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AQA FP1 Further Pure 1 17th May 2013 Official Thread Watch

1. Roots question: 2x²+3x-6 = 0 (A = alpha, B = beta)
a) Solve A+B and AB
-> A+B = -3/2, AB = -6/2 = -3
b) Show A³+B³ = -135/8
-> (A+B)³ - 3AB(A+B) = (-3/2)³-3(-3)(-3/2) = -135/8
c) Find equation with roots A+A/B² and B+B/A²
-> Sum of roots: A+B + (A/B² + B/A²)
= -3/2 + (B³+A³/A²B²) = -3/2 + ((-135/8)/(-3)²) = -27/8
-> Product of roots: (A+A/B²)(B+B/A²) = AB + (B/A+A/B) + (AB/A²B²)
= -3 + (A²+B²/AB) + (-3/(-3)²) -> A²+B² = (A+B)² - 2AB = (-3/2)² - 2(-3) = 33/4. Thus product roots = -3 + ((33/4)/-3) + (-3/(-3)²) = -73/12
So we get the equation: x²+27/8x-73/12 = 0, but we want INTEGER coefficients, so multiply by the lowest common multiple which is 24, hence 24x²+81x-146 = 0
2. (Original post by KBarney)
I thought thats what mine shows, doesnt what you put show a stretch in the x direction? Can you explian how you got to that awnser of the roots then?
Putting [1 0 0 3] means that the stretch is just 1 in the x-direction (i.e stays the same) and the 3 is the stretch in the y-direction as it was stretched 3x in y-direction and none across if that makes sense? and i put the answer to the roots question above.
3. (Original post by Annie_o)
Yeah exactly, same. Not sure how I'll do in M1 sometimes I do really well, others not so good. M2 is horrible which is why I needed fp1 to go well...

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Good luck on M2! M1 should be okay you just need to watch out for how they word stuff, I did the Jan 2013 as a mock and I hated how they worded that boat question but I got it in the end :P
4. anyone got the AQA D1 Jan 2013 paper?
5. (Original post by mathsRus)
anyone got the AQA D1 Jan 2013 paper?
No mark scheme though sorry.

EDIT: oh, I thought I'd attached it. Hold on....
Attached Images
6. AQA-MM1B-QP-Jan13.pdf (181.2 KB, 141 views)
7. (Original post by mathsRus)
anyone got the AQA D1 Jan 2013 paper?
(Original post by Vernish)
No mark scheme though sorry.

EDIT: oh, I thought I'd attached it. Hold on....
You attached the M1 one lol. :P

Here's the D1 one.
8. Woops!
9. What really put me off was the amount of answering space there was, especially in the summations question. I was only given 1.5 pages for the lot of the sigma summation questions, which is ridiculous.

10. (Original post by AlanDu)
What really put me off was the amount of answering space there was, especially in the summations question. I was only given 1.5 pages for the lot of the sigma summation questions, which is ridiculous.

Yeah I had to ask for extra paper for the summation as well, I don't get how they expect us to use only 2 pages to do all those questions it's just insane...
11. (Original post by matt242o1552)
Roots question: 2x²+3x-6 = 0 (A = alpha, B = beta)
a) Solve A+B and AB
-> A+B = -3/2, AB = -6/2 = -3
b) Show A³+B³ = -135/8
-> (A+B)³ - 3AB(A+B) = (-3/2)³-3(-3)(-3/2) = -135/8
c) Find equation with roots A+A/B² and B+B/A²
-> Sum of roots: A+B + (A/B² + B/A²)
= -3/2 + (B³+A³/A²B²) = -3/2 + ((-135/8)/(-3)²) = -27/8
-> Product of roots: (A+A/B²)(B+B/A²) = AB + (B/A+A/B) + (AB/A²B²)
= -3 + (A²+B²/AB) + (-3/(-3)²) -> A²+B² = (A+B)² - 2AB = (-3/2)² - 2(-3) = 33/4. Thus product roots = -3 + ((33/4)/-3) + (-3/(-3)²) = -73/12
So we get the equation: x²+27/8x-73/12 = 0, but we want INTEGER coefficients, so multiply by the lowest common multiple which is 24, hence 24x²+81x-146 = 0
I don't know how but for the sum of the roots I got -9. I got what you got for the product of the roots though. Grrr I'm really annoyed because those questions are my favourite ( should get 4 of the 6 marks though I'm hoping
12. Has anyone found a mark scheme yet?
13. (Original post by kingmango)
Has anyone found a mark scheme yet?
The earliest anyone can have access to the official mark scheme is teachers via e-AQA 10 days after the exam takes place (according to AQA's website.) So 27th May for us!

14. With all the answers I've seen on all comments, I believe I may have smacked d exam maybe 100%

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Given that sin(π/12) = (√3 - 1) / (2√2), you can take out the √2 and put it into a seperate fraction, then separate the remaining fraction to get:

(1/√2)(√3/2 - 1/2)

Which is the same as cos(π/4)(cos(π/6) + cos(2π/3)).
What I did was to use Sin(π/12) = Cos(π/2 - π/12)
Sin (
π/12) = Cos(5π/12)

But Cos(5
π/12) = Cos(π/6 + π/4)

But Cos(a+b) = Cos(a)Cos(b) - Sin(a)Sin(b)

Therefore,
Cos(
π/6 + π/4) = Cos(π/4)Cos(π/6) - Sin(π/4)Sin(π/6)

But Cos(
π/4) = Sin(π/4) and Cos(π/3) = Sin(π/6)

Cos(π/6 + π/4) = Cos(π/4)Cos(π/6) - Sin(π/4)Sin(π/6)

Cos(
π/6 + π/4) = Cos(π/4)Cos(π/6) - Cos(π/4)Cos(π/3)
= Cos(
π/4) [Cos(π/6) - Cos(π/3)]

But -Cos(
π/3) = Cos(2π/3)

Therefore,
Cos(
π/6 + π/4) = Cos(π/4) [Cos(π/6) + Cos(2π/3)] = Cos(5π/12) = Sin(π+12)

Therefore, a = 1/6 and b = 2/3.
16. (Original post by don_ayo)
What I did was to use Sin(π/12) = Cos(π/2 - π/12)
Sin (
π/12) = Cos(5π/12)

But Cos(5
π/12) = Cos(π/6 + π/4)

But Cos(a+b) = Cos(a)Cos(b) - Sin(a)Sin(b)

Therefore,
Cos(
π/6 + π/4) = Cos(π/4)Cos(π/6) - Sin(π/4)Sin(π/6)

But Cos(
π/4) = Sin(π/4) and Cos(π/3) = Sin(π/6)

Cos(π/6 + π/4) = Cos(π/4)Cos(π/6) - Sin(π/4)Sin(π/6)

Cos(
π/6 + π/4) = Cos(π/4)Cos(π/6) - Cos(π/4)Cos(π/3)
= Cos(
π/4) [Cos(π/6) - Cos(π/3)]

But -Cos(
π/3) = Cos(2π/3)

Therefore,
Cos(
π/6 + π/4) = Cos(π/4) [Cos(π/6) + Cos(2π/3)] = Cos(5π/12) = Sin(π+12)

Therefore, a = 1/6 and b = 2/3.
Are you allowed to use Core 4 trig identities in FP1?
17. (Original post by fizzbizz)
Are you allowed to use Core 4 trig identities in FP1?
I guess so

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18. (Original post by sohailkm96)
Good luck on M2! M1 should be okay you just need to watch out for how they word stuff, I did the Jan 2013 as a mock and I hated how they worded that boat question but I got it in the end :P
Thank you! Yeah I'm not overly worried about M1 it's normally just like one question that can be a bit nasty. M2 is horrible though

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19. hey guys in the trigonometry i made a very silly mistake by using both degree and 2kpi and in the limit question i made a wrong sign -2/x + 5/2x^2 instead of -2/x - 5/2x^2 and it leads to wrong answer 9/2. So how many marks will i lose for each of the questions ?
20. (Original post by mathsRus)
anyone got the AQA D1 Jan 2013 paper?
I did the AQA D1 paper this January got 88UMS. Which is pretty good considering I didn't bother revising much coz decision isn't proper maths. Why do you ask
21. (Original post by sohailkm96)
Yeah I had to ask for extra paper for the summation as well, I don't get how they expect us to use only 2 pages to do all those questions it's just insane...
I finished the summation question with about 3/5ths of the second page left

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