VCE Methods Question Thread!

[BubbleWrapMan]

Y= e^(4x^2-8x)


Graphs similar to this, are we required to graph them cas free?

With rate of decay/ average rate of change.... Do we need to write units?

No and no

[Alwin]

With rate of decay/ average rate of change.... Do we need to write units?

Hmm, I have heard of people losing marks in SACS because they didn't write km/h or bacteria/min or cm³/s etc.
Textbook answers generally include units too.

However, I have never seen it asked for in exams. Generally they would ask for the value, in which case no units are required. Or, they would ask (for example) "What is the average rate of change in m/s?" Since they've provided you with units already, technically there is no need to write m/s in your answer and they would deduct marks if you don't write it.

[BubbleWrapMan]

Since they've provided you with units already, technically there is no need to write m/s in your answer and they would deduct marks if you don't write it.

Very much this. Also, units generally aren't the focus of the question, so there's pretty much never any need to convert between units (e.g. metres to kilometres), just because it's not something VCAA wants to test you on in a methods exam.

That said, units are generally important in any calculations (unless you're working in Math Land where everything is unitless), so it's definitely a good idea to be mindful of it. Take this for example:

http://edition.cnn.com/TECH/space/9909/30/mars.metric.02/

"NASA lost a $125 million Mars orbiter because a Lockheed Martin engineering team used English units of measurement while the agency's team used the more conventional metric system for a key spacecraft operation".

Obviously an extreme case, but it hopefully gets the point across. Also it's kind of hilarious.

Personally I'd try to write down units as much as possible, since it forces me to go back and read the question, which is also good practice.

[Alwin]

Very much this. Also, units generally aren't the focus of the question, so there's pretty much never any need to convert between units

http://edition.cnn.com/TECH/space/9909/30/mars.metric.02/
"NASA lost a $125 million Mars orbiter because a Lockheed Martin engineering team used English units of measurement while the agency's team used the more conventional metric system for a key spacecraft operation".

This is Methods, not Further  =P

Wow.. 125million is just a bit.. much haha. I like that point tho +1

[BubbleWrapMan]

This is Methods, not Further  =P

'choo mean?

[shadows]

Thanks.

 velocity and acceleration.  Acceleration is just the derivative of the derivative (velocity)
With acceleration ex. km/m^2.   

Why is it squared. Is it required we understand concepts about acceleration and velocity? Thought its more of a physics thing.


Say f(x) is a negative cubic which has two t.ps (both above x axis and occur to the right of the y axis) is a function that models population.


The question tells us to find what value that would occur in which the population is a minimum.

Wouldn't it be minimum at the x intercept?
Apparently it's minimum is at the minimum t.p. but the y value of the x intercept is lower.

Help I am confused. And thanks for your help. .

[BubbleWrapMan]

Thanks.

 velocity and acceleration.  Acceleration is just the derivative of the derivative (velocity)
With acceleration ex. km/m^2.   

Why is it squared. Is it required we understand concepts about acceleration and velocity? Thought its more of a physics thing.


Say f(x) is a negative cubic which has two t.ps (both above x axis and occur to the right of the y axis) is a function that models population.


The question tells us to find what value that would occur in which the population is a minimum.

Wouldn't it be minimum at the x intercept?
Apparently it's minimum is at the minimum t.p. but the y value of the x intercept is lower.

Help I am confused. And thanks for your help. .

Acceleration only needs to be understood as being equal to , which is the second derivative as you said.

The reason it's is because it's the rate at which velocity changes with respect to time. When you measure the rate at which something changes, you express it generally as . If the quantity that's changing is distance, then you get . If you measure velocity per time unit, velocity itself has units of , so this divided by time units gives .

You're right about the cubic question - they should be more specific and say 'local minimum' or something to that effect, since the global minimum is obviously when it hits zero.

[jono88]

The x co-ordinate of the point on the curve of y=root(x^2-4x) at which the gradient is zero.

So i find dy/dx=x-2/root(x^2-4x)  Let that equal 0. How do i prove that there are no x-coordinates at which the gradient is 0?

[Jeggz]

The x co-ordinate of the point on the curve of y=root(x^2-4x) at which the gradient is zero.

So i find dy/dx=x-2/root(x^2-4x)  Let that equal 0. How do i prove that there are no x-coordinates at which the gradient is 0?

The way I would approach this is to say that although when , this point does not exist on the graph. Why? Because if we look at the domain of it is . And because the point x=2 doesn't fall in this domain, there are hence no x-coordinates at which the gradient is 0.

[brightsky]

you have (x-2)/sqrt(x^2-4x) = 0, where x<0 or x > 4
now if you solve this normally, you would get x - 2 =0, meaning x = 2
but x = 2 does not fall within the domain of dy/dx.
so there are no x-coordinates at which gradient = 0.

[jono88]

Ahhh........ look at the domain of (x-2)/sqrt(x^2-4x), thanks guys

[shadows]

How does 2(cos(x))^2 - 2(sin(x))^2

Equal 4(cos(x))^2 - 2

[b^3]

Hint: Make use of

Spoiler

[Stick]

[Alwin]

(Image removed from quote.)

MERRY CHIRSTMAS STICK:

Re: Methods [3/4] Question Thread!

I uploaded solutions there ^^

Considering just uploading the whole booklet now lol.