Mathematics: Post your doubts here!

[Scafalon40]

Sure....hope u get it now.
View attachment 23276

Ok dude that helps alot! Thanks. This is as far as I got
The spaces:
_ _ _ _ _ _ _ _
1/3 in the first slot----->got it
the next tile should not be matching, so 2/3 in the second------>got it
now the next tile after that should not match the second tile. The probabiltiy that the next tile matches the second is 1/3, and the probability that it doesn't is 2/3. So 2/3 in the third slot. And this goes on...
Point out any fault in my reasoning, if you would please.

 

[PhyZac]

Ok dude that helps alot! Thanks. This is as far as I got
The spaces:
_ _ _ _ _ _ _ _
1/3 in the first slot----->got it
the next tile should not be matching, so 2/7 in the second------>got it
now the next tile after that should not match the second tile. The probabiltiy that the next tile matches the second is 1/3, and the probability that it doesn't is 2/3. So 2/3 in the third slot. And this goes on...
Point out any fault in my reasoning, if you would please.

Well,
In first slot it is 1 ! ( because it cud be any! no restrictions)
Now from second onwards it is 2/3 ! because a different color to first is 2/3 and so on!
We dont start with 1/3 and it is 2/3 not 2/7

 

[salvatore]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s07_qp_1.pdf
Please help me solve no. 3.. I'm totally confused!
Thanks

PhyZac I need urgent help

 

[Scafalon40]

Well,
In first slot it is 1 ! ( because it cud be any! no restrictions)
Now from second onwards it is 2/3 ! because a different color to first is 2/3 and so on!
We dont start with 1/3 and it is 2/3 not 2/7

oops corrected the 2/7, typing mistake
The reason I'm starting with 1/3 is because there is the probability of choosing any of the 3 tiles is 1/3. No?

 

[PhyZac]

oops corrected the 2/7, typing mistake
The reason I'm starting with 1/3 is because there is the probability of choosing any of the 3 tiles is 1/3. No?

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

 

[PhyZac]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s07_qp_1.pdf
Please help me solve no. 3.. I'm totally confused!
Thanks

PhyZac I need urgent help

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)

 

[Steel Arm]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s07_qp_1.pdf
Please help me solve no. 3.. I'm totally confused!
Thanks

ok so
1-tan^2x
1+tan^2x

this can be written as
1-((sin^2x)/(cos^2x))
1+(the same as above)

now the 1 in denominator and numerator can be written as ((cos^2x)/(cos^2x))

by using this u get that
cos^2x - sin^2x
cos^2x + sin^2x

the denominator is equal to 1 obv...so we work with numerator only
since cos^2x = 1-sin^2x....
u get 1-sin^2x-sin^2x
which is equal to
1-2sin^2x
Hence Shown!!!

Hope i helped!!!

 

[salvatore]

Thanks a lot both of you PhyZac Steel Arm
I don't get the 'multiply every term by cos²x' and 'cos²x/cos²x = 1'.. but I'll try to figure it out

 

[PhyZac]

Thanks a lot both of you PhyZac Steel Arm
I don't get the 'multiply every term by cos²x' and 'cos²x/cos²x = 1'.. but I'll try to figure it out

Write it on paper...u will get my point!

 

[salvatore]

Write it on paper...u will get my point!

Oh yeah.. now I get it.. I should have written it on a paper.
Thanks!

 

[Ahmedm96]

need good notes for permutatons and combnations

 

[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