Mathematics: Post your doubts here!

[Alice123]

b (i) For getting a even number u need the number to end with even number (ofc) well in that number we have 2 4 6 8 as even,
now we consider each separtely
with 2 as end
we have 1 44 687
we rearrange 6! / 2! (we permutate 6 and we need to divide with 2 cuz there are 2 4s)
with 6 and 8 as end it is same thing as with 2
so we get 6!/2! and 6!/2!
with 4 as end we wont have 2 4s, so it will be only 6!
now add
6! + (6!/2!)*3 = 1800

i will try to solve rest soon In Sha Allah

b (ii) to get a number between 20 000 and 30 000 we have to start with number 2 and only, (we cant have a number smaller than 30000 starting with 3 ryt!)
so basically we have 2 and 4 blank
2_ _ _ _
so we permutate 4 from the left 5 numbers
we get 5P4 = 120!

(c) wat a tricky one!
anyway,
see, now since all have same prob, u get that each prob is 1/3

so we start any color and then take any of the other two in next shot
I am not sure if u got my point,
so we 1 * (2/3 )^7

first try is one, becuz all is possible..and power is 7 since 8 - 1 = 7

May Allah bless u with good grades...

 

[A star]

p(x<6)= 63/600
p(z< (6-mean0/s.d) = 63/600
(i)Do the same for the other set of values. You'll get to equations. Solve them simultaneously to get the answer.
(ii) P(X< mean-s.d) + P(X> mean + s.d)
This gives u the probability of length being more than a s.d from the mean. Multiply the result by 1000 to get expected number in 1000

i got that much but in the ms the value of z is 1.253 for 6 and i am not getting that value of z for my equation

 

[Scafalon40]

Fine fine, now lets say
any tile would be 1/3
now the probabilities when we start with a grey as an example would be
1/3 x (2/3)^7
and when start with black it will be
1/3 x (2/3)^7
and when we start with white it will be
1/3 x (2/3)^7

so basically [3 x (1/3 x (2/3)^7)]
3 x 1/3 = 1

got it. thanks

 

[A star]

need good notes for permutatons and combnations

buy the statistics 1 book by Steve Dobss its a great book and explains 90 percent of your questions in it are repeaed in past papers in diffrent wordings and figures

 

[Yousif Mukkhtar]

Can someone explain these two questions of 2 past papers:
Q5 i) Just q i
http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_w08_qp_1.pdf
Q4 part i)
http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_s09_qp_1.pdf

 

[VelaneDeBeaute]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w08_qp_1.pdf

Nov 08/Q5/(i)
Look at the function. It involves the cos function. We know that cos 0=1, cos 90=0, cos 180=-1, cos 270 =0, cos 360 =1.
If you substitute these values in place of cos x, you'll find that with the value of cos x as -1, we get a + b which might be the highest value.
Hence, we equate a + b =10.
Similarly, if cos x is taken by a 1, then f(x) =a - b (least value). Hence a -b = -2.
There you go, two simultaneous equations. Solve and get the answer.

 

[VelaneDeBeaute]

Q4 part i)
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s09_qp_1.pdf

When a function as such is written, the 'a' is the amplitude of the wave i.e. its maximum height/displacement from the mean position. Hence, a = 9 -3 =6.
For a normal sine curve, b = 1. However, if we compare a normal curve with the given, we find that this one completes two wave cycles in a time period of 2 pi. Therefore, b = 2.
'c' is the value of how high or low the mean position of the wave is when compared to the line y = 0. Here the graph is raised +3 respective of the line y = 0, hence c = 3.

 

[asexamskillme111]

http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20(9709)/9709_s10_qp_43.pdf

Can someone explain the last two parts of question 7 for me please? Thank you.

 

[princess787]

hey cn any1 understand 9709_w12_qp_12 question 7 ii) ? i expand (k-1) square and (2k-2) square and then add everything including k square.. i get the equation 6k square minus 10k and plus 5... bt the ms says plus 4... not idea how... in d column aside in the ms... its written "Sum of 3 squares (doesn't need =1)" dont knw wat it means.. pls help

 

[princess787]

dear XPC Bot..... wenevr i post a doubt u post some blank comment... u alright? or got any problems? :/

 

[aleezay]

i got that much but in the ms the value of z is 1.253 for 6 and i am not getting that value of z for my equation

P(X<6)=0.105 Let (6-mean)/sd be a
P(Z<a)=0.105
a is negative (im not sure how you've been taught to determine whether a is -ve or +ve. What we do is that if both the sign is less than, i.e <, and the probability is less than 0.5, or if both are more than, then a is -ve)
1- Fi(a)= 0.105
Fi(a)= 0.895
a= -1.253

 

[yousef]

The identities you have to know is tanx = sinx/cosx
and sin^2x + cos^2x = 1
and from the above u can also see cos^2x = 1-sin^2x

Now this is very messy, i would suggest to write what you see in paper...since it isnt neat on pc. And check Steel Arm post below...it is nicely represented !

1-tan^2(x) / 1+tan^2(x)
1-[ sin^2(x) / cos^2(x)] / 1 + [sin^2(x) / cos^2(x)]
now multiply every term with cos^2(x)
cos^2(x) - sin^2(x) / cos^2(x) + sin^2(x)
cos^2(x) - sin^2(x) / 1
(1-sin^2(x)) - sin^2(x)
1-2sin^2(x)

can any one help me bro's ???
q no. 1 q5 (ii)


http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s10_qp_11.pdf

 

[abcde]

can any one help me bro's ???
q no. 1 q5 (ii)


http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s10_qp_11.pdf

AoA! You could maximize the expression (2 sin^2 x - 3 cos^2 x) by maximizing the value with the positive coefficient and minimizing the value with the negative coefiicient. Max (sin^2 x) = 1 and min(cos^2 x) = 0. So, the max value of f(x) = 2(1) - 3(0) = 2.

To minimize the expression, minimize the value with the positive coefficient and maximize the value with the negative coefficient. Min(sin^2 x) = 0 and max(cos^2 x) = 1. So, the minimum would be = 2(0) - 3(1) = -3.

Tee hee!

 

[yousef]

AoA! You could maximize the expression (2 sin^2 x - 3 cos^2 x) by maximizing the value with the positive coefficient and minimizing the value with the negative coefiicient. Max (sin^2 x) = 1 and min(cos^2 x) = 0. So, the max value of f(x) = 2(1) - 3(0) = 2.

To minimize the expression, minimize the value with the positive coefficient and maximize the value with the negative coefficient. Min(sin^2 x) = 0 and max(cos^2 x) = 1. So, the minimum would be = 2(0) - 3(1) = -3.

Tee hee!

thanks dude ... thats not the way we got taugh in school ... so probably i wont understand it ::: any way thanks for helping ......... if there is other way .. it will be much better ..if not (thanks )
can u do no. 1

 

[salvatore]

http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_s07_qp_1.pdf
Please help me solve qn no. 8 (i & ii).. an explanation will be appreciated.

Thanks!

 

[abcde]

thanks dude ... thats not the way we got taugh in school ... so probably i wont understand it ::: any way thanks for helping ......... if there is other way .. it will be much better ..if not (thanks )
can u do no. 1

No problem, dude. Even if it isn't the way you were taught, I hope it made some sense.
Q5. Use the identity sin^2 x = 1 - cos^2 x over here and you'll have it solved.
(P.S. Just a bit of advice: If you learn to adapt to new methods, things can work quite smoothly for you. )

 

[Just visiting]

Can anyone please help me in solving this question and if he/she would be extra clear when explaining
Thanks in advanc

 

[Rutzaba]

dear XPC Bot..... wenevr i post a doubt u post some blank comment... u alright? or got any problems? :/

xpc bot is a way of advertising
u cant post a blabk post at xpc

 

[19islandprincess96]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w11_qp_33.pdf
Can someone help me?
Q10) i)
I made an equation in u but I don't understand how to integrate it.

 

[19islandprincess96]

No problem, dude. Even if it isn't the way you were taught, I hope it made some sense.
Q5. Use the identity sin^2 x = 1 - cos^2 x over here and you'll have it solved.
(P.S. Just a bit of advice: If you learn to adapt to new methods, things can work quite smoothly for you. )

I am jumping into you conversation out of nowhere but I had the same problem... My question is, how'd you know that max (sin^2 x) = 1 and min(cos^2 x) = 0?