Level 2 Further Maths - Post some hard questions (Includes unofficial practice paper)

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Reply 80

Junglious

Anyone dreading the further maths paper tomorrow?

Reply 81

Notnek

Original post by Pretish

this isn't even in our spec???

Yes it is - I know the spec very well. The last part of the working requires a diagram but it's all doable with Level 2 FM methods.

(edited 6 years ago)

Reply 82

_gcx

Study Forum Helper

Original post by Pretish

wait, is 'hopital's rule the one where u put all the numbers over the highest value (x)

Spoiler

Reply 83

alyttelton

Original post by chinkinator

hey man can u show me your working out? I somehow got p= -2, q=4

I got p = 3 and q = 9 as well.

1) find the difference in x coordinate of B and C, so:
(2q - 2) - (q + 2) = q - 4
Because that's 20%, times it by 5 to find the difference in x through the whole line, so 5q - 20

Another way to find the x difference is by subtracting the A coordinates from C, so
-(-3p) + (2q - 2) = 3p + 2q - 2

They are equal to the same thing, so 5q - 20 = 3p + 2q - 2, which is the same as
3q - 3p = 18.

2) Do the same thing for the y coordinates, you will end up with 9p - 3q = 0.

3) Simultaneously solve both equations now.

Reply 84

3317752

Original post by _gcx

Spoiler

it doesn't lol. Too advanced. What i did was put everything over n and cancel it out, then made n equal to 0 so i got the remaining value.

Reply 85

Blackjoker1506

Original post by Loci Pi

Cool! Happy birthday :smile:

My birthday is the day before the calculator paper.

So, in other words, it's today?

Reply 86

_gcx

Study Forum Helper

Original post by Pretish

it doesn't lol. Too advanced. What i did was put everything over n and cancel it out, then made n equal to 0 so i got the remaining value.

Ah, that's not quite the same :P

Reply 87

3317752

Original post by Blackjoker1506

So, in other words, it's today?

calculator is later lol

Reply 88

3317752

Original post by notnek

Yes it is - I know the spec very well. The last part of the working requires a diagram but it's all doable with Level 2 FM methods.

if the paper uses unknowns such as p and q, is it ok to use x and y but write as a key at the top of the lines. It makes it easier as i get confused easliy within p and q

Reply 89

Notnek

Original post by Pretish

if the paper uses unknowns such as p and q, is it ok to use x and y but write as a key at the top of the lines. It makes it easier as i get confused easliy within p and q

Yes that's fine. Just say e.g. "Let x = p and y = q". But make sure you don't get mixed up and if you're asked for p and q values then write p = ... and q = ... at the end.

Reply 90

TheMightyBadger

Original post by notnek

This is the hardest one I've posted so far and requires a very good undrstanding of transformation matrices. Don't worry if you can't do this one.

The transformation matrix

\displaystyle \mathbf{P}^3

represents a clockwise rotation of

150^o

about the origin.

\displaystyle \mathbf{Q} = \begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}

The unit vector

\displaystyle \begin{pmatrix}0 \\ 1\end{pmatrix}

is transformed by the matrix

\displaystyle \mathbf{Q}\mathbf{P}

to give the vector

\displaystyle \begin{pmatrix}-\cos \theta \\ \cos \alpha \end{pmatrix}

.

Find the value of

\theta

and

\alpha

Spoiler

Reply 91

thekidwhogames

Original post by _gcx

Spoiler

Truly a beautiful weapon. Makes finding limiting value in FM much quicker then cancelling by highest power or whatever the method is (I forgot)

Reply 92

3317752

Original post by notnek

Yes that's fine. Just say e.g. "Let x = p and y = q". But make sure you don't get mixed up and if you're asked for p and q values then write p = ... and q = ... at the end.

ok thanks then. Also, can u post a solution for ur last quesiton in spoilers? I want to see how it works out.

Reply 93

username3113306

Original post by notnek

This is the hardest one I've posted so far and requires a very good undrstanding of transformation matrices. Don't worry if you can't do this one.

The transformation matrix

\displaystyle \mathbf{P}^3

represents a clockwise rotation of

150^o

about the origin.

\displaystyle \mathbf{Q} = \begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}

The unit vector

\displaystyle \begin{pmatrix}0 \\ 1\end{pmatrix}

is transformed by the matrix

\displaystyle \mathbf{Q}\mathbf{P}

to give the vector

\displaystyle \begin{pmatrix}-\cos \theta \\ \cos \alpha \end{pmatrix}

.

Find the value of

\theta

and

\alpha

does theta = 150 degrees and alpha = 60 degrees

Reply 94

Notnek

Original post by TheMightyBadger

Spoiler

I don't think this is right. If you are trying to use methods outside Level 2 FM then this is the wrong approach.

Lots of hints for anyone strugging with the matrices question:

Spoiler

Reply 95

TheMightyBadger

Original post by notnek

I don't think this is right. If you are trying to use methods outside Level 2 FM then this is the wrong approach.

Lots of hints for anyone strugging with the matrices question:

Spoiler

Reply 96

Notnek

Original post by TheMightyBadger

Spoiler

Reply 97

Notnek

Original post by Pretish

ok thanks then. Also, can u post a solution for ur last quesiton in spoilers? I want to see how it works out.

I'm going to have to leave it to others to post solutions. If there's a question that no one can do then I'll post a solution.

Reply 98

B0redBrioche

Original post by notnek

This is the hardest one I've posted so far and requires a very good undrstanding of transformation matrices. Don't worry if you can't do this one.

The transformation matrix

\displaystyle \mathbf{P}^3

represents a clockwise rotation of

150^o

about the origin.

\displaystyle \mathbf{Q} = \begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}

The unit vector

\displaystyle \begin{pmatrix}0 \\ 1\end{pmatrix}

is transformed by the matrix

\displaystyle \mathbf{Q}\mathbf{P}

to give the vector

\displaystyle \begin{pmatrix}-\cos \theta \\ \cos \alpha \end{pmatrix}

.

Find the value of

\theta

and

\alpha

I'm completely lost, could you link in some revision resources for transformations of matrices?

Reply 99

Notnek

Original post by B0redBrioche

I'm completely lost, could you link in some revision resources for transformations of matrices?

The best thing to use is your textbook if you have one. The problem with revision resources for a topic like this is that most revision resources will be A Level and go through methods that you don't need.

I'll probably post a full solution to this question a bit later and explain all the methods. This question is harder than any matrices question that's been in a Level 2 FM paper so try those questions first.