C4 (Not MEI) - Thursday June 21 2012, PM

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For 1. e) use the chain rule, so let $u= \sqrt x$

$\frac{dcos \sqrt{x}}{dx}=\frac{dcos \sqrt{x}}{du} \times \frac{du}{dx}$

For 3. a) think about two angles which you can subtract to get $\frac{\pi}{12}$, whose sines and coses you know. Then apply the addition formula. Ans:


You can use these same angles in the tan addition formula since you are finding tan of the same angle. (And you should be familiar with tan of the angles used above.)

I've got a way of doing b).
Look at page 204/205.

For $0< \theta< \frac{ \pi}{2}$, $\sin \theta < \theta < \tan \theta$.
In a) we found that

$\sin \frac{ \pi}{12} < \frac{ \pi}{12} < \tan \frac{ \pi}{12}$

or $\frac{ \sqrt 2(\sqrt 3 -1)}{4} < \frac{ \pi}{12} < 2 - \sqrt 3$

Multiplying by 12 yields the result they require.

8. b) Set the derivative form a) to 0 and then expand sin2t using the double angle addition formula. Then factorise and simplify a little.

Set cost and (2sint -1) to zero and solve for t in the required interval.
Other than the solution form a), there are only two others.

Thank you for your help!

1(e): I did do that! Although I didn't get the right answer will try it again, maybe the answer at the back of the book isn't right

Ah right I see what you mean about the last part, it's pretty much just x12 then?

8(b): "expand sin2t using the double angle addition formula." - 2sintcost -cost=0

What's the 'addition formula bit?

We just equate the solutions of the eq in 8b to the dy/dx formula of 8a and do some simplifying and get the values of 't' (int he range needed)?

I've got the answer in the back of the book for 1 e).

Yes.

The Double angle formula you need is $sin2x=2sinxcosx$
Its just a special case of the addition formula with $\alpha= \beta$

You do
$\dfrac{dy}{dx}=0=cost(2sint -1)$

For 2.
Once you find the derivative simplify using the double angle formula for sin (that I showed earlier) and you should end up with 6cost.
What do you know about the values cost can take?

For 7. b)
Alpha is just a particular value for the parameter.
Let t be alpha, then what values do y and x take?
Differentiate the Cartesian eqn with respect to x (Implicit differentiation is required).
Simply sub in your values to find dy/dx.

Now find the eqn of the normal by the usual method.

does anyone have the C4 june 11 past paper and mark scheme?

Im quite stressed for this exam!! Can anyone help me with writing a differential equation from a desciption given in an exam and also vectors.. the ones where they are perpendicular ... Im 'dotting them' with the wrong thing :/

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hope you're ready for tomorrow, why?
Because I am spendig a full day on the OCR book
Will be doing a mash of C4 and C3! (C4 all morning and C3 in the evening) my plan is to finish every single one of them damn questions in the misc section

Ps I shall need a ton of your help lol

How's the C4 coming along people?

Canny, canny. I'm concentrating on FP2 and S2 at the minute as I feel like I've got C4 nailed

Only thing I dislike with C4 is making the binomial expansion valid and what values x can and cannot be.

Excuse my ignorance, what does 'canny canny' mean?

Oh dear, didn't realise I'd used that.

Basically, it means 'well' in that context

Ah, ok.