Mathematics: Post your doubts here!

[eureka!]

cool Hassan
Could you help me with question 5? Thanks!

 

[manya]

 

[Rizwan Javed]

View attachment 57018

(i)
y= (1-x)^0.5 / (1+x)^0.5
dy/dx = ( ( (1+x)^0.5) * (-1/2√(1-x) ) - ( (1-x)^0.5 * (1/2√(1+x) ) ) ) / (1+x)
after solving ....
dy/dx= -1 / ( 1+x ) ( √(1-x^2) ) = m

the gradient of normal = -1/m
so, gradient of normal = ( 1+x ) ( √(1-x^2) ) (shown)

 

[Rizwan Javed]

View attachment 57018

(ii)
gradient of normal : (1+x) (√(1-x^2)) --- (1)

differentiating (1) wrt to x

dy/dx = (1)(√(1-x^2)) + (1+x)(1/2√(1-x^2))*(-2x)
for max values , dy/dx = 0, so

0 = (1)(√(1-x^2)) + (1+x)(1/2√(1-x^2))*(-2x)
0 = 1 - x - 2x^2

(x+1) (2x-1) = 0

either x = -1 or x = 1/2

since the x-coordinate of P is +ive, so x=-1 is rejected.

hence the x-coordinate of P is 1/2

 

[Uttam Shrestha]

Get Mathematics pastpapers 2015 in http://uttamshr.cf. Other pastpapers from this site. Hope it will be helpful.

 

[manya]

(i)
y= (1-x)^0.5 / (1+x)^0.5
dy/dx = ( ( (1+x)^0.5) * (-1/2√(1-x) ) - ( (1-x)^0.5 * (1/2√(1+x) ) ) ) / (1+x)
after solving ....
dy/dx= -1 / ( 1+x ) ( √(1-x^2) ) = m

the gradient of normal = -1/m
so, gradient of normal = ( 1+x ) ( √(1-x^2) ) (shown)

jazakallah khair. i see ur method is a bit different than asked in the question but in ms they are giving point for this method as well. however, i noticed a mistake ie the minus sign with the power of the differenciated one since its gonna be (1-1/2)=-0.5

 

[cool Hassan]

Hi eureka!
As u can see that the mass is attached to the disc via a string
So it must have the same angular velocity as that of the disc
Where as it has different "linear velocity" from that of the disc
Now..
As Angular velocity=2π/T where T is "time period"
Now as we know that the angular velocity of disc and mass is same
So the value of T for both must be "same"
Hence
Distance travelled by point A on the disc in one revolution i-e in time T
Equals to 2πr=2π(0.5)
Now as the question says that linear velocity of mass is 1.6 times that of point A on disc
Hence
2π(0.5)/T=(1.6*(2π(0.5+0.8sin theta)))/T
"T" cancels out
Now you can solve the equation to find the value of theta
(b) this part is simple
T cos theta= weight of particle
Solve it and get the value of T
(c) for this part u need to form two equations and solve them simultaneously to get the ans
As v=r* angular velocity (omega)
Firstly consider the point A on disk let the veloctiy of that point to be "x" and the angular velocity of point A and particle to be "y"
For point A => x=0.5y
For particle =>1.6x=(0.5+0.8sin theta) y
Solve these equations to get the value of "y"
U will get the value of angular velocity..
Hope u understood..

 

[Ankitaagg]

do we get a formula sheet for stats and pure maths in as level???
if yes please upload the file.
thank you

 

[zahra azam]

Can any one name a helpful highly recommended reference book for math?

 

[Rizwan Javed]

Can any one name a helpful highly recommended reference book for math?

Which module?

 

[zahra azam]

Which module?

I am doing edxcel
N i am taking C1 C2 and S1

 

[Rizwan Javed]

I am doing edxcel
N i am taking C1 C2 and S1

I thought you're asking about CIE A Level Maths. I can't help you with edexcel

 

[zahra azam]

I thought you're asking about CIE A Level Maths. I can't help you with edexcel

Which one do u use for cie
Doesnt matter course is almost the same

 

[Rizwan Javed]

For P1 I use 'Advanced Level Mathematics : Pure Mathematics 1 by Hugh Neil and Douglas Quadling'.
For P3 I use 'Advanced Level Mathematics : Pure Mathematics 2 & 3 by Hugh Neil and Douglas Quadling'.
FOr Stats, S1 I use : 'Concise Course in Adcanved Level Statistics by J.Crawshaw and J.Chambers'

Btw I have a few books for edexcel Mathematics in pdf format. If you want I can upload them for you.

 

[manya]

someone plz help me with part b ii

 

[lemonrsiow]

Hi guys can anyone help me with this question?
manya squareroot each root you got from a that's the answer.

 

[manya]

Hi guys can anyone help me with this question?
manya squareroot each root you got from a that's the answer.

View attachment 57043

yeah but why taking roots of the roots of z will give roots of z^2

 

[Umna.Asim]

Can someone give me topic wise past papers for APGP and Vectors? Pleasseeee

 

[My Name]

Can someone give me topic wise past papers for APGP and Vectors? Pleasseeee

Check here:
https://www.xtremepapers.com/community/threads/the-ultimate-maths-thread-for-a-as-level.36407/
https://www.xtremepapers.com/commun...2-and-p3-combined-topicals-for-a2-here.41944/

 

[sj0007]

Ummmmm hey is there any rule, in vectors, that if a.b is negative, the angle is obtuse?