IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => IB => Math => Topic started by: astarmathsandphysics on October 06, 2008, 10:59:23 am

Title: Maths/Physics help
Post by: astarmathsandphysics on October 06, 2008, 10:59:23 am
Post your IB questions here to get the answers back asap from someone with 3 maths/physics degrees.
Title: Re: Maths/Physics help
Post by: milton on November 18, 2008, 02:35:55 pm
Whats the formula/method for perpendicular distance of a point to a plane?
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on November 19, 2008, 09:47:59 am
I will give an example. Point(2,3,1) and plane 9x+8y+7z=4.

The equation of the line from the point to the plane is r=(2,3,1)+t(9,8,7)
so for this line x=2+9t
                       y=3+8t
                       z=1+7t
Substitute these into equation of plane

9(2+9t)+8(3+8t)+7(1+7t)=4
49+194t=4 so t=-45/194
and r intersects the plane at the point (2,3,1)-45/194(9,8,7)=(-17/194,222/194,-121/194)

Now find the distance between (2,3,1) and the point just found using the formula sqrt((x1-x2)^2+(y1-y2)^2+(z1-z2)^2)
Title: Re: Maths/Physics help
Post by: milton on November 20, 2008, 09:38:24 am
My memory is sketchy, but I found a tough question, worth 15 marks.

Serious car accidents on a road follow a Poisson distribution and have a mean of 2 per week.

a) What is the mean in a 4-week period

b) Given that 1 year has 13 four-week periods, what is the probability of nine of those 13 four-week periods having atleast 1 serious car accidents

c) If the probability of a car crash in 'n' weeks is 0.99, what is n
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on November 20, 2008, 09:52:19 am
My memory is sketchy, but I found a tough question, worth 15 marks.

Serious car accidents on a road follow a Poisson distribution and have a mean of 2 per week.

a) What is the mean in a 4-week period

b) Given that 1 year has 13 four-week periods, what is the probability of nine of those 13 four-week periods having atleast 1 serious car accidents

c) If the probability of a car crash in 'n' weeks is 0.99, what is n

a)8
b)The poisson is scalable so the probability distribution now is Po(eight) so P(X=k)=e^-8*8/k!. the probability that x>=1 accident in 1 month is 1-e^-8*8^0/0!=1-e^-8
Now we have a binomial B(13,8e^-1) so P(x=9)=13!/(4!9!)*(e^-8)^4(1-(e^-8))^9

C) The probability of a no car crashese is 1-e^-2
So solve 0.01=(1-e^-2)^n

n=ln(0.01)/ln(1-e^-2)
Title: Math Conversion Question
Post by: omarsubei on November 22, 2008, 05:05:59 pm
Hi, I'd be grateful if you can tell me how to convert metres per minute squared (acceleration) to feet per second squared (also acceleration) and vice versa. I just can't do it!!! Thanks
Title: Re: Math Conversion Question
Post by: astarmathsandphysics on November 22, 2008, 05:10:18 pm
Hi, I'd be grateful if you can tell me how to convert metres per minute squared (acceleration) to feet per second squared (also acceleration) and vice versa. I just can't do it!!! Thanks


Divide by 3600 to change meters per minute squared into meters per second squared then Times by 3.3 since there are 3.3 feet in every meter
Title: Re: Maths/Physics help
Post by: omarsubei on November 22, 2008, 05:14:23 pm
Thanks a LOT. Wow, you're quite fast at responding.
Title: Re: Maths/Physics help
Post by: lolo on February 01, 2009, 09:30:00 am
heyy am still stuck in vectors
i dont get it  ???
so if i have a question like this how do i solve it?
pointA and B have coordinates (4, 1) and (2, -5), respectively. Find a vector equation for the line which passes through the point A, and which is perpendicular to the line AB.

really appreaciate ur help
thanks :)
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 01, 2009, 01:25:22 pm
heyy am still stuck in vectors
i dont get it  ???
so if i have a question like this how do i solve it?
pointA and B have coordinates (4, 1) and (2, -5), respectively. Find a vector equation for the line which passes through the point A, and which is perpendicular to the line AB.

really appreaciate ur help
thanks :)


gradient of line from A to B =change in y/change in x=(-5-1)/(2-4)=3 so gradient of perpendicular =-1/3

y=mx+c

y=-1/3x+c Put point A in to this equation.
1=(_1/3)4+c
so c=7/3 and y=-1/3x+7/3
Title: Re: Maths/Physics help
Post by: lolo on February 01, 2009, 02:01:16 pm
wooww!! omg i actually get it nw!! :D
u r smart lol

thankooo soooo much :D
really appreciate it ..
:)
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 01, 2009, 02:11:18 pm
Thanks. Post all your maths questions.
Title: Re: Maths/Physics help
Post by: saifalan on February 01, 2009, 03:32:16 pm
Good way to learn maths. But, alas, there isnt a good way to write down all the mathematical notations down
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 01, 2009, 09:07:00 pm
There is - we have latex now. Look at the pi button- that is the latex code thingy, but I dont know how to use it yet.
Title: Re: Maths/Physics help
Post by: saifalan on February 02, 2009, 01:05:05 pm
 ;D if u havnt found a way to use it yet, it is as well as not there.
Title: Re: Maths/Physics help
Post by: lolo on February 05, 2009, 12:11:37 pm
i have another question plz:

there were 1240 tickets sold for a concert. Of these, 780 were sold at $24.50 each, while the remainder were sold at a reduction of 20%. Find the total money taken in ticket sales.

thanks :)
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 05, 2009, 02:33:12 pm
i have another question plz:

there were 1240 tickets sold for a concert. Of these, 780 were sold at $24.50 each, while the remainder were sold at a reduction of 20%. Find the total money taken in ticket sales.

thanks :)
(780x24.5)+ 0.8x(1240-780)x24.5=28136
Title: Re: Maths/Physics help
Post by: lolo on February 08, 2009, 05:50:09 am
thanks .. bt i reli dnt get what u did  ???.. cn u plz explain
thanks :)
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 08, 2009, 07:35:13 am
780 sold at 24.50 so revenue =780x24.5=19110

The remainder have a discount of 20% iethey cost 24.50x0.8=19.60. There are 1240-780=460 of these so revenue =19.60x460=9016

Total revenue =19110+9016=28126
Title: Re: Maths/Physics help
Post by: omarsubei on February 11, 2009, 11:45:41 pm
Please help me with this question and explain to me why the answer is what it is:

A force of magnitude F1 accelerates a body of mass m from rest to a speed v. A force of
magnitude F2 accelerates a body of mass 2m from rest to a speed 2v.
The ratio: (work done by F2)/(work done by F1) is:

A. 2.
B. 4.
C. 8.
D. 16.

Thanks
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 12, 2009, 08:38:02 am
Please help me with this question and explain to me why the answer is what it is:

A force of magnitude F1 accelerates a body of mass m from rest to a speed v. A force of
magnitude F2 accelerates a body of mass 2m from rest to a speed 2v.
The ratio: (work done by F2)/(work done by F1) is:

A. 2.
B. 4.
C. 8.
D. 16.

Thanks
The accelerations are eqaul sinceF2/2m=F1/m therefore from v^2=u^"+2as, s=v^2/2a sobody 2 travels 4 times as far as body 1.
(work done by F2)/(work done by F1)=F2*4s/F1*s=4

Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 12, 2009, 08:45:15 am
One question about Statistics

The height of certain plants are normally distributed. The plants are classified into three categories.

The shortest 12,92% are in cat a
The tallest 10,38% are in cat C
All other plants are in between r and t cm and are cat B

Given that the mean height is 6.84 cm and the standard deviation is 0.25 find t and r

PS> With explanations if possible, i m not an expert on statistics
I had this question a couple of days ago from one of my sudents.

For 12.92 % z=-1.13 so -1.13=(r-6.84)/025 so r=0.25*-1.13+6.84=6.5575
For10.38 we must do 1-.1038=0.8962 and z=1.26 s0 1.26=(t-6.84)/0.25 so t=1.26*0.25+6.84=7.155
Title: Re: Maths/Physics help
Post by: omarsubei on February 12, 2009, 10:14:17 am
Please help me with this question and explain to me why the answer is what it is:

A force of magnitude F1 accelerates a body of mass m from rest to a speed v. A force of
magnitude F2 accelerates a body of mass 2m from rest to a speed 2v.
The ratio: (work done by F2)/(work done by F1) is:

A. 2.
B. 4.
C. 8.
D. 16.

Thanks
The accelerations are eqaul sinceF2/2m=F1/m therefore from v^2=u^"+2as, s=v^2/2a sobody 2 travels 4 times as far as body 1.
(work done by F2)/(work done by F1)=F2*4s/F1*s=4


That's the answer I came up with, but strangely the mark scheme says the answer is C (8). I was thinking maybe because it's asking about the "Work" done by F, and that there is distance involved (W=Fd), that the distance in F2 is double that of F1 because it's twice as fast?
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 12, 2009, 10:49:39 am
Can you copy and pasty the question
Title: Re: Maths/Physics help
Post by: omarsubei on February 12, 2009, 11:09:47 am
I've attached it as a word document. Thank you.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 12, 2009, 11:19:22 am
Please help me with this question and explain to me why the answer is what it is:

A force of magnitude F1 accelerates a body of mass m from rest to a speed v. A force of
magnitude F2 accelerates a body of mass 2m from rest to a speed 2v.
The ratio: (work done by F2)/(work done by F1) is:

A. 2.
B. 4.
C. 8.
D. 16.

Thanks
The accelerations are eqaul sinceF2/2m=F1/m therefore from v^2=u^"+2as, s=v^2/2a sobody 2 travels 4 times as far as body 1.
(work done by F2)/(work done by F1)=F2*4s/F1*s=4


That's the answer I came up with, but strangely the mark scheme says the answer is C (8). I was thinking maybe because it's asking about the "Work" done by F, and that there is distance involved (W=Fd), that the distance in F2 is double that of F1 because it's twice as fast?
0.5(2M)V^2/0.mvv^"=8 THEquestion is badlty worded
Title: Re: Maths/Physics help
Post by: omarsubei on February 12, 2009, 11:31:28 am
Sorry I don't understand. Could you please explain.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 12, 2009, 11:32:49 am
f2 is not twicw F1
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 12, 2009, 11:34:03 am
u hve to work out the ratiof2/f1 first.
Title: Re: Maths/Physics help
Post by: omarsubei on February 12, 2009, 11:38:24 am
You're making me feel even more confused. :-\
The ratio of F2/F1 is 4. How does the "work"  make that 8?
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 12, 2009, 11:41:08 am
The diazstance is also doubled
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 12, 2009, 11:42:42 am
The disatnce is aLSO DOUBLED
Title: Re: Maths/Physics help
Post by: omarsubei on February 12, 2009, 11:43:29 am
OK ok ok. Thanks a lot
Title: Re: Maths/Physics help
Post by: omarsubei on February 13, 2009, 11:25:19 am
I just can't get this question:

A container is filled with a mixture of nitrogen and oxygen. What is the ratio of the rms (root mean squared) speed of oxygen molecules to that of nitrogen molecules? (Molar mass of oxygen=32 g mol-1 ; molar mass of nitrogen=28 g mol-1

I'll tell you the answer this time :P : 0.935
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 13, 2009, 11:37:26 am
I just can't get this question:

A container is filled with a mixture of nitrogen and oxygen. What is the ratio of the rms (root mean squared) speed of oxygen molecules to that of nitrogen molecules? (Molar mass of oxygen=32 g mol-1 ; molar mass of nitrogen=28 g mol-1

I'll tell you the answer this time :P : 0.935
All the molecules have the same kinetic energy
therefore0.5m(ox)v(ox)^2=0.5M(nit)v(nit)^2
therefore rms(ox)/rms(nit)=sqrt(m(nit)/(ox))=sqrt(14/16)=0.93
Title: Re: Maths/Physics help
Post by: omarsubei on February 13, 2009, 11:59:49 am
Wow. I see. THhnk you very much
Title: Re: Maths/Physics help
Post by: omarsubei on February 19, 2009, 12:15:09 pm
I swear, if you solve this question, you're just a born genius! I've been trying it the whole day and I'm not getting the answer, which is 72.
I HATE Permutations and Combinations. Here it is:

"Mr Blue, Mr Black, Mr Green, Mrs White, Mrs Yellow and Mrs Red sit around a circular table for a meeting. Mr Black and Mrs White must not sit together.

Calculate the number of different ways these six people can sit at the table without Mr Black and Mrs White sitting together."
 
Title: Re: Maths/Physics help
Post by: crucio on February 19, 2009, 12:46:13 pm
u sure the ans is 72? im gettin 144...lol  :D
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 19, 2009, 12:59:31 pm
Soppose mr black site down fist then mrs white can site in one of 3 possible seats - draw it!. The other 4 guests can sit in 4! different ways with respect to oder. 3x24 =72
Title: Re: Maths/Physics help
Post by: omarsubei on February 19, 2009, 01:36:29 pm
Soppose mr black site down fist then mrs white can site in one of 3 possible seats - draw it!. The other 4 guests can sit in 4! different ways with respect to oder. 3x24 =72

Wait wait wait. I DID DRAW IT, a few million times too. Ya but what if Mr. Black changes his seat. He can also sit in six different places can't he. It's a permutation isn't it? Please explain more. There is actually a solution, but it's even more complex than yours:

"The number of different ways six people can sit around a circular table
is 5! = 120.   (M1)
The number of different ways these six people can sit around a circular
table with Mr Black and Mrs White together is 4! × 2 = 48.   (A1)
Therefore, the number of different ways these six people can sit around
a circular table with Mr Black and Mrs White NOT together is
120 – 48 = 72   "

Why can they sit in 5! ways, not 6!   ???????
Title: Re: Maths/Physics help
Post by: omarsubei on February 19, 2009, 01:39:59 pm
Oooooooh, wait I think I get it. Is it because it doesn't matter where Mr. Black sits first, because the question is asking about the different "ways" they can sit i.e. their positions with respect to each other?
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 19, 2009, 01:59:26 pm
Exactly. If it mattered there answer would be 6x72=432
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 19, 2009, 02:00:42 pm
You are making it soooooooooooooo compilated but it is exactly as I say.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 19, 2009, 02:02:06 pm
Oooooooh, wait I think I get it. Is it because it doesn't matter where Mr. Black sits first, because the question is asking about the different "ways" they can sit i.e. their positions with respect to each other?

Exactly
Title: Re: Maths/Physics help
Post by: avrila on February 24, 2009, 10:55:03 am
Can you please help me with this:

1. Find the fourth vertex of the parallelogram:
A(2,1,0) B(3,2,-1) C(0,-1,1)

2. Find the shortest distance between point A (3,5,6) and line (x-7)/2=y-5=(z-12)/6

Thanks in advance...
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 24, 2009, 12:19:05 pm
Can you please help me with this:

1. Find the fourth vertex of the parallelogram:
A(2,1,0) B(3,2,-1) C(0,-1,1)

2. Find the shortest distance between point A (3,5,6) and line (x-7)/2=y-5=(z-12)/6

Thanks in advance...

AD=BC=(0,-1,1)-(3,2,-1)=(-3,-3,2) so D=A+(-3,-3,2)=(-1,-2,2)

2.eequation of line=(7,5,12)+t(2,1,6). Suppose they intersect at (a,b,c) then (a-3,b-5,c-6) is at right angles to (2,1,6) but (a,b,c) is on line so (a,b,c)= (7+2t,5+t,12+6t)
 and (4+2t,t,6+6t).(2,1,6)=0 ie  44+41t=o so t=-44/41 sthe sub into  (7+2t,5+t,12+6t) to find a and use pythagoras theorem in 3D to find distance between A and (a,b,c)
Title: Re: Maths/Physics help
Post by: avrila on February 27, 2009, 10:19:21 pm
Next question..

How would i solve this system of equations by hand of course. Is it possible?
625A -125B +25C -5D +E =4.5
112A -34.3B +10.6C -3.25D+E=2.25
0.00391A -0.0156B +0.0625C -0.25D +E=6.25
92.4A + 29.8B +9.61C + 3.10 D + E= 1.40
625A +125B +25C +5D +E =3.85

Help would be very much appreciated. Thanks.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 27, 2009, 10:24:27 pm
My impression is that for IB you would expected to use your calculators solve function. You are doing ib?
Title: Re: Maths/Physics help
Post by: avrila on February 27, 2009, 11:11:12 pm
Ya.. I'm doing IB. The question is not from IB though. Someone ask me and I'm just curious to answer. I try them but it seems little bit complex. Just wondering if you could solve the problem.. There must be a way right. Someone said use augmented matrices. I usually do this but up to three only not till 5x5 matrices.

Well, I'll keep on trying. Do tell me if you manage to solve this.. Thanks.
Title: Re: Maths/Physics help
Post by: avrila on February 28, 2009, 06:17:12 am
What is arbitrary point in vector?
A question ask, Find the position vector of an arbitrary point R which lies on the line.

I just want to know what is arbitrary point at the moment. ..
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 28, 2009, 08:25:26 am
Yes use augmented matrices. Row reduce and the inverse is on the right hand side. The multiple the vector on right hand side of the original system of equations by the inverse you have found and the answer is the vector  you have found
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on February 28, 2009, 08:35:02 am
Yes use augmented matrices. Row reduce and the inverse is on the right hand side. The multiple the vector on right hand side of the original system of equations by the inverse you have found and the answer is the vector  you have found
suppose the equation of a line is r(t) =2i+4j-k+t(5i-2j+7k) the arbitrary point vector is (2+5t,4-2t,-1+7t)
Title: Re: Maths/Physics help
Post by: avrila on March 01, 2009, 01:05:33 am
P=(4,1,-1) Q=(3,3,5) R=(1,0,2c) S=(1,1,2)

Find C so that QR and PR are orthogonal.
I know that I have to use dot product. QR.PR=0
But I got a weird value of C. Is my method correct? How do you do this.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on March 01, 2009, 07:54:44 am
P=(4,1,-1) Q=(3,3,5) R=(1,0,2c) S=(1,1,2)

Find C so that QR and PR are orthogonal.
I know that I have to use dot product. QR.PR=0
But I got a weird value of C. Is my method correct? How do you do this.
QR=(-2,-3,2c-5) and PR=(-3,-1,2c+1)
QR.PR=6+3+(2c-5)(2c+1)=9+4c^2-8c-5=4c^2-8c+4=0 solution is c=1
Title: Re: Maths/Physics help
Post by: avrila on March 01, 2009, 02:08:23 pm
Ya.. I know where my mistake is. I misplace one of the sign and ruin the question.. Thanks.
Title: Re: Maths/Physics help
Post by: avrila on March 02, 2009, 02:43:57 am
Plane pi has equation r.(2i +j + 2k)= 36
Point B and C has position vectors (i +3 +2k) and (3i +2j + k) respectively.

>Find the position vector of the point where the line OB meets pi and find the perpendicular distance from B to pi.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on March 02, 2009, 11:33:31 pm
Plane pi has equation r.(2i +j + 2k)= 36
Point B and C has position vectors (i +3 +2k) and (3i +2j + k) respectively.

>Find the position vector of the point where the line OB meets pi and find the perpendicular distance from B to pi.
OB=t(1,3,2) so subsitute into pi x=t, y=3t, z=2t

We have (t,3t,2t).(2,1,2)=36 so 9t=36 and t=4 and the line meets pi at(4,12,8). The distance is \surd(3^2+9^2+6^2)=3\surd14
Title: Re: Maths/Physics help
Post by: avrila on March 03, 2009, 04:30:40 am
Ok.I got it until (4,12,8). And this is the coordinates where OB meets the plane. In other words, it is the point of intersection between the line and the plane.

But to find the distance from B to pi, why we just use the same coordinate? B has it owns coordinate right?...
Can you please explain.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on March 03, 2009, 07:50:48 am
I corrected my post
Title: Re: Maths/Physics help
Post by: avrila on March 03, 2009, 10:02:40 am
Ok.. I got the answer but it is slightly different.
For the distance, instead of 3,6,9 I got 6,3,6. After substitute this in the distance formula, I got 9 as the answer.

Hope I am in the right track.
Title: Re: Maths/Physics help
Post by: radam on March 26, 2009, 06:29:29 pm
This is an extract from the Physics specimen 09 HL paper 2:

"A digital camera is used to take a photograph of a plant. The CCD in the camera has 1.6*10^-7 square pixels. Each pixel has an area of 2.3*10^-10m^2. A particular leaf of the plant has an area of 3.5*10^-2 m^2. The image formed on the CCD is 1*10^-3 m^2. Two indentations on the lead are seperated by 0.50mm. Deduce that it is unlikely that the images of the two indentations will be resolved"

The marking scheme states that you should calculate the magnification as (1*10^-3/2.5*10^-2)=0.04, and so my question is, isnt this formula the area magnication, in which case the linear magnification would be sqrt(0.04)= 0.2? The only problem is that if you use the square-root then you get the distance of seperation as greater than the minimum distance to be just-resolved... is their a problem in the question or is my method incorrect?

Thanks a lot in advance :)


Title: Re: Maths/Physics help
Post by: astarmathsandphysics on March 26, 2009, 06:55:59 pm
Have been very busy all day. Will do this when I come back tonight.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on March 27, 2009, 08:30:26 am
This is an extract from the Physics specimen 09 HL paper 2:

"A digital camera is used to take a photograph of a plant. The CCD in the camera has 1.6*10^-7 square pixels. Each pixel has an area of 2.3*10^-10m^2. A particular leaf of the plant has an area of 3.5*10^-2 m^2. The image formed on the CCD is 1*10^-3 m^2. Two indentations on the lead are seperated by 0.50mm. Deduce that it is unlikely that the images of the two indentations will be resolved"

The marking scheme states that you should calculate the magnification as (1*10^-3/2.5*10^-2)=0.04, and so my question is, isnt this formula the area magnication, in which case the linear magnification would be sqrt(0.04)= 0.2? The only problem is that if you use the square-root then you get the distance of seperation as greater than the minimum distance to be just-resolved... is their a problem in the question or is my method incorrect?
Thanks a lot in advance :)
The distance between the indentations is 0.2*0.5mm=0.1mm=10^(-4), and the length of a side of a pixel is sqrt(2.3*(10^-10))=1.5*10^(-5). I see the same problem. I think it must be a mistake in the question.
Title: Re: Maths/Physics help
Post by: radam on March 27, 2009, 01:08:36 pm
Hmm i figured as much... thanks a lot for your help :)
Title: Re: Maths/Physics help
Post by: omarsubei on April 10, 2009, 09:28:39 pm
Hi it's been a while.
As usual I'm getting a different answer to the markscheme,
"A circle has equation x^2 + (y-3)^2 = 4 . Knowing that y= +/- (4 - x^2)^0.5 , find the volume of revolution of the shaded region about the x-axis.
The mark scheme says 144, and I got 237
PLEASE HELP!
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on April 10, 2009, 09:30:27 pm
Hi it's been a while.
As usual I'm getting a different answer to the markscheme,
"A circle has equation x^2 + (y-3)^2 = 4 . Knowing that y= +/- (4 - x^2)^0.5 , find the volume of revolution of the shaded region about the x-axis.
The mark scheme says 144, and I got 237
PLEASE HELP!


Surely y= 3+/- (4 - x^2)^0.5
Title: Re: Maths/Physics help
Post by: omarsubei on April 10, 2009, 09:33:24 pm
Ya I know I just wanted to make it less time consuming for you
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on April 10, 2009, 09:37:53 pm
What region is shaded? If you cant say which paper the question is on can you describe it?
Title: Re: Maths/Physics help
Post by: omarsubei on April 10, 2009, 09:56:05 pm
The whole circle is shadad
Title: Re: Maths/Physics help
Post by: omarsubei on April 10, 2009, 10:04:18 pm
It's an integration question, to do with integral of the function squared multiplied by pie, if that helps
Title: Re: Maths/Physics help
Post by: omarsubei on April 10, 2009, 10:08:56 pm
Do you mind if we do this on msn, I think it'd be much easier
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on April 10, 2009, 10:22:17 pm
V=pi\int(3+sqrt(4-x^2))^2dx-pi\int(3-sqrt(4-x^2))^2dx
     =pi\int12sqrt(4-x^2)dx
Use the substition x=2sint then dx=2costdt
     =12pi\int2cost.2costdt=12pi\int(2+2cos2t)dt=12pi(2t+sin2t)

The limits are changed from \pm 2 to \pm pi/2

We have V=12pi((2pi/2+sinpi)-(-2pi/2+sin-pi))==24pi^2

Title: Re: Maths/Physics help
Post by: omarsubei on April 10, 2009, 10:27:29 pm
WHAT???!! 6pi?? I just got it anyways, my bounds were wrong, they need to be from -1 to 1, and I was doing -2 to 2. Thanks anyways. Appreciate it.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on April 10, 2009, 10:32:51 pm
I dont understand. If the limits are +-1 how can the whole circle be shaded?

I looked up the volume of a tours here. It is consistent with my answer.
http://whistleralley.com/torus/torus.htm
Title: Re: Maths/Physics help
Post by: omarsubei on April 10, 2009, 10:38:24 pm
I guess you have to split it into the two equations + and -, that way you can have the whole circle shaded
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on April 10, 2009, 10:42:30 pm
That is what I did to get two integrals.
Title: Re: Maths/Physics help
Post by: omarsubei on April 10, 2009, 10:47:09 pm
Ya I looked at that. I don't understand their method, but I can see that in your method, you put the same equation twice, you need to put one of them as +square root... and the other as -square root..., if you see what I mean
Title: Re: Maths/Physics help
Post by: omarsubei on April 10, 2009, 10:50:19 pm
I don' get how you went from step one to two, how'd you put the integrals together?
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on April 10, 2009, 10:51:49 pm
You are right. I corrected my mistake.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on April 10, 2009, 10:55:03 pm
I don' get how you went from step one to two, how'd you put the integrals together?

Exapnad the brackets and simplify. You can just add the integrands. The squared terms cancel and for one term I get--=+
Title: Re: Maths/Physics help
Post by: radam on April 23, 2009, 01:11:11 pm
Hey;

I'd appreciate some help with this question;

(from the previous subsection b is an imaginary root of the equation z^5-1=0 and b^4+b^3+b^2+b+1=0)
________________________________________
Q 13, PART B, MATH HL NOV 08

c) If u=b+b^4 and v= b^2+b^3, show that

i) u+v=uv=-1
ii) u-v= sqrt(5) , given that u-v>0
_______________________________________

for i) Proving that u+v=-1 is not difficult... but i have no idea how to prove that uv=-1, or for ii) how u-v is sqrt(5).

Help would be greatly appreciated :)
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on April 23, 2009, 01:53:03 pm
Hey;

I'd appreciate some help with this question;

(from the previous subsection b is an imaginary root of the equation z^5-1=0 and b^4+b^3+b^2+b+1=0)
________________________________________
Q 13, PART B, MATH HL NOV 08

c) If u=b+b^4 and v= b^2+b^3, show that

i) u+v=uv=-1
ii) u-v= sqrt(5) , given that u-v>0


_______________________________________

for i) Proving that u+v=-1 is not difficult... but i have no idea how to prove that uv=-1, or for ii) how u-v is sqrt(5).

Help would be greatly appreciated :)

i)uv=(b+b^4)(b^2+b^3)=b^3+b^4+b^6+b^7 now use b^5=1 ie B^6=b and B^7=b^2 so we have b^3+b^4+b +b^2=-1 too.

I will answer the second part as soon as I come back, but I have to go RIGHT NOW and teach some maths.

ii)(u-v)^2=u^2-2uv+v^2=(b+b^4)^2-2(b+b^4)(b^2+b^3)+(b^2+b^3)^2=b^2+2b^5+b^8-2b^3-2b^4-2b^6-2b^7_+b^4+2b^5+b^6
b^5=1 so we have b^2+2+b^3-2b^3-2b^4-2b-2b^2+b^4+b=(b^2+b^3-2b^3-2b^4-2b-2b^2+b^4+b)+4
=-(b^3+b^4+b +b^2)+4=5
Title: Re: Maths/Physics help
Post by: radam on April 23, 2009, 02:04:40 pm
Ah thanks!

I forgot that b^5=1;

I was thinking about the question with that bit of insight; and i was wondering if my method below is correct:

(u-v) is the same as sqroot (u-v)^2 (since u-v>0)

(U-v)=u^2-2uv+v^2= b^8+2b^5+b^2+2+b^4+2b^5+b^6

since uv=-1, and b^5=1

This gives b^4+b^3+b^2+b-6= 5

Hence  (u-v)^2= 5

u-v= sqrt(5)

The answer seems correct, but I'm wary of squaring as it normally adds complications to the matter... is there an easier and less time consuming way to do it?

Again thanks a lot for your help! With my math exam 2 weeks away, its a life-saver!
Title: Re: Maths/Physics help
Post by: Clerk on April 28, 2009, 11:00:43 pm
Hi. I'm a standard level physics student. Does anyone know if I have to know how to "Solve problems using the equation of state of an ideal gas". There are some past papers exercises, but I think that this part of the syllabus is now only for high level. Please help me!
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on April 28, 2009, 11:06:34 pm
Ah thanks!

I forgot that b^5=1;

I was thinking about the question with that bit of insight; and i was wondering if my method below is correct:

(u-v) is the same as sqroot (u-v)^2 (since u-v>0)

(U-v)=u^2-2uv+v^2= b^8+2b^5+b^2+2+b^4+2b^5+b^6

since uv=-1, and b^5=1

This gives b^4+b^3+b^2+b-6= 5

Hence  (u-v)^2= 5

u-v= sqrt(5)

The answer seems correct, but I'm wary of squaring as it normally adds complications to the matter... is there an easier and less time consuming way to do it?

Again thanks a lot for your help! With my math exam 2 weeks away, its a life-saver!

I can't think of a simpler way to do it.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on April 28, 2009, 11:07:12 pm
Post your questions and I will answer asap
Title: Re: Maths/Physics help
Post by: IGSTUDENT on June 08, 2009, 10:11:13 am
Can u pls suggest a good book for IB Higher maths ?Aslo for Chemisty HL?
Title: Re: Maths/Physics help
Post by: omega007 on June 08, 2009, 11:43:55 am
This is going to help you with the books.

http://en.wikibooks.org/wiki/IB_Textbook_Reviews
Title: Re: Maths/Physics help
Post by: IGSTUDENT on June 08, 2009, 12:58:37 pm
Thanks a lot.Will have a look.
All the same some of you who are already doing it..any suggestions?
Title: Re: Maths/Physics help
Post by: IGSTUDENT on June 08, 2009, 12:59:18 pm
Thanks a lot.Will have a look.
All the same some of you who are already doing it..any suggestions?
Title: Re: Maths/Physics help
Post by: sippah on October 23, 2009, 01:24:10 pm
can you please help with some ideas for practicals i can design and carry out in my school, something simple would be preferred that can ablso be done at home because i am swamped in the area man so please help me.
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on October 23, 2009, 01:52:24 pm
You mean ib physics?
Title: Re: Maths/Physics help
Post by: sippah on October 23, 2009, 02:40:47 pm
yes i mean IB physics so please any ideas you have that i could build on would help.

thanx in advance
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on October 23, 2009, 03:30:17 pm
I sent you an email
Title: Re: Maths/Physics help
Post by: sweet777 on May 12, 2010, 03:13:06 am
sir, do you know where i can get the 2009 math and physics paper from?
Title: Re: Maths/Physics help
Post by: Monica on May 12, 2010, 03:15:52 am
Did you check freeexampapers.com?
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on May 12, 2010, 08:47:48 am
ibpapers.info
They make you pay or do a survey
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on May 12, 2010, 08:49:03 am
Sorry ibpapers.net
Title: Re: Maths/Physics help
Post by: sweet777 on May 13, 2010, 04:02:31 am
i got math 2009 papers...i got them from freeexampapers..but then i checked fep for physics..dey dnt physics 2009...i checked the other websites which are mentioned..and u have to pay for them, and earn credits..and all that.....so i guess its fine...il manage....wid 2008...thanks By the way!!!! :D
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on May 13, 2010, 09:35:31 am
We will get all the papers in the next update.
Title: Re: Maths/Physics help
Post by: azhaan on May 15, 2010, 06:48:51 pm
hey,
im an igcse grade 10 student
and i have to choose my IB subjects now,
so im taking
HL-math, physics, economics
SL- english, french abinition, history
any suggestion?
are these subjects to hard or not helpful
PS: i want to do business or finance in university
Title: Re: Maths/Physics help
Post by: Burnside on May 18, 2010, 01:20:55 pm
@azhaan

HL maths and physics are considered the two hardest courses in IB. I'm not saying they will be too hard for you, however if you're taking those two subjects I'd suggest taking up chemistry instead of the double humanities (chemistry and physics have quite a bit of overlap).
Title: Re: Maths/Physics help
Post by: azhaan on May 20, 2010, 03:09:58 pm
@azhaan

HL maths and physics are considered the two hardest courses in IB. I'm not saying they will be too hard for you, however if you're taking those two subjects I'd suggest taking up chemistry instead of the double humanities (chemistry and physics have quite a bit of overlap).
thanks but is it easier to score in history HL than physics HL???
Title: Re: Maths/Physics help
Post by: Burnside on May 23, 2010, 01:02:25 pm
I'm not doing history so it's hard to judge. However from my experience I can make a few comments about certain subjects.

Subjects that have a large gap between SL and HL content:
Physics
Mathematics
Chemistry
Biology
All Languages

Small gap between SL and HL content:
Economics
Geography
English

Subjects that are hard conceptually:
HL maths
HL Physics

Subjects that are hard due to the sheer content you need to remember:
Economics
Biology
History
HL Chemistry (SL chem is easy)


If you do HL Physics, SL Chemistry will be a breeze due to alot of the concepts already being covered in physics.
Title: Re: Maths/Physics help
Post by: sasukeuchiha on May 25, 2010, 09:54:04 pm
can someone please answer the question 23 31 and 33 of June 2007's P1 physics (with explanation)
http://www.freeexampapers.com/FreeExamPapers.com_.php?__lo=TyBMZXZlbC9QaHlzaWNzL0NJRS8yMDA3IEp1bi81MDU0X3MwN19xcF8xLnBkZg== (http://www.freeexampapers.com/FreeExamPapers.com_.php?__lo=TyBMZXZlbC9QaHlzaWNzL0NJRS8yMDA3IEp1bi81MDU0X3MwN19xcF8xLnBkZg==)
Title: Re: Maths/Physics help
Post by: astarmathsandphysics on May 25, 2010, 10:45:00 pm
23. 300m/s - one sound goes to boy direct and the other thravels an extre 2*150m to wall and back
31. Total power =0.5 so cost =0.5*8*2=8 cents
33 Use right jhand grip rule and remeber like currents attract
Title: Re: Maths/Physics help
Post by: azhaan on May 26, 2010, 05:53:50 pm
I'm not doing history so it's hard to judge. However from my experience I can make a few comments about certain subjects.

Subjects that have a large gap between SL and HL content:
Physics
Mathematics
Chemistry
Biology
All Languages

Small gap between SL and HL content:
Economics
Geography
English

Subjects that are hard conceptually:
HL maths
HL Physics

Subjects that are hard due to the sheer content you need to remember:
Economics
Biology
History
HL Chemistry (SL chem is easy)


If you do HL Physics, SL Chemistry will be a breeze due to alot of the concepts already being covered in physics.
thanks a lot you are really helpful!!
taking history HL and physics SL finally :)
hope it will help