Mathematics: Post your doubts here!

[Rutzaba]

Can anyone help me with co prime numbers which are also said as relatively prime number??? Ho2 do u find out the ways that can be expressed? ?

dude u post a question hre once and once ok? we will find u k?

 

[farhan143]

I have a difficulty in solving q-6, b (i) of O/N 2012


can someone explain me, how to solve it..
not just the solution..
the explanation as well

THANKS in adavance.
FARHAN

 

[Dug]

I have a difficulty in solving q-6, b (i) of O/N 2012
View attachment 22407

b. (i)
Because it looks less tedious, I am going to find the no. of arrangements where the number is odd and then subtract it from all possible arrangements.

For odd numbers, the last digit has to be odd. This gives us two possibilities.

_ _ _ _ _ _ 1 or _ _ _ _ _ _ 7

No. of odd arrangements = (6!/2!) + (6!/2!) = 720

No. of even arrangements = No. of all possible arrangements - No. of odd arrangements
= 7!/2! - 720
= 1800

 

[snowbrood]

Prove that if (c-b).a=0 and (c-a).b=0, then (b-a).c=0. Show this can be used to prove the following geometric results:
1) The lines through the vertices of a triangle ABC perpendicular to the opposite sides meet in a point (the orthocentre)
2) The tetrhedron OABC has two pairs of perpendicular opposite edges, the third pair of edges is perpendicular.
Prove also that, in both cases, OA^2 + BC^2 = OB^2 + CA^2 = OC^2 + AB^2.

 

[PhyZac]

Assalamu Alikum Wa Rahmatullahi Wa Barakatoho...littlecloud11
Can someone solve Question 6 part (i)

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s10_qp_32.pdf

 

[littlecloud11]

Assalamu Alikum Wa Rahmatullahi Wa Barakatoho...littlecloud11
Can someone solve Question 6 part (i)

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s10_qp_32.pdf

Re-arrange the eq-
ln y = 2x+1/x
differentiate both sides
1/y dy/dx = [2x- 1(2x+1)]/x^2 {use u/v formula for RHS and ln y = 1/y dy/dx for LHS}
1/y dy/dx = 2x-2x -1/ x^2
1/y dy/dx = -1/x^2
dy/dx = (-1/x^2)/ (1/y)
dy/dx = -y/x^2

 

[Translucent231]

Co prime numbers are numbers which have no factor common ,

like 2 and 3 are coprime 16 and 25 are coprime but 2 and 4 are not co prime...
8 and 5 are coprime and so on..

 

[PhyZac]

Re-arrange the eq-
ln y = 2x+1/x
differentiate both sides
1/y dy/dx = [2x- 1(2x+1)]/x^2 {use u/v formula for RHS and ln y = 1/y dy/dx for LHS}
1/y dy/dx = 2x-2x -1/ x^2
1/y dy/dx = -1/x^2
dy/dx = (-1/x^2)/ (1/y)
dy/dx = -y/x^2

Thank You so much !!!!! JazakAllah khiaran !! May Allah grant you and your family with highest grades in this life and hereafter. Ameen !

Alhamdulilah i got it !!

 

[snowbrood]

i dont get the second part the angle one. answer is 119.9 or60.1

 

[daredevil]

i dont get the second part the angle one. answer is 119.9 or60.1

As OA --> 4i
OC --> 2j
OD --> 3k
and it is a cuboid so:

OG --> 2j+ 3k
OA --> 4i
AG = OG - OA = -4i + 2j + 3k

and OB = 4i + 2j


that said... now use the scalar product to find the angle between them
(ai)(bi) + (aj)(bj) + (ak)(bk) = lal . lbl . Cos (angle between a and b)

where a and b are AG and OB respectively and LaL --> magnitude of vector a

solving this:
put in all the values and u'll get it down to:
-12 = (20)^1/2 . (29)^1/2 . Cos (angle between them)
Cos (angle b/w them) = -0.49827...
angle b/w them = 119.8858...
= 119.9

 

[maham khan]

h

Assalamoalaikum Wr Wb!

Post your doubts here. Make sure you give the link to the question paper when posting your doubts.


May Allah give us all success in this world as well as the HereAfter...Aameen!!

And oh yeah, let me put up some links for A level Maths Notes here.

Check this out! - Nice website, with video tutorials for everything! MUST CHECK

My P1 Notes! - Only few chapters available at the moment!

Maths Notes by destined007

Some Notes for P1 and P3 - shared by hamidali391

A LEVEL MATHS TOPIC WISE NOTES

MATHS A LEVEL LECTURES

compiled pastpapers p3 and p4 - by haseebriaz

Permutations and Combinations (my explanation)- P6

Permutations and Combinations - P6

Vectors - P3

Complex No. max/min IzI and arg(z) - P3

Sketcing Argand Diagrams - P3 (click to download..shared by ffaadyy)

Range of a function. - P1

help needed with question 3 of a level s1 paper 62 may june 2012

 

[kronix6]

Hi can anyone please slove 61/o/n/2010 question 3 part 2. and m/j/61/2012 question 6 part 2. and can u explain plx why in 2012 paper we have taken p(-1<x<+1) and why we have only taken p(x<1.645) in octnov 2012 paper. i will be grateful.

 

[PhyZac]

Asslamu Alikum Wa Rahmatulahi Wa Barakatoho.......!!! littlecloud11

Can anyone please solve question 8 part (ii)

http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_s09_qp_3.pdf

 

[Omar99]

question no. 9
oct/nov 2012 p32

 

[Omar99]

Assalamoalaikum Wr Wb!

Post your doubts here. Make sure you give the link to the question paper when posting your doubts.


May Allah give us all success in this world as well as the HereAfter...Aameen!!

And oh yeah, let me put up some links for A level Maths Notes here.

Check this out! - Nice website, with video tutorials for everything! MUST CHECK

My P1 Notes! - Only few chapters available at the moment!

Maths Notes by destined007

Some Notes for P1 and P3 - shared by hamidali391

A LEVEL MATHS TOPIC WISE NOTES

MATHS A LEVEL LECTURES

compiled pastpapers p3 and p4 - by haseebriaz

Permutations and Combinations (my explanation)- P6

Permutations and Combinations - P6

Vectors - P3

Complex No. max/min IzI and arg(z) - P3

Sketcing Argand Diagrams - P3 (click to download..shared by ffaadyy)

Range of a function. - P1

oct/nov 2012
p32

 

[littlecloud11]

Asslamu Alikum Wa Rahmatulahi Wa Barakatoho.......!!! littlecloud11

Can anyone please solve question 8 part (ii)

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s09_qp_3.pdf

dx/dt = x^2 (10−x)/100
Cross multiply
∫100/ (x^2 10−x) dx = ∫ dt
use your answer to part (i) for the LHS
∫1/x + 10/x^2 + 1/(10-x) dx = ∫ dt
lnx - 10/x - ln|10-x| = t + c -------1
when x=1, t=0
ln1 - 10/1 - ln| 10-1| = 0 + c
-10 - ln9 =c
substitute the value of c in eq 1
lnx - 10/x -ln|10-x| = t - 10 - ln9
t = -10/x + 10 +ln9 +lnx - ln|10-x|
t= -10/x + 10 + ln | 9*x/ (10-x)|

 

[PhyZac]

dx/dt = x^2 (10−x)/100
Cross multiply
∫100/ (x^2 10−x) dx = ∫ dt
use your answer to part (i) for the LHS
∫1/x + 10/x^2 + 1/(10-x) dx = ∫ dt
lnx - 10/x - ln|10-x| = t + c -------1
when x=1, t=0
ln1 - 10/1 - ln| 10-1| = 0 + c
-10 - ln9 =c
substitute the value of c in eq 1
lnx - 10/x -ln|10-x| = t - 10 - ln9
t = -10/x + 10 +ln9 +lnx - ln|10-x|
t= -10/x + 10 + ln | 9*x/ (10-x)|

Thank you thank you thank you soooooo much !!!!!!!!!!! Jazki Allah khairan !!! THANKS ALOT for your help, i am sorry for tagging all time !! May Allah reward you with best grades , Ameen. May Allah have mercy on you and your family, Ameen. May Allah bless you and your family with happiness and success, Ameen. May Allah grant you with Jannah tul firdous Ameeen!!!!

 

[littlecloud11]

Thank you thank you thank you soooooo much !!!!!!!!!!! Jazki Allah khairan !!! THANKS ALOT for your help, i am sorry for tagging all time !! May Allah reward you with best grades , Ameen. May Allah have mercy on you and your family, Ameen. May Allah bless you and your family with happiness and success, Ameen. May Allah grant you with Jannah tul firdous Ameeen!!!!

You tagging me is worth it just for the good wishes I get afterwards.
So tag away!
And thank YOU.

 

[PhyZac]

Assalamu Alikum littlecloud11

Can anyone solve question 10 part (ii)

http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_s09_qp_3.pdf

 

[littlecloud11]

Assalamu Alikum littlecloud11

Can anyone solve question 10 part (ii)

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s09_qp_3.pdf

Sin^2(θ) = [1 - Cos 2(θ)]/2
so, sin^2 (2θ) = [1 - Cos 2(2θ)]/2
sin^2 (2θ) = [1 - Cos 4θ]/2

Now substitute sin^2 (2θ) as [1 - Cos 4θ]/2 for the integration:
1/4∫ sin^2 2θ =1/4 ∫[1 - Cos 4θ]/2
= 1/4 * 1/2 ∫1 - Cos 4θ
= 1/8 [θ - Sin 4θ/4]
put the limits
=1/8 [(π/2 -0) - (0 -0)]
=π/16
so A = π/16