How to Cram for a Math or Engineering Exam in 24 Hours

Posted on September 24, 2012 by


Seeing as how I write a lot about deliberate practice and appear to be pretty disciplined and routine in my approach you wouldn’t be surprised to find out that I was a Biomedical Engineering major in college.  I think you would be surprised to find out that I rarely went to class and regularly pulled all-nighters to cram for my engineering and math exams.

The truth is that most of my classes did not require attendance and it was not a factor in your grade.  Most times grades were a combination of Homework, Mid-term and Final exam scores.  The homework was always less than 20% of the total so your grade mostly depended on your ability to score better than average on the Mid-term and Final Exam.

I frequently put off studying for major engineering exams until the day before.  I still remember the rush I experienced as I tackled Mech-E Thermodynamics in a 24hr period.  When I opened the book the day before the exam I literally had to break it in it was so new.   By then I was a junior and had experience cramming for these types of exams.  I went on to get an A on that exam and in that class.

Here are the steps I used to cram for engineering and math exams.  If I was able to go back to school right now I would use these same techniques but I would distribute them over the entire semester instead of cramming last minute.

Remember the Goal

I think a lot of people lose track of the goal when studying for an exam.  My goal was to get a B or better on all my exams and in my classes.  I would have loved to get an A but I realized that there was a big difference between the amount of work it takes to get a B and the additional effort it takes to get an A.

I wasn’t planning on going to Law school or Medical school so having a super high GPA wasn’t critical for my success.  I did need to have a Good Enough GPA and that is what I focused on.

Once you are in a position where you are cramming for an exam it stops being about learning the material or understanding the concepts.  You need to figure out how to pass the exam.  That is how you are being measured and graded.  In most cases that means learning how to solve the problems for that subject.

Collect Your Study Materials

If you are anything like me it is a week before the big mid-term and you haven’t even cracked the book yet.  You do have a copy of the book, right?  Because you are going to need that.  You better buy the solutions manual too.

I would collect all the materials I could get my hands on.  Syllabus, lecture notes, exam and homework solutions.  I would throw all that in a big 3-hole binder.  Anything you can find related to the class goes in the binder.  The more problems with solutions that you can find the better.

Go to a Place without Distractions

You need to find a quiet place to study.  At Hopkins there was one floor in the library, “D Level,” that was renowned for quiet and focused study.  No talking was allowed and there was no chit-chat going on between students. If there weren’t any desks available on D-level I would look for an open classroom in one of the engineering buildings.  I almost always did this after the library closed and I really enjoyed working by myself in a large quiet classroom.

You will probably be tempted to join your friends who are planning to meet up and study together.  Avoid this situation at all costs.  It is a trap!

I never understood why people would work in groups or in crowded study rooms. I found it so distracting to be around so many different people. Plus you have to listen to all of them trying to learn and teach these concepts and you don’t know if they are right or wrong!  Talk about confusing the brain…

First Pass Through Everything

Now that you have your study materials and a quiet space begin reviewing all the materials quickly to build a mental framework.   I would use the syllabus, class notes, textbook, etc to figure out what the overarching ideas of the course were.  This gives the brain a framework to start organizing ideas.  The brain likes relationships and if you can figure out where a certain idea fits in to the larger framework then it is going to have an easier time remembering and understanding it.

You need to read through the textbook quickly.  How do you read an engineering textbook in a couple hours?  Well, you scan it.   Avoid all the superfluous stuff that talks about real life examples and a day in the life of type stuff.  This is a distraction.

You are looking for theorems, formulas, rules, claims, truths, facts.  If it isn’t highlighted, bolded, in Italics, or underlined than it probably isn’t that important.  Write the most important stuff down in your own notes for reference.

Review Homework and Exam Solutions

Once you have a rough framework built it is time to start scanning through the old exams and homework assignments to confirm what material will be included on the exam. Don’t worry too much about trying to understand or solve them yet.  Just look to see what parts of the book they align with.  Usually this is pretty clear.  If there are 5 problems on an exam they are usually tied directly to certain sections or key concepts of the book.

This is when you will realize that some concepts or chapters aren’t covered at all.  You will be happy that you didn’t go to deep and try to memorize everything in the book.  The truth is these textbooks often cover way more material then the professor ever teaches or tests to.

Pay attention to how the professor structures his exams.  You will find that most professors make similar exams each year with slight variations of the problems. If you see a pattern you can use this information to guide which types of problems you practice.

Learn How to Solve the Problems

Don’t waste your time working on problems without solutions.  They provide little to no value and may hinder your progress.  If you can’t get immediate feedback after trying the problem then you don’t know if you are doing them correctly and you may create bad habits.

Don’t struggle too hard to try to “figure out” or solve the problem.  It is a waste of energy.  Look at the solution.  The technique for solving the problem is right in front of you.  That is what you need to learn.  What was the leap that the professor made that wasn’t obvious?

I like to go through each problem and solution and work them out side by side but using my own notation and hand-writing.  Professors will often skip simple steps to make their solutions look neater.  I like to write these steps down because it will help establish my work flow.

Practice, Practice, Practice

Once you have worked through a couple problems with solutions it is time to try solving a problem without a solution.  Feel free to reference your notes and solutions of other problems.  The goal here isn’t to make it too hard but to force you to apply some of the skills that you just learned.  Eventually you will want to start working on problems without any notes.  This is the real test of what the exam situation is going to be like.

Once you have learned a problem solving technique you need to close the book, put away your notes and practice solving exercises.  As you work through problems pay attention to where you are getting stuck or making mistakes repeatedly.  You will want to review your notes and solutions and correct your technique.

Consolidate Key Concepts

Throughout this process you should be taking notes.  When I scan through a text book I will normally have 10-15 pages of hand-written notes.  After doing the practice problems I would have 15-20 additional pages of solutions.

Now it is time to consolidate all that down to one page of reference information.  Start writing key formulas, rules, concepts, etc.  What information do you want to reference?  What ideas or rules are you having trouble remembering.

Some professors will allow open book or open notes.  It is a mistake to bring in all your notes and textbook and think that it is going to be helpful.  You need to consolidate and distill that information down to key pieces of info.

If you aren’t allowed to bring in your notes then you are going to memorize this single page of info.  Don’t worry; you are already most of the way there.  You distilled 300 pages, down to 30 pages, down to 1 page.  You already have it mostly memorized.

Strategies for Taking the Actual Exam

Whether you pulled an all-nighter or have been studying for weeks here are a couple rules I would follow on the day of the exam:

Plan on showing up 20-30 minutes early.  This gives you plenty of time to find a comfortable chair, get out your pencil and calculator, and review your notes.  It also decreases the chance that you would be delayed and actually show up late for an exam.

Review your single page of notes.  If there are any formulas or concepts that you are struggling to memorize you may want to focus on them in the final minutes right before the exam.  As soon as the exam starts write down those notes you were struggling to remember.  Throughout the exam certain notes from your sheet will bubble up into your mind and you should write them down in the margins of the exam.

Once the exam starts you need to remain calm.  It is easy to freak out and feel like you are going to forget everything you just crammed in the last 24 hours.  Take a deep breath and start reviewing the exam.  Scan the entire test.  Read any instructions carefully.  Figure out how many problems there are.  Does it look similar to the old problems you were studying?

Start with a familiar problem.  You want to get a quick win.  Solve that problem and move on to the next most familiar.  Work your way through each problem.  If you find yourself stuck on a particular problem skip it and come back to it later.  You want to get the brain in a state of flow and you don’t want to waste too much time.

Once you have worked all the problems as far as you can it is time to muscle through and try for partial credit.  Write statements that explain why you did something.  Reference material that made it on to your one page of notes.  Often you can get full credit on a problem if you explain why you made a certain decision.

Some people would say that you should go back and check your work now…  I have never done that.  In my opinion if you made the mistake once you will probably make it again. Besides, I just want to go home and go to bed.

If you enjoyed this post you might also enjoy:
Spaced Repetition: How to Learn Anything and Never Forget It
Sensory Overload: How Your Brain Triages Information
Pushing Through a Learning Plateau
3 Lessons Skiing Taught Me About Learning

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