Edexcel M2/M3 June 6th/10th 2013

My thoughts on the two papers:-

M3 UK Version
Q1) The simplest sort of horizontal circles question. Very reasonable first question to get people started.
Q2) Acceleration depending on t. Needs two simple integrations and solving a quadratic; I had to re-read the question to check it was OK to ignore the negative solution for t. I'm pretty sure it was, but it would have been nice of them to make it more obvious by saying the motion started at t = 0. Otherwise O.K.
Q3) A slightly unusual conical pendulum question in that instead of being given the tension, you had to find it by considering Q. Otherwise quite easy if you have practiced conical pendulums.
Q4) Reasonable energy question. Important to read carefully; the second answer would be different if the string had been replaced by a spring.
Q5) I think this one was rather nasty. Originally I did all the integration by hand, and it takes ages (if you can stay awake through the boredom). It would be even worse if you multiplied out the 4th power of the bracket instead of (implicitly or explicitly) changing variable to u = x + 1. I also made a sign mistake (pointed out by The Burgeoning - thanks). The question only gives a reasonable rate of return on your effort if you use a calculator to do the definite integrations. I've now changed my answers to do it that way. However, I've just noticed that it says "use algebraic integration", so now I'm worried that they actually might want you to do it the long way. (I've put that version at the end of my answers.)
Q6) SHM with two (unequal) horizontal strings. The first two parts fall nicely to the standard method that I teach my students, and the last part to the reference-circle method, or to just substituting into x = a cos(wt).
Q7) A rather awkward type 2 vertical circles/projectile question. The awkwardness is mainly in trying to use the working done in part (a) to get the initial conditions for the projectile motion in part (c). The critical value of theta is negative and of size greater than 90 degrees. I was tempted to do the Newton and CofE afresh for point B instead of reusing the earlier working. Also, getting x and y in terms of t is going to take a while if you use uvast (or suvat, as some weird people call it ) or if you integrate, find the constant of integration and then substitute back, 4 times! This is where "iauic" (integrate and use initial conditions) comes in useful.

M3 International version.
Q1) Horizontal circles inside a smooth cone. Quite quick, especially if you use Newton perpendicular to the normal reaction so that you don't have to find it.
Q2) Acceleration depending on t, one integration, followed by finding the work done. This would be horrendous if you tried to find the work done by integrating power with respect to time (which was my first, stupid, idea). Instead use WEP (I made 2 careless errors in one line! Thanks, Goodkwong.)
Q3) Newton, Hooke for (a), CofE for (b). The quadratic factorises over decimals, but it might be quicker to use the formula or a calculator. Reasonable.
Q4) Rather unusual; I had to think about this one. For (a), write v as dx/dt, then svauiafc (separate variables and use initial and final conditions). Part (b) is the second time recently that they have asked you to find an acceleration using vdv/dx, (rather to than use that formula to set up a differential equation). This might throw people who hadn't seen the previous example.
Q5) Another vertical circles/projectile question. A bit easier than the UK version for two reasons - you didn't need to solve simultaneous equations to find out where the particle left the circle, and you didn't have the same awkwardness in getting the angle of elevation for the projectile motion. Also, uvast could be used conveniently. (Nevertheless, I got this one wrong, leaving out the 1/2 when substituting into the no-v formula. Thanks again, Goodkwong. By the way, how's Badkwong?) As with Q5 of the UK paper, making sensible use of the more advanced facilities of modern calculators (in this case, solving quadratic equations), shortened the answer very significantly.
Q6) The first part was quite reasonable so long as you decided to get y-bar by integration and get x-bar from it by symmetry. The integration would be much more awkward if you did it the other way around. Second part falls to the table method as usual. Third part is simple moments.
Q7) Similar to Q6 of the UK paper overall, but a bit more awkward because you want the time until a particular speed was achieved, instead of a particular position.

I found both papers fairly challenging time-wise, because of the way that they now seem to ask questions that take a long time to do using traditional methods, but are quick using the more advanced calculator facilities. It would have been nice to be given prior warning of this change in style; I don't remember seeing any. Certainly both papers seemed on the hard side.

Sorry to have taken a long time to reply to people - I've had internet problems at home, and at work there is still teaching going on. (Also we've had a lot of leaving parties - more people have left this term than we usually have leaving in a period of many years, for some reason.) I may not be able to reply to people's individual queries till tomorrow. Many apologies.

I couldn't be bothered to sub in the value of v since it would take effort to do without any tools and still make it clear,...

btw any chance you could possibly determine how many marks i would of lost for the stupid mistake on question 5 COM? it was 13 marks and i think i would lose 8 at worse but just want to get a better idea i guess

For Q5:
Answer should be 0.5497
(1/2)g(t^2)= (1/2)(49/5)(t^2) rather than just (49/5)(t^1/2)

I had got the same answers for all other questions(but making silly mistakes during the exam)

For Q6:
I would like to know how many marks would I lose if I use "a" rather than "a/2" in Q6 for CG of the rectangle when calculating the CG of lamina in part (b)...then in part(c)...

May I still get the method marks of part (b) and (c) = 2+1 = 3 marks (or more?) out of 8?

For Q5:
And I would also like to know if I get the time wrong in Q5 because when I use both [ v^2=u^2 - 2gh ] and [ v=u+at ] to find time t, I wrote "2gh" into "gh" forgetting to add the "2", leading to wrong time t and thus wrong ans of 0.515m.

Would I still get the method marks of about 4 out of 8?

For Question 5-

The answer should be 547/363? Just done it on my calculator...

the paper was fair, M3 is just damned hard, ran out of time for the last part of the last question, resisting looking at the unofficial mark scheme thanks for asking

What about mass. Did you do the same for finding the mass i.e. M = ρπ∫y² dx.
If so, I would say you would lose all the answer marks but will get a few method mark, especially if your method of proving the thing was correct. You would probably get about 5-6-7-8 / 13(might be 14 not sure).

what do you think will be the raw mark needed for 100/98/96 ums- i bungled a tiny part of the last question because i mixed up the cos and sin for the last part i have realised. I am praying also that there is error carried forward.
i really want either 100/98/96- its just that i hated the fact that the questions were easy- just took a bloody long time- I spend ages doing Integration by parts but since nobody seems to be commenting on this im assuming everybody used the bloody integrate function shortcut on their calculators which greatly pisses me off. Will you be penalised if you dont show working out for that part- i hope so because its just unfair that some people can do that instantly with the right calculator which in any case is banned- i would have finished quicker also if it wasnt for that bloody question and would have had time to check last part.
Conclusion: IS this a test of understanding of mechanics or a test of bloody numerical analysis? why cant they just use simple numbers with questions that actually stretch?
Oh and of course- boundary prediction- what do you reckon?
Thanks for posting your solution too.

what do you think will be the raw mark needed for 100/98/96 ums- i bungled a tiny part of the last question because i mixed up the cos and sin for the last part i have realised. I am praying also that there is error carried forward.
i really want either 100/98/96- its just that i hated the fact that the questions were easy- just took a bloody long time- I spend ages doing Integration by parts but since nobody seems to be commenting on this im assuming everybody used the bloody integrate function shortcut on their calculators which greatly pisses me off. Will you be penalised if you dont show working out for that part- i hope so because its just unfair that some people can do that instantly with the right calculator which in any case is banned- i would have finished quicker also if it wasnt for that bloody question and would have had time to check last part.

Conclusion: IS this a test of understanding of mechanics or a test of bloody numerical analysis? why cant they just use simple numbers with questions that actually stretch?

Oh and of course- boundary prediction- what do you reckon?

Thanks for posting your solution too.

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My guess is you could lose several marks and still get 100% - you can most years, and I think this paper was harder than usual.

I totally sympathise about the calculators. But you're wrong about those with a definite integration facility being banned. I noticed that Q7 of M3 January 2012 involved an inordinate amount of boring integration for not very many marks. So we checked the regulations and found that it's only symbolic, indefinite, integration that is banned. So we changed our college's standard A-level calculator to one that could do it. (It also had advantages for statistics.)

But you might just be in luck and get some credit for wading through the integration by parts instead of using the calculator. The question mentioned "algebraic integration".


You could argue that, once everyone knows it's OK, using things like definite integration by calculator might allow them to ask more questions that really test out understanding and ingenuity. The transitional period is awkward, though.


A touch lower than normal, but not massively so.


No problem!

Im going to sound very stupid here, but what does it mean by algebraic integration? I used integration by part, will I be okay?


Posted from TSR Mobile

You said earlier that you thought you might lose 6 to 8 marks. If I've understood the mistake correctly, that seems over-pessimistic. I'd have said losing 6 marks would be a bit harsh for what is essentially one minor mistake.

Thankyou for replying,
If it changes anything i used by parts when integrating hence i did the same mistake twice:
one for when i subbed in 0 for (x+1)^5/5 and also when i subbed in 0 into (x+1)^6/30.
So would losing 6 marks still be harsh on that basis? losing 6 marks for that would be absolutely fantastic

Definitely.
So would expanding the power of the bracket using the binomial theorem, but that would be very time-consuming.

I have to say i completely agree with you about the centre of mass question - As far as im concerned you're not even allowed to use a calculator which can integrate in the exam. Integration by parts took so long for me and that question stressed me out so much that I ended up doing (ρπ∫xy dx / ρπ∫y dx) instead of (ρπ∫y²x dx / ρπ∫y² dx) so im bound to have lost loads of marks for that question...... And because I spent so long on that question i didn't even have time to do 7c which I really don't believe was as hard as everybody made it out to be, it just required you to use your brain and do some thinking.

Edexcel definitely need to fix up and stop giving questions where the centre of mass is some bloody three digit numerator and denominator and it wasn't even a show that question so how the hell would you have known if you were actually doing the right thing?

My teacher said I could have done that. LOl Only an idiot or a madman would have done such a thing. You'd be sitting there all night.

I hate using parts if I can avoid it, I think I used a substitution or recognised it as an f'(x)f(x) or something like that (can't remember exactly but I remember getting the answer). I never use the calculator for definite integrals I always do it algebraically and then evaluate the limits at the end, I think calculators are cheating 😏😏