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1. To my knowledge, any appendices or footnotes/bibliography do not count toward the total word count; but the 4000 word maximum rule still applies.
2. How about analyzing the change of the angle of the shadow relative to some axis as time changes? This could initiate some interesting mathematical concepts, possibly in the areas of trigonometry and vectors.
3. It would be the sum of the fractional uncertainty in the distance (determined by the least count of the ruler) and the fractional uncertainty in time. For time, since you're analyzing a video played back, the least count would be determined by the number of seconds elapsed after each frame. For example, if the video was replayed at 100 fps, the least count = 1/100 fps = 0.01 s
4. I was able to push my way through that last probability question. For the first part, all it was was setting the sum equal to one, and then solving for cos θ. Then they asked for tan θ which is just (sin θ) / (cos θ) and since you're already given cos θ, just solve for sin θ using sin2 θ + cos2 θ = 1. The harder part was the last one where you had to integrate it. The problem I got stuck on on Paper 1 was number 9, when they asked you to find the values of k.
5. I'm from TZ1 and I actually thought Paper 2 was harder than Paper 1! But Paper 1 was still pretty hard especially question nine, which I found quite tricky. On Paper 2, I messed up on number 7 ("Find when the total distances are equal") and I blanked on number 10 ("Find when the distance between h(x) and y = x is maximum). Did anyone get 23:00 for the high tide question in number 8?
6. That's a good start. Now you just need to simplify the complex fraction:
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