## Time Pressured Examinations

It is with utmost regret that I inform you that even after under a thousand hours of exam writing experience under my belt, I still haven't quite mastered the fine art of managing the so-called "time pressured examinations". But I'm getting better. Nonetheless, I think I got some interesting thoughts that I'd like to share with you.

What's a time pressured exam anyway? A time-pressured or time-sensitive exam is an examination that isn't necessarily intended to be completed. The anticipated duration of the exam will generally be non-trivially longer than the amount of time alloted. The number of questions will be far more than you think you can handle.

At Waterloo, which is the school I go to, the norm seems to be 3-hour exams in 2.5 hours. However, with time pressured exams, we'd often see 3.5 hour exams compressed into 2.5.

Why are time pressured (TP) exams hard? They aren't exactly "hard" in the traditional meaning of the word "hard" per se. But they're hard for other reasons. For one, you can't score a 100%, at least not easily. And this fact alone tends to annoy a lot of people.

Also, from a very young age, we're generally taught to start with the first question and keep working through the exam until we hit the last. This time-tested traditional "algorithm" doesn't quite work that well for TP exams, and this too annoys a lot of people, because now we have to invent a new algorithm. And to make matters worse, we now have to do it on our own. How alarming.

TP exams are essentially a special class of optimization problems known as scheduling problems. The problem statement is as follows: Given a list of questions and the marks allotted to each question, determine the order in which the questions must be tackled in order to maximize total marks obtained, subject to the constraint of insufficient time.

I've had to sit through a number of interesting time pressured exams. Sometimes, they tell us in advance it's going to be time pressured, like the GRE. Sometimes they don't, like the IB Paper 1 and Paper 3 exams. In all honesty, the most exciting TP exam I've ever had was the final exam for the Fall 2006 offering of MSCI 331. Ironically, it was an introductory course in optimization. How very meta.

I personally feel time pressured exams are better than regular exams. For
one, we don't have to know *all* the material taught in the course to
get the best grade in the class. With regular exams, if we don't know the
answer to even one question, we could be in big trouble.

TP exams, on the other hand, tend to test us on what we know rather than what
we *don't* know. But they're hard. We not only need to know which
topics we're most comfortable with, we also need to know *how*
comfortable we are with them.

Time pressured exams tend to work particularly well for math and
engineering-oriented exams. They're very good at weeding out the bunch who
crammed things into their heads the night before, because these students
would take too long to solve each problem. On most math and engineering
exams, given enough time, we could probably nail down the answer regardless
of difficulty by re-working everything from first principles. So
examiners *need* to provide inadequate time to see who knows what the
best.

Questions on a TP exam require tons of prior practice for us to have the right intuitions and the right speed. The Spring 2007 offering of MATH 212 Advanced Calculus 2 was one such gem: people who only studied a week before the exam all got low-80s or lower. And they all wished they had more time. If they did, they would've easily secured a 90.

A time pressured exam is best approached like a desert littered with diamonds. And we're given a fixed amount of time to spend at the desert. What do we do? We obviously scout the areas with the highest density of diamonds first.

What most of us do is approach TP exams like a pacman chomping away at a line of dots. We try to go in order, in a rather mechanical fashion, and when we get stuck on one of the earlier problems (usually the first or second), we get put off, lose hope, and complain. Or sometimes we stress that we may not have time to finish the entire exam, and the stress reduces our performance and causes us to make unintentional and silly arithmetic or algebraic errors that we wouldn't usually make.

The point we constantly miss is that the exam was *designed* to not be
finished on time. It's not that we don't know the material well enough; even
the *prof* probably couldn't finish the exam on time.

What I usually do on a time pressured exam is to invest the first five
minutes of my time to *read* each question thoroughly. If there are
only five questions on the exam, then I write down the order in which I plan
to tackle the questions right away. If there are more questions, I write down
approximately how long I think it would take me to solve the problem in
minutes. If I don't feel like I can solve a particular problem, I just cross
it off and don't bother with it. *I do not try to solve every
problem.* I'll just end up wasting time if I did that. Then I divide the
grades allotted to each question by the amount of time I feel it would take
me to solve them. Then I rank the questions by decreasing value of these
quotients and tackle the problems in that order. If I get stuck anywhere, I
immediately proceed to the next question. This way, I solve the problems I
know for sure first, then I try the challenging ones later if I have time
left.

That's certainly one approach, and arguably the simplest. But there are more. Lots more in fact. We just have to come up with a clever game plan a day ahead of the exam. Of course, if our heuristic takes us more than 5 minutes to execute, we're defeating the purpose of the heuristic in the first place.

We definitely want to stay *calm* during a time pressured exam. We'll
have a tendency to constantly look at the clock. We'll have a tendency to
freak out as time starts to run out and we still have 4-5 unanswered
questions. However, we need to have the composure of a bomb diffusal expert:
anxious but calm, tense but confident, uncertain but steady. You have to
remember that if *you* can't finish the exam on time, neither can
others. You just have to do relatively better than the rest of the class.

TP exams are fun games profs like to play with us. Our job is to win it.