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

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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 ?

Reply 421

Dapperblook22

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.

Reply 422

mickel_w

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%

Reply 423

32908

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???

Reply 424

1/2(p^2-p)

Original post by Mowerharvey

Cos x = 13/35 for me

i got the same as you

Reply 425

df97

Original post by Adam_98

I have pretty much all the same answers! :biggrin:

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?

(edited 7 years ago)

Reply 426

KB_97

Original post by Mowerharvey

Cos x = 13/35 for me

Same I got this. Please someone clarify that this is correct

Reply 427

mickel_w

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..

Reply 428

-jordan-

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.

Reply 429

CaoimheMee

Can any one remember the first question??

Reply 430

spmenz123

Last year C4 was 63 for an A*. I think this may be lowered to 62/61, anyone agree?

Reply 431

mickel_w

Original post by KB_97

Same I got this. Please someone clarify that this is correct

i got this too.

Reply 432

C0balt

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

Reply 433

Dapperblook22

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?

Reply 434

mertyuiop

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

Reply 435

125_

Original post by lIoydy

Yeah something like that.. I hope that's what I put

Yes!

Reply 436

tanyapotter

does anyone remember the two parametric equations that you had to find dy/dx for?

Reply 437

df97

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