[f1mad]

(Original post by Oromis263)
Just finished the January 2007, it's definitely worth taking a crack at, I felt it had a fair few challenging components, but also really showed a lot of applications of the core elements of the exam.

Just had a quick glance; it definitely tests application. It's a pretty nice paper if you take the former into account.

[Mikeyyy!]

I really dislike proof by induction.
Can anyone outline the steps in order to do it? So far i'm thinking this:
1. Try for an integer to show it's true (usually n=1)
2. If true, assume true for n=k.
3. Try n=k+1. Is this where you input k+1 into n, and add k+1 to the end. Rearrange and hope you get the same as just replacing n with k+1?

Sorry if this is confusing, really struggling with proof by induction.
Hoping to get and 80% aggregate over this and FP3 in the next few weeks!!

[ebmaj7]

(Original post by Mikeyyy!)
I really dislike proof by induction.
Can anyone outline the steps in order to do it? So far i'm thinking this:
1. Try for an integer to show it's true (usually n=1)
2. If true, assume true for n=k.
3. Try n=k+1. Is this where you input k+1 into n, and add k+1 to the end. Rearrange and hope you get the same as just replacing n with k+1?

Sorry if this is confusing, really struggling with proof by induction.
Hoping to get and 80% aggregate over this and FP3 in the next few weeks!!

I tend to do:

1. Assume true for n = k.

2. Then "for n = k+1".

3. You're going to use the assumption you've made somewhere in proving it works for n = k+1.

4. I tend to make a note in pencil on the corner of the page of what I'm aiming for and then do some maths to try and "fudge" that result if I'm struggling.

5. Then "for n = 1".

6. Finally end by saying "P(n) implies P(n+1) and P(1) is true.

[Dangerous Theory]

I struggle sometimes with questions that want, say, the sum of alpha cubes (not the sum of alphas, cubed). Alpha squares is fine , but i don't know a rule for cubes, and I end up with long expansions and trial and errors for like 2 marks (which implies it should be straightforward).

[member910132]

(Original post by Dangerous Theory)
I struggle sometimes with questions that want, say, the sum of alpha cubes (not the sum of alphas, cubed). Alpha squares is fine , but i don't know a rule for cubes, and I end up with long expansions and trial and errors for like 2 marks (which implies it should be straightforward).

If you are looking for something like this for the roots cubed
then I don't think there is one to the best of my knowledge however if a cubic equation had roots v, n and m then
can be written as and the same equation can be set up with n and m. Now because they all equal 0 we can add all the three questions to give us 0 hence we get:
which may look useless now but when you get a question you should note that a is often 1 and you have already worked out for a previous part of the question and it becomes quite easy.

I can't remember which paper it was but one in particular really grilled the above issue, they asked for the value of the sum of the roots to the 5th power each eg,. I don't want to explain the method because I think it would be better if you tried it for your self.

On the issue of argand diagrams, I have noticed that sometimes the last 2-3 marker where they expect us to use some trig or basic geometry to workout some length or angle can get time consuming and tricky but I think these general rules might help out. I am not 100% on the second one but I can confirm the first holds:

1. If z1 and z2 are points on a argand diagram then the point (z2-z1) is the 4th vertex of a parallelogram with sides O, (z2,z1 and z2-z1)

2. The second rule is exactly the same as the firts but with (z1+z2) replacing (z2-z1) - but am not 100% sure on this.

Once we know it's a parallelogram then it makes it easier to find some angles or lengths I think.

Edit: Also it is worth noticing that just as a quadratic has imaginary roots if , in a cubic equation if the three roots squared is less than 0 then that means that there is at least 1 imaginary root and if all the coefficients are real then there must be complex conjugates in which case there must be at least 2 imaginary roots.

[Dangerous Theory]

(Original post by member910132)
If you are looking for something like this for the roots cubed
then I don't think there is one to the best of my knowledge however if a cubic equation had roots v, n and m then
can be written as and the same equation can be set up with n and m. Now because they all equal 0 we can add all the three questions to give us 0 hence we get:
which may look useless now but when you get a question you should note that a is often 1 and you have already worked out for a previous part of the question and it becomes quite easy.

I can't remember which paper it was but one in particular really grilled the above issue, they asked for the value of the sum of the roots to the 5th power each eg,. I don't want to explain the method because I think it would be better if you tried it for your self.

On the issue of argand diagrams, I have noticed that sometimes the last 2-3 marker where they expect us to use some trig or basic geometry to workout some length or angle can get time consuming and tricky but I think these general rules might help out. I am not 100% on the second one but I can confirm the first holds:

1. If z1 and z2 are points on a argand diagram then the point (z2-z1) is the 4th vertex of a parallelogram with sides O, (z2,z1 and z2-z1)

2. The second rule is exactly the same as the firts but with (z1+z2) replacing (z2-z1) - but am not 100% sure on this.

Once we know it's a parallelogram then it makes it easier to find some angles or lengths I think.

Edit: Also it is worth noticing that just as a quadratic has imaginary roots if , in a cubic equation if the three roots squared is less than 0 then that means that there is at least 1 imaginary root and if all the coefficients are real then there must be complex conjugates in which case there must be at least 2 imaginary roots.

Thank you for the explanation of equations, both about sum of cubes, and the roots. Very helpful! So much stuff is omitted from the FP2 PDF!

[member910132]

Does anyone know whether we need to be able to prove the differentials of inverse trig functions and prove the integral found in the formula book.
I know we can quote them with proof but are we going to get asked a question like prove

[Oromis263]

(Original post by member910132)
Does anyone know whether we need to be able to prove the differentials of inverse trig functions and prove the integral found in the formula book.
I know we can quote them with proof but are we going to get asked a question like prove

It's quite possible, but it doesn't hurt to learn it! It may even boost confidence/understanding etc if you learn how to derive something properly. I have myself.

[Dangerous Theory]

(Original post by member910132)
Does anyone know whether we need to be able to prove the differentials of inverse trig functions and prove the integral found in the formula book.
I know we can quote them with proof but are we going to get asked a question like prove

Honestly? I would put little past them. The range of questions they come up with is pretty expansive. These papers seem to really test your ability as a mathametician in general, and not just the particular syllabus. Some of the things they ask are so odd and obscure.

[Iepnauy]

(Original post by Dangerous Theory)
Honestly? I would put little past them. The range of questions they come up with is pretty expansive. These papers seem to really test your ability as a mathametician in general, and not just the particular syllabus. Some of the things they ask are so odd and obscure.

Completely agree with you =/. With a couple of days until the exam I'm still not getting decent marks . It's becoming worrying and stressful.

[Dangerous Theory]

(Original post by Iepnauy)
Completely agree with you =/. With a couple of days until the exam I'm still not getting decent marks . It's becoming worrying and stressful.

I know right? There are always a good few questions that I don't have a problem getting full marks on, but at the same time there are ones that I have never come across before and they just stump me. Usually, if I spend a few hours on a paper I can start to answer MOST things, but I dread to think what it'll be like in the exam. This is the paper I think most of all, requires much more time, because I have to REALLY think about everything I know so far and how it can be applied.

[f1mad]

I'm pretty confident.

The latter end of the De Moivre's questions throw off me though, somewhat.

I did the Jan 2012 paper today, wasn't too bad as I expected.

[Oromis263]

(Original post by member910132)
Does anyone know whether we need to be able to prove the differentials of inverse trig functions and prove the integral found in the formula book.
I know we can quote them with proof but are we going to get asked a question like prove

The June 2009 paper requires you to prove the arctanh equation. Just doing it now. EDIT: Sort of, it's a bit different I think but it was actually extremely simple.

[member910132]

(Original post by f1mad)
I'm pretty confident.

The latter end of the De Moivre's questions throw off me though, somewhat.

I did the Jan 2012 paper today, wasn't too bad as I expected.

Mind if I ask what you got ?

[member910132]

Might be worth memorising all of these.

When I write it equals something I mean the graph looks just like that. eg sinh x looks just like tan x but with no asymptotes. cosh x looks just like x^2 +1.

This was posted from The Student Room's iPhone/iPad App

[f1mad]

(Original post by member910132)
Mind if I ask what you got ?

71/75 .

[member910132]

(Original post by f1mad)
71/75 .

59 was needed for an A* so you probably got full UMS.
Source:
http://store.aqa.org.uk/over/stat_pd...OUND-JAN12.PDF

Edit: where did you loose the marks, I thought the last question was quite unclear tbh

[Oromis263]

(Original post by f1mad)
71/75 .

That's a nice score where did you drop marks? Reviewing that paper, it's actually relatively simple. I blame the fact that I had two exams prior to FP2 on the same day that I used all my energy on. Ah well, should beast it this time, I've got no exams around it at all.

[Iepnauy]

Can someone help me with the June 2010 paper?
Question 4 b ii.
I don't see how they've done it, even with the mark scheme, how did they get +30? :/

[f1mad]

(Original post by member910132)


59 was needed for an A* so you probably got full UMS.
Source:
http://store.aqa.org.uk/over/stat_pd...OUND-JAN12.PDF

Edit: where did you loose the marks, I thought the last question was quite unclear tbh

(Original post by Oromis263)
That's a nice score where did you drop marks? Reviewing that paper, it's actually relatively simple. I blame the fact that I had two exams prior to FP2 on the same day that I used all my energy on. Ah well, should beast it this time, I've got no exams around it at all.

Yeah, it was the last question. This is my first time sitting it .

EDIT: It would be 100 UMS. You needed at least 66 raw mark to get 100 UMS.