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

OP

Original post by thekidwhogames

Find nth term of numerator and denominator so 6n2-n-2/4n2-1. Apply l'hopitals rule to get the limit to infinity to get 3/2.

By the way I have a feeling that I haven't replied to one of your posts. Please tag me again if this is the case.

I've received a lot of quotes/PMs recently so I'm finding that I'm forgetting some of them.

Reply 62

Original post by notnek

ABC is a straight line where BC is 20% of AC. In the diagram below, the coordinates of A, B and C are shown.

p

and

q

are positive numbers.

Find the value of

p

and

q

.

Spoiler

Reply 63

OP

Original post by thekidwhogames

Spoiler

Correct!

Reply 64

Original post by notnek

Wow I didn't expect L'hopitals rule to be used for this :smile:

But you can factorise and cancel that fraction which is a more GCSE/A Level way of doing this.

Haha I saw the opportunity so I took it. And yeah that method was possible but l'hopitals rule saves a lot of time 😂😂

Reply 65

Blackjoker1506

11

FURTHER MATHS IS ON MY BIRTHDAY TOMORROW!!!!

:frown:

Reply 66

Original post by notnek

By the way I have a feeling that I haven't replied to one of your posts. Please tag me again if this is the case.

I've received a lot of quotes/PMs recently so I'm finding that I'm forgetting some of them.

NotNek you're messing with my sly eyes lol. I've got that question wrong so many times because my eyes keep replacing the p and q's. xD

Reply 67

Original post by Blackjoker1506

FURTHER MATHS IS ON MY BIRTHDAY TOMORROW!!!!

:frown:

Happy birthday. Truly the best gift - I wish I was put in for FM 😂😂

Reply 68

Original post by thekidwhogames

Happy birthday. Truly the best gift - I wish I was put in for FM 😂😂

do u do triple science? or double?

Reply 69

alyttelton

4

Original post by thekidwhogames

Find nth term of numerator and denominator so 6n2-n-2/4n2-1. Apply l'hopitals rule to get the limit to infinity to get 3/2.

Nice to see people using different methods!
I found the second difference of the numerator and also of the denominator, turned out to be 12/8. Simplified it to 3/2 after.

Reply 70

SamanyuTir

4

Original post by notnek

Sequences. It's definitely grade A^ and I've seen a question like this but easier in textbooks but not in an exam (yet).

Here are the first five terms of a sequence:

\displaystyle \frac{3}{3},\frac{20}{15}, \frac{49}{35}, \frac{90}{63}, \frac{143}{99}

The

n

^th term of the sequence is

u_n

. Find the limiting value of

u_n

as

n\rightarrow \infty

.

1.5???

Reply 71

Original post by notnek

Correct!

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

Reply 72

Original post by Pretish

do u do triple science? or double?

I'm doing the new spec 9-1 science next year and triple

Reply 73

alyttelton

4

Original post by SamanyuTir

1.5???

Yep. If I were you I'd leave it as 3/2 though

Reply 74

boi_

12

Original post by thekidwhogames

Spoiler

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

Reply 75

Loci Pi

16

Original post by Blackjoker1506

FURTHER MATHS IS ON MY BIRTHDAY TOMORROW!!!!

:frown:

Cool! Happy birthday :smile:

My birthday is the day before the calculator paper.

Reply 76

OP

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

.

Reply 77

OP

Original post by SamanyuTir

1.5???

Correct

Reply 78

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

.

this isn't even in our spec???

Reply 79