Mathematics: Post your doubts here!

[A star]

Q 6i)
and
Q9ii)

yelps for help

when scaler product less then 1 we sayy acute if greater then 1 then obtuse
other is simple integration

 

[PANDA-]

when integrating with limits we donot add c.
when integrating without limits we add c

I don't really understand the meaning of limits to be honest.

 

[Sarah22]

r u sure about c3?cn u tell me it is in which year

Thank you soo much.. The paper is Oct/Nov 2005, question 8 & 9

 

[iKhaled]

I don't really understand the meaning of limits to be honest.

in integration limits r the values u put on the top of that sign ∫ and on the bottom of it

 

[GorgeousEyes]

@GorgeousEyes
9i) if OAB is a straight line then OA is a part of OB,
Therefore, by comparing the two vectors we can that OB is twice of OA
p = 2

unit vector = each vector/ magnitude of vector
= (2i+ j + k)/(2^2 +1 +1)[square root]
= (2i+ j + k)/[square root]6

ii) Remember that the dot product of perpendicular vectors is '0'
therefore, OA.AB = 0
(pi + j + k) . ( [4-p]i, j, [p-1]k) = 0
p*(4-p) + (1*1) + (1*(p-1)) = 0
5p - p^2 = 0
solve quadricatically p= 0 or 5

iii) if you can roughly draw the diagram you will realise that AB = OC
therefore c = b-a
I hope you can work that out.

[i may have made some calculation errors in ii but the methods generally correct]

And next time could you please give the link of qp please

Thanks

 

[Sarah22]

1. May/June 2006, question 7
2. Oct/Nov 2006, question 10-Part (v)
It would be great help.. Thank you..

 

[A star]

1. May/June 2006, question 7
2. Oct/Nov 2006, question 10-Part (v)
It would be great help.. Thank you..

link would be nice

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_11.pdf 9iii) how to find the value of D the ms just states the answer not the method pls reply asap those who can as ii want to finish maths and do phy for rest of the nite

 

[falcon678]

link would be nice

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_11.pdf 9iii) how to find the value of D the ms just states the answer not the method pls reply asap those who can as ii want to finish maths and do phy for rest of the nite

on it!

plus coordinates of B?

 

[Maz]

I don't really understand the meaning of limits to be honest.

Limits mean the the values of x between which the graph stretches.
For instance if the dy/dx is given as = 3x^2, the integration of this will give us y=x^3. it is correct however dy/dx= 3x^2 can also be gotten from y=x^3+2 or =x^3+4, there are multiple answers therefore we add "+c".
I hope that makes sense.

 

[A star]

on it!

plus coordinates of B?

just explain the last part of this question thankyou

 

[sma786]

(6)^2 /(2x-3)^2
so make the integ . --> 36 (2x-3)^-2 -- > 36(2x-3)^-1 / -2
and by using the limits 2 and 3 --> -6-(-18)= 12 pi

so why do we divide by -2?

 

[GorgeousEyes]

1. May/June 2006, question 7
2. Oct/Nov 2006, question 10-Part (v)
It would be great help.. Thank you..

no . 7 : You have to divide the like diamond shape to 2 traingles
so u can use tan to get BOT --> -Tan15/8 -- > ans x pi / 180 --- >to get AOB : ans x 2 -- > 2.16
ii . pe :15+15+ 2.16 x8 = 47.28
iii.get the hyp and by it bring tha area of the 2 traingles and subtract it from 2.16 x 8^2 x 0.5 --> 120-69012 =50.88 .

 

[sma786]

how to find the equation y+2= -4/3(x-3)
i found the correct gradient (-4/3) but i got the equation : 3y+4x=-19

 

[GorgeousEyes]

so why do we divide by -2?

because the coefficient of x is 2 and the new power is -1 so -1 x 2= -2 .

 

[Maz]

link would be nice

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_11.pdf 9iii) how to find the value of D the ms just states the answer not the method pls reply asap those who can as ii want to finish maths and do phy for rest of the nite

Hope you remember that m1*m2 = -1
i.e. the products of two gradients is equal to -1 if the two lines are perpendicular.

 

[falcon678]

just explain the last part of this question thankyou

dude it wld be sumthing like tht v ve to translation vector here....v just ve to find the side parallel to AD...lets say it is BC....v find itz translation vector n apply it on A to find the value of D.....i hope u got it?

 

[Tkp]

Thank you soo much.. The paper is Oct/Nov 2005, question 8 & 9

it was a tough question.c by putting the value of k=10 u will get anohter point q amd frm that point find the gradient
and u need to find the gradient of the curve also which is dy/dx
dy/dx=12/x
dy/dx=-12/x2
by putting x =2 u will get 3
then to find the angle difference tan theta2m-tan(theta1m)
so for the 1st by calculating u will get m=-2
so tan(3)-tan(2) and thats the answer

 

[syed1995]

sin 2x + 3 cos 2x = 0
3cos2x = sin2x
3=sin2x/cos2x
3= tan2x

0<x<360
0<2x<720

tan2x=-3
2x = tan-1(3)
2x=180-71.6=108.4, 360-71.6=288.4 in 1st revolution
2x = 108.4+360=468.4 , 288.4+360=648.4 in 2nd revolution
so 2x = 108.4,288.4,468.4,648.4
and x = 54.2,144.2,234.2,324.2

We won't go into third revolution as that exceeds 720.. 468.4+360 = GREATER than 720.

Tan negative in second and 4th quadrant..


The curve y =10/(2x + 1)− 2 intersects the x-axis at A. The tangent to the curve at A intersects the y-axis at C.
(i) Show that the equation of AC is 5y + 4x = 8

Intersects X axis at A.. y=0 at A..
0=10/(2x+1) -2
solve that.. you get x=2.. so A = (2,0)

differentiate curve equation and put x=2 to get the gradient..

Now use that gradient.. according to MS the gradient is -4/5 ..

Then use the gradient and the point which you have.. (2,0) to get the equation...

y-y1=m(x-x1)
y-0=-4(x-2)/5
5y=-4x+8
5y+4x=8 Answer

 

[Maz]

how to find the equation y+2= -4/3(x-3)
i found the correct gradient (-4/3) but i got the equation : 3y+4x=-19

find the equation from what?

 

[GorgeousEyes]

1. May/June 2006, question 7
2. Oct/Nov 2006, question 10-Part (v)
It would be great help.. Thank you..

q. 10 -- > x-3squarerootx =10
square root x is half x , so u knw reducing equation to quadritic ?
put the equation --> x-3squarerootx-10 on calculator
ans = square root x =5 and square root x = -2
but we want x so --> x=(5)2 and x= (-2)^2