0-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 total average max standard deviation MT1 0 0 3 5 15 18 33 30 104 30.8 40 6.6 MT2 0 0 4 14 37 29 11 9 104 25.8 40 6.0 pb1 8.9 10 1.6 pb2 3.8 10 2.8 pb3 7.5 10 2.2 pb4 5.5 10 1.9
0-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 total 0 0 3 5 15 18 33 30 104
A remark on my marking scheme for question 1 (b) (computing d/dt|_{t = 1} [u(t) x v(t)]): There were a quite a few students who "came up" with a v(t) that satisfied the requirements of v(1) and v'(1), and then with this explicit v(t),
- either took the cross-product of u(t) x v(t), and then the derivative, or
- just used d/dt [u(t) x v(t)]) = u'(t) x v(t) + u(t) x v'(t)
Either way, (providing no mistakes) obviously they will get the correct answer when evaluating at t = 1. But there is some sort of reasoning error that we can determine v(t) just from v(1) & v'(1).
If everything was otherwise correct, I gave 4/5. If there were more errors, it would be 2/5 or 3/5 (depending on severity).