Further Mathematics: Post your doubts here!

[Sareeeeeto]

please guys help me with S1 and C2

 

[Isotope42]

Help plz solve this step by step, I can't integrate this, need help

I will give you a hint. Use a variable substitution for the expression inside the parenthesis.

 

[Sakib]

hey guys, I'm pretty new to the forum. Do you think I can finish the syllabus in 4 months and sit for the exam in O/N-13 session?(I have zero knowledge of the syllabus)

 

[fahaddewan]

accha, how long does it usually take for a student who has physics,chemistry and math, to complete Further Maths syllabus?( CIE ofcourse)

 

[studen12345]

hey guys, I'm pretty new to the forum. Do you think I can finish the syllabus in 4 months and sit for the exam in O/N-13 session?(I have zero knowledge of the syllabus)

no u cannot

 

[Sakib]

Can someone please explain to me how you read of the amplitude from the given information. Thanks

Taking velocity=0 and solving for t, yields, t=0.655. putting it in the equation of x yields, x=-1. At fixed point A, acceleration=0. So at initial point, x=12. so difference from fixed point to point where v=0 is the amplitude.{12-(-1)}=13.

 

[AbbbbY]

hey guys, I'm pretty new to the forum. Do you think I can finish the syllabus in 4 months and sit for the exam in O/N-13 session?(I have zero knowledge of the syllabus)

Myself and a lot of my friends are struggling having studied it for about a year now. In all honesty, I don't think.

 

[Sakib]

To all the brave and perhaps lunatic guys who took Further Mathematics, I believe we should all be more regular in this thread. Further Mathematics is considered as the most difficult subject of A levels but if we all try together and help one another we could reduce the difficulty. No matter if there are 5 people studying this subject, I request all of you to regularly and actively participate in this thread so that we can ask questions to one another and have them quickly solved. Please visit this thread at least twice a day, ask questions if you face problem and answer others' questions if you know. That way all of us will be benefited. Ex- Lecom40 asked a question on May 5th and it was answered on May 24th. That's unexpected. If you could be regular he would have had his answer a long time back. So I once again ask all of you to help each other and make this thread an active one, please.

 

[AlphaCentauri]

To all the brave and perhaps lunatic guys who took Further Mathematics, I believe we should all be more regular in this thread. Further Mathematics is considered as the most difficult subject of A levels but if we all try together and help one another we could reduce the difficulty. No matter if there are 5 people studying this subject, I request all of you to regularly and actively participate in this thread so that we can ask questions to one another and have them quickly solved. Please visit this thread at least twice a day, ask questions if you face problem and answer others' questions if you know. That way all of us will be benefited. Ex- Lecom40 asked a question on May 5th and it was answered on May 24th. That's unexpected. If you could be regular he would have had his answer a long time back. So I once again ask all of you to help each other and make this thread an active one, please.

Great. I'm in, for I reckon I'll need help.


http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics - Further (9231)/9231_s06_qp_2.pdf

Starting with this. No 11 Either.
No need to work out the question, it'll be enough if someone could identify the forces (+ directions) for me please.

 

[Sakib]

Tension in the string, Radially inwards, Component of weight(at the position where OP makes an angle of (π/3) with the upward vertical), also radially inward. But I could not show (ii) of the same question. Somebody help me.

 

[anythin576]

Can anyone tell me the method of finding the centroid of a 2d and a 3d shape. My teacher didn't teach me this and I just read it in the syllabus. Please mention any questions from past papers if you have some in your mind so I could practice. Thanx in advance..

 

[Sakib]

If you have "Mathematics-Mechanics and Probability" by Bostock and Chandler see chapter 15(pg-514). It has an excellent explanation to find centroid using Integration. As it shows, the formula varies depending on the shapes. Generally formula is, for X coordinate, {integration of (xy)dx}/Area under curve, and for Y coordinate, {integration of (.5y^2)dx/Area under curve}. But as I have already said, formula varies depending on the shape and even limits. O/N 10 p1 Q 3.
For 3D shape, X coordinate= {integration of (pie*x*y^2)dx/volume of shape}. Generally the curve is rotated about the x-axis, hence Y-coordinate is 0.

 

[anythin576]

If you have "Mathematics-Mechanics and Probability" by Bostock and Chandler see chapter 15(pg-514). It has an excellent explanation to find centroid using Integration. As it shows, the formula varies depending on the shapes. Generally formula is, for X coordinate, {integration of (xy)dx}/Area under curve, and for Y coordinate, {integration of (.5y^2)dx/Area under curve}. But as I have already said, formula varies depending on the shape and even limits. O/N 10 p1 Q 3.
For 3D shape, X coordinate= {integration of (pie*x*y^2)dx/volume of shape}. Generally the curve is rotated about the x-axis, hence Y-coordinate is 0.

Thanx a lot Sakib. I desperately needed that information. I don't have the book you mentioned but I have the book Mechanics for A level Bostock and Chandler (the green book). However I have found the two formulas on wikipedia http://en.wikipedia.org/wiki/Centroid#By_integral_formula.

 

[Sakib]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics - Further (9231)/9231_s06_qp_2.pdf

No one has been able to do No. 11 either part(ii) of this paper? If anyone has, please help me with it.

 

[AlphaCentauri]

Tension in the string, Radially inwards, Component of weight(at the position where OP makes an angle of (π/3) with the upward vertical), also radially inward. But I could not show (ii) of the same question. Somebody help me.

Yes, yes, I got that too. Thank you so much. I'd taken the angle vertically downwards, but I haven't been able to prove part ii either. :/

I'll think about it once my test is over. If I get it, I'll post here.

 

[AlphaCentauri]

June 09 P 2 No 1.

I don't get that transverse acceleration. Shouldn't differentiating d@/dt once give you d^2@/dt^2?

Where @ : theta.

 

[Sakib]

June 09 P 2 No 1.

I don't get that transverse acceleration. Shouldn't differentiating d@/dt once give you d^2@/dt^2?

Where @ : theta.

It surely will, but is d^2@/dt^2 accelaration? In the question d@/dt is given which is angular velocity. Using v=wr, where w=angular velocity, find the velocity(l sin@). Then find the tangential(dv/dt) and radial component(v^2/l) of acceleration and pythagoras yields the resultant acceleration which is also l sin@. So magnitude same.

Note- Be careful when calculating dv/dt. If you find dv/dt= l cos@ (which I did initially and it took me an hour to realize it) you are wrong.
BTW, what test?

 

[AlphaCentauri]

It surely will, but is d^2@/dt^2 accelaration? In the question d@/dt is given which is angular velocity. Using v=wr, where w=angular velocity, find the velocity(l sin@). Then find the tangential(dv/dt) and radial component(v^2/l) of acceleration and pythagoras yields the resultant acceleration which is also l sin@. So magnitude same.

Note- Be careful when calculating dv/dt. If you find dv/dt= l cos@ (which I did initially and it took me an hour to realize it) you are wrong.
BTW, what test?

Yeah, I did get dv/dt= l cos@ but I still can't understand why it's wrong.. l cos@ sin@ is the first differential of 0.5 sin^2 @. No?

Sort of a mock exam... which I should've done Saturday, but couldn't upto now because too many things disturb my mind.
I deserve it. I trusted people blindly. Lesson for life. Don't ever do that. Excuse me the rant.

 

[Sakib]

v=l sin@, means, v is expressed in terms of @. So, dv/dt has to be calculated by chain rule(O level differentiation). dv/dt=(dv/d@)*(d@/dt). What you calculated is dv/d@. d@/dt is sin@, as given in the question.So, dv/dt=l cos@ sin @. Hope that answers it.
About that trust thing, that's one lesson everyone learns first hand. I haven't yet been in such a situation so far and I hope I never have to.
Back to Further Mathematics, O/N 04, P-2, Q-11 Either. The whole question has baffled me. But I guess, if anyone could solve (i) for me, I may be able to proceed. So anyone?

 

[AlphaCentauri]

v=l sin@, means, v is expressed in terms of @. So, dv/dt has to be calculated by chain rule(O level differentiation). dv/dt=(dv/d@)*(d@/dt). What you calculated is dv/d@. d@/dt is sin@, as given in the question.So, dv/dt=l cos@ sin @. Hope that answers it.
About that trust thing, that's one lesson everyone learns first hand. I haven't yet been in such a situation so far and I hope I never have to.
Back to Further Mathematics, O/N 04, P-2, Q-11 Either. The whole question has baffled me. But I guess, if anyone could solve (i) for me, I may be able to proceed. So anyone?

Thanks. Yeah, right. I got it now.
I'll try that for you soon. As I've some time.