Edexcel A2 C4 Mathematics June 2016 - Official Thread

When doing an integration question that asks for the region R for example. If you area is negative, is it ok to leave it as negative??

First you deal with the $x$

So you would have

$0 < 2x < 720$

Then if you're adding/subtracting anything

$-60 < 2x-60 < 660$

Then once you have your values you do it in the opposite order

so $\dfrac{(x+60)}{2}$

If its asks for the area of the region, then no - you need to give it as a positive answer.

Oh ok, so when should you leave it as negative?

When it asks you to integrate something without context. "Evaluate this integral" or "do this integral" or w/e.

Hi, I think the question attached is improper, if so why don't you carry out long division before finding the partial fractions?
Thanks

It is improper - however, it is accounted for by the 'A' term.

so do you do long division to find the A term?

Proceed as normal - multiply both sides by (x-1)(x+2). Work out B and C first and then you should be able to work out what A is after that.

Thanks, very strange because on some questions you have to do long division first, why is it different here?

Thanks, very strange because on some questions you have to do long division first, why is it different here?

I do not know, sorry

Another way of looking at it (without long division) is to use a tricks like so:

$(x-1)(x+2) = x^2 + x -2$

$\frac{2x^2+5x-10}{x^2 + x -2}$ =$\frac{(2x^2+2x -4) + (3x-6)}{x^2 + x -2}$ as we wanted to find a multiple of the bottom on top, and then add the rest of the fraction that isn't in the first.

$= 2 + \frac{(3x-6)}{x^2 + x -2}$ =$= 2 + \frac{(3x-6)}{(x-1)(x+2)}$

Not useful now but with integration it's useful, as the second fraction can be turned into something that looks like $\frac{kf'(x)}{f(x)}$ where k is some constant, which can be integrated to give klnmod(f(x)) and then the final term is a constant that can be integrated using partial fractions. This is, of course, useless in C4 but the more you know...

How does the c4 mark scheme work, for example on the question where they ask to find cartesian equation from parametric equations, if I work it out using a different method to the mark scheme but get the same answer, do I get all the marks?

Depends on if your method is mathematically sound or not. Though if you end up with the same answer chances are your Maths is correct. You would be fine.