Mathematics: Post your doubts here!

[Rutzaba]

in sha Allah

 

[Jiyad Ahsan]

someone pleaaase give me s1 problems.. i need to solve problems !!! doesnt anybody have any s1 problems ? gimme gimmeeee !! i think im high on sugar

 

[hassanhijazi1995]

awful the last 2 questions were hell !!!
the stupid complex number thing wasnt even printed properly.. it said the Re > 0.. which was supposed to mean that the real part was greater than zero.. WTH !? was i supposed to guess that Re meant real part?

no dude Re means real and it's mentioned in the question + it did came in the past years!

 

[Zenia ZZ]

oh its because since all the presents are going to be distributed among 11 players so 11! and then dividing the presents 5 pens = 5!, 4 diaries= 4!, 2 notebooks = 2!
so you have 11! / 5! x 4! x 2!
the purpose of factorial ' ! ' is that it works like 11 x 10 x 9 x 8 x .... as the players get the gifts the total number of gifts and the players waiting to recieve the gift decreases..
do you get it?

yp thank you so much

 

[kreacher]

permutations and combinations good techniques..any body got notes on these???

 

[Zenia ZZ]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s11_ms_62.pdf
Q3 anyone ? please . I also want to know the rules of these types of questions .

 

[Jiyad Ahsan]

permutations and combinations good techniques..any body got notes on these???

ok i'll put it in very simple words for you, permutations is 'arrangement' whenever you have to arrange something or put it in sequence.. it always means permutations
In permutations if you have say 10 people who can sit on a bus which has say 18 seats.. okay so you have 18 places where you can arrange 10 people so the number of ways in which the people can sit in the bus is 18P10.. if there were 18 people and 18 seats it would be 18! which is basically 18P18.. and so forth

similarly combinations just means the ways a thing or a number of things can be 'selected/chosen' the difference of course being that here the sequence 'DOES NOT' matter
example you have to find the number of ways that a commitee of 6 people can be chosen from 8 men and 8 women if there have to be 4 men and 4 women then all you have to do is 8C4 x 8C2,
8C4 shows 4 men chosen from 8 and similarly 8C2 shows 2 women chosen from 8..

try to do the question 4 from june 11 paper 61.. its all permutation
and Q7. november 10 paper 62.. its all combination.. thats all the hints im giving you right now.. try them and if you get stuck just ask

 

[syed1995]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_61.pdf
i dnt understand 4ii... u dnt hav to do it..... jus explain Jiyad Ahsan

In 7 days.. Atleast 1 day it snows .. so you will find the probability of that.. (X>=1) .. meaning 1-P(X=0) where p = 0.21

then use that value as p .. for 1 period of 7 days... p comes as 0.808

Now it takes 4 periods where it asks the probablity for exactly 3 periods where it rains..

4C3*(p)^3*(1-p)
=0.4052

 

[Alice123]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_62.pdf
no 5iii

 

[panoramafolks]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_61.pdf
i dnt understand 4ii... u dnt hav to do it..... jus explain Jiyad Ahsan

sorry for poor editing...

 

[TaffsAsLevel]

it went terrible... the 1st 7 questions made me feel like i wud get full marks n then ....... felt like murdering the a***hole who made the question

OMGG exactlyyy, first page was easy and complex number is something new, the sketch was fine, and vector first part is easy only second part where they gave angle 60 degrees, then trigonometric subs, especially differential I couldn't eliminate the logarithmic

 

[Jiyad Ahsan]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s11_ms_62.pdf
Q3 anyone ? please . I also want to know the rules of these types of questions .

umm ok this is a method known as assumed mean, you basically take a number and assume that it is the mean of a set of numbers (lets say we have 16, 17, 19, 21, 22) so I 'assume' the mean is 20 and the i calculate the difference of every number from that assumed mean. first lets just do it. then i'll explain this in statistical sense
so the five numbers are
16, 17, 19, 21, 22 and the assumed mean was 20, so find the difference for each of these numbers from 20,= -4, -3 ,-1, 1, 2 these are the respective differences

so you add all the differences and you have -5
so you have the sum of (x - 20) = -5
since there were five numbers, divide -5 by 5
x-20 = -5/5
x-20 = -1
x = 19 (voila, this is the real mean)

so when in your question they give you
Σ(x-45) = -148 (45 here is the assumed mean)
x-45 = -148/36
x-45 = -4.11
x = -4.11 + 45
x = 40.89 (the real mean )
= 40.9 (to one d.p.)

so the formula for the mean is
[ Σ(x-a) ]/ n , a is the assumed mean and n is the number,

similarly in the question there is given Σ(x-45)^2 = 3089
the variance is calculated by
Σ(x-a)^2/n _ ( Σ(x-a)/n )^2

so according to the question we have,
3089/36 _ ( -148/36 )^2 . . keep in mind that it is (-148/36) whole squared

=85.8 - (-4.11)^2
=68.90

since standard deviation is sqrt of variance
s.d = sqrt (68.90)
s.d = 8.30

 

[Jiyad Ahsan]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_62.pdf
no 5iii

(2C2 x 9C4) + (2C0 x 9C6)
= 186 + 84
= 210

total 11 questions right? you have two conditions, either both questions or none
well say first you choose both the questions so you'd have 2C2 multiplied by the rest 4 questions will be chosen from the 9 remaining so 9C4
the other condition if 2C0 (you dnt choose both questions) multiplied by the all the 6 questions chosen from the remaining p so 9C6
add both conditions

 

[Alice123]

(2C2 x 9C4) + (2C0 x 9C6)
= 186 + 84
= 210

total 11 questions right? you have two conditions, either both questions or none
well say first you choose both the questions so you'd have 2C2 multiplies by the rest 4 questions will be chosen from the 9 remaining so 9C4
the other condition if 2C0 (you dnt choose both questions) multiplied by the all the 6 questions chosen from the remaining p so 9C6
add both conditions

stupid mee... my brain's nt working ... thanks

 

[Jiyad Ahsan]

stupid mee... my brain's nt working ... thanks

we all have those 'brain not working' days, kher ogae

 

[Alice123]

we all have those 'brain not working' days, kher ogae

yea !!! can u help me with 7iii the same year??? i'll sleep after that.......

 

[Jiyad Ahsan]

yea !!! can u help me with 7iii the same year??? i'll sleep after that.......

P(X < 34.6)
P (Z < 34.6-41.1/3.4 )
P (Z < -1.912)
=Φ (-1.912)
=1 - Φ (1.912) as Φ(-a) = 1 - Φ(a)
=1-0.9713
=0.0287
=0.028

multiply that by 0.95
=0.95 x 0.028
=0.0266 (reasons and explanation below)

since its given that the probability that 5th symphony rhyme is more than 34.6 = 0.05
therefore the probability that it is less than 34.6
= 1 - 0.05
=o.95
probability that 5th and 6th are less than 34.6
= 0.028 x o.95
= o.o266

 

[Alice123]

P(X < 34.6)
P (Z < 34.6-41.1/3.4 )
P (Z < -1.912)
=Φ (-1.912)
=1 - Φ (1.912) as Φ(-a) = 1 - Φ(a)
=1-0.9713
=0.0287
=0.028

multiply that by 0.95
=0.95 x 0.028
=0.0266 (reasons and explanation below)

since its given that the probability that 5th symphony rhyme is more than 34.6 = 0.05
therefore the probability that it is less than 34.6
= 1 - 0.05
=o.95
probability that 5th and 6th are less than 34.6
= 0.028 x o.95
= o.o266

why arent we using mean n sd frm 7ii??? Im sorry if u find my qs stupid...
PS my brain's actually nt working
EDIT: got it thanks

 

[Jiyad Ahsan]

by the way if someone could please explain (hopefully before our paper ) why and when (in what conditions) in normal distribution do we subtract from 1,
from what i've learned till now..
Φ(-a) = 1 - Φ(a) here to remove the negative sign
P(Z > a) = 1 - Φ(a) here (apparently) to remove the greater than ( > ) sign

also there was something about the fact that we cant read values less than o.5 off the table, so you had to 1 minus that too.. can someone explain please..

 

[abbey789]

that was easy

Let me know how did you do that? did you get x=2a?
Well for my school many got stuck after one point