[CIE] All Pure Mathematics (P1, P2 and P3) doubts here !

[leebux101]

may june 2003 Q5 , what are the complex numbers and how to do part i)
please asap! =D thanks a gziliion in advance! =D

[ShiningStar]

I have a question:
State the range of values of x for which the expansion (1-4x)^-3 is valid. ( Q3 Paper 9202/1/O/N/01)
What I did is:
-1<1-4x<1
-2<-4x<0
0<x<1/2
Please correct me if there is anything wrong...
What I don't understand here is that how is 1/4 accepted, as if x=1/4 then there is a 0 in the denominator which is going to give (Math Error)?? 
Thanks!

[ShiningStar]

may june 2003 Q5 , what are the complex numbers and how to do part i)
please asap! =D thanks a gziliion in advance! =D

The complex numbers are: u=2i, w=(cos(2pi/3) + sin(2pi/3)i)
5.i) w= -1/2 + (root3/2)i, what I did is that I solved the brackets where cos(2pi/3) = -1/2 and sin(2pi/3)i = (root3/2) i
uw= 2i(-1/2 + (root3/2)i) = -root3-i
u/w = 2i/(-1/2 + (root3/2)i) then you multiply it by its conjugate (-1/2 - (root3/2)i) to get it in form x+iy
Hope it helps

[leebux101]

thankyou sooooooooooooooooooooooooooo much!! honestly! =D
i am sorry i cant help u in ur question.. =(

[leebux101]

also for same questio  part iii
how do u get the angle at the vertices! please. =)

[ShiningStar]

also for same questio  part iii
how do u get the angle at the vertices! please. =)

You don't have to find the angle at the vertices, you can find the lengths of UB, UA and AB and see if they are equal then it is an equaliteral triangle..!

[leebux101]

in the marking scheme it says that u have to get the angle at atleast two vertices as 60
secondly, can u do q10 part iii from the same paper! please!!

[leebux101]

please! anyone! i need this reallyyy quickly!

[ShiningStar]

in the marking scheme it says that u have to get the angle at atleast two vertices as 60
secondly, can u do q10 part iii from the same paper! please!!

Use the Identity in the 10.i) to replace cosec2x, so it will become:
Integration cotx - cot2x dx (with the same limits)
=(ln(sinx) - 1/2 ln(sin2x)) then substitute with the limits

[leebux101]

thakyouuuuuuuuu sooooooo much!
+repp!! =D =D

[THEIGBOY]

can someone explain how to do questions like -->
question 5 paper 33 june 2010 part ii
and
question 3 paper 33 octover/nov 2010 part ii


and how to do question 10 on may june 2010 paper 33
Thank you very much

[TJ-56]

Does anyone know why the root (-1\3) in question 10 (ii) in paper May June 2008 is rejected?  The mark scheme just states that “Having rejected the root (-1\3) for a valid reason" lol, well what is this reason?
Thanx in advance.

[leebux101]

can someone do ON03 q 7 iii)
arii!! where u at man!
we need ya here! =P

[SkyPilotage]

can someone do ON03 q 7 iii)
arii!! where u at man!
we need ya here! =P

Its A circle with radius=2 units and center u.

[SkyPilotage]

Does anyone know why the root (-1\3) in question 10 (ii) in paper May June 2008 is rejected?  The mark scheme just states that “Having rejected the root (-1\3) for a valid reason" lol, well what is this reason?
Thanx in advance.

That is because if you substitute t=-2 and t=-1/3 in the position vector of P ; the dot product of AP.AB should be +ve since the angle is acute.. If its -ve the angle is obtuse...Therefore if you use t=-2 you will get it +ve, and t=-1/3 will be -ve meaning obstuse angle which is incorrect..