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# OCR MEI FP3 2016 Exam

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1. Couldn't find one so I have created one. How did it go?

I did vectors, MVC and groups. I was hoping for near 100% but for the vectors questions I couldn't figure out how to get the point on the lines that give the shortest distance, which seemed to be about 10 marks overall. As a result I ran out of time for the last part of the groups.
2. Finally someone created a thread for this! I did vectors, differential geometry and multivariable calculus.

I didn't like that they gave a context for the vectors. For differential geometry I got 8/3 for radius of curvature. Fortunately I managed to get a squared expression so could square root it. It was 9t^2+1 I think
3. i couldn't get the shortest distance points either i'm so gutted
what did you get for the first part of the vectors question?
4. (Original post by rubycstoddart)
i couldn't get the shortest distance points either i'm so gutted
what did you get for the first part of the vectors question?
Can't remember the answer to the first part. Shortest distance was root 5.

Spoke to a friend. You can calculate the points for the shortest distance by doing the cross product of the directions, which gives you the perpendicular direction between the two lines, and find where that intersects with both lines to get the points.
5. What answers did people get for MVC and groups?
6. For the points with the shortest distance, you cross the directions to get the perpendicular to both lines.
Then you solve 3 simultaneous equations with 3 parameters where the general point on one line (a known point+lambda×direction) equals the general point on the other line + a parameter×perpendicular between the line. You find the parameters and substitute back to the equations of the lines to find the points.
7. For the groups question did anyone put 2 subgroups for the group? Elements were order 1,2,4,4 if im not mistaken
8. (Original post by groovy_q)
For the groups question did anyone put 2 subgroups for the group? Elements were order 1,2,4,4 if im not mistaken
Don't forget that the whole group and the group consisting of just the identity element are subgroups too.
9. Would i get the mark if i just wrote the subgroup order 2 and the group itself and missed the identity? (question was 1 mark
10. Vectors was poor. Parts I and II were fine but III and IV our Further Maths Cohort generally found tough.

Apart from that it was pretty decent.

Muy Bein! I got the same answers to those in Diff Geom too!
11. (Original post by willutalk)
Vectors was poor. Parts I and II were fine but III and IV our Further Maths Cohort generally found tough.

Apart from that it was pretty decent.

Muy Bein! I got the same answers to those in Diff Geom too!
Great! Do you remember what was the centre of curvature? I was confused because (0,2) seemed to have two graph sections crossing it so I didn't know which one we had to find the centre of curvature for.

Edit: just remembered I got 8.31 for the first question. Did anyone else get it too?
12. The answer to the first question was sqrt(69). So yes, 8.31 was correct.
13. I thought the paper was mostly good overall.

I did vectors, MVC and Markov chains. From reading this thread it seems like everyone had the same problem I did with the vectors question. I came back to it at the end and must have spent a good 25 minutes trying anything that might work.

I thought all the other questions were very nice though. MVC had the small changes method for determining the nature of stationary points that came up last year, so I'm glad I did the 2015 paper a couple of times.
14. But for the final part of th vectors question, I think you had to solve simultaneously the equations of the lines to get a λ and μ. If you then take the magnitude of each direction vector and multiply by their respective λ or μ you get 27 and 28.5 which are proportional to the speeds of the two planes. They will therefore collide on current course and speed.

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