(There’s more tips here)

Some of these tips may sound cliché and I’m sure many of you have heard them elsewhere (from your professors and T.A.’s) . But that’s because they really do work. The cost of a one semester course at Western is around $500. Plus a lot of time spent on homework, assignments and exams. It’s worth spending few extra minutes following the tips I’ve mentioned below. It could mean the difference between passing or failing

Before the Exam

Read over the old exams

Past exams are the best indicator of what to expect on your exam. Assuming that you’re not reading this moments before the exam, you should use old exams to study from. Exams usually follow a pattern from year to year. Take a look at several past years exams and see if you can spot any patterns. Perhaps one question type shows up every year. Maybe there’s always the same number of convergence problems in the multiple choice section. You may even notice a particular problem showing up more than one year. Also, be aware that exam problems can be worded differently than homework problems. If you’ve never seen this kind of phrasing, it can be intimidating.

The best use of past exams is to set aside some time to yourself (without interruptions), put away your textbook, cover up the answers and solve the exam with no outside help. By mimicking actually exam conditions you’ll have a good indication of what you know and what you don’t know. Chances are that the problems you have trouble solving will all come from the same section.

Be careful, however: Sometimes there are slight changes made to the course curriculum. (Some old exams for Calculus make reference to linear and quadratic approximation – a topic that’s no longer part of the course)

Know what will be on the exam

I don’t mean know the formulas (although you do need to know all the formulas). What I mean is that you should know which topics were taught in the course and which topics were emphasized the most. For example, integration by parts was one of the first topics taught in Calculus 1301. It shows up in a lot of different sections. So, you can be pretty sure that there will be some integration by parts on the exam. If you finish the exam and haven’t used integration by parts, then you have done some questions wrong. Likewise, if you identify which topics were the most important, you should expect them to show up at least once. If they don’t, you might want to look back and make sure you haven’t made any errors. Of course, this doesn’t guarantee that every topic taught will be on the test. But a good cross-section should. Arc length of polar curves made up a smaller part of Calculus 1301. And while I may not expect to necessarily see a question involving the arc length of a polar curve, I should expect to see some kind of question involving arc length. Keep in mind that material covered after the midterm will be emphasized more strongly on the final. Since you’ve already been tested on the pre-midterm material, it won’t show up as strongly on the final. In most courses, the post-midterm material accounts for 2/3 of the final and the pre-midterm material accounts for the remaining 1/3.

Get lots of sleep and eat a good meal before the exam

Having pulled a few all-nighters myself, I can say that this really does make a difference. An extra hour of sleep will serve you many times better than an extra hour of studying at 3 a.m. At 3 a.m., your brain is no longer processing information. If it’s the day before the exam and you aren’t feeling ready, go to bed a few hours earlier and wake up earlier the next day to study after your brain has been refreshed. You will notice the difference. Your brain needs sleep and food to function and this is especially true in mathematics.

During the Exam

Write down your formulas as soon as the test starts

As soon as you get the exam, jot down those formulas that you’ve been memorizing. Especially if you’ve only half memorized them. If there’s some formulas you only half know, then keep repeating them to yourself in your head until the professor says to start the exam, and then scribble them down so you don’t forget. Formulas are necessary to do mathematics. It’s no good when you’re in the middle of the exam and can’t remember any of the double angle formulas or how to integrate the secant function.

Read over the entire exam before you start writing

Reading over the entire test gives you an idea of which questions will require the most time and which should be quick and simple. You may even see one or two that you can answer right away. When you read over the whole exam, your mind will unconsciously be working on the harder questions without you even realizing it. There’s been several exams where I’ve read over the problems before starting. Then, in the middle of the exam, I’d have some kind of epiphany about a question that was completely unrelated to the one I had been working on.

Start by solving the problems you know

There’s always one or two problems on the test that are meant to be easier than the rest. Always start with these. If you aren’t sure how to solve a problem, skip it and come back to it later. In the meantime, your mind will unconsciously be thinking about it and you might have better luck when you’ve had time to digest it.

Start with the “Show All Work” section

After you’ve gone through and solved the questions you are 100% positive about, tackle the “show your work” section. If your exam doesn’t have any show your work problems, start with the hardest problems on the test. Trust me - you don’t want to be two hours into the test, feeling completely drained, and just starting the most difficult questions. You’ll be tired and asking yourself “Do I want to stay and keep working at this question, or do I want to go home and sleep?” and as time goes on, it’ll be easier to give up. If you get the most difficult problems out of the way from the start, you won’t have this problem.

Use lots of words!

Yes, math is full of equations and numbers, but you still have to use words to explain what you’re doing. The professor marking your exam doesn’t know that you know that sine is always between -1 and 1. So, write that down if you’re using it in a problem. And, don’t just write in point form! Write in clear, english sentences: “Since |sin(x)| is always between 0 and 1, we can apply the Squeeze Theorem.” Pretend you’re explaining what you’re doing to a high school student. Or a four year old. The professor is going to be marking hundreds of these exams. You want to make it as easy for him or her as possible.

Show all your steps

Don’t ever ever ever skip steps. If you skip steps it tells the professor that you got lost somewhere, didn’t know what the next step was and guessed what the final answer should be. “Show All Work” means just that – show everything.

Go slowly!

Go slowly. There’s no marks based on the speed you solve a problem. Write out each step and don’t try to do five things at a time - don’t cross multiply and simplify in the same step. The more things you try to do at once, the more likely you’ll make a silly mistake.

Always write something. Never leave a question blank!

Do you have no clue how to solve a problem? Always write something down. Even if you just draw a diagram of the situation that a word problem describes. Or if you take the derivative (or integral) of some function involved in the problem (if it’s a Calculus course). A generous professor or T.A. might award you some part marks - wich is a lot better than getting a zero.

Remember, the topics should appear in order

Questions on the exam usually appear in each section in the order they were taught. This can help give you some idea of what techniques to use. If you’re stuck on a problem and you just finished one involving Taylor Series, it might help to remember that Binomial Series was taught just after Taylor Series. Maybe you should consider using Binomial Series on the problems you’re stuck on. Of course, this won’t be true all the time. But, if you’re completely lost on a question, it can help.

Don’t Panic!

So you looked over the entire exam to find the easy problems to start with – and you found there weren’t any. (It’s happened to me a few times). Don’t panic! If you start panicking, you’re mind goes blank and it’s downhill from there. Relax. Take a deep breath. Choose a problem to start with. Go slowly and read the whole question. A problem can look hard on the surface, but after taking some time to think about it and break it down, it’s not so bad. Does the question look like one that you’ve seen on the homework? Or in class? Or on an assignment? Try relating it to things that you’ve seen before. Also, remember that the professors would only ask a question if you had the tools necessary to solve it. If you’re not sure what to do, just try something - anything. If you just jump into a problem and take things one step at a time, things will usually work out. The questions are set up to work out nicely - even if they don’t seem that way at first. Don’t focus on mapping out in your head every step to the solutions. Just think to yourself “what’s the first thing I can do with this problem”. Once you make that first step, stop a minute and see what you can do from there.

Read the Questions Carefully

Really. A single word can change the entire approach you should take. A 10 mark question can be worth 3% of your final grade. If you misread it, then you don’t have a chance of solving it right. Take an extra 20 seconds and read the problem slowly and carefully. And then re-read it. You have plenty of time – the professors usually determine that it should take between an hour and an hour and a half to complete the exam.

After the Exam

Spend time after you’re finished to review your work

Never ever leave early! If you finish the questions, start at the beginning and double check your work. Cover up the answer you found the first time and re-do each problem to make sure you get the same answer. I can’t count the number of times I left an exam early and, moments after I left the room, I realized that I did one or two questions completely wrong.