Mathematics: Post your doubts here!

[i_try9621]

Hey everyone I'm new on Math AS and would appreciate your help

The thread is so lengthy so if someone can help me and provide me notes for PURE MATH 1 and MECHANICS 1 I've checked some links but always directs me to 404 error .
Thanks in advance .

Btw is it hard to get A in AS Math ? I'm terrified from it

It's definitely not hard to get an A in AS Math although I believe M1 can be a bit tricky and P1 is really easy if you have done Add Maths in O-levels

 

[i_try9621]

Need help with Q24 part 2

 

[DragonCub]

View attachment 61674 Need help with Q24 part 2

Special thanks to i_try9621 for spotting the mistake! (Post #17891)

 

[i_try9621]

jhz

View attachment 61675

why did you consider a to be (1,2,-1) because this is a direction vector, isn't it? I have tried this sum and my ans was 7x + y - 5z = 17 and I took a to be (1,0,-2) from the line l.

 

[DragonCub]

jhz

why did you consider a to be (1,2,-1) because this is a direction vector, isn't it? I have tried this sum and my ans was 7x + y - 5z = 17 and I took a to be (1,0,-2) from the line l.

Sorry, I made a silly mistake... I meant to take the point on line r but misread it. (There is no j in there but I mistook k as it, and s as k, so I came up with the wrong one.)
Yes, you are right, it should be (1, 0, -2) or (6, -5, 4), and both will arrive at d = 17.

The answer should be as you stated.
Good job finding the error

 

[i_try9621]

Sorry, I made a silly mistake... I meant to take the point on line r but misread it. (There is no j in there but I mistook k as it, and s as k, so I came up with the wrong one.)
Yes, you are right, it should be (1, 0, -2) or (6, -5, 4), and both will arrive at d = 17.

The answer should be as you stated.
Good job finding the error

And thanks for helping me out

 

[i_try9621]

Need help with Q29) part 3

 

[DragonCub]

View attachment 61685 Need help with Q29) part 3

This part does not seem to be solvable.

From the information given we can obtain the following pieces of info:
1. "N is the foot of the perpendicular from B to l" --> N is on line l.
2. "The plane containing A, B and N" --> A and N are both on the plane --> Line l is on the plane.
3. "The line l ... is parallel to OB" --> OB's direction is the same as l --> (and since B is on the plane) Vector OB is also on the plane

--> Point O (the origin) is on the plane.

This is sufficient to mean that, if the plane's equation is in the form of ax + by + cz = d, the right-hand side must be d = 0.

This deduction is, however, contradictary to the requirements of the question.

So unless there is a typo in the question, this part does not have a solution.

------------------------------------------------------------

P.S.
I may have made some mistake during the deduction process. If anyone finds any, do not hesitate to notify me of it.
Also, if you have a marking scheme or solution manual ready at hand, please let me know. I am interested to see the provided solution.

 

[i_try9621]

This part does not seem to be solvable.

From the information given we can obtain the following pieces of info:
1. "N is the foot of the perpendicular from B to l" --> N is on line l.
2. "The plane containing A, B and N" --> A and N are both on the plane --> Line l is on the plane.
3. "The line l ... is parallel to OB" --> OB's direction is the same as l --> (and since B is on the plane) Vector OB is also on the plane

--> Point O (the origin) is on the plane.

This is sufficient to mean that, if the plane's equation is in the form of ax + by + cz = d, the right-hand side must be d = 0.

This deduction is, however, contradictary to the requirements of the question.

So unless there is a typo in the question, this part does not have a solution.

------------------------------------------------------------

P.S.
I may have made some mistake during the deduction process. If anyone finds any, do not hesitate to notify me of it.
Also, if you have a marking scheme or solution manual ready at hand, please let me know. I am interested to see the provided solution.

In 2. How is it that the line l is on the plane?
Also the answer on the markscheme says it's 7x + 8y - 11z = -38

 

[DragonCub]

In 2. How is it that the line l is on the plane?
Also the answer on the markscheme says it's 7x + 8y - 11z = -38

Both A and N are on line l, and both the points are on the plane, so l must be on the plane too.

Also, I tested the answer on the MS using the points and found it to be inconsistent.
Using B's coordinates, (3, -1, -4), we can see that:
7 * 3 + 8 * (-1) + (-11) * (-4)
= 21 - 8 + 44
= 57
The equation shows that B is not on the plane.

 

[Thought blocker]

In 2. How is it that the line l is on the plane?
Also the answer on the markscheme says it's 7x + 8y - 11z = -38

I guess you have a wrong ms. And the question u have posted, check Qten of s06 paper three.

 

[i_try9621]

I guess you have a wrong ms. And the question u have posted, check Qten of s06 paper three.

yup it's wrong, thanks for the help

 

[Shuddho Ukil]

Stuck on this M1 problem from 2009. I solved it but my question is, why aren't we considering the kinetic energy acting on the body?
Its from 9709_s09_qp_04.

 

[DragonCub]

Stuck on this M1 problem from 2009. I solved it but my question is, why aren't we considering the kinetic energy acting on the body?
Its from 9709_s09_qp_04.

The whole process was done at constant speed of C. This means C's kinetic energy does not change at all.

 

[SpawnX-1200]

Hi guys trust you are doing well. I would really need some help for the 2 questions I've attached below.

 

[DragonCub]

Hi guys trust you are doing well. I would really need some help for the 2 questions I've attached below.

 

[SpawnX-1200]

Thanks Sir! It's brilliantly done, but if I may. For the 1st question my only concern is why did you only take the absolute value for a=3 and did not also consider the case where $a$ can be equal to -3 ?

 

[DragonCub]

Thanks Sir! It's brilliantly done, but if I may. For the 1st question my only concern is why did you only take the absolute value for a=3 and did not also consider the case where $a$ can be equal to -3 ?

 

[SpawnX-1200]

View attachment 61731

True shame on me xD.

Your help was very much appreciated, also I see you manage to write your equations beautifully. I'm new to the forum and I know it's a bit off topic but does the forum support latex to write the mathematics?

 

[DragonCub]

True shame on me xD.

Your help was very much appreciated, also I see you manage to write your equations beautifully. I'm new to the forum and I know it's a bit off topic but does the forum support latex to write the mathematics?

Glad to see you find my answer helpful.
As of now, the rich text editor in the forum doesn't quite support insertion of equations. I used MS Word instead, and converted the lines to images. You can see that the answer I provided was actually image files.