# M2 Solutions

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Sorry about the delay dudes. Just got paper and done it now. Seems to be similar to alot of the answers on the forum. Hope you all did well. Not sure about these as I have done them as I go along as such they are unchecked. Best I could do though. All the best, Dan

Question

1) Vector Calculus (5 marks)

9 metres

2a) Magnitude of Impulse (4marks)

5.83 Ns

2b) Angle to i vector: (2 marks)

31 degrees nearest degree

2C) Kinetic energy gained (2 marks)

45 J I think (not sure here) THIS IS WRONG SEE BELOW

3a) Centre of Mass: (5 marks)

19a/15

3b) m in terms of M: (4 marks)

m = 7M/45

4a) Prove T = 980 N (5marks)

Proof (easy)

4b) Find reaction (6 marks)

R = 784 N THIS IS WRONG SEE BELOW

4c) No weight (1 mark)

5a) Show uT = 10 (2 marks)

Proof Easy

5b) Find u (5 marks)

u = 7m/s

5c) Find tan @ (5marks)

tan @ = about root 2

So @ would be 60 degrees or so??!!!

6a) Working ( 4marks)

324 J

6b) Speed (5 marks)

9.3m/s

6c) Magnitude or R (1mark)

32N

6d) Mag acceleration (4 marks)

d) 0.59m/s

7) Speeds of particles: (7 marks)

7a) (1-2e)/3u and (1+e)/3u

b) Range of e (2 marks)

0<e<0.5

7c) Another collision (6 marks)

Prove that speed of particle A away is less than that of that of particle B. As such it will catch and collide with A causing a third collision QED

Not certain about a couple of these as I have tried to work them out as I type this up. Hope everyone did well. All the best, Mensandan

Question

1) Vector Calculus (5 marks)

9 metres

2a) Magnitude of Impulse (4marks)

5.83 Ns

2b) Angle to i vector: (2 marks)

31 degrees nearest degree

2C) Kinetic energy gained (2 marks)

45 J I think (not sure here) THIS IS WRONG SEE BELOW

3a) Centre of Mass: (5 marks)

19a/15

3b) m in terms of M: (4 marks)

m = 7M/45

4a) Prove T = 980 N (5marks)

Proof (easy)

4b) Find reaction (6 marks)

R = 784 N THIS IS WRONG SEE BELOW

4c) No weight (1 mark)

5a) Show uT = 10 (2 marks)

Proof Easy

5b) Find u (5 marks)

u = 7m/s

5c) Find tan @ (5marks)

tan @ = about root 2

So @ would be 60 degrees or so??!!!

6a) Working ( 4marks)

324 J

6b) Speed (5 marks)

9.3m/s

6c) Magnitude or R (1mark)

32N

6d) Mag acceleration (4 marks)

d) 0.59m/s

7) Speeds of particles: (7 marks)

7a) (1-2e)/3u and (1+e)/3u

b) Range of e (2 marks)

0<e<0.5

7c) Another collision (6 marks)

Prove that speed of particle A away is less than that of that of particle B. As such it will catch and collide with A causing a third collision QED

Not certain about a couple of these as I have tried to work them out as I type this up. Hope everyone did well. All the best, Mensandan

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#2

your answers are mostly correct but i think you have made a few errors.

firstly, the change in kinetic energy is 35J

secondly, the reaction has vertical and horizontal component, one of which is 392N and the other is 784N, so the magnitude of this is sqrt[392^2 + 784^2] = 877N

Also i dont know how you got the answer for tan psi that you did but it should be 7/4.

Other than that i think the rest is correct, i did the exam and found it fine. The only dodgy area is the last part of the last question where there are many different methods for showing the required result.

firstly, the change in kinetic energy is 35J

secondly, the reaction has vertical and horizontal component, one of which is 392N and the other is 784N, so the magnitude of this is sqrt[392^2 + 784^2] = 877N

Also i dont know how you got the answer for tan psi that you did but it should be 7/4.

Other than that i think the rest is correct, i did the exam and found it fine. The only dodgy area is the last part of the last question where there are many different methods for showing the required result.

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#3

yeah, i agree with the response, you had to take 10 away from 45 for one, to get 35J.

Also on the magnitude of impulse, I have left it as (5i + 3j) So i take it I lose a mark there?

Also on the magnitude of impulse, I have left it as (5i + 3j) So i take it I lose a mark there?

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#4

yeah unfortunately you lose 1 or 2 depending on the mark scheme.

Because it said magnitude it should have been sqrt[3^2 + 5^2]

= sqrt34

but hey its only 1 or 2 out of 75!

Because it said magnitude it should have been sqrt[3^2 + 5^2]

= sqrt34

but hey its only 1 or 2 out of 75!

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Yeah that sounds more like it. Forgot to use Pythagoras on the 2 forces to find the resultant, silly really a very M1 thing to know. Not sure what I did on the tan @ bit but never mind, got that @=60 then wrote down nonsense about [email protected] = root 2. As you say should be 1.75. can't imagine where I got that from. Just glad to hear that people seem to have mostly the same. I just did P1 and P2 and M1 this year as my AS level. I will be sitting M2 later on didn't do it this time. Not done the course yet but have been looking at M2 text book, got a copy of the exam paper from school and decided to have a go, seems fairly friendly. I think I will be ready by next June when I will sit M2 / M3 to finish A2. My next exam is P3 which I will do in January, hope it is not like this years, I could only cope with about 60% of that. Then it will be on to Further Maths modules. I think I will be able to cope with these modules by then. Hope everyone else did well on this module, all the best, Dan.

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#6

well looks like i've bagged an A in this exam at least, considering all the marks I could have lost, its hopefully about 90%.

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You have finished Maths now, Byb3 right. Were the upper Vi modules okay??? Which ones did you do for A2. Reason I ask is I want to know if any particular module needs more effort than others. I plan on doing P1-3 and M1-2, and M3 or S1 for Maths then further Maths, I have done P1, P2, M1 already and have decided to do P3 in Jan and maybe S1 , leaving M2 M3 and further maths modules.

I think I did pretty well in P1, M1, P2, if this is the case which exam would you recommend I revise for hardest next year. Dan

I think I did pretty well in P1, M1, P2, if this is the case which exam would you recommend I revise for hardest next year. Dan

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#8

First year I did, S1 M1 P1 (Applied Maths)

Second year, P2, P3, M2

Out of P3, S1 and M2...

P3 is pretty hard to start off with, all the trig differentiation and integration you have to remember, but apart from that its fine.

M2 is a pile of piss basically, the rigid bodies chapter got me stumped for a while before it clicked and then it was pretty easy from then on. Oh yeah, and Centre of mass, that just does my head in.

S1, being my worst module at 76% deserves a fair bit of work I would say. I would recommend practicing on those Sxy, Sxx Syy formulas, because if you can recall them off hand it makes the test much easier. I think normal distribution also deserves a helping hand. I never quite got the grip of venn diagrams myself

I would say S1 and P3 deserve most work. M2 is pretty simple.

Second year, P2, P3, M2

Out of P3, S1 and M2...

P3 is pretty hard to start off with, all the trig differentiation and integration you have to remember, but apart from that its fine.

M2 is a pile of piss basically, the rigid bodies chapter got me stumped for a while before it clicked and then it was pretty easy from then on. Oh yeah, and Centre of mass, that just does my head in.

S1, being my worst module at 76% deserves a fair bit of work I would say. I would recommend practicing on those Sxy, Sxx Syy formulas, because if you can recall them off hand it makes the test much easier. I think normal distribution also deserves a helping hand. I never quite got the grip of venn diagrams myself

I would say S1 and P3 deserve most work. M2 is pretty simple.

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#9

Oh yeah I was just about to add...

I was thinking about staying back at college for another year, to perhaps do a full further maths A-level course.

My problem is that I am fine with maths, but Im basically **** at Physics, and Biology isn't much better. You might say that physics is maths, but if you take physics you'll find it is nothing like that.

I'm hoping to get a B in biology, but it will be a C, and physics is definitely nothing better than a C.

As I have a B in biology after AS level, I am considering resitting the A2 modules, as well as the whole further maths course in one year (P4, P5, P6, M3, S2, and I think D1). What are peoples recommendations on going to uni on just 1 maths a level?

Regards,

I was thinking about staying back at college for another year, to perhaps do a full further maths A-level course.

My problem is that I am fine with maths, but Im basically **** at Physics, and Biology isn't much better. You might say that physics is maths, but if you take physics you'll find it is nothing like that.

I'm hoping to get a B in biology, but it will be a C, and physics is definitely nothing better than a C.

As I have a B in biology after AS level, I am considering resitting the A2 modules, as well as the whole further maths course in one year (P4, P5, P6, M3, S2, and I think D1). What are peoples recommendations on going to uni on just 1 maths a level?

Regards,

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Hmmm I thought Stats was a bit iffy. I think I might just do M3 as my final A2 module, then do P4-6, M4-6 as further Maths. Perhaps take S1 as an extra module, incase there is another P3 out there next year. Chances are there will be, if I could get a good grade in S1 (70% + easily) it could be used to make up for any bad module either in A2 or further maths if one of them is a bit dodgy, cheers mate, sounds like you did good in Maths. Hope everything else went well too. If everyone doesn't hang out here much during the Summer I hope everyone drops in to share on results day. Good luck at University, cheers Dan

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#11

I joined college late in January and decided to do P1-3 and M1 - 3 in June! (i actually did it for the fun of it thinking "well if something goes rong ill resit") I just coodnt believe how easy the Modules were (P3 was hard along with M2 but it seems ive got the answers right somehow!!). Now im expecting way above an A. I am already doing further maths (havnt started P4 though). You think I should give a go at S1 and S2 and P1 again for an AS level stats ("IF" i didnt slump in math

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#12

nice one dan,i got question 3 wrong but i got the right method for both parts i think,would i get method marks?

Also how would you do the last question? I swear it asked us to prove that they dont collide again? So we have to prove that B is smaller than A and that therefore it wont catch up to A in order to collide?

Also how would you do the last question? I swear it asked us to prove that they dont collide again? So we have to prove that B is smaller than A and that therefore it wont catch up to A in order to collide?

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#13

Dan,i got question 3 wrong but i got the right method for both parts i think,would i get method marks?

Also how would you do the last question? I swear it asked us to prove that they dont collide again? So we have to prove that B is smaller than A and that therefore it wont catch up to A in order to collide?

Also how would you do the last question? I swear it asked us to prove that they dont collide again? So we have to prove that B is smaller than A and that therefore it wont catch up to A in order to collide?

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#14

Yeah you got most of the marks for method (called M1 marks) but you'll probably lose a few acuuracy (A1) marks, depending on what exactly you did wrong, and how lenient the mark scheme is with follow through marks for errors.

The question required you to show there would be another collision be demonstrating that the speed of A was faster than the speed of B and therefore would catch up and collide again. In terms of how many marks you'll get for this bit I don't know but unfortunately I dont think it will be many (maybe 3/6). Still if you got everything else right your well on course for an A

The question required you to show there would be another collision be demonstrating that the speed of A was faster than the speed of B and therefore would catch up and collide again. In terms of how many marks you'll get for this bit I don't know but unfortunately I dont think it will be many (maybe 3/6). Still if you got everything else right your well on course for an A

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#15

I did somthing highly stupid in 5 b). I resolved vertically and found that u = 7m/s. So far, so good.

However, then in a state of momentary madness I also resolved horizontally, before finding the resultant of the two. Don't ask me why - bad cheese the night before or something. Will I lose any marks for the extra crap at the end of my answer? (the first half of it is right).

However, then in a state of momentary madness I also resolved horizontally, before finding the resultant of the two. Don't ask me why - bad cheese the night before or something. Will I lose any marks for the extra crap at the end of my answer? (the first half of it is right).

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#17

um, dan, i dont understand; ru in lower 6? if so, how and why are u doing A2 papers when u havent been taught them yet?!

ru just like well, well clever?

ru just like well, well clever?

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I work through the modules in advance so that when we do go through it, it is like revision for me. Saves doing too much revision near the exams (which never works for me as there is nooneto ask). Will do M2 and P3 in January, school is very flexible. Let me do papers when I think I am ready. Got a lot of papers to do to get further maths exam. Just finished AS this year adn will do rest of course next year in Jan and June. All the best dudes, Dan

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#19

mensadan doesn't your school have workshops you can attend, mine does and they have been a great help (apart form D1 stuff, the guy hasn't finished the course yet!) hope you can find the help you need to get you through P6 it's not as easy as it looks in the books (so says my friend Pat)

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