AQA Further Maths FP2 [Exam discussion thread] - Tuesday 16th June 2014

Pretty sure the identities are in the formula book/can be found by dividing through by cosh and sinh etc? But it comes out as:
cosh²x - sinh²x = 1 therefore
1 - tanh²x = sech²x
coth²x - 1 = cosech²x therefore
cosh2x = 2cosh²x - 1
cosh2x = 2sinh²x + 1
(hopefully those are actually right!) along with sinh2x = 2sinhxcoshx I can't think of any others?

There's very little that's not in the formula book off the top of my head, other than sinhx = e^x - e^-x and coshx = e^x + e^-x...

$\cosh^2 x - \sinh^2 x \equiv 1$
$\sinh(A+B) \equiv \sinh A \cosh B + \sinh B \cosh A$
$\cosh(A+B) \equiv \cosh A\cosh B + \sinh A\sinh B$

Use the circular identities and replace cos with cosh and sin with sinh, use Obsborne's rule to get the signs right(where there is a $\sin^2$, replace with a $-\sinh^2$).

Pretty sure the identities are in the formula book/can be found by dividing through by cosh and sinh etc? But it comes out as:
cosh²x - sinh²x = 1 therefore
1 - tanh²x = sech²x
coth²x - 1 = cosech²x therefore
cosh2x = 2cosh²x - 1
cosh2x = 2sinh²x + 1
(hopefully those are actually right!) along with sinh2x = 2sinhxcoshx I can't think of any others?

There's very little that's not in the formula book off the top of my head, other than sinhx = e^x - e^-x and coshx = e^x + e^-x...

Do you have to know the double angle stuff? it's not in the formula book, but yeah you can just use Osborne's rule with the normal trig double identities and derive them

Beat me to it. I think the top ones are correct, but don't have time to check. The bolded ones are incorrect.
$\sinh x = \frac{1}{2}(e^{x} - e^{-x}), \cosh x = \frac{1}{2}(e^x + e^{-x})$

Lol just realised you can divide by cosh and sinh to get the other ones, thanks. btw, that's supposed to be over 2

They come in handy a lot in integration, but I think at A-level they always ask you to derive the specific expression required from first principles(using exponentials). Doesn't hurt to know them just in case and I'm not sure. Yep.

Oops you wouldn't believe how often I forget those halves, thanks!

Remember the halves when you derive similar expressions for sin and cos in exponentials too.

When do you do that?

Using complex numbers to prove trig identities.
Do $z+z^{-1}$ and $z -z^{-1}$ ring any bells? Where $z=e^{i\theta}$.

Chapter 3...method of differences and proof by induction.

The textbook is pretty darn poor.

I'll just keep practicing but even then what if they give us an induction type we've never done? If that's even possible.

Agreed.

I don't think they're allowed to set difficult method of differences and induction questions. Method of differences they'll always give you the function and get you to sum the series. For induction they only ask you to sum a series or prove divisibility or de Moivre's theorem.

Which years had the hardest papers?

Judging by the grade boundaries (62 for an A*) June 11 was pretty bad
edit Jan 12 as well was only 59 for a A*

Thanks, I'll do them. Have you done any of the old papers, pre-2010? are they worth doing or are they too easy?

What is the concluding statement for proof by induction?

I always wrote True for n=1, n=k and n=k+1. Therefore true for all integers.

But my teacher marked this wrong? (he said you don't write n=k) What should you write to give the examiner no complaints at all