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# AQA A2 Mathematics Pure Core 4 MPC4 - 17th June 2016

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All the answers I can remember putting. No idea if any of them are correct so feel free to comment:

A= -5/2
B= 9/2

-1+7X-22X^2/3

theta = 99.6° , 260.4°
(Rejecting cos0 = 1 as solutions are outside the range)

-3X +2+9/(whatever the factor was)

9/2ln3-69/2

181grams
330days

P=2/15

R=1/3

S=4/15

CosX=1/5

(2,0,-1)

C = (8,-18,-31)
D = (-4,18,29)

e^4/2

sin3x-3xcos3x = ......+pi

Posted from TSR Mobile
Thanks bud. People like you amaze me. For the binomial one when you say 22X^2/3 , does this also mean 22/3*X^2 ?
2. (Original post by Pingu7)
why FP2 for the last question?
Standard integrals are part of the FP2 spec. The last question was essentially deriving a standard integral.
3. (Original post by -jordan-)
Around 300 definitely correct. It started at 10 grams and after 100 days it was down to 8. So in 100 days it's at roughly 80% of the original value. So 10*(0.8)^3=5.12 (to the power of 3 as it's the half life is approximately 100 days x 3) which is approximately half of the original 10.
but the rate of decay isn't constant? So it won't take the same amount of time for it to decay from say 100% to 80% as it will for it to decay from 80% to 60%
4. (Original post by -jordan-)
2tanϴ = 3x

Differentiating it implicitly

2sec^2ϴ * (dϴ/dx) = 3

(dϴ/dx) = 3/(2sec^2ϴ)
= 3/(2(1+tan^2ϴ))
= 3/(2+2tan^2ϴ)
= 6/(4+4tan^2ϴ)

And from the question tanϴ=3x/2
Therefore tan^2ϴ = 9x^2/4
Putting this into (dϴ/dx) gives

(dϴ/dx) = 6/(4+4(9x^2/4))
= 6/4+9x^2 as required
I got to k=3 exactly the same method as you but then don't understand how it ended up at 6???
5. (Original post by Mowerharvey)
Cos x = 13/35 for me
i got the same as you
All the answers I can remember putting. No idea if any of them are correct so feel free to comment:

A= -5/2
B= 9/2

-1+7X-22X^2/3

theta = 99.6° , 260.4°
(Rejecting cos0 = 1 as solutions are outside the range)

-3X +2+9/(whatever the factor was)

9/2ln3-69/2

181grams
330days

P=2/15

R=1/3

S=4/15

CosX=1/5

(2,0,-1)

C = (8,-18,-31)
D = (-4,18,29)

e^4/2

sin3x-3xcos3x = ......+pi

Posted from TSR Mobile
I have pretty much all the same answers! except I think i might've put 69/2-9/2ln3 and also i couldn't do last vectors question and think i butchered vectors part a, got like 4/rt390 lol. For the "....." on last bit does -18x/(4-9x^2)^2 look familiar?
7. (Original post by Mowerharvey)
Cos x = 13/35 for me
Same I got this. Please someone clarify that this is correct
8. can someone post a written solution for the half life, because i found a new constant K since it was a different element decaying and worked from there to get 600 days..
9. (Original post by mickel_w)
but the rate of decay isn't constant? So it won't take the same amount of time for it to decay from say 100% to 80% as it will for it to decay from 80% to 60%
You loose the same percentage in the same time period.
10. Can any one remember the first question??
11. Last year C4 was 63 for an A*. I think this may be lowered to 62/61, anyone agree?
12. (Original post by KB_97)
Same I got this. Please someone clarify that this is correct
i got this too.
13. (Original post by Pingu7)
why FP2 for the last question?
(Original post by Dapperblook22)
Standard integrals are part of the FP2 spec. The last question was essentially deriving a standard integral.
What he said
14. I think worst case scenario I got 68/75, as I did not get part C of the vector question in the end and I missed writing the angle in it's simplest form... UMS predictions?
15. (Original post by ThusSpakeAlex)
were 5/3 and 1/3 your lamba values?
I thought -1/3 and -5/3 but im not sure. The quadratic i solved was something like 35x^2-70x+35=140/9
16. (Original post by lIoydy)
Yeah something like that.. I hope that's what I put
Yes!
17. does anyone remember the two parametric equations that you had to find dy/dx for?
18. (Original post by CaoimheMee)
Can any one remember the first question??
partial fractions and binomial expansion, i think answers are as follows:
A=-5/2 B=9/2
-1+7x-22/3x^2
not sure on limit, think some people have something like mod x < 4/3
19. (Original post by tanyapotter)
does anyone remember the two parametric equations that you had to find dy/dx for?
x=[4+e^(2-6t)]/4
y=e^3t/3t or something
20. Does anyone remember what info they gave you in the half life question?

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