Mathematics: Post your doubts here!

[TheJDOG]

http://maxpapers.com/syllabus-materials/mathematics-9709-a-level/attachment/9709_s14_qp_42/

can someone help me solve question 5?

Hi,
5)
i) they want the KE gain of the whole system, we know that KE=1/2mv^2
We know block A mass= 5 kg and B= 16 kg
So KE of whole system = (1/2)5v^2 + (1/2)16v^2 = 10.5v^2 J

ii) a) we need the loss of PE of the system. We know that PE= mgh and we know they moved a distance of x
We also know that the loss of PE of the system= Loss of b - gain of A
Well, logically B lost PE it moved downwards, so PE Loss of b= mgh= 16(10)(x) J
Also, A gained PE it moved up the slope, use basic trigonometry to find the distance it moved vertically up in terms of x.
So PE gain of A= mgh= 5(10)(xsin30) J
Loss of PE of the system= 16(10)(x) - 5(10)(xsin30)= 160x - 25x= 135x J

b) here we need the work done against friction. We know that f=uR and work = FxD
given u= 1/root3
We have to resolve, take y axis perpendicular to slope. We have R acting upwards along y axis and we have the component of weight of A acting downwards along y axis. Now R= Wcos30=50cos30= 25root3.
So friction = uR= (1/root3)(25root3)= 25 N
So work done against friction = 25x J since it moved a distance of x

iii) we know that Gain in KE= Loss in PE - work done to oppose friction
So 10.5v^2= 135x - 25x
10.5v^2 = 110x
Multiply both sides by 2
21v^2= 220x

 

[cadburrylover]

can someone tell me when continuity correction has to be done for calculation mean/variance for a histogram data in s1?

 

[The Sarcastic Retard]

can someone tell me when continuity correction has to be done for calculation mean/variance for a histogram data in s1?

When the given data is not continuous, you to correct it using upper and lower bounds to plot histogram and calculate the mean, varaiance, SD, or anything asked.

 

[Mayarzawaydeh]

http://onlineexamhelp.com/past-pape.../9709-mathematics-a-as-level-past-papers-2014

Hi. can someone please take a look at s14_qp_13 question 7 (i) ?
I seem to never get it right.

 

[TheJDOG]

http://onlineexamhelp.com/past-pape.../9709-mathematics-a-as-level-past-papers-2014

Hi. can someone please take a look at s14_qp_13 question 7 (i) ?
I seem to never get it right.

Hey, in 7) were given vectors OA, OB and OC.
We have to show that angle BAC is = cosinverse (1/3)
This angle is at the vertex A, draw a quick sketch it'll make things clear.
This angle is between vectors AB and AC also, a quick sketch will help you.
We know that Costheta= A.B/|A|.|B|
Where theta is the angle between the two vectors, and modulus is their lengths.
Now find AB, we know that AB= OB - OA= (0,-1,7) -(2,1,3) = (-2,-2,4)
Find AC= OC - OA= (2,4,7)- (2,1,3)= (0,3,4)
Now substitute in the equation, Costheta= (-2,-2,4).(0,3,4)/root((-2)^2+(-2)^2+(4)^2).root((0)^2+(3)^2+(4)^2)
Make theta the subject, Costheta = 10/(root24).(5)
Theta = cosinverse(1/root6)
I think there's something wrong here, ms says OB - OA= (4,-2,4) but how ? I think there's a typo in the first number of the given OB :/ or I might have a silly mistake who knows

 

[lxelle]

Hey, in 7) were given vectors OA, OB and OC.
We have to show that angle BAC is = cosinverse (1/3)
This angle is at the vertex A, draw a quick sketch it'll make things clear.
This angle is between vectors AB and AC also, a quick sketch will help you.
We know that Costheta= A.B/|A|.|B|
Where theta is the angle between the two vectors, and modulus is their lengths.
Now find AB, we know that AB= OB - OA= (0,-1,7) -(2,1,3) = (-2,-2,4)
Find AC= OC - OA= (2,4,7)- (2,1,3)= (0,3,4)
Now substitute in the equation, Costheta= (-2,-2,4).(0,3,4)/root((-2)^2+(-2)^2+(4)^2).root((0)^2+(3)^2+(4)^2)
Make theta the subject, Costheta = 10/(root24).(5)
Theta = cosinverse(1/root6)
I think there's something wrong here, ms says OB - OA= (4,-2,4) but how ? I think there's a typo in the first number of the given OB :/ or I might have a silly mistake who knows

hi! Could you help me with further statistics? Ques 7ii please https://thol.sunway.edu.my/examdbase/alv/math/p7/math_p7_n02.pdf Thanks.
And this question too, A fair coin is tossed 5 times and the number of heads is recorded.
The number of heads is doubled and denoted by the random variable Y. State the mean and variance of Y.

 

[sara kamal]

http://maxpapers.com/wp-content/uploads/2012/11/9709_May-June-2011-All-Question-Papers.pdf
please explain Q5 b of paper 61
thanks in advance.

 

[Mayarzawaydeh]

Hey, in 7) were given vectors OA, OB and OC.
We have to show that angle BAC is = cosinverse (1/3)
This angle is at the vertex A, draw a quick sketch it'll make things clear.
This angle is between vectors AB and AC also, a quick sketch will help you.
We know that Costheta= A.B/|A|.|B|
Where theta is the angle between the two vectors, and modulus is their lengths.
Now find AB, we know that AB= OB - OA= (0,-1,7) -(2,1,3) = (-2,-2,4)
Find AC= OC - OA= (2,4,7)- (2,1,3)= (0,3,4)
Now substitute in the equation, Costheta= (-2,-2,4).(0,3,4)/root((-2)^2+(-2)^2+(4)^2).root((0)^2+(3)^2+(4)^2)
Make theta the subject, Costheta = 10/(root24).(5)
Theta = cosinverse(1/root6)
I think there's something wrong here, ms says OB - OA= (4,-2,4) but how ? I think there's a typo in the first number of the given OB :/ or I might have a silly mistake who knows

Thank you very much!!

 

[sara kamal]

3 The times taken by students to get up in the morning can be modelled by a normal distribution with
mean 26.4 minutes and standard deviation 3.7 minutes.
(i) For a random sample of 350 students, find the number who would be expected to take longer
than 20 minutes to get up in the morning. [3]
(ii) ‘Very slow’ students are students whose time to get up is more than 1.645 standard deviations
above the mean. Find the probability that fewer than 3 students from a random sample of 8
students are ‘very slow’.

please explain part 2,i didnt get what does question mean???

 

[asadalam]

Anyone have examiner reports of W14 papers?

 

[asadalam]

Hey, in 7) were given vectors OA, OB and OC.
We have to show that angle BAC is = cosinverse (1/3)
This angle is at the vertex A, draw a quick sketch it'll make things clear.
This angle is between vectors AB and AC also, a quick sketch will help you.
We know that Costheta= A.B/|A|.|B|
Where theta is the angle between the two vectors, and modulus is their lengths.
Now find AB, we know that AB= OB - OA= (0,-1,7) -(2,1,3) = (-2,-2,4)
Find AC= OC - OA= (2,4,7)- (2,1,3)= (0,3,4)
Now substitute in the equation, Costheta= (-2,-2,4).(0,3,4)/root((-2)^2+(-2)^2+(4)^2).root((0)^2+(3)^2+(4)^2)
Make theta the subject, Costheta = 10/(root24).(5)
Theta = cosinverse(1/root6)
I think there's something wrong here, ms says OB - OA= (4,-2,4) but how ? I think there's a typo in the first number of the given OB :/ or I might have a silly mistake who knows

I think its a typo cuz 0 and 2 can never give an i vector of 4,i also did it and got the ans as cos-1 (1/(square root 6).There has to be a typo in the question.

 

[qwertypoiu]

yeah

 

[TheJDOG]

hi! Could you help me with further statistics? Ques 7ii please https://thol.sunway.edu.my/examdbase/alv/math/p7/math_p7_n02.pdf Thanks.
And this question too, A fair coin is tossed 5 times and the number of heads is recorded.
The number of heads is doubled and denoted by the random variable Y. State the mean and variance of Y.

Hey, I don't know Statistics unfortunately, I study Mechanics instead

 

[Ahmed Aqdam]

dx=2u du
Substitute x and dx to get ∫2ucosu du. Integrate by parts.
2u(sin u) - ∫sin u(2)
2u sinu + 2 cos u
Limits will be 0 and p as when x is 0 u is 0 and when x=p^2 then u=p. Area of R is equal to 1 so equation will be equated to 1.
(2p sinp + 2 cosp) - (0 + 2)=1
2p sinp +2 cosp -2=1
Make sinp the subject to get sinp= (3-2 cosp)/2p

 

[a12345]

Mathematics AS level Paper 1 Complete notes
Please reply if you found them helpful.

http://cieoandalevelnotes.blogspot.com/2015/04/mathematics-level-paper-1-notes-as-level.html?m=1

thanks the notes were very helpful best of luck for your exams!

 

[TheJDOG]

Papajohn here you go, I hope its clear

 

[hammadullah]

thanks the notes were very helpful best of luck for your exams!

thank you and good luck to you too

 

[ashcull14]

in my ans i get +2 instead of -1 cn smone point out my mistake??

 

[Mayarzawaydeh]

View attachment 52293
in my ans i get +2 instead of -1 cn smone point out my mistake??

if you're writing 4x^2 +8x+3 in the form of a(x+b)^2+c. I suggest you fully expand the form of -->a(x+b)^2+c and compare it to your quadratic equation.
example, the full expansion of a(x+b)^2+c is ---> ax^2 + 2abx+ab^2+c.
comparing it to your quadratic equation would be like:

• 4x^2 = ax^2, cancel the x^2 on both sides gives you a=4.
• 8x= 2abx (substitute a here) , 8x= 2 (4)bx, cancel x on both sides gives you b=1.
• 3=ab^2+c (substitute both a and b here) , 3= (4)(1)^2 +c, gives you c= -1

hence overall substitute all values you found in the form of a(x+b)^2+c gives you 4( x+1)^2 -1
I hope this helps.

 

[ashcull14]

can someone resolve the forces and xplain plzz?