*Exam Reflection*

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## June 30, 2011

### Exam Reflection – Results!

Looking back at previous entries, I believe my expectation for the marks I’d receive goes something like this:

Intro to Geometry >> Japanese writing > Probability B = Probability A > Games & Decisions > Geometry and Motion > Differential equations > Linear Algebra > Japanese Oral >> Analysis

In fact, the results (final exams only, Japanese is blended) went more like this:

Geo & Motion > Introduction to Geometry > Probability B >> Probability A > Japanese > Linear Algebra > Analysis > Differential Equations > Games & Decisions

So the most surprising ones were Geo & Motion, where I scored far, far beyond what I expected (I suspect mark adjustment) and Games & Decisions, where I scored some distance below. I also underestimated my Analysis mark by around 50%.

Details: I took 145.5 CATS, scored an average mark (in the final exams) of 78, with a sdev of 10.9, which is pretty damn large, really.

Individual comments:

For GeoMo I eschewed doing past papers, instead reading through the notes and worked examples, and doing some of the worked examples. This paid dividends – I was very well prepared. It also didn’t take that much time. I feel having the worked examples helped tremendously. Unfortunately, most modules lack these.

The difference between my Prob B and Prob A mark is around ±10% – quite large. While I suspected I’d done better initially in Prob B during the exam, I thought I’d corrected my mistakes. Not having lecture notes hindered me in this course: my own notes, despite apparently being in chronological order, wibble and wobble all over the place. As an example, I didn’t know (and still don’t!) anything about bivariate conditional/marginal distributions – I presume we looked at it briefly, and I skipped over that section.

Finally, a graph of exam marks against date of exam.

The graph shows a few things: for one, my belief that I was doing better on exams as time went on looks pretty wrong from here; second, the four day exam stint didn’t appear to have much effect on my marks despite the wild zagging between below 70 and above 90%, and finally that looking at the rest of my marks the coursework propped me up a fair bit. Geometry & Motion was the only module where I did better in the exam than the coursework.

I’ll conclude by saying that my mark for Programming for Scientists, a cool 95.75%, narrowly beats out Geometry and Motion for the top spot. That course was pretty ridiculous.

## June 14, 2011

### ST114 Games & Decisions Exam Reflection

I feel I’ve become both more relaxed and more flippant as the exams went on – I also feel that generally I performed better on the later ones. Having questions in which a girl believes she can predict her marks down to the last percentage point are more fun to do.

This was one of the exams, like Analysis, in which I did more than the bare minimum of questions: i.e. all 3. Unlike Analysis I was able to give complete answers to all three.

I began confidently with the question on Games, but couldn’t remember the exact graph method, flipped and flopped around, tried to work out the final answer a different way, got something else, gave up and moved on.

I then moved back to answer the first question, drew a tiny decision tree, and gave an answer on discounting a 69 vs a 70, assuming you have your estimated marks perfect. This part was fun.

I then rushed through the second, trying to recall definitions, and giving an example of a man who is certain that any given coin comes up both heads and tails at the same time (he’s wrong). For the last part, I misread min as max (NTS: don’t do that), forgot how the log function worked, forgot how functions in general worked (I saw min(log(r),100) as min(log(min(r,100)),100)), but I think I was able to sort it out. Narrowly finished on time. Enjoyed the exam. Probably worse than Prob, but around there. More fun, though.

## June 09, 2011

### MA134 Geometry and Motion Exam Reflection

Like most of the exams that weren’t Analysis, this exam also went well. I wasn’t quite able to derive the final result on one of the questions and my notation was messed up because I didn’t realise that r’ with respect to x and r’ with respect to y would be different and so my attempt to save on writing instead confused the whole situation.

I eschewed the normal “do past papers” style of revision because there are no answers, and doing past papers without answers is even more of a waste of time than doing past papers normally. And doing past papers without answers after the syllabus has changed is even more of a waste of time than that.

Instead, I read through the lecture notes again, doing some of the examples. These lecture notes incidentally happen to be very readable. And concise. I also did some of the exercises from the example sheets, because those had answers. I also read through answers for the questions I couldn’t be bothered to/didn’t have time to do (this was the morning of the exam). It’s very useful to have a lot of worked, short example questions. I can understand a rationale for not giving students example sheet answers (if you never change the questions, they could sell/distribute them to new first years) but it’s still a pain.

As for how it went – probably better than Linear Algebra, but worse than Probability. I did enjoy this course, though.

## June 08, 2011

### MA133 Differential Equations Exam Reflection

From this I’ll conclude that I’d memorised less than I thought I had, but I was able to derive more than I thought I would be. So overall +.

I wasted ~ 20 minutes due to pointless mistakes – swapping x and y,not changing a sign through an entire bracket…but I found them in the end. There were likely more I didn’t see. I also wasted a lot of time trying hopelessly to figure out how to answer certain questions :)

Overall I think it went better than Linear Algebra but worse than probability. Only one more exam to go until I get a break of at least a day! Hooray!

## June 07, 2011

### MA125 Introduction to Geometry Exam Reflection

The exam could not feasibly have gone much better. The questions – straightforward, for the most part, but entirely possible. A 14-mark walkthrough of proving Ceva’s theorem – a proof I already knew. Could have done with being a bit harder, I guess.

I didn’t do anywhere near as much revision for this as for other courses, but then again the course is also significantly shorter.

I think my reading Euclid long ago has aided my ability to construct proofs in some way, but considering it was “nonexistent” before that I can’t say by how much. I still believe it was useful, though.

## June 06, 2011

### MA1312 Analysis II Exam Reflection

So, that went poorly.

Could I have done more revision? Yes, most certainly. Would the sort of revision I had intended to do have helped? No.

Points:

I missed cases or failed to accurately read questions in some cases. There’s not much help for this – it’s something I try not to do :)

I forgot how to prove the latter part of the Extreme Value Theorem, despite only doing it the day before.

I couldn’t see how to solve some questions.

Improvements:

I should become more comfortable with Taylor polynomials to the level at which I’m willing to use them even if they aren’t explicitly specified. Currently I avoid them out of some vague sort of discontent.

Current mark expectation:

Japanese writing > Probability B = Probability A > Linear Algebra > Japanese Oral > Analysis

## June 02, 2011

### Linear Algebra MA106 Exam Reflection

This year’s exam was written by a different person (Daan Krammer) to the previous years’ and so naturally it differed. In particular, the last question wasn’t a series of true/false, which I preferred for easy marks and occasional interesting point (and nice tricks – an identity map is not always an identity matrix, for one).

As before, I did past paper questions, got bored quickly, and flipped through the markschemes the morning of the exam. I did find a much better (shorter) “ranks are equivalent” proof than the one I’d previously learnt, so it wasn’t a complete waste of time.

The first question was standard fare even for previous papers. One question was awkwardly phrased, so I decided to take it literally. The second dealt with surjectivity and injectivity – a new topic for exams, but one I’m pretty sure was dealt with in assignments. The third contained a matrix proof where I couldn’t be bothered to memorise the subscripts involved, in the hope it wouldn’t come up – ah well. The fourth contained a horrible “find this 5×5 matrix determinant” that I got terribly wrong. The last part of four was an interesting original proof in which I used parts of my old rank-equivalent proof, mostly relating to bases of row spaces and the like. The fifth, which I didn’t do, was full of questions that would be easy to work backwards. I was turned off by the hint to the second part, which I couldn’t comprehend in the time limit.

Overall I think I did pretty well, but I may have got large swathes of it incorrect. Nonetheless, it was a more interesting exam than the previous ones – original proof questions are very fun if you get them.

### Probability A/B – ST111/2 Exam Reflection

Probability was the first Maths exam I took this term, on the 31st. I had a bunch of past papers, but the lecture notes were still incomplete. No answers were provided for any assignment bar the last, but I got most of the marked questions right, and probably most of the rest of the questions as well.

I did…around 3 past papers of the old style, and one or two newer ones. I skipped some of the questions of PGFs and the like that aren’t in the syllabus. Before the exam, I felt like I’d done enough revision – more that I didn’t feel like doing any more.

The exam itself was split into two parts: A and B. A bore some resemblance to past papers but had a fair few questions on the theory, the like of which hadn’t come up before. I was glad I picked Games & Decisions at this point, as the extra work on basic probability helped.

I think I did pretty well on Prob A, overall. I was able to answer all of the questions, which is a good sign. I wasn’t exactly sure what “basic set operations” were, though, especially when Probabilities are added to the mix.

Probability B was different. I couldn’t remember how to find joint or marginal densities, the version of Markov’s inequality was different to the one I knew, and I thought that a question asking for an expected number of offers relating to “a” (nonspecific) cdf F meant to average over all possible cdfs, so one question was right out. 4 past paper sub-questions came up, so that was very convenient. Couldn’t remember exactly how to find P(X < Y) given distributions, did a double integral that seemed reasonable at the time.

Overall, I think this exam went very well, although as it was the first I did more revision on it than I have for many other subjects (there were more past papers available, too). I think I did *too much* revision – I could quite easily have done substantially less and got a similar mark. I am planning on doing more Stats later, though, so no harm.