AQA Mathematics GCE, AS, 27th May 2010 MFP1

For those of us sitting the Further Pure 1 exam this Thrusday: good luck!

I shall be posting pictures of the paper & solutions when I get hold of them, unless someone else gets there first :P

Reply 1

Sawwah

8

yeah i didnt do the core 2 but apparently our teacher said it was really hard! im nervous now!!!

Reply 2

rob...

OP

I really should be revising right now, but I really cannot think striaght!
It's like the more I want to revise, the less I do :biggrin:

Reply 3

*A_S_H*

am trying to revise for it now
and its just really hard wen it comes to doing the practice papers :frown:

having problems with doing the trig general equations in the past papers although they appeared so straight forward in the textbook exercise

Reply 4

Septimoose

I actually found Pure Core 2 to be really easy... and the Pure Core 1 that I re-sat.

However, I have no chance in Further Pure 1. It's on the same day as Physics and Statistics, and I haven't revised for it... In summary, I'm screwed.

Reply 5

rob...

OP

*A_S_H*

am trying to revise for it now
and its just really hard wen it comes to doing the practice papers :frown:

having problems with doing the trig general equations in the past papers although they appeared so straight forward in the textbook exercise

Hey again ASH :smile:

It's a load of BULL what they do in the past papers...
I learnt the general solution to sine graphs, with the 180n +(-1)^n(theta) , then I was told that in the mark schemes you need to substitute n=2m & n=2m+1 to get two general solutions! That's not simplification at all, it's just further complicating things...

Reply 6

rob...

OP

Septimoose

I actually found Pure Core 2 to be really easy... and the Pure Core 1 that I re-sat.

However, I have no chance in Further Pure 1. It's on the same day as Physics and Statistics, and I haven't revised for it... In summary, I'm screwed.

I'm hiding from stats until June next year :woo:

I'm hoping to get 100% on PC2, but the exam took my quite a while to finish so I considered it to be difficult... I posted my solutions and the questions to pure core 2 on my forum by the way, post #301-303 on page 16!

Reply 7

AshDUOL

I've got FP1 on Thursday, decided to resit it just cos it's so early and out of the way. Didn't resit P2 so don't know how bad that was :frown:

Revision for FP1 starts tomorrow, good luck to you all :biggrin:

Reply 8

rob...

OP

AshDonson

Revision for FP1 starts tomorrow, good luck to you all :biggrin:

That's not the attitude! REVISION STARTS NOW! or maybe in a few hours time... :yep:

Reply 9

*A_S_H*

rob...

Hey again ASH :smile:

It's a load of BULL what they do in the past papers...
I learnt the general solution to sine graphs, with the 180n +(-1)^n(theta) , then I was told that in the mark schemes you need to substitute n=2m & n=2m+1 to get two general solutions! That's not simplification at all, it's just further complicating things...

hi
yeah exactly so confusing
Rob can you please check this out, you seem intelligent i hope you can help with this step by step diffrential equation using euler's formula
http://www.thestudentroom.co.uk/showthread.php?p=25410536#post25410536

Reply 10

rob...

OP

OK, so our first coordinate is (0 , 1), and were looking for the (0.4 , __):
y(n+1) = y(n) + hf(x(n)) where f(x(n)) is the derivative. THUS y(n+1) = 1 + 0.2(1) = 1.2
Now we have our first approximation: (0.2 , 1.2)

Now you need to preform Euler's method once more to find an aproximation at x = 0.4
So: y(n+2) = y(n+1) + hf(x(n+1)), where f(x(n+1)) is the derivative. THUS y(n+2) = 1.2 + 0.2(root[1+0.2^2]) = 1.404
Now we have our approximation of y at x=0.4: (0.4 , 1.404)

That table method's nice, I remember by teacher telling us about it once but i never bothered listening :frown:

I think Ill take a look at conics now!

Reply 11

mickyM

What does this matrix represent? I can't get it out...

[ 1 root(3)]
[ -root(3) 1]

Reply 12

rob...

OP

mickyM

What does this matrix represent? I can't get it out...

[ 1 root(3)]
[ -root(3) 1]

It's a rotation of 60 degrees clockwise, folowed by an enlargement of scale factor 2. Would you lke me to explain why??

OK, well when I first saw the matrix, what attracted my attention the most was the '-' in the bottom left corner. It's because of this that i realised it was a rotation, the matrix for which is:

cosX -sinX
sinX cosX

Since the top left, and bottom right corners are bother exactly the same, they will have exactly the same value, e.g. (1)
The next thing I though was what angles correspond to root(3) & 1; the answer of course is 30 or 60 degrees {you should know that cos60 = 1/2 & sin60 = root(3)/2}.

The next step was to realise that the -sin was in the wrong place, which implies a clockwise rotation, of 60degrees, or of course an anticlockwise rotation of 300degrees. Then to compensate for the missing 1/2 the matrix must also be an enlargement too, namely of scale factor 2.

Yes please (:

OP

One thing to remember about combinations of transformations, is that the second transformation comes first in the order of multiplication, folowed by the first. This is a common mistake, and one that I've made quite a few times too! So don't be fooled :wink:

Reply 15

kais58

could you give me a hand on this matrix,
1,3^0.5
3^0.5,-1

I think its a refelection in y axis then rotation 60degs anticlockwise. you?

Reply 16

rob...

OP

kais58

could you give me a hand on this matrix,
1,3^0.5
3^0.5,-1

I think its a refelection in y axis then rotation 60degs anticlockwise. you?

It's a reflection in the line y=tan(30), folowed by an enlargement of scale factor 2 I believe, one moment...

The top left and bottom right corners are different, which leads to reflection in the line y=tan(x). This has a matrix:
cos(2x) sin(2x)
sin(2x) -cos(2x)

When x=30, cos(2x) = (1)/2
When x=30, sin(2x) = (3^1/2)/2
If you enlarge this matrix by scale factor 2, the '/2's cancel out, thus giving you your matrix. Your method may work too though, but I'd have to put a bit more thought into that one!

Reply 17

kais58

how did you work that out? btw I had a sub for matrices and gen solns who failed completely :smile:

EDIT: where are those general matrices from?
ie
cos(2x) sin(2x)
sin(2x) -cos(2x)

Reply 18

rob...

OP

OK

Well If you look in the formula book: http://www.mathsnetalevel.com/download/AQA_formula_book.pdf These were in your formula book last year (page 16 for edexcel), so i presume they still will be in this new exam?
on page 6 are the matrices for matrix transformations.

The main hint that a matrix gives you about what type it is, it the place of the negative sign(s)
If the top left and bottom right are the same, then it's generally a rotation
If the bottom left and top right are the same, then it's probably a reflection in y=tan(x)

Then next thing to do is look at the angles, I presume you know that cos60 = 1/2, cos30 = root(3)/2? & sin60 = root(3)/2, sin30 = 1/2?

Reply 19

kais58

oh yeah, I forgot the formula book is actually useful in Fp1...

AQA Mathematics GCE, AS, 27th May 2010 MFP1

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