(Finalised) Official BOS Mathematics Trial Examinations. (2 Viewers)

[Sy123]

The reason this took so long for me is that I differentiated and tried to go on further when I was differentiating that theta expression, but with x^2 in the denomiantor for some strange reason, I did this about 3 times to check if I did a silly mistake, I then realised I was differentiating what Im not supposed to be, I then differentiated the real thing and I got it in a small amount of time

ಠ_ಠ

Curse my inability to see my mistakes, it cost me way too much time on this question.

Solution

But another thing, is there a way in saying that because the parametric equations of a circle are
(Acos t, Asin t)

Can we go on further by doing something with that and ending up with something to do with SHM due to reasoning?
Like I can say that due to:

x=Acos t

Hence it moves in SHM?

EDIT: Also its a cool result :>

 

[Carrotsticks]

Yes that is an alternative way to observe SHM with respect to time, nice work =)

The last part was actually "Explain why theta = t", but then there were problems regarding negative time due to restrictions.

 

[deswa1]

Yes that is an alternative way to observe SHM with respect to time, nice work =)

The last part was actually "Explain why theta = t", but then there were problems regarding negative time due to restrictions.

See haha I'm legit the master of working out questions the long way ... Need to work on that- luckily I can generally do maths quickly so time isn't an issue normally.

 

[bleakarcher]

Here you go.

*Moves about in Simple Harmonic Motion.

Carrot how do you come up with this questions lol?

 

[Sy123]

Carrot how do you come up with this questions lol?

Yeah you should make a textbook carrot, Im serious

 

[Carrotsticks]

Scrapped this Conics question because you didn't really need any knowledge of conics to do it.

 

[king chopper]

Carrot, will you be able to please upload the exam + solutions to here after it is sat on the 24th?
Can't make the date and would really like to try the 3u paper

 

[karnbmx]

Carrot, can I attend too please?

 

[Carrotsticks]

Carrot, will you be able to please upload the exam + solutions to here after it is sat on the 24th?
Can't make the date and would really like to try the 3u paper

I will make a thread afterwards, for people to discuss their own solutions. And uploading the exam, other people can scan it etc. Need to finalise a few things before uploading it here.

Carrot, can I attend too please?

Added.

 

[Carrotsticks]

Adding some more scrapped questions soon. They're all over the place, so may take some time.

 

[Carrotsticks]

Scrapped because it was too 'standard'.

Last line should say: Prove that PSQ is collinear. Also, was going to put a problem regarding the limiting value of theta as T gets infinitely large, but it was trivially zero anyway.

 

[Carrotsticks]

BTW the X and Y are swapped the wrong way around. Typo'd that one.

Should be (acosx,bcosx), but doesn't make much difference here.

 

[Sy123]

Adding some more scrapped questions soon. They're all over the place, so may take some time.

Any more 3U ones? =)

 

[Carrotsticks]

Any more 3U ones? =)

I'll look around the computer.

 

[Carrotsticks]

 

[Carrotsticks]

Also, please CONFIRM your attendance to the 3U Examination now by sending me a PM. So I can confirm numbers.

The Extension 1 Mathematics Exam is on MONDAY 24th September (in 2 days).

 

[Carrotsticks]

Cash Prize for highest score in Extension 1 and Extension 2 Mathematics.

Thoughts?

 

[barbernator]

Cash Prize for highest score in Extension 1 and Extension 2 Mathematics.

Thoughts?

source of cash?

 

[Carrotsticks]

Either from BOS or funded from the Library.

 

[bleakarcher]

Carrot, I think there is a mistake part b). If you solve the quadratic for x=cos(2pi/5) i.e. solve 8x^2-9x+1=0 the solutions are 1 and 1/8, neither of which is the value of cos(2pi/5).