OCR FP1 (Non-MEI) 14th May 2015

UNOFFICIAL MARKSCHEME1) 2x^2 +2y^22) n/2(2n-3)(n+3)3) matrix: inverse of A = 1/2 * (1 -a) (0 2)3ii) P matrix: P = ( 1 0 ) ( 2 1-2a)4) Proof by Induction 5i) circle center -2,0 radius 2 and a halfline from the point -2, 0 with an argument of 5pi/6 with positive x axis. 5ii) -(2+ root3) +i5iii) shaded within the circle in between the line and the negative x axis6i) diagram, cant show here6ii) rotation of 3pi/2 anticlockwise followed by a stretch scale factor 2 parallel to the x acis ( 0 1 ) ( 2 0 ) (-1 0 ) ( 0 1 )7i) + or - (3+2i)7ii) x= 5+2i or -1-2i8i) QED8ii) 7/2 -2/n -1/n -1/n+18iii) 5/49i) a= 1 or 59ii) yes a solution9iib) no solution and equations are inconsistent10i) 0= u^3 +8u^2 +16u -910ii) 29let me know if you have any corrections, some answers may be incorrect!

Wow thanks so much!
Got all those (I think)!!
However on 8ii they wouldn't penalise for simplifying (-1/n -2/n) to -3/n would they?

UNOFFICIAL MARKSCHEME
1) 2x^2 +2y^2
2) n/2(2n-3)(n+3)
3) matrix:

inverse of A = 1/2 * (1 -a)
(0 2)
3ii) P matrix:

P = ( 1 0 )
( 2 1-2a)

4) Proof by Induction
5i) circle center -2,0 radius 2 and a halfline from the point -2, 0 with an argument of 5pi/6 with positive x axis.
5ii) -(2+ root3) +i
5iii) shaded within the circle in between the line and the negative x axis
6i) diagram, cant show here
6ii) rotation of 3pi/2 anticlockwise followed by a stretch scale factor 2 parallel to the x acis
( 0 1 ) ( 2 0 )
(-1 0 ) ( 0 1 )

7i) + or - (3+2i)
7ii) x= 5+2i or -1-2i

8i) QED
8ii) 7/2 -2/n -1/n -1/n+1
8iii) 5/4

9i) a= 1 or 5
9ii) yes a solution
9iib) no solution and equations are inconsistent

10i) 0= u^3 +8u^2 +16u -9
10ii) 29

let me know if you have any corrections, some answers may be incorrect!

They shouldn't. They usually put oe in the mark scheme for those questions. As long as you showed your cancelling they should give you the mark.

brill, thanks again. Also, instead of rotation followed by x stretch, would it have been possible to do y stretch followed by rotation?

Got all of them apart from 5ii and 10ii

You're right with 5ii - I foolishly got -root15 + i so I'll probably get one of the two marks there
For 10ii. I somehow got 53 but that was quite a horrific question so I'm not dwelling too much on it!

Any thoughts as to how this paper compared to last years? I think the grade boundaries might be a little similar but I'm trying not to get my hopes up.

Much nicer than last years IMO- the cubic polynomial question in June 14 was awful. Probably similar grade boundaries I reckon.

Guys for 10i I got a different wrong equation u^3 -16u^2+24u-9 due to a silly mistake in my expansion and I used those values in my answer to question 10ii but my working is correct for 10ii, do you think my error will be carried forward and how many marks do you think I would have lost. Thanks

Yes, as long as you made sure to state which was P and which was Q. As in, if you said P (the first one) was a rotation and then Q was an enlargement in y you wouldn't get it, it'd need to be the other way around.

For the rotation it can also be expressed as a rotation 90 clockwise, centre the origin right?

UNOFFICIAL MARKSCHEME
1) 2x^2 +2y^2
2) n/2(2n-3)(n+3)
3) matrix:

inverse of A = 1/2 * (1 -a)
(0 2)
3ii) P matrix:

P = ( 1 0 )
( 2 1-2a)

4) Proof by Induction
5i) circle center -2,0 radius 2 and a halfline from the point -2, 0 with an argument of 5pi/6 with positive x axis.
5ii) -(2+ root3) +i
5iii) shaded within the circle in between the line and the negative x axis
6i) diagram, cant show here
6ii) rotation of 3pi/2 anticlockwise followed by a stretch scale factor 2 parallel to the x acis
( 0 1 ) ( 2 0 )
(-1 0 ) ( 0 1 )

7i) + or - (3+2i)
7ii) x= 5+2i or -1-2i

8i) QED
8ii) 7/2 -2/n -1/n -1/n+1
8iii) 5/4

9i) a= 1 or 5
9ii) yes a solution
9iib) no solution and equations are inconsistent

10i) 0= u^3 +8u^2 +16u -9
10ii) 29

let me know if you have any corrections, some answers may be incorrect!