Mathematics: Post your doubts here!

[Zishi]

AoA. Can anyone pls explain how we solve the question # 8? and also explain generally how we solve these type of question. I cant solve these easily.thank you
http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s11_qp_11.pdf

This is the Series and Sequences question. Do you know how to solve questions related to arithmetic and geometric series? All you need to do in this question is to apply the formulas of series. Hint: Model 1 represents arithmetic series and Model 2 represents geometric series.

 

[Zishi]

And also in the question # 4 part (ii) to find the angle, why do we take: tanx= -3 ,where -3 is the gradient and also in Qs#9 Part(i) (a) how do we find the range??
.the paper is http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s11_qp_12.pdf
pls can someone explain these to me soon? thank you.

Q4: Because the gradient is Δy/Δx and we usually draw a right angle triangle to find the gradient. Tangent theta is Perpendicular(Δy) divided by base(Δx).
Q9: Range is the max and min values of f(x), cos^2 x has a minimum value of 0 and max value of 1. Put those values in f(x) expression to get min and max values of f(x)
(P.S I appeared in this paper in May/June 2011 )

 

[Hammad Siddiqi]

qstn 9 iia) we have proved that cos4θ 4 cos2θ = 8cos^4θ - 3

so for solving cos4θ 4 cos2θ =1 we can solve 8cos^4θ - 3 =1

8cos^4θ - 3 =1
8cos^4θ = 1+3
8cos^4θ = 4
cos^4θ = 4/8
cos^4θ = 1/2 take square root on both sides

cos^2θ = 0.707 take square root again

cosθ = 0.84 now θ = cos-1(0.841 = 0.572 Ans

Hey agar online aao to June 06 P3
Q6 (ii) solve krlo...
ms itni kharab hai k samagh nhi aarahi...
maine answer verify krna hai

 

[bamteck]

Prove the identity :

tan A + cot A = 2/sin2A

Thank you very much ...

 

[Anoushay]

Q4: Because the gradient is Δy/Δx and we usually draw a right angle triangle to find the gradient. Tangent theta is Perpendicular(Δy) divided by base(Δx).
Q9: Range is the max and min values of f(x), cos^2 x has a minimum value of 0 and max value of 1. Put those values in f(x) expression to get min and max values of f(x)
(P.S I appeared in this paper in May/June 2011 )

Yeah,i Figured the tangent question out when i did it again. but Thanks for explaining that and the cos one.

 

[Anoushay]

This is the Series and Sequences question. Do you know how to solve questions related to arithmetic and geometric series? All you need to do in this question is to apply the formulas of series. Hint: Model 1 represents arithmetic series and Model 2 represents geometric series.

yes,i know how to solve arithmetic and geometric series but i kind of have a block with these type of questions. Can you do solve a little?

 

[Zishi]

Prove the identity :

tan A + cot A = 2/sin2A

Thank you very much ...

The LHS can be written as sinA/cosA + cosA/sinA. Take the LCM and simplify it into a simpler fraction, i.e (sin^2 A + cos^2 A)/(sinAcosA). sin^2 A + cos^2 A = 1 and sinAcosA = ½sin2A(using the double angle formula). I hope you get it now.

 

[xhizors]

Yeah,i Figured the tangent question out when i did it again. but Thanks for explaining that and the cos one.

well i dont know it may help you or not
you can even find out the angle with b/w two lines with the formula --> tan(x)=|(m2-m1)/1-m1m2)|

where m1 and m2 are the gradients of the lines

 

[Zishi]

yes,i know how to solve arithmetic and geometric series but i kind of have a block with these type of questions. Can you do solve a little?

Okay, for Model 1, use the Sum formula with n= 40, d and a= 1000. Multiply the sum by 0.05 to get the money which will go to charity. As for Model 2, again use the formula with r=1.1 and n=40. Multiply that sum by 0.05(5%) to get the answer. Do you get it now?

 

[Nikesh]

Prove the identity :

tan A + cot A = 2/sin2A

Thank you very much ...

LHS. tanA + cotA
--> sinA/cosA + cosA/sinA
--> (sin^2A + cos^2A) / (cosA.sinA)
--> 1/sinA.cosA
Multiply numerator and denominator by 2
--> 2/2sinA.cosA
-->2/sin2A (sin2A = 2sinAcosA)
hence proved

 

[leadingguy]

Prove the identity :

tan A + cot A = 2/sin2A

Thank you very much ...

sina/cosa + cosa/sina now take lcm

sin^2a + cos^2a /(cosa.sina)
1/(sina.cosa ) now remember the identity sin2a = 2sina.cosa

so we have to multiply the denominator by 2 to gt 2sina.cosa


when multipling denominator numenator should also be muliplied by

1*2/(sina.cosa )*2 = 2/2sina.cosa = 2/sin2a proven

 

[leadingguy]

http://www.xtremepapers.com/papers/...AS Level/Mathematics (9709)/9709_s06_ms_3.pdf
http://www.xtremepapers.com/papers/...AS Level/Mathematics (9709)/9709_s06_qp_3.pdf

question 6 part ii)

can any one solve it with each and evry step?? a detailed explanation is needed here

 

[hm12]

http://www.xtremepapers.com/papers/...S Level/Mathematics (9709)/9709_w10_qp_11.pdf

question 7 part(i) and part(iii)

i really have a lot of problem finding ranges and domains of function can anyone help me with it? how do we find them?

 

[Dug]

AoA wr wb
9709_s04_qp_4
Q6 ii
help plz

 

[Jimmy Russels]

Assalamalaikum. These are probably stupid questions so don't laugh Can anyone help me?
Qs.1) Find the values of k such that the straight line y=2x+k meets the curve with equation x^2+2xy+y^2=5 exactly once.

Qs.2) An Open cylindrical wastepaper bin, of radius r cm and capacity Vcm^3 is to have a surface area of 5000 cm^3.
(a) Show that V=1/2r(5000πr^2)
(b) Calculate the maximum possible capacity of the bin.

 

[aaakhtar19]

AoA wr wb
9709_s04_qp_4
Q6 ii
help plz

The minimum value of force will give the maximum speed

and force is minimum when its equal to resistance so force = 400

speed = power / force
speed = 20000 / 400
speed = 50
hope you got it *^_^*

 

[Dug]

the ms says put acceleration=0 wht does that mean

 

[aaakhtar19]

the ms says put acceleration=0 wht does that mean

at acceleration = 0
force = resistance
b'coz::
force - resistance = ma
force - resistance = m * (0)
force - resistance = 0
force = resistance

 

[aaakhtar19]

http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s06_ms_3.pdf
http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s06_qp_3.pdf

question 6 part ii)

can any one solve it with each and evry step?? a detailed explanation is needed here

in part (ii) just do these steps
let f(x) = 1 + e^x - 2cot(x)
then f(0.5) = -1.0123
then f(1.0) = 2.4341

The change of sign between the values of f(x) means f(x) cuts the X-axis between this interval

 

[Anoushay]

well i dont know it may help you or not
you can even find out the angle with b/w two lines with the formula --> tan(x)=|(m2-m1)/1-m1m2)|

where m1 and m2 are the gradients of the lines

Thankyou.