Advanced Higher Maths 2011-2012 : Discussion and Help

Can anyone help me on these questions:

find the integral of 4x (1-x^2)^1/3 using the substitution 1-x^2=t^2

So guys, quick question.

If I have a question on integration by substitution, and it recommends a substitution, do I have to use that?

$\int \frac{x}{\sqrt{1-x^2}}dx$

They suggest $Let x = sin\theta$.

But I think it's easier to do $Let u = 1-x^2$

I can solve it both ways (and have done), I'm just wondering if they'd penalise you for using an alternate substitution, as long as you got to the same answer.

Thanks.

.

Yes you must use their substitution. It may have been intended for it not to be the easiest possible so as to increase the difficulty of the question.

P.S.: It's even easier if you substitute $u^2 = 1 - x^2$

I suppose it depends on the wording of the question?

Does anyone know about the rules on using different notation for differentiation. Personally I prefer Leibniz notation, but questions are usually given in functional notation.

Can I just use Leibniz for my working, and then give my answer like f'(x)=something, or do I have to use the notation provided in the question?

Thnks

Damn it. Ah well. Thanks. Silly SQA. I'd have thought they wouldn't mind students doing it an alternate way, since it shows that you're actually thinking.

Ah yes... I didn't think of that, actually. That does make a lot of sense. Either way's easier than their substitution, anyway.

I guess it doesn't matter, since I can do it either way, it's just me being awkward, really.

Results for the Unit 1 NAB today - 100%

Same

I think Maths education from algebra to calculus in secondary schools needs a serious overhaul in the way it is taught, I think...anyone agree? Here's my thought processes:

-I realised I was rearranging equations the wrong way in 5th year, I was taught it "change the side, change the sign" and that was it. I'd get stuck on a question and the reason I'd get it wrong was because of my algebra skills. I'd take a number over to the other side and be told "It's wrong because you just can't do that, it doesn't work that way!" but I was never told the way it works! It wasn't until I stumbled upon a YouTube video that showed someone rearranging an equation in it and he said "I can move this to the other side by dividing the entire equation by..." and it all clicked what I was ACTUALLY doing to the equation...had I been taught this, rather than a little "rule", I'd never have encountered any problems and my understanding of mathematics would have been much better.

-The mechanical approach to doing mathematical problems NEEDS to end. All through my life, even now at Advanced Higher, I am consistently told "Here's this problem, and this is how you do it." "Well why do you do THIS bit?" "You just do."
I'd like to know reasons as to why things work, or what I'm actually doing to something so that I can apply that same principle to something else when I encounter it. I'm sick of not being given reasons for stuff, such answers infuriate me!

-I still don't know what a logarithm is...all I know is its the inverse of an exponent...and again, the only reason I know what differentiation (and the entire field of differential calculus) is is because I've did my own research into it. Sure, you show us what to do, and we'll be able to do it; it doesn't mean we understand it. They need to stop teaching it like pupils are too stupid to understand mathematical concepts and start giving them some understanding, rather than giving them a hammer and telling them to hit away at a wall without saying why.

To be honest, thank **** for the internet, and resources like Khanacademy, or I wouldn't actually understand anything in the entire field of Mathematics, and would just be doing it because I've been told to do it that way.

Help on questions pleaseee, just cant get my head around how to do it.......

Sodium is freely filtered from plasma into the first part if the kidney tubule. The sodium concentration in the initial tubular fluid is therefore the same as plasma (140mM). A normal person filters fluid into the kindey ata rate of 0.125L/min. Sodium that enters the kidney tubule leaves by one of two routes, by reabsorption into the plasma or by excretion into the urine.
A subject excretes 1.3ml/min urine witha sodium concentration of 90mM (millimoles per llitre).

1.
Assuming the normal values given in the first paragraph, what is the rate (millimoles/min) at which sodium enters the kidney tubule. Answer to 2 decimal places.

2.
What is the rate at which sodium is excreted?

3.
What is teh rate at which sodium is reabsorbed by the kidney

4.
What percent of filtered sodium is reabsorbed?