Maths Methods 3/4 Help Thread 2011

[paulsterio]

factor of k from the y-axis...don't you put it in the top left?

Yes, "from the y-axis" means that the x-co-ordinate is changing

[Anon123]

do we need to know point of inflections in methods?
And the definition/formula of velocity and acceleration?

IIRC, there will be a focus (question) regarding velocity and acceleration, etc, apparently in some VCAA bulletin/supplementary thingamabobs (omg this is a word now) which i cant find

[nacho]

whats the difference between the period of an absolute trig function and the normal trig function?
How exactly do you determine it?
Eg. y = |3sin(x)|
as opposed to
y = 3sin(x)
?

[paulsterio]

whats the difference between the period of an absolute trig function and the normal trig function?
How exactly do you determine it?
Eg. y = |3sin(x)|
as opposed to
y = 3sin(x)

You halve the period, because if you graph it, you can see that it now repeats itself twice whist the original (non-absolute) graph repeats itself once

Edit: Thanks b^3

[b^3]

With the mod functions, we know that everything that is below the x-axis is flipped above the x-axis. So with 3sin(x), it will first be flipped at pi. Really I think the best way is to draw it and see where it starts to repeat. So the period of |3sin(x)| will be . It's a bit like rectifying diodes with a bridge rectifier. It makes it DC current and flipps everything about the x-axis but the frequency doubles as the period halfs.

Hope that helps.

EDIT: beaten by a minute, and Paul you typed in nacho's quote box.

[#1procrastinator]

is the derivative refer to the gradient at an actual point or the function you get when you differentiate or both?

[nacho]

Need some urgant help

q. A particle moves in a straight line and its displacement at time n from the origin O is given by x = -2sin(2npi). The average speed of the particle from n =0 and n=0.75

similar q.
q. Position x(n) = 1 + sin(npi)
Find the distance travelled for n from 0 to 3.

[b^3]

Need some urgant help

q. A particle moves in a straight line and its displacement at time n from the origin O is given by x = -2sin(2npi). The average speed of the particle from n =0 and n=0.75

similar q.
q. Position x(n) = 1 + sin(npi)
Find the distance travelled for n from 0 to 3.

Speed is given by the gradient of velocity Vs time graphs, so the average speed is the gradient from 0 to 0.75
i.e. avg speed = rise/run = (-2sin(3pi/2)+2sin(0))/.75-0
=2/.75
=8/3 units/sec REFER to post below.

x(0)=1+sin(0)=1
x(3)=1+sin(3pi)=1
So that is at the endpoints, now find turning points to find the extremes that it reaches.
x'=n*cos(npi)
ncos(npi)=0
npi=pi/2,3pi/2, 5pi/2
n=1/2,3/2,5/2

x(1/2)=1+sin(pi/2)=2
x(3/2)=1+sin(3pi/2)=0
x(5/2)=1+sin(5pi/2)=2

       0   1/2    3/2     5/2  3
2                                   
            /    \              /     \
1         /       \           /       \
                     \        /     
0                     \     /

So from 0->1/2, it travels 2-1=1
From 1/2 to 3/2 it travels 2-0=2
From 3/2 to 5/2 it travels 0--2=2
From 5/2 to 3 it travels 2-1=1
Total distance = 1+2+2+1=6 units

Lets hope there are not mistakes there.

EDIT: Missed the last tp, added it.

[nacho]

hey i got the same for q.1
although the solutions say it is not the answer, the answer is 8

q2 is correct, why is it ive never seen this type of question
is it asked on exams often?

[b^3]

Wait I realistd what I did wrong for 1.

For 2, I've  come across it on sacs before but not exams yet?

[b^3]

Using the same method as 2, the total distance travelled is 6 units (2+4=6).
Then speed = distance/time-6/.75=8unit/sec

EDIT: The above method would work for Velocity, but this is speed so we have to work it out in parts (i.e. adding the distances) then average the whole thing.

[Andiio]

Just for extra clarification:
If a Q asks to find the derivative of something in its SIMPLEST FORM, and say the result you get is 2x+2, would you factorise that to get 2(x+1) just in case? Or is it feasible to simply leave it as 2x+2

[paulsterio]

Just for extra clarification:
If a Q asks to find the derivative of something in its SIMPLEST FORM, and say the result you get is 2x+2, would you factorise that to get 2(x+1) just in case? Or is it feasible to simply leave it as 2x+2

They're both fine, it doesn't really matter

It's like is (x-1)(x-2)(x-3)(x-4) really considered simplest form? :S

But in all cases, as long as its reasonably simplified it's ok

[Andiio]

Would you factorise just in case you get some super 'anal' VCAA examiners? D:

[paulsterio]

No I personally wouldn't factorise, because you can easily argue that factorised is NOT simplest form, I've always thought of simplest form as no brackets

But I highly doubt they will ask for "simplest form" - haven't seen it on VCAA yet? :S