exam. I guess it shows that only 3% of people got full marks for question 2.

Did it on last page.

[LiquidPaperz]

thanks for that.

However i dont under the process of minusing both equations, ive never come across this before, as ive only had to make them equal each other or simultaneously solve.What does minusing the equations tell us? and what does minusing michael - kate and kate - michael represent?

and making it equal to 3, would this tell us when y is equal to 3?

[redcracker]

you are effectively finding at what times they are 3 km apart
so the difference in distance = 3
that is to say: distance of m minus distance of k = 3

[Splash-Tackle-Flail]

When using random samples in exam 2, do we write CAS speak to show the working out? As in first I'd allocate each sample a number, then could I say
Menu, Prob …..?

Also, how strict are they with marking wrong working if the answer is correct, for example in last years exam for Question 4b, I thought the points were (3,13.6) and (13,21.7), and then used gradient formula to get 0.8. However the exam report read the graph's second point as (13,21.. Since when rounded to 1dp, the answers are the same, would I get the marK?

[keltingmeith]

When using random samples in exam 2, do we write CAS speak to show the working out? As in first I'd allocate each sample a number, then could I say
Menu, Prob …..?

NEVER use "CAS speak". Ever. Not once. Don't even do it as a last resort. Don't do it in practice even though you'll do better in the exam. Just don't. Just write that you've used your CAS as an intermediate between steps. Or, write full working out, but then just use your CAS to evaluate it.

[LiquidPaperz]

why is abd and dcb not similar?

[keltingmeith]

why is abd and dcb not similar?

Only one angle is the same - you have no proof they both have another angle the same, so you cannot say that they are similar.

[LiquidPaperz]

ok that makes sense.

just a few more questions in the course
1) if its not a transition matrix what makes it different to a transition matrix, other then columns adding to 1? can it be raised to a power for steady state? etc..
2) what essentially does Sx mean other then the spread around mean, is there anything too add? how can it be affected?
3) a quick question, if you look at the attached. Say this question asked, what is the total revenue of the 203 hot chocolates, would i sub 203 into the second revenue one, or sub 200 in the first and 3 in the second
4) also questions like, mark has a  fixed cost of 1000 and $10 for the first days, and $20 for every day after, find the equation that shows cost a after 10 days, how do we do this?

[redcracker]

ok that makes sense.

just a few more questions in the course
1) if its not a transition matrix what makes it different to a transition matrix, other then columns adding to 1? can it be raised to a power for steady state? etc..
2) what essentially does Sx mean other then the spread around mean, is there anything too add? how can it be affected?
3) a quick question, if you look at the attached. Say this question asked, what is the total revenue of the 203 hot chocolates, would i sub 203 into the second revenue one, or sub 200 in the first and 3 in the second
4) also questions like, mark has a  fixed cost of 1000 and $10 for the first days, and $20 for every day after, find the equation that shows cost a after 10 days, how do we do this?

re: 3
200 into first equation then every one after 200 (so the remaining 3) sub into second equation

[LiquidPaperz]

Are you sure, because I've seen some answers that say otherwise, and some that say what you say, so conflicting views

[LiquidPaperz]

and how does this work??

how can you square it?

[LiquidPaperz]

and also this. why dont we use m = y2-y1/x2-x1 this seem to work all the time?

[keltingmeith]

and how does this work??

how can you square it?

First line is from the fact that they're similar triangles (I'd need to see the triangles to explain why), the second line is just a cross multiplication of the first line.

and also this. why dont we use m = y2-y1/x2-x1 this seem to work all the time?

They are doing this - just in different words.