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

[EMO123]

Thanks emo

any time

[$H00t!N& $t@r]

need help with q 2, 6(ii) and 10 O/N 2010 variant 12

Here is the link: http://www.xtremepapers.me/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_w10_qp_12.pdf

 

[........]

This is explained clearly in mark schemes .

[polltery]

the marked one is done! but i need help with the second one.. cant really understand how do i integrate it :/

[elemis]

Re-arrange :

6(3x-2)^-0.5

Concentrate only on (3x-2)^-0.5.

Add one to the power :

(3x-2)^0.5

Differentiate and adjust.

[Vin]

need help with q 2, 6(ii) and 10 O/N 2010 variant 12

Here is the link: http://www.xtremepapers.me/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_w10_qp_12.pdf

 

Q2
Right hand side

tan²x sin² x  

=tan²x (1 - cos² x)

=tan² x - tan²x cos²x

As tanx = sinx / cosx
cos x = sinx/ tanx

=tan²x - tan²x *

=tan²x - sin²x

[Vin]

the marked one is done! but i need help with the second one.. cant really understand how do i integrate it :/

There's a formula to integrate functions of the form (ax + b)ⁿ

f(x) = (ax + b)ⁿ

if f(x)  = y

y = (ax + b)ⁿ





= (ax + b)ⁿ⁺¹
   ----------        x
   n + 1  


DO NOT forget to multiply by 1/a

[Vin]

need help with q 2, 6(ii) and 10 O/N 2010 variant 12

Here is the link: http://www.xtremepapers.me/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_w10_qp_12.pdf

 

Q6 ii)

y = kx² +1   &  y = kx

equate the two to get k = 4 (follow up from the previous- but k² - 4k = 0 )
equate k=4 in kx² - kx +1 = 0 to get x = 1/2
equate x = 1/2 in one of the equations to get the y coordinate

Q 10

Expressing h in terms of x

Vol = 4 cm3 (given)

vol of object = x * 0.5x * h
4 = 0.5 * h * x^2
Change the sub. of formula to h to get h = 8/x²

Total Surface area (consider each side and add them up to make things easy)

= 2xh + 2*0.5*xh + 0.5 * x* x + 4/5 x * 5/4 x

solve, and substitute h = 8/x² to get the desired answer.

ii)

dA/ dx = 1.5 * 2 * x + 24 * -1 * * x ^-1-1

= 3x - 24/x^2

equate this to zero to obtain the stationary point as 2

d²A/ dx² = 3 - 24 * -2 * x ^-2-1

= 3 + 48/x^3

equate x =2 to get 9
since 9 > 0, point of minima

[physichemaths]

help me with question j08 question8? anyone?

[HUSH1994]

MJ 2010 P13,Q6 part 1,i did AB.BC but in the MS it was AB.CB,how do u know which order do u use?

[elemis]

help me with question j08 question8? anyone?

Since the area of the triangle equals to tanx  :

0.5*TN*PN = tanx

This can be re-written as :

0.5*x*y = tanx

The gradient of the tangent is simply :

dy/dx  = y/x

Finding the reciprocal of both sides :

dx/dy = x/y   

Re-arranging :

y*dx/dy = x

Substituting into original equation :

0.5*y²*dx/dy = tanx

Moving everything around :

0.5*y²*dx/tanx = dy

0.5*y²*dx*cotx = dy

0.5*y²*cotx = dy/dx

Done !

[SkyPilotage]

MJ 2010 P13,Q6 part 1,i did AB.BC but in the MS it was AB.CB,how do u know which order do u use?

Pretty Simple,
When they ask for angle ABC you either do BA.BC  or AB.CB
You just have to either go from inside to outside or outside to inside.
More ex: -Angle DAC You either do DA.CA or AD.AC
Ofcourse you have to use the corresponding modulus of each!
             -Angle PQR You can use QP.QR or PQ.RQ
Hope it clears things up

[HUSH1994]

Thanks alot,i thought if ABC then AB.BC,thanks and a +rep for you

[Arthur Bon Zavi]

Have a look at some other papers (paper 1 of p1) to have your doubts fully cleared.

By the way, VECTORS was a cakewalk for you.

[HUSH1994]

i know,tbh all the pure is a piece of cake,but there are always some questions that need thinking,i got 69/75 in this papers and i finished it in 1hour 10 mins,my biggest problem is signs,esp in binomial series :S