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OCR (not OCR MEI) FP1 Answers June 2009

OCR (not OCR MEI) FP1 Answers June 2009

1. 958888125 (3 marks)

2. a = -3 and b = 2 (4 marks)

3. (i) 11 - 29i (2 marks)

(ii) 1 + 41i (2 marks)

4. -7/8 (4 marks)

5. (i) u3−25u2−70u−49=0u^3 - 25 u^2 - 70u - 49 = 0 (3 marks)

(ii) -70 (2 marks)

6. (i) 323 \sqrt 2 and −π4\frac{-\pi}{4} (2 marks)

(ii)(a) Circle centre 3 - 3i radius 3 root 2 (3 marks)

(ii)(b) Half line starting at 3 - 3i at angle pi/4 above real axis (3 marks)

(iii) Shade region outside this circle and between half line and the horizontal (3 marks)

7. (i) Show using method of differences (2 marks)

(ii) Show (2 marks)

(iii) Hence show sum (6 marks)

8. (i) Parallelogram with vertices at (0,0) (2,1) (3,1) (5,2) (3 marks)

(ii) S=(1011)S = \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix} (2 marks)

(iii) T=(1201)T = \begin{pmatrix} 1 & 2 \\ 0 & 1 \end{pmatrix}

Shear with x axis invariant in which the image of the point (1,1) is (3,1) (6 marks)

9. (i) determinant = 2a (a-1) (3 marks)

(ii) a = 0 and a = 1 (3 marks)

(iii)(a) yes infinite number of solutions as first 2 equations sum to produce the 3rd

(iii)(b) no because x + y + z cannot be both 2 and -1 so the equations are inconsistent (4 marks)

10. (i) u2=7u_2 = 7

u3=19u_3 = 19

Show ... (3 marks)

(ii) un=1+2(3n−1)u_n = 1 + 2 (3^{n-1}) (2 marks)

(iii) Induction (5 marks)

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Reply 1
Avatar for laurie344
laurie344
Nice, I think I did pretty well :smile:
Reply 2
Avatar for _MaThs_
_MaThs_
Can't you do the answers for AQA C3 Answers :biggrin:
Reply 3
Avatar for firepowa999
firepowa999
Mr M
OCR (not OCR MEI) FP1 Answers June 2009



(iii)(a) yes infinite number of solutions as first 2 equations sum to produce the 3rd

(iii)(b) no because x + y + z cannot be both 2 and -1 so the equations are inconsistent (4 marks)



Mr M would i get any marks for saying that there are no solutions (for part iii)b) without giving an explanation why?
How many marks will i loose in question 9 for finding the determinant as 2a^2-2a+1 snf therefore only getting a=1 as a solution??
_MaThs_
Can't you do the answers for AQA C3 Answers :biggrin:


Don't have the paper - sorry!
Reply 6
Avatar for 02bradan
02bradan
Was the circle centre (3,-3) treating it as (x.y)? For 6?
I got the second line being from the circles centre to the circumference (literally the radius) and no further...

I couldn't find Un in time! and so couldn't do the induction!!
strothersdale
How many marks will i loose in question 9 for finding the determinant as 2a^2-2a+1 snf therefore only getting a=1 as a solution??


2 or 3 if you include part (ii)
Reply 8
Avatar for laeof
laeof
14
Thankyou :smile:
What do you reckon the grade boundries on this paper would be?
Mr M
2 or 3 if you include part (ii)


Thanks a lot. The rest of the paper was okies i think. Much appreciated you posting the answers again :smile::smile:
02bradan
Was the circle centre (3,-3) treating it as (x.y)? For 6?
I got the second line being from the circles centre to the circumference (literally the radius) and no further...

I couldn't find Un in time! and so couldn't do the induction!!


I improved my answer here to make it easier to understand.
AshleyT
Thankyou :smile:
What do you reckon the grade boundries on this paper would be?


Not sure. I think it was slightly more difficult than Jan 2009.
Reply 12
Avatar for laeof
laeof
14
Mr M
Not sure. I think it was slightly more difficult than Jan 2009.

Yeah :smile:. Jan was 57 for an A so i think this one may be 56.
Thanks. How does the substitution for 5(i) work? I substituted them in but I couldn't get rid of the u^(3/2). I didn't do as bad as I thought when I had finished but I couldn't do 5 or the induction and I got some of the parts of the Argand diagram wrong.
gangsta316
Thanks. How does the substitution for 5(i) work? I substituted them in but I couldn't get rid of the u^(3/2). I didn't do as bad as I thought when I had finished but I couldn't do 5 or the induction and I got some of the parts of the Argand diagram wrong.


keep the u^1.5 part on one side and move the other stuff to the other side then square both sides
thank you! Mr M would i get any marks for saying that there are no solutions (for part q.9 iii)b) without giving an explanation why?
firepowa999
thank you! Mr M would i get any marks for saying that there are no solutions (for part q.9 iii)b) without giving an explanation why?


yes 1 mark i think
Mr M
keep the u^1.5 part on one side and move the other stuff to the other side then square both sides


Thanks. :frown: I was thinking of squaring it all but it didn't work out. I should have rearranged first.
Reply 18
Avatar for Sh4w
Sh4w
9
Many thanks Mr. M, I got 0/6 on the transformation T but apart from that nearly everything right :smile:
Sh4w
Many thanks Mr. M, I got 0/6 on the transformation T but apart from that nearly everything right :smile:


well done

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