AQA FP4 25th May 2016 Discussion Thread

Emi1998

For Q6 (c) of the Jan 11 paper, could anyone explain why we take landa to equal 2, I know it's something to do with the direction cosines but what is it?

Think it's because the magintude of the direction vector is 25, so you use landa as 2 to obtain the "50 unitS" away which it tells you in Q

Reply 41

Emi1998

7

Can anyone show their working for Jan 09 8ci please

Reply 42

milsy.afrochic

anyone else getting slightly concerned about how few resources there are for FP4?? I mean the AQA textbook is just awful

Reply 43

Qcomber

OP

3

Original post by milsy.afrochic

anyone else getting slightly concerned about how few resources there are for FP4?? I mean the AQA textbook is just awful

Check on the opening page, there is a link to douis.net which has some useful notes for fp4.

Reply 44

username1560589

20

Original post by milsy.afrochic

anyone else getting slightly concerned about how few resources there are for FP4?? I mean the AQA textbook is just awful

There are two books titled Further Pure Mathematics that I found had better explanations of FP4 and other topics.

Reply 45

pic

1

Q) show that the only real value of U for which the simultaneous equations has a solution other than x=y=z=0 is -1:

(2+U)x-y+z=0
x-2Uy-z=0
4x-y-(U-1)z=0

..... So obviously determinant of the matrix only can =0 when U=-1, and when you work that through you get a common line and thus another solution. Buuuuut how would I set this out? Would I need to look at the equations first to show that the only unique solution is x=y=z=0? Or is it only asking me to look at the non-unique solutions ?

Reply 46

AHRocks187

How would you guys go about finding the shortest distance between a point and a plane, assuming you only know the point co-ordinates and the parametric equation of the plane? Just trying to brush up on geometry techniques as expecting a hard question on this this year

Reply 47

MathedUp!

1

Original post by AHRocks187

For Q6 (c) of the Jan 11 paper, could anyone explain why we take landa to equal 2, I know it's something to do with the direction cosines but what is it?

This video may help
https://youtu.be/BXooSxwMkM0

Lots more on this topic here
https://www.youtube.com/playlist?list=PL0sgfvQGLNJv-H5zNrF0fe6mkKFQ6Dala

Reply 48

pic

1

Original post by AHRocks187

How would you guys go about finding the shortest distance between a point and a plane, assuming you only know the point co-ordinates and the parametric equation of the plane? Just trying to brush up on geometry techniques as expecting a hard question on this this year

[AP.N] / [N]

AP is direction connecting a point to the plane. N is the direction of the normal to the plane, work this out by the vector product of the 2 directions of the plane you have.

edit: [h] being magnitude of h.

Reply 49

EwanatTSR

8

So how is everyone feeling about Wednesday morning then? Just over 48 hours away!

Reply 50

TeeEm

19

Link for FP4 material

http://www.madasmaths.com/archive_maths_booklets_further_topics_linear_algebra.html

_IYGB 9.jpg

Reply 51

C0balt

16

Original post by TeeEm

Link for FP4 material

http://www.madasmaths.com/archive_maths_booklets_further_topics_linear_algebra.html

_IYGB 9.jpg

Thank you. I hope all is well with you.

Reply 52

MahirYuksel

Can someone give me a simple explanation on how to find the distance between two planes. A GENERAL method please.
Thanks ever so much!

Reply 53

C0balt

16

I wish I sat 2014 paper, I liked all the questions but it had a generous 100UMS cap!

Reply 54

Mm68

I know this might be more fp1 but I've seen it come up in fp4, how are you supposed to work out the enlargement of a transformation matrix, for example if it's
2 -2
2 2
It would be a enlargement 2rt2 but how do you work that out.

Reply 55

pic

1

Can anyone work through a "find the invariant lines of this matrix" question? Or tell me the best method, the one my teacher said isn't on mark schemes and seems to be a bit dodgy

Reply 56

MahirYuksel

Original post by Mm68

I know this might be more fp1 but I've seen it come up in fp4, how are you supposed to work out the enlargement of a transformation matrix, for example if it's
2 -2
2 2
It would be a enlargement 2rt2 but how do you work that out.

So you would compare it to any matrices you know, to me, this looks like a rotation matrix.
Compare elements.
I would let 2/h=costheta and 2/h=sintheta
draw a pythagoras triangle and find h through sohcahtoa.
then it will be 2rt2(2/2rt2,-2/2rt2... and so on inside.
so h x all the elements over h in the matrix, so they cancel.
so enlargement 2rt2, and work out the angle of rotation.
cheers

Reply 57

student0042

7

Original post by Mm68

I know this might be more fp1 but I've seen it come up in fp4, how are you supposed to work out the enlargement of a transformation matrix, for example if it's
2 -2
2 2
It would be a enlargement 2rt2 but how do you work that out.

Just do pythagoras on the first row.

\sqrt(2^2+2^2) = 2 \sqrt(2)

Reply 58

Qcomber

OP

3

Original post by MahirYuksel

Can someone give me a simple explanation on how to find the distance between two planes. A GENERAL method please.
Thanks ever so much!

The planes would have to be parallel.
You can follow the steps in this video. It's for a point but you will see the method would be the same for the distance between 2 planes
http://www.examsolutions.net/maths-revision/further-maths/vectors/plane/point_shortest-dist/tutorial-1.php

Reply 59

EwanatTSR

8

Does anyone know an easy method for finding eigenvalues in a 3x3 matrix? I use the Gaussian Elimination process but it is very confusing and a huge space for error.

AQA FP4 25th May 2016 Discussion Thread

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