Next year I am likely to be teaching Mechanics 3 to my further mathematicians and so I thought I should have a go at this years exam paper (1 person sat it at school so I had a copy of it). After seeing this video I was a little nervous as I hadn’t looked at this since I did my A Levels, however I didn’t find it too bad with a bit of help from my old A Level textbook:

Question 1 I thought was pretty straightforward – once I had refreshed my memory of how to calculate elastic potential energy it was just an energy conservation question. Please excuse that I have written Hooke without a capital letter.

Question 2 was nice, as long as you could remember how to find volumes of revolution, and then use this to find \(\bar{x}\)

For Question 3 I realised that sometimes I have no intuition with the mechanics questions. Even though it was asking you to find the tensions in each string I still expected them to come out equally – of course in hindsight this clearly wouldn’t have made much sense. The circular motion stuff came back to me quicker than I expected to be honest, and this question dropped out quite nicely.

Question 4 was a nice power type question, I thought it was very like an M2 question, just with the complication of non constant acceleration. I really like how the question required you to use the Trapezium rule. As a numerics guy I think how the numerical methods are presented at A Level is incredibly sad. The trapezium rule is great, and it could be used so much in the applied modules – students wouldn’t like being asked to use something from Core 2 in other modules though. I think I may have to write about the Trapezium rule……

Question 5 is a nice centres of mass of a 3D solid. It considers a spindle formed of two cones. In hindsight it would have made more sense for me to work out the Center of mass using moments from A instead of taking moments from B

I can remember loving questions like Question 6 when I did A level, and I still quite enjoy showing that a particle connected to two springs exhibits simple harmonic motion. Like many questions as long as you are comfortable with applying F=ma and solving simultaneous equations it is fairly straight forward.

The final question considers a particle moving on the surface of a sphere and uses conservation of energy and F=ma. I wouldn’t be surprised if some students forgot to add the horizontal distance moved whilst on the sphere in the final part.

Great post Tom, M3 is one of my favourite modules to teach, but I’ve not got any sitting it this year so thsnks for sharing.

I was surprised there is a whole mechanics paper from edexcel without a hidden 3,4,5 triangle, and I love the fact you use centre and center interchangeably in your workings for question 7!

Thanks š yeh I was surprised there wasn’t a 3,4,5 triangle. Haha I hadn’t realised that – it’s what comes from years of reading American English maths papers! What is your view on the use of the trapezium rule in a question?