Maths Methods 3/4 Help Thread 2011

[b^3]

harro,
question;
what is adequate when explaining questions like
'Explain why A  = 5, B = 3/2 and n = 2pi

and you have the graph of the equation:
d = Asin(nx) + B
which shows Amplitude is 10, vert translation is 10, and repeated after 2pi.
Do you just say
"Max height minus min height divided by 2 = 10, therefore amplitude = 10" ?

I think it's a well known rule/definition that for any y = Asin(nx), you have amplitude = 2A and period = 2pi/n. So you can just state those and it should be fine.

Also, if your graph repeats after 2pi, n = 1, not 2pi. Just clearing that up!

Amplitude = 2A? The difference between the maximum and minimum will be 2A but the amplitude is still A is it not?

Ah, it may be different for methods, but peak amplitude is A, and peak to peak amplitude is 2A. I can't remember which one VCAA uses. You're probably right though.

Yeh peak is just A and peak-to-peak is 2A (if I remember right from unit 3 physics).

[nacho]

Question:
The approximate area under a curve over a particular interval is found by using left endpoint rectangles. An over estimate for the actual area under the curve over the interval will be found if its equation is.

A. y = e^x
B. y = (x)^0.5
C. y = (x)^(3/2)
D. y = -e^x
E. y= -e^-x


no answer here

[burbs]

I have a feeling this is one of the first times I have posted on the methods board :/
Some queries from VCAA exams:

VCAA 06 exam 2
MC:
16) f'(x)=g'(x)+3, f(0)=2 and g(0)=1
Then f(x) is given by?
Not sure how to do this one.

[BlueSky_3]

The answer is D. This is because the function is decreasing for x is an element of R and so using left end point approximations will give you an overestimate.

[BlueSky_3]

@ Burbs: split up the integrals so that you get f(x) = g(x) + 3x + c and substitute the relevant points given to work out the c value. Which should work out to be 1.

[nacho]

The answer is D. This is because the function is decreasing for x is an element of R and so using left end point approximations will give you an overestimate.

solutions say u are wrong

[BlueSky_3]

Oh shucks my mistake yeah the answer is (E). I was under the impression that D was y=e^(-x) 

[nacho]

Oh shucks my mistake yeah the answer is (E). I was under the impression that D was y=e^(-x) 

ah cool, i see what you are saying now anyway,
thanks

[b^3]

The answer is D. This is because the function is decreasing for x is an element of R and so using left end point approximations will give you an overestimate.

solutions say u are wrong

The answer should be E. since we need it to either be decreasing with the gradient increasing or increasing with the gradient decreasing. For D the graph is decreasing but the gradient is increasing.

EDIT: now beaten

[ech_93]

I'm confused with question 21 on vcaa exam 1 2007,
it says:
Question 21
{x: cos2(x) + 2cos (x) = 0} =
A. {x : cos (x) = 0}
B. {x : cos (x) = -1/2}
C. {x : cos(x) = 1/2}
D. {x : cos(x) =0} U {x : cos (x) = -1/2}
E. {x : cos(x) = 1/2} U {x : cos (x) = -1/2}

What is that even asking...... :/

[dc302]

I'm confused with question 21 on vcaa exam 1 2007,
it says:
Question 21
{x: cos2(x) + 2cos (x) = 0} =
A. {x : cos (x) = 0}
B. {x : cos (x) = -1/2}
C. {x : cos(x) = 1/2}
D. {x : cos(x) =0} U {x : cos (x) = -1/2}
E. {x : cos(x) = 1/2} U {x : cos (x) = -1/2}

What is that even asking...... :/

It's asking you to equate two sets of numbers. The first is the set of x such that cos(2x) + 2cosx = 0. All you have to do is find the values of x that satisfy this equation. So start by simplying cos2x with the double angle formula and then proceed from there..

edit: sorry did you mean (cosx) ^2 or cos(2x)? Either way, the method is the same.

edit 2: i'm going to assume it is (cosx)^2. In that case:

if (cosx)^2 + 2cosx = 0, we factorise to get:

cosx (cosx + 2) = 0

so either cosx = 0 or cosx = -2. The latter is impossible, so the set equates to the set of x such that cosx = 0, which is A

[ech_93]

Oh yeah, I wrote the question out wrong, meant to be ^2. Thanks!

[Bozo]

The area, correct to three D.P bounded by  the y axis with equations f(x)=cos(2x)+2   and   g(x)=e^x

[Greatness]

Find the point of intersection, g(x)=f(x), x=0.7387
Find the integral from 0 to 0.7387 of ( f(x) - g(x) ) dx = 0.882
Is that correct?

[Bozo]

It is. I'm just wondering, how do i do it the way you flip it all i.e. x=f(y)