The CO 370 Midterm
On Feb 22 2010, I wrote the hardest exam of my entire undergraduate career. The 2-hour CO 370 midterm exam designed by Prof. Ricardo Fukasawa of the combinatorics and optimization department at the University of Waterloo was perhaps one of the best well-designed exams I had ever seen to date.
I felt that the questions were all solidly hard but yet entirely fair. They were all direct applications of material we had either seen in class or in the assignments, usually both.
I put in about 9 hours of total study time for this midterm worth 30% of the final grade. I thought that was quite generous. But I was able to be so generous only because of the free Reading Week that just preceded it. I was looking forward to getting as close to 100% on this midterm to enhance my buffer for the 50% final, in case I didn't do too well on it.
The truth was that almost everyone in the class, including me, could have gotten 100% on this midterm exam given sufficient time. At this point you should be thinking to yourself, hmm, that certainly smells like a time pressured exam to me. And it was! The midterm was a 3 to 3.5 hour exam compressed into 2 hours. Now we're talking!
It was at this point that I realized how useful all my analysis and pondering over time-pressured (TP) exams over the last 5 years was going to be. I cleared my throat, rolled up my sleeves, released a brand-new piece of lead at the tip of my mechanical pencil, and got down to work. I spotted four equally-valued questions at 25 marks each, for a total duration of 2 hours. That was half-an-hour per question tops.
I quickly took 5 minutes to skim through the questions and determine a total oder on the questions. The questions were definitely arranged in random order. On purpose of course. Within minutes, I was able to sort the questions in ascending order of difficulty: 4, 3, 1, 2. Phew!
Five minutes into the exam, I quickly scanned the room to see how people were doing. Everyone seemed to be scurrying to put pen on paper. It was at this point that I realized the class as a whole was probably going to end up doing pretty badly on the exam. They hadn't realized what was coming at them. They hadn't realized what they were dealing with was a TP exam. They were certainly going to run out of time, no doubt.
In a TP exam, it is crucial that you take time at the start of the exam to figure out the order in which questions must be answered to maximize final grade. Remember, TP exams are like a beach littered with diamonds everywhere. So you want to head towards the areas with the highest density of diamonds first. Approaching a TP exam sequentially, from first question to last, is perhaps the worst thing you could do for your grade.
Half-way through the exam, I could actually feel my head getting hot during the exam. I don't think I've ever sweat any exam before. This was a first. I kept getting visions of how my brain was like a giant 3 GHz Intel quadcore microprocessor with 8 gigs of unpartitioned ECC memory, with each cell, tissue and muscle in my brain acting like a tiny resistor, releasing a microwatt of heat upon each computation. Luckily, there was a water fountain right outside the exam hall so I could be constantly sipping on chill water every few minutes to keep cool.
The marks were of course unevenly distributed throughout the exam. This is a hallmark of every time pressured exam. The marks for each sub-question were allotted not based on the amount of time it would take a student to solve it or how difficult the problem was, but based on how important the prof thought the concept was, or based on how many concepts the question was amalgamating. It's a perfectly legit way to assign marks, but if you didn't realize what was happening, you'd have been in for a surprise.
A point I had failed to address in my previous blog post on TP exams was the idea that there is an initial investment of reading, parsing, making sense of, understanding, and building a mental, conceptual model of the problem in your head before you can even attempt to solve it. This is an important yet time-consuming step.
A lot of subjects are like this with long-winded stories about the problem statement in English with a lot of useless info in between. Translating the word problem to a mental mathematical framework that is concise and precise takes time. So the faster you can do this, the more time you'll have left to actually solve the problem. This is a higher-order skill that can only be obtained by the experience of solving hundreds of practice problems the day before the exam.
The midterm exam consisted of only 4 typos. And we were interrupted by the prof for corrections and clarifications just twice. Not too shabby. At the end day, I approached the exam by eating my own dog food. Time pressured exams are my specialty, and I think people who had spent time thinking about them before hand were at a significant advantage compared to people who still think it is unacceptable and unfair if they can't finish an exam on time.