Edexcel M2/M3 June 6th/10th 2013

I don't see why anyone would go into an edexcel maths exam without a calculator which does numerical calculus and more importantly has a table function.
I typically spend a at least ten minutes of my exam time checking answer using the table function to brute force check my functions for sense.

What's the Cal?

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Once you've solved a question you can type in a function and then get solution for 30 different values of x in a table. Its basically impossible to get intercepts or turning points wrong when that tables lets you do a decent sketch of even the most convoluted function.

But you can't draw graphs, histograms, box plots?


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A table of x and y values makes drawing a graph trivial. I've only done S1 but I don't think the stats stuff is that great.
I'm sure there's allowed (expensive) graphical calculator that could.

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Once you've solved a question you can type in a function and then get solution for 30 different values of x in a table. Its basically impossible to get intercepts or turning points wrong when that tables lets you do a decent sketch of even the most convoluted function.

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 Important to read carefully; the second answer would be different if the string had been replaced by a spring.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 sat the UK version of M3 but what I sat was completely different to what you outlined

Does this mean that your school gave you the version that was replaced?

I don't know. .... the questions were as follows as far as I can remember:
1. Simple vertical string/spring hanging from a ceiling
2. Finding an angle of an inclined plane
3. Centre of mass part a asked to prove by integration the centre of mass of a hemisphere then had to use this in part b then it was in equilibrium in part c
4. Two horizontal springs attached to each other and had to work out tension in both springs and then prove it was in SHM
5. Was vertical circles question
6. Kinematics
7. Simple horizontal circle question

I think Tiny Hobbit must be right; it sounds like someone in your school's exams office must have missed the message from Edexcel about using the replacement paper.

I don't know how they are going to set grade boundaries on this paper, given that so few people sat it. Your school's Maths Department and Head Teacher should know about it, and should be fighting your corner to make sure that the grade boundaries don't disadvantage you.

Don't worry too much about it - you shouldn't suffer because of someone else's mistake.

I'm sure it'll be fine, the results shouldn't suffer because surely they'll just set new boundaries based on those who sat that paper (there were four of us) but perhaps others have taken it too.

It wasn't in the form f(x)f'(x)

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.

Yes, full marks, no problem. You would have to use this method if the angle hadn't been a right-angle, but as it is, the other method is a bit easier.

I don't claim to be a expert on grade boundaries, but my instinct is that the paper was a bit harder than recently, so they should be depressed a little bit from the notional 60/75 and 67.5/75.