Mathematics: Post your doubts here!

[PANDA-]

Is it only me or is solving P1 papers very very boring?
I can't finish a whole paper without taking like 3 breaks in between, it's just that boring lol.

 

[Sarah22]

Hi...
1. A function f is defined by f : x → (2x − 3)3 − 8, for 2 ≤ x ≤ 4.
(i) Find an expression, in terms of x, for f(x) and show that f is an increasing function. [4]
(ii) Find an expression, in terms of x, for f−1(x) and find the domain of f−1. [4]
I want the domain part..

2. The equation of a curve is xy = 12 and the equation of a line l is 2x + y = k, where k is a constant.
(i) In the case where k = 11, find the coordinates of the points of intersection of l and the curve. [3]
Ans: ((1.5,8) & (4,3))
(ii) Find the set of values of k for which l does not intersect the curve. [4]
Ans: -√96 < k < √96
(iii) In the case where k = 10, one of the points of intersection is P (2, 6). Find the angle, in degrees
correct to 1 decimal place, between l and the tangent to the curve at P. [4]
Ans: 8.1° or 8.2°
The (ii) and the (iii) part pls..
It would be great help..
Thank you..

 

[Tkp]

Hi...

Thank you..

domain of f-1 is range of fx
so the ramge of fx is >-8 and its the domain also


Xy=12
2x+y=k
2x+12/x=k
2x2+12-kx=0
2x2-kx+12=0
B2-4ac<0
A=2,b=-k,c=12
K2-96<0
K<+-√96
So -√96<k<+√96

 

[Tkp]

Hi...
Thank you..

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

 

[Alice123]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w03_qp_6.pdf
help needed in qs 4i n ii

 

[Muhammad Muneeb]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_11.pdf
q4...

 

[A star]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w03_qp_6.pdf
help needed in qs 4i n ii

4i ) probability of success is (0.05) and failure is (0.95) .
he must fail in all the tries to not complete collection hence (0.95)^5
4ii use binomial approximation =5C1 x (0.15)^1 (0.95)^4

 

[A star]

shouldnt u guys concentrate on p1 now :/

 

[A star]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_11.pdf
q4...

Q4 to find k use the value of M=3.2kg and r= 10 in the formulae
(3.2)=k(10)^3
3.2/1000=k or k=2/625
now use the formulae
dM/dt = dM/dr x dr/dt
here dr/dt =0.1 (given)
find dM/dr =3kr^2 put the value of k and r you will get 0.96
therefore
dM/dt= 0.96 x 0.1 =0.096

 

[immie.rose]

(i) Sketch, on a single diagram, the graphs of y = cos 2q and y = 1
2 for 0 ≤ q ≤ 2p. [3] ( where q= theta)
(ii) Write down the number of roots of the equation 2 cos 2q − 1 = 0 in the interval 0 ≤ q ≤ 2p. [1]
Ans=4
(iii) Deduce the number of roots of the equation 2 cos 2q − 1 = 0 in the interval 10p ≤ q ≤ 20p. [1]
Ans=20

Someone please explain part (iii)!

 

[A star]

(i) Sketch, on a single diagram, the graphs of y = cos 2q and y = 1
2 for 0 ≤ q ≤ 2p. [3] ( where q= theta)
(ii) Write down the number of roots of the equation 2 cos 2q − 1 = 0 in the interval 0 ≤ q ≤ 2p. [1]
Ans=4
(iii) Deduce the number of roots of the equation 2 cos 2q − 1 = 0 in the interval 10p ≤ q ≤ 20p. [1]
Ans=20

Someone please explain part (iii)!

well part ii you found out there are four roots in a cycle that is 0-2p well there are 5 such cycles in 10p to 20p (20-10)/2=5
so if 4 : 1
theta: 5 sycles cross multiply you will get 20

 

[immie.rose]

well part ii you found out there are four roots in a cycle that is 0-2p well there are 5 such cycles in 10p to 20p (20-10)/2=5
so if 4 : 1
theta: 5 sycles cross multiply you will get 20

JazakAllah

 

[shafayat]

Help Me please ! the part one of this question :/

 

[A star]

Help Me please ! the part one of this question :/

is it p1?

 

[shafayat]

3 The first three terms in the expansion of (1 − 2x)^2(1 + ax)^6, in ascending powers of x, are 1 − x + bx^2.

Find the values of the constants a and b. [6]

I don't know how to multiply after expansion !! please can anyone help ?

 

[shafayat]

is it p1?

yeah !

 

[A star]

Help Me please ! the part one of this question :/

parti r= 1/(1/3tan x) hence r=3/tan(x)^2 it must be r must be less then 1 to be convergent hence
3/tan(x)^2 <1 hence tanx < under root 3 hence x< tan^-1 (under root of 3 ))
am i rite?

 

[iKhaled]

3 The first three terms in the expansion of (1 − 2x)^2(1 + ax)^6, in ascending powers of x, are 1 − x + bx^2.

Find the values of the constants a and b. [6]

I don't know how to multiply after expansion !! please can anyone help ?

how man..u dont know how to multiply 2 brackets..like for example u never ever multiplied (1+3x)(1+2x)..i dont think so :S

 

[shafayat]

g(x) = 8 − (x − 2)^2, for k ≤ x ≤ 4, where k is a constant.
(iii) find an expression for g−1(x),

how to find g inverse? Cuz I have no idea y they don't take plus or minus when they square root ! they only take plus , can someone explain me ? please

 

[shafayat]

how man..u dont know how to multiply 2 brackets..like for example u never ever multiplied (1+3x)(1+2x)..i dont think so :S

duhh Multiplication and then how to equate them ? if you can please explain me how to find a and b please