Mathematics Question Thread

[EEEEEEP]

Find the exact area bounded by the curve y=e^2x, the x-axis and the lines x=2 and x=5.

sorry, i know these are really easy but i've had a mind blank

thanks heaps

To find the exact area, we need to integrate y=e^2x and then apply the values of x =2, and x =5.

The integration of y=e^2x = 1/2 * e^2x (We can test this using differentiation, but it should be right =)

The actual application of the integral bounds equals to:
((e^10)/2) - ((e^4)/2) ... note, this isn't in the form of the answer with a lot of decimals.

Remember that the integral of e^x = e^x.

If you do a calculation with a calculator, unless it's a whole number, you will get a sequence of about 9 or 10 digits on screen. This is not an exact answer BUT an approximation.

[Never.Give.Up]

Thanks for that EEEEEEP

Also, Find the exact gradient of the normal to the curve at the point where x=2.

and,



thanks heaps!

[RuiAce]

Thanks for that EEEEEEP

Also, Find the exact gradient of the normal to the curve y=x-e^-x at the point where x=2.

and,



thanks heaps!

Putting \(x=2\) into \( \frac{dy}{dx} = 1 + e^{-x} \) just gives \( m = 1 + e^{-2} \).

(After subbing in, note that \( \ln 1 = 0\).)

[Never.Give.Up]

Putting \(x=2\) into \( \frac{dy}{dx} = 1 + e^{-x} \) just gives \( m = 1 + e^{-2} \).

(After subbing in, note that \( \ln 1 = 0\).)

thanks RuiAce!!v kind of u

im getting one wrong stationary point here....
Find the stationary points on the curve and determine their nature. for some reason i keep getting x=0,3, when its x=0,-3...

thankyou!!

[RuiAce]

thanks RuiAce!!v kind of u

im getting one wrong stationary point here....
Find the stationary points on the curve and determine their nature. for some reason i keep getting x=0,3, when its x=0,-3...

thankyou!!

Which gives 0 and -3

[LaraC]

Hey!

Could someone please help me with two general rules. I'm a tad confused sorry! 

How to integrate a to the function of x??
And how to differentiate a to the function of x??

E.g, the question 3^(2x-1).

Could someone please explain how to both differentiate and integrate this as well as tell me the rules involved??

Thanks so much!!!!

[Dragomistress]

Hey,
I was wondering how are state-rankers given state-ranks if a vast majority of people are able to obtain 100 raw in Mathematics.

[RuiAce]

Hey,
I was wondering how are state-rankers given state-ranks if a vast majority of people are able to obtain 100 raw in Mathematics.

They go into the school's internal results as well.

Hey!

Could someone please help me with two general rules. I'm a tad confused sorry! 

How to integrate a to the function of x??
And how to differentiate a to the function of x??

E.g, the question 3^(2x-1).

Could someone please explain how to both differentiate and integrate this as well as tell me the rules involved??

Thanks so much!!!!

[Dragomistress]

What is their criteria for internals?

[jamonwindeyer]

What is their criteria for internals?

This is quoted from NESA:

If students are equal on the highest HSC marks in a course, then the following process is used to determine the recipient(s):

1. take an average of each student's exam mark and assessment mark after alignment to performance bands, each to one decimal place

2. take an average of each student's exam mark and assessment mark before alignment to performance bands, each to two decimal places

3. if an extension course, use the marks awarded for other courses in the subject area.

[skisso]

Helloo!

I was wondering if there was a quicker way of doing probability questions without drawing tree diagrams because they are really time consuming and messy.

Thanks heaps

[RuiAce]

Helloo!

I was wondering if there was a quicker way of doing probability questions without drawing tree diagrams because they are really time consuming and messy.

Thanks heaps

Personally, I've somewhat developed the ability to visualise the important branches of a tree diagram in my head.

If they start throwing you off with those "with or without replacement" questions then you might not have much of a choice. Having said that, you don't lose marks for omitting the tree diagram, so you can always just draw a draft tree diagram (or even just 1/4 of it) on the question booklet to use as a reference. You're also quite limited in 2U because you don't have access to perms and combs.

If there's any specific problems causing you grief, please provide them.

[skisso]

Personally, I've somewhat developed the ability to visualise the important branches of a tree diagram in my head.

If they start throwing you off with those "with or without replacement" questions then you might not have much of a choice. Having said that, you don't lose marks for omitting the tree diagram, so you can always just draw a draft tree diagram (or even just 1/4 of it) on the question booklet to use as a reference. You're also quite limited in 2U because you don't have access to perms and combs.

If there's any specific problems causing you grief, please provide them.

Okk thank you
I was doing this question when I wrote this:

[RuiAce]

Okk thank you
I was doing this question when I wrote this:

Yeah, I'm afraid that one is a bit more of a tough one.

With perms and combs at your side, this would be much easier. But because we cannot do that in 2U, the only 'shorter' way I can think of would be this.



Note, of course, 'shorter' is debatable here. It's up to you if you'd take this suggestion on board.

[skisso]

Yeah, I'm afraid that one is a bit more of a tough one.

With perms and combs at your side, this would be much easier. But because we cannot do that in 2U, the only 'shorter' way I can think of would be this.



Note, of course, 'shorter' is debatable here. It's up to you if you'd take this suggestion on board.

Yeah I guess its easier to do the combinations like that with more practice
Thank you