Get Practise in a Timed Environment
Date Written: June 18, 2024; Last Modified: June 18, 2024This advice probably doesn’t apply to you if you don’t struggle with time on exams.
When doing practise exercises or practise exams, time yourself. Be aware of how you are spending your time and where you’re spending it. Are you spending a lot of time writing out, erasing, and rewriting computations? Are you spending too much time trying to remember the conditions of a certain theorem? Are Taylor expansion problems just impossible for you to work out, no matter how hard you try? Or maybe you are just a slow writer and can’t get everything on the page in time?
When studying, it’s easy to focus on the math and content altogether and forget that timing is a component of the test-taking environment, and it deserves respect. Moreover, it’s helpful for guiding how one spends their time both while studying and on the exam itself.
On one hand, if you’re spending too much time on problems involving concepts X and Y, perhaps this is a sign that you should spend some time reviewing concepts X and Y. If you’re spending too much time writing out and messing up computations in general, you should figure out a system for yourself (e.g. mnemonics) that aid with those computations.
To back this point up, when I was studying for the analysis qual, I realised that I was spending an inordinate amount of time with inequalities involving fractions (if \(a< b\) and \(c< d\), is \(\frac{a}{c}< \frac{b}{d}\) or \(\frac{a}{d}< \frac{b}{c}\)?). I would write down the wrong inequality half the time, and I would have to spend time fixing my proof (often having to start over altogether). Or I would just get the problem wrong.
I would never have realised this was an issue if I wasn’t timing myself! Without the time pressure, I had the attitude of, “Well I figured out the issue and fixed it, so I’m good”. This is a fine attitude for doing homework, but it wasn’t helpful for exam preparation.
The second point is that on exam day, it’ll be easier to budget your time. If you know you always take forever on Taylor expansion problems, you should probably avoid the Taylor expansion problems. If you know writing out computations takes forever, skip them, and fill them in at the end if you think it’s absolutely necessary! (This point is a shadow of the more general advice of writing solutions iteratively.)