OCR Core 4 - Fri 11th June 2010.

a = 4i + 3j - 2k and b = -7i + 5j + 4k
is a.b like 4x-7 + 3x5 + -2x4 here?? i thought its between the direction vectors? not position vectors
and i still dont understand how to find the angle from my first answer?

and for the second one ive got dx = 1/2 u, so i know to swap the dx with this 1/2 u but just dont understand what to do with the (4x-8)(2x-5)^7 part, i realise the (2x-5)^7 becomes u^7 but what about the 4x-8? thanks

does anyone have jan 2010 paper? i've got the mark scheme but no paper

gonna need high ums for A* and kinda need it lol gl me.

just learnt how to integrate cos^2(x) and revising vectors now.

glgl hope it turns out well for everybody.... :]

Does anyone know where I could find OCR Core 4 June 2005 Mark Scheme?

I can't find it anywhere online!

Cos^2x can be integrated using cos2x. But do you know why you can take 1/2 out of the integration?

how do you integrate cos²2x ??

As I've never seen the one with cos4x before (it looks complicated) here's how I derive it.

You have the trig identities:

sin²x+cos²x=1

and your formula for cos(2x)=cos²x-sin²x

Then you sub in sin²x from your first identity to your second which gives:

cos2x=2cos²x-1

so cos²x=1/2(cos2x+1)

(I think. Don't have a calculator to check From memory you can do the same with sin²x, except it's sin²x=1/2(sin2x-1)).

When you integrate this you can just take 1/2 out yeah.