My tutor very kindly sent me a solution document for the past paper from 2008, so this morning I’ve been working through the my first ever practice exam for a maths course! I was quite curious to see what the exam paper was like, since all the exams I’ve taken with the OU so far have been in computing/programming. Luckily it seems like maths exam papers follow roughly the same pattern that the computing exams do – about a dozen short questions, one for each course unit, and then a few longer questions that require combinations of techniques from various units. And nicely, you only have to do two out of the four longer questions available, so I’m happy to say that I’ll be able to avoid at least some of the graph-sketching questions!

I haven’t done much revision so far for MS221, just a few problems from the exercise books provided for each block, so I’ve used the 2008 past paper as a kind of diagnostic tool, to find out which areas I’m confident in already, and which ones I’m completely incompetent at. Guess which there are more of?

Here’s how a rough outline of what’s in the 2008 paper (hopefully this won’t constitute copyright infringement!):

## Part 1

• Question 1: Finding a closed form for a recurrence system
• Question 2: Identifying and sketching a conic
• Question 3: Stating the rule for some isometries, and for a composite isometry, and then using the double-angle and half-angle formulas to show a result
• Question 4: Classifying fixed points of a curve, then sketching the graph of the curve and using graphic iteration construction
• Question 5: Identifying basic linear transformations, applying them to a vector, and stating an invariant line for each one
• Question 6: Finding eigenvalues, eigenlines and eigenvectors.
• Question 7: Differentiation
• Question 8: Integration
• Question 9: Finding and manipulating Taylor series about 0, and classifying stationary points
• Question 10: Finding the modulus and argument of a complex number, converting them from Cartesian to polar form and vice versa, and using the formula for powers of complex numbers.
• Question 11: Using Euclid’s Algorithm and working with exponential ciphers.
• Question 12: Combining variable propositions, finding a case for which a given proposition is false, and finding the converse of a proposition.

## Part 2

• Question 13: Looks like it’s about conics, but I haven’t done this one yet.
• Question 14: Linear transformations
• Question 15: I haven’t done this one yet either, but it looks like it involves differentiation, integration and stationary points.
• Question 16: Groups

I decided to do all the short questions and then two of the long questions, to simulate what the actual exam will be like – and I was pleasantly surprised to find that I didn’t run out of time (though this is probably due to the fact that there were quite a few questions I couldn’t complete!). I did manage to get something down for all the questions (except the two long questions I opted not to do), but there were quite a few where I couldn’t quite remember how to apply the appropriate techniques – yes, even with the handbook right next to me!

In particular, I seem to have completely lost any competence I ever had with the material from Block B; which is unfortunate, since that’s what Question 14 was pretty much all about! I also need a lot more practice working with Taylor series, I got myself in a complete muddle trying to substitute into the standard Taylor series about 0. It’s weird, though, because I remember really enjoying those two topics, so I assumed that I wouldn’t have any trouble with them. I seem to be alright at Blocks A, B and D, but the contents of Block B have apparently disappeared entirely from my memory!

I think the area I was strongest in was the Block D stuff, which is unsurprising really since it’s the material I’ve learned most recently, and it was my favourite part of the course. I was pretty confident with the calculus questions too, except for integration by substitution, which I’ve mostly forgotten how to do. So I’m mainly going to concentrate on Blocks A and B for the first week or so of my revision for MS221, and then see how I do at the next past paper next weekend. Hopefully my copy of the Black Badge Press solutions booklet will have arrived by then!