Mathematics: Post your doubts here!

[daredevil]

well as an aid roughly sketch the graph and you will find graph varies between -1 and 3 which is the range

drawing the graph like we normally do for cos graphs?? taking 4 values on x-axis like (pie)/4 and stuff??

 

[iKhaled]

Any mechanics people here? !

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w10_qp_41.pdf

Q6 (i) (c) and (ii) ?

JazakAllah

hey there!

for 6 c(i) you need to find the ratio of the speed at the ground to the speed at B. we have the kinetic energy at both points. At B the kinetic energy is 1.6j and at the ground it will be 6j so

1/2mv^2 = 1.6
v = 4 ( this is the speed of the object at B)

1/2mv^2 = 6
v = √60 ( this is the speed of the object on the ground)

ratio = v at G / v at B = √60/4 = 1.94

(c) initial energy at X is the potential energy = 2H all of this will be converted to kinetic energy when it reaches the ground so the final energy at the ground will be 2H which is all kinetic energy so 1/2m(VG)^2 = 2H
so VG^2 = 20H

now we will calculate the value of V at B (VB)

initial energy at x:

Ep = 0.2(10)(H) = 2H

final energy at B :
Ek = 1/2(0.2)(VB)^2
Ek = 0.1VB^2

EP = 2(H-2.2) = 2H - 4.4

2H = 0.1VB^2 + 2H - 4.4
VB^2 = 20H - 44

we got both VB^2 and VG^2 now we can use our ratio VG/VB= 2.55

VB^2/VG^2 = 6.5025
20H - 44/20H = 6.5025

solve for H and u will get it as 0.385 subtract it from 3 and u will get the answer 2.62

 

[qwerty123123]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s11_qp_12.pdf
Question 9 i)a)
I always get lost when I see questions like these :c
Help please?

Just go to your calculator table function and type in:

f(x) = 3 − 4(cos(x))^2
type in your limits and step.
So start = 0
end = pi
step = pi/4
Now you can immediatly see the highest and lowest value's of f(x) i.e. your range so it is: -1=<f(x)<=3

OR

Since you know that the max value of cos^2(x) = 1 and the min is 0, you know that 3-4(0) = 3 and 3-4(1) = -1 Hence your range is -1=<f(x)<=3

 

[WayneRooney10]

Can someone please solve (Nov 2012, P13) Q2, and Q7 part (ii), with full working and explanations? Thank you. There seems to be some problem with the mark scheme.

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w12_qp_13.pdf

 

[daredevil]

Can someone please solve (Nov 2012, P13) Q2, and Q7 part (ii), with full working and explanations? Thank you. There seems to be some problem with the mark scheme.

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w12_qp_13.pdf

i don't know how to write so much maths here cz it gets all confusing but i'll try
look if f is a decreasing function then dy/dx should be <0
find dy/dx of this funciton which wen i calculated it was pretty wierd: -
dy/dx = -3(1-x^2)/x^4

is this wat u r getting too?

 

[Rutzaba]

I usually get confused when we are asked to find the range of trigonometric functions.. its just too complicated for me! What do I have to consider when solving such questions?

Look at these two functions:
f(x) = 3 - 2sinx for 0 ≤ x < pi
f(x) = 3 - 2sin(1/2x) for 0 ≤ x < pi.

How different would the range of the two functions be?
regards salvatore

 

[tom ed]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w11_qp_63.pdf
q2

 

[mominzahid]

volume of rotation of this graph will be (pie) x integration of the square of the equation in terms of y

the equation will be (y^2 - 1)/3 ........... check if its ryt.
take the square of this equation and integrate it.
use integration limits to calculate integrant and then multiply it by pie.
if u dont' get it then tell me and i'll c wat i can do to further explain

The answer I get if i do it this way is 4pi/9 or 1.89 whereas the marking scheme gives the answer 1.5Pi or 4.71. :/

 

[Rutzaba]

The answer I get if i do it this way is 4pi/9 or 1.89 whereas the marking scheme gives the answer 1.5Pi or 4.71. :/

mai solve karun? poora?

 

[Rutzaba]

I usually get confused when we are asked to find the range of trigonometric functions.. its just too complicated for me! What do I have to consider when solving such questions?

Look at these two functions:
f(x) = 3 - 2sinx for 0 ≤ x < pi
f(x) = 3 - 2sin(1/2x) for 0 ≤ x < pi.

How different would the range of the two functions be?
regards salvatore

HELLO SOLVE SOMEONE!
A star syed1995 iKhaled daredevil

 

[A star]

i don't know how to write so much maths here cz it gets all confusing but i'll try
look if f is a decreasing function then dy/dx should be <0
find dy/dx of this funciton which wen i calculated it was pretty wierd: -
dy/dx = -3(1-x^2)/x^4

is this wat u r getting too?

yup thats what i got and its not wierd is it .
i guess i solved wierder then this
i

 

[Rutzaba]

The answer I get if i do it this way is 4pi/9 or 1.89 whereas the marking scheme gives the answer 1.5Pi or 4.71. :/

one eq is y=2
square = 4
integrate 4x for the limits 0 and 1
you get 4
4(1) - 4(0) =4
then sec eq (3x+1) ^1/2
square = 3x+1
integrate (3/2) x^2 +x apply limits 0 and 1
(3/2) (1)^2 +(1) - (3/2) (0)^2 +(0)

5/2
then (4- 5/2) pi
1.5 pi ^_^

 

[A star]

Can someone please solve (Nov 2012, P13) Q2, and Q7 part (ii), with full working and explanations? Thank you. There seems to be some problem with the mark scheme.

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w12_qp_13.pdf

Q2 find f '(x) and see that you will get two terms in x with neg sign hence for all positive values of x it will be a decreasing function
7i
y=5-x
y=11-x^2
sub y you will get 5-x=11-x^2 solve it and take the positive value of x as p and its y coordinate as q

 

[tom ed]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w11_qp_63.pdf
q2 and q6 plz

 

[qwerty123123]

I usually get confused when we are asked to find the range of trigonometric functions.. its just too complicated for me! What do I have to consider when solving such questions?

Look at these two functions:
f(x) = 3 - 2sinx for 0 ≤ x < pi
f(x) = 3 - 2sin(1/2x) for 0 ≤ x < pi.

How different would the range of the two functions be?
regards salvatore

The range for those two functions is going to be the exact same, the only thing that is changing is the period.
-2sin(x) means the graph will be flipped and the amplitude will be twice.
3+ means the graph will be translated +3 in the y direction so the range for both is 1=<f(x)<=5

 

[Maz]

I usually get confused when we are asked to find the range of trigonometric functions.. its just too complicated for me! What do I have to consider when solving such questions?

Look at these two functions:
f(x) = 3 - 2sinx for 0 ≤ x < pi
f(x) = 3 - 2sin(1/2x) for 0 ≤ x < pi.

How different would the range of the two functions be?
regards salvatore

qwerty123123 gave you the correct answer, but if you are still confused as to how to go about it then here goes.
What i do is substitue the whole sinx, sin(1/2x), or for that matter cosx or any other cos or sin function by 1 for the maximun value and -1 for the minimum value. I guess you can check it.
And then it's child's play.
3 - 2(1) = 1 & 3-2(-1) = 5 for both of them.
It's only applies for sin/cos not for tan.

 

[Rutzaba]

The range for those two functions is going to be the exact same, the only thing that is changing is the period.
-2sin(x) means the graph will be flipped and the amplitude will be twice.
3+ means the graph will be translated +3 in the y direction so the range for both is 1=<f(x)<=5

qwerty123123 gave you the correct answer, but if you are still confused as to how to go about it then here goes.
What i do is substitue the whole sinx, sin(1/2x), or for that matter cosx or any other cos or sin function by 1 for the maximun value and -1 for the minimum value. I guess you can check it.
And then it's child's play.
3 - 2(1) = 1 & 3-2(-1) = 5 for both of them.
It's only applies for sin/cos not for tan.

salvatore

 

[qwerty123123]

qwerty123123 gave you the correct answer, but if you are still confused as to how to go about it then here goes.
What i do is substitue the whole sinx, sin(1/2x), or for that matter cosx or any other cos or sin function by 1 for the maximun value and -1 for the minimum value. I guess you can check it.
And then it's child's play.
3 - 2(1) = 1 & 3-2(-1) = 5 for both of them.
It's only applies for sin/cos not for tan.

Good point, that would be a quicker method.

 

[Yousif Mukkhtar]

Can someone explain Q7) b) i)
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_11.pdf

 

[igcsedude_Jor]

hello
can someone please explain to me everything i need to know about completing the sqaure and coefficient?
please can someone explain to me this: w12 qp 11 question 10 parts 1 and 2 (btw whats domain?) and question 4
and this: w2008 q1, q5, and q10 part 3
thank u soo much