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AQA FP4 Unofficial Mark Scheme 2018

Hey guys! The chances of this getting completed is slim to none, I’m not confident with my answers so I won’t put many on here but I’ll try and summarise the questions so if anyone wants to contribute they can

1) Area/Volume of shape after being translated by MN^2 [4 marks]

1.5cm^3

2) Find matrix A and describe the corresponding transformation [4 marks]

Rotation 164 degrees about the z axis

3) a) Find determinant of P [1 mark]

b) Calculate P inverse [5 marks]

4) Think this was the value of p given that the angle between the line and the plane was 30 degrees [5 marks]

p = -1 or 17

5) a) Solving the 3 equations in terms of k to get a single point [5 marks]

b) Finding the 2 values of k where the equations have no unique solution [3 marks]

-3 and 4.5

c) Finding the number of solutions and configurations of the planes in each of these cases [4 marks]

4.5: Inconsistent, 0 solutions

-3: Consistent, Infinite number of solutions

6) a) Volume of Parallelepiped [2 marks]

30

b) Vector equation of plane [3 marks]

c) Equation of second plane in form r.n = d [3 marks]

d) Equation of line of interaction of both planes [3 marks]

7) a) Factorise the determinant [6 marks]

y(x-y)(x y)(x y z)(2y x)

b) Value of z if x = 2, y = 3 and matrix is singular [2 marks]

z = -5

8) a) Value of ac - 3b = 1 [1 mark]

b) i. Find values for a b and c [4 marks]

a = 4 b = -3 c = -2

ii. Equation of invariant line which passes through (0,2) [3 marks]

(I think that’s how this question was set out)

9) a) Find eigenvalues in terms of p and q [3 marks]

b) i. Show that (some vector I can’t remember) is an eigenvector and state the corresponding eigenvalue [2 marks]

ii. Show the other eigenvector is independent of p and q [2 marks]

c) I didn’t even read this I didn’t have time to finish. [6 marks]

Think these marks only add up to 71 but it was something like that

If anyone could help fill this out that would help! I’ll edit this post as necessary, sorry I can’t quote many of my answers, I’m not very confident at all, I really hated that it paper!

Hope it went well for everyone :yep:

(edited 5 years ago)

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M8 wut

Total cancer

I died, I am dead
I have got straight A*s... And I missed 15 marks. I am worthless. Kill me.

Reply 4

EmilySarah00

Original post by Rowanstruggling

I died, I am dead
I have got straight A*s... And I missed 15 marks. I am worthless. Kill me.

Literally same don’t worry I’m also done for

Reply 5

Rowanstruggling

Original post by EmilySarah00

Literally same don’t worry I’m also done for

Would you say that was the worse thing you have ever experienced?

Reply 6

dbowgen1234

No that was a really easy paper, grade boundaries are gonna be really high

Reply 7

dbowgen1234

Question 1, detN was 1/17 so the det of the whole thing was 3/17 so then 3/17*8.5 = 1.5cm^3

Reply 8

AndyLad21

Original post by dbowgen1234

Question 1, detN was 1/17 so the det of the whole thing was 3/17 so then 3/17*8.5 = 1.5 Icm^3

Yes deemssss

Reply 9

georgieb42

Question 9 was almost exactly the same as a question on a really early paper, I'll try and find it

Reply 10

leedsnd

Original post by dbowgen1234

Question 1, detN was 1/17 so the det of the whole thing was 3/17 so then 3/17*8.5 = 1.5cm^3

AGREED

Reply 11

EmilySarah00

(You know it’s bad when you got question 1 wrong)

Reply 12

georgieb42

I'm pretty sure the answers for 5a were:
z=-4
y=-16/(2k-9)
x=(2k+12)/(2k-9)
or something like that??????

then 5b was 9/2 and -3

5c was consistent for -3 and inconsistent for 9/2

Reply 13

Rowanstruggling

Original post by EmilySarah00

(You know it’s bad when you got question 1 wrong)

You know it's bad when you get question 4,5,6,7,8,9 wrong 😎

Reply 14

EmilySarah00

Original post by georgieb42

I'm pretty sure the answers for 5a were:
z=-4
y=-16/(2k-9)
x=(2k+12)/(2k-9)
or something like that??????

then 5b was 9/2 and -3

5c was consistent for -3 and inconsistent for 9/2

Yeah I got that for b and c but didn’t cancel the fractions for a!

Reply 15

Mathew_Willis

not sure how you go ? for question 2 and 6 but apart from that good job m9

Reply 16

georgieb42

this is june 2006 q8 which is basically the same as q9, just set b=q, p=a
plus they used actual values in this instead of n, but the principle is the same

Reply 17

chen881020

I didn’t even have time to do that one so I just skipped at all!

Reply 18

georgieb42

there was a volume question somewhere and the volume was 30

for the shear question it was a=4, b=-2, c=-3 or something and the invariant line was y=-x+2

for q4 I got p=1 and -17 ?????

determinant factorised to something like y(y-x)(y+x)(x+y+z)(x+2y) which gives z=-5 when the matrix is singular

determinant of P was 7k+14 for q3a