Mathematics: Post your doubts here!

[PhyZac]

PhyZac if u can!? Please!

Umm, okay, sure, but can you list your priorities? Like those are so many..

 

[WayneRooney10]

Can anyone solve this identity for me? cos4x-4cos2x+3=8sin^4x

 

[AlishaK]

Umm, okay, sure, but can you list your priorities? Like those are so many..

start from the first one... do it at ur pace. no hurry. but if possible before the exam? only if u're good with it?
Jazak Allah Khair! Thanks so much!
Cheers!

 

[Muhammad Muneeb]

i) 7!/2!
ii) consider 1 3 and 7 to be in a box and consider that box to be one dash
_ * 7 *6*5*4*3*2*1

number if dashes 8 and inside the box 3!
so 8!*3! /2! because 2 comes twice thats y we divide

iii) that means they wud end at 2,2,6,8
6! *4 /2!

what i didnt get was why we divided by 2! in part, formula or something i m missing?

 

[PhyZac]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w10_qp_63.pdf
(can someone please explain question (1 , 4 , 6 and 7 )
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w10_qp_61.pdf
(question 1 , 6 and 7(ii , iv , v)) http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s10_qp_63.pdf
(question 6 (ii))

AlishaK
First paper.
1) Normal distribution (because this is continuous variable, not discrete)
The mean weight, and variance. (Since X ~ N(mean, variance) )
Suggestion
Weight, 60
Variance, I dont know how to suggest a variance, but I would say 100.

4) (i) Mean, 63.5
Because, you first take the mean of the value given, 245/70 = 3.5 ; you then add 60 (because it was subtracted, don't subtract before dividing)

(ii) 945,
We know know that the mean of E(x-60) is 3.5
Now to get mean of E(x-50) we ad 10 getting 13.5
Then to E(x-50) we multiply with 70, getting 945

(iii)http://papers.xtremepapers.com/CIE/...d AS Level/Mathematics (9709)/9709_y13_sy.pdf
Check the syllabus in link above and go down to Statistics formulas

You will find this formula


therefore
10.6 = √E(x^2) /n - x`^2
E(x^2) = n(10.6^2 + x`^2 )
n=70
so,
70 (10.6^2 + 13.5^2) [P.S. we calculated mean is 13.5 above]
=20623

This for now, will continue later, In Sha Allah.

 

[PhyZac]

what i didnt get was why we divided by 2! in part, formula or something i m missing?

the number "2" is repeated twice, so you have to divide with 2!
if repeated trice the divide 3! and etc..

 

[talha-_-khan]

Q)Find the tangent of the angle b/w the line "7y=x+2" and "x+y=3"

i got the answer
find the grad of 7y=x+2 which is 1/7
find the grad of "x+y=3" which is -1
then we need to do tan(A-B) = tan [(1/7)-(-1)] = [(1/7)-(-1)]/[1+((1/7)*1)] = 4/3

 

[MustafaMotani]

I got the diameter and radius... I was wondering how would we find out the mid- point and I just understood!! We had to use the coordinate geometry formula for mid-point of the two points! Can't believe I didn't think of that before ! Thank you soo much. May Allah bless you and grant you success in this life and in the Hereafter

thanx for the prayers..

 

[mominzahid]

Hi can someone please explain q8 (i) and i(i), q9 (ii) only and q10 (ii) 0nly.. thanks
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w12_qp_32.pdf

 

[Esme]

Hi can someone please explain q8 (i) and i(i), q9 (ii) only and q10 (ii) 0nly.. thanks
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w12_qp_32.pdf

Wow only ?

 

[Rutzaba]

what i didnt get was why we divided by 2! in part, formula or something i m missing?

because 2 comes twice thats y we divide

if we have to find the number of ways in which the word book can be arranged for example it will be 4!/2!
because o comes two times yea?
if for example there is a bag in which there are 3 red balls and 4 blue ones...
then it will be 7! / (4!*3!) because blue gets repeated 4 times and red 3 times... get it? tell me if u dun

 

[PhyZac]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w10_qp_63.pdf
(can someone please explain question (1 , 4 , 6 and 7 )
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w10_qp_61.pdf
(question 1 , 6 and 7(ii , iv , v)) http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s10_qp_63.pdf
(question 6 (ii))

AlishaK

6) (i) 14P12 = 4.36 x10^10 [P.S, use calculator]
See, there are 14 places, and thus we permutate 12. (This is more like a rule)

(ii) Here I got stuck, but Alhamdulilah, I found littlecloud11 post, below.

View attachment 25598

The students cannot take the window seats in the first row because the 3 business people have to be seated there. Each married couple must be seated in a different row, but they have to be on the same side of the isle. So one of the couples have to take two window seats so that both couples are in different rows. So you see, only 5 window seats remain, and the students have to take these 5 seats in any order. So it's 5! and not 9P5.

(iii)I got stuck again, but Alhamdulilah found this post below

I know what you mean, the question is worded quite awkwardly so don't blame yourself for not getting it.
Its basically asking you to take the total number of way for the passengers to be seated, and since it uses the word and you then multiply those ways and divide them by the result in part (i).
Hence, there being 3 front row seats for Mrs. Brown --> 3P1.... For Mrs. Lin, she must sit behind a student, and for her to do so she cannot be in the front and since there are 10 seats available for this to be true --> 10P1.... now for the STUDENTS, Mrs. Lin must be behind 1 student, which means this student must be infront of her, which leads to only 1 possibility for that student to be seated. BUT we do not know which student this is, since there are 5 students and we need to choose 1, we do ------> 5P1 =5.

Hope this helps

Now, the only this left is, 9 people are left, (12- (Mrs Lin + a student + Mrs Brown))
And 11 seats left (14 - 3)
so x 11P9
and divided by total number of permutation the answer we got at (i)

Later, will continue In Sha Allah.

 

[Esme]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_33.pdf

Q5ii) How do we do these type of questions ? There others like this.. eg find the value of y as x becomes very large..

 

[Soldier313]

https://docs.google.com/file/d/0Bzq5n8R79M6_bEFMLWFERFBVdW8/edit?usp=sharing

Check this up what i meant!!

Wow jazakAllah khair for this! it's exactly what I wanted to see...

 

[iKhaled]

Hi can someone please explain q8 (i) and i(i), q9 (ii) only and q10 (ii) 0nly.. thanks
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w12_qp_32.pdf

for question 9(ii)

u have the found 2 roots = 1-√2i and 1+√2i
so the 2 factors of the polynomial that has been found are (u-(1-√2i)) and (u-(1+√2i)) if u multiply these factors together u will get a quadratic equation of u^2-2u+3 now u have the polynomial equation as u^4 + u^2 + 2u + 6....u or x it doesnt matter they are all letters after all anyway apply long division or whatever way u have learnt to find the other quadratic equation..then from that other equation u will find the other 2 roots then boom u have 4 roots found

 

[kiara15]

i had some ambiguity in below quest:
1) P(Z>a)=0.8888 , a is negativ,
1-fi(-a)=o.8888
1-[1-fi(a) ]=o.8888
the other solution of quest i found:
2)p(z<t)=0.25, t is negativ
fi(-t)=0.25
1-fi(t)=0.25..
can anyone tell me this difference and concept how to solve such type of quest plzzz

 

[kiara15]

i had some ambiguity in below quest:
1) P(Z>a)=0.8888 , a is negativ,
1-fi(-a)=o.8888
1-[1-fi(a) ]=o.8888
the other solution of quest i found:
2)p(z<t)=0.25, t is negativ
fi(-t)=0.25
1-fi(t)=0.25..
can anyone tell me this difference and concept how to solve such type of quest plzzz

 

[kiara15]

i had some ambiguity in below quest:
1) P(Z>a)=0.8888 , a is negativ,
1-fi(-a)=o.8888
1-[1-fi(a) ]=o.8888
the other solution of quest i found:
2)p(z<t)=0.25, t is negativ
fi(-t)=0.25
1-fi(t)=0.25..
can anyone tell me this difference and concept how to solve such type of quest plzzz

 

[mominzahid]

for question 9(ii)

u have the found 2 roots = 1-√2i and 1+√2i
so the 2 factors of the polynomial that has been found are (u-(1-√2i)) and (u-(1+√2i)) if u multiply these factors together u will get a quadratic equation of u^2-2u+3 now u have the polynomial equation as u^4 + u^2 + 2u + 6....u or x it doesnt matter they are all letters after all anyway apply long division or whatever way u have learnt to find the other quadratic equation..then from that other equation u will find the other 2 roots then boom u have 4 roots found

Hey thanksss.... What about other questions? can u solve them please?

 

[MustafaMotani]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_33.pdf

Q5ii) How do we do these type of questions ? There others like this.. eg find the value of y as x becomes very large..

from part i) u would have got
y = 70 e^(e^(-3t) -1)

p = mass at time t / initial mass x 100
p = 70 e^(e^(-3t) -1) / 70 x 100
p = e^(e^(-3t)-1)) x 100


now if yu see if t becomes very large the expression e^(-3t) would approach zero .
look at it this way
e^(-3t) = 1/e^(3t)
see if denominator becomes very large the fraction becomes too small i.e. it approaches zero.
thus if e^(-3t) aproaches zero then e^(-3t)-1 approaches -1
thus e^(e^(-3t)-1) approaches e^(-1)

so p = e^(-1) x 100

take yur time reading this post..