WJEC C4 June 2011

How did you all find it ?

These are my answers..

1 a) -3/ (x+2) ^2 + 1 / (x+3)

b)0.246

2a) Gradient was 2, gradinet of normal was -1/2.
Equation was 2y + x =7

3a) 0, 180, 35.26, 215.26

b) 50.21, 309.79, 25.53, 123.95

4 a) Show the tangent...

5a) Coordinates

b) i had 18 pi

6) 1 - 6x+ 27x^2

7a) forogt

b) 0.24

8 a) dn/dt = kn

b) A is e^c

c) When t=20. N=233

9a) 7

9b) Mew = -3.2
Landa= 0.4


10 (3x-2)^2 < 0


Same answers?

A few questions:

For the vectors question, I managed to get the right values for lambda and mu but I messed up the rest of the question - any marks?

In the second question, do you think there are any follow through marks if you get part of the question wrong?

I didn't think the paper was too bad. I forgot to incude x = 0 or 180 in the second question when I canceled my $tan(x)$'s, but that would only have lost me one or two marks. I forgot how to do the binomial expansion when it was one thing minus another... So I just did the expansion for the first part, and then did it for the second, and subtracted my result for the first from the second. Does anyone know if that's a valid way of doing it or not?

The proof was pretty standard... the vetor question wasn't too bad, either. Paramatric and Implicit differentiations where standard, as was the integration by parts and integration by substitution.

I didn't really like getting a zero value for the constant with the partial fractions... but apart from that, it was OK. the $Rcos(\theta - \alpha)$ question was OK... So was the volume of revolution. I think that the geometric representation was to say that it was a sphere with radius 3? But I'm not 100% sure.

It would be good if someone couple upload a copy of the paper, so we can jog our memories :P

The tanx=0 almost stomped me when I realised I divided (Extremely forbidden by law for finding solutions) so had to write on a new booklet to show it xD. integration was nice. The 0 in one of my partials made me check twice! I recrossed multipled and found it went to the original function so it was fine xD

1) same 2) same 3) I had 0,180 and 35.26, you left out -35.26 (144.64?) and your other value wasnt in range.
4) Assume we had the show q correctly.
5) had 36pi and interpreted as the volume of a sphere (plug the calculator to the volume of a sphere with your radius found and gives the same number)
6)did you forget to multiply the first expansion by 4?
7) a) was integration by parts of xsin2x b) same
8)same
9)b) I had mew same but lambda, I had a minus answer to yours
10) same

Right the vector one: Everyones got different answers so lets sort this out:

The line passes through the point with position vector 8i + 3j - 7k and is parallel to the vector 2i + j + 2k.

i) Write down the vector equstion of line L1?
ii) the line L2 has vector equation r = 4i + 7j + 5k + mew(-2i + j + 3k)

Show they dont intersect?

I got the vector eqn as r = 2i + j + 2k + lambda(8i + 3j + 7k) I think, although I've just realised I maybe should have turned the 2i + j +2k around so it was all minuses? I don't know
Then I got lambda = -1 and mew = -3 if I remember correctly, then subbed into the k eqn, one side was -4 and the other was -5 so they don't intersect

Oh right. I thought you had to work out the vector equation. So the position vector is the vector inside the bracket? Ahh ****ttt

Sorry I had a minus too. The question is. The line passes through the point with position vector 8i + 3j - 7k and is parallel to the vector 2i + j + 2k.

i) Write down the vector equstion of line L1? What is that ?

And 6) No i didnt. I multiplyed by 4. Anyone else have the same answer as me in the expansion: 3 + 10x -29x^2

Your expansion is correct

Wow you've just made me feel so much better thought I'd totally screwed up this paper. I have many of the same answers as both of you but I'm going to list them all anyway.

1.a) -3/(x+2)^2 +1/(x-3)
b) 0.246 (3dp)

2. gr of normal = -1/2
equation y-3=-1/2(x-1)

3.a) okay i messed this up :/
b) 25cos($-73.74)
23.53' or 123.95' $= theta

4.a) show equation
b)i) A(2root3, 0) B(0,8)
ii) show length

5.a) okay I've got this question different too...
A(-3,0) B(3,0) C(0,3)
b)i)162pi = 508.94 (2dp) :/
ii) what?

6. 3 + 2x -29x^2 +... Valid for |x|< 1/3

7.a) -x/2.cos(2x) + sin(2x)/ 4 + c

8.a) dn/dt = kn
b)show equation .. i used t= 0 and n=A so work out c and get the equation
c)i) show k
ii)233.031 (3dp)

9.a) a=7
b)i) r=8i +3j -7k + landa ( 2i +j +2k) ???
ii) can't rember what i got landa and mu as but got lhs as -4 and rhs as -5 therefore don't intersect

10. (2x-3)^2 <0 contradiction etc


Right hope this helps

Sorry I had a minus too. The question is. The line passes through the point with position vector 8i + 3j - 7k and is parallel to the vector 2i + j + 2k.

i) Write down the vector equstion of line L1? What is that ?

And 6) No i didnt. I multiplyed by 4. Anyone else have the same answer as me in the expansion: 3 + 10x -29x^2