Struggling to study for a math exam? Don’t sweat it! The key to math exams is understanding that professors write them. And the key to professors is understanding that they are not some sort of objective, divinely-inspired beings that can perfectly assess how well you learned the course material. They are smart people that need to write exams to make sure you study and get a grade. By seeing exam-taking from the perspective of a professor, you can improve your score.
The tough part about writing math exams
Writing questions to test people’s knowledge of a subject is harder than it seems. My brother and I once held a trivia night for and it took us four hours to write twenty questions. Don’t believe me? Pick a topic and see how long it takes to write five questions of varying difficulty. The task is significantly harder for professors. They must assign As, Bs, and Cs to smart college students who all received the same information throughout the semester. For more qualitative courses, like English and History, it is much easier to distribute grades. Essays have so many nuances that it is easy to assign grades on a spectrum. This is not the case for math classes in which answers are either right or wrong.
How questions are written for math exams
To overcome this, professors write certain problems that are nearly impossible to solve based solely on information from the class. This is why you often hear that the average grade on a physics test was 40%, but you never hear that the average grade for an essay was 40%. It is also why you never hear a Physics professor apologize that his class wasn’t able to perform well on 60% of the material tested. The exam was designed to be that way. Encountering these exams is extremely frustrating as a student. I suspect they are also a major reason why students drop out of STEM courses in their freshman year. For those willing to put in a little extra studying time, however, math exams are usually the easiest to perform well on.
“…you often hear that the average grade on a physics test was 40%, but you never hear that the average grade for an essay was 40%.“
As discussed above, the objective of the ‘impossible’ math question is to manage the grade distribution. Since almost no student can get the question right, the professor is able to give credit based on how well a student set up the approach to the problem. (In my experience, it is typically the professors that preface an exam with “I don’t care about the answer, I care about the path you took to get there” that ask questions the furthest from the course material). In taking this approach, grading a difficult math question is much like grading an English essay. The professor has wiggle room to assign different scores to different students.
How to study for math exam questions
Luckily for students, professors cannot include questions that are so far removed from the course material that they are unfair. Doing so would lead to too many complaints and possibly scrutiny from members of an academic committee. So professors must write questions that are 1) tied closely enough to the course material to be legitimate and 2) difficult enough that few students can get it right. To meet these criteria, most professors opt to make available to students previous versions of exams, which contain the difficult question types. Practice exams serve as a perfect out for professors when someone challenges the relevance of a question. More importantly, they are a perfect way for enterprising students to identify and master the most difficult questions. Want to know the best way to study for a math exam? Take the practice exam!
The recommended approach to study for math exams
For whatever reason, I’ve found that very few students go through these previous exams thoroughly when preparing for a test. Here’s the recommended approach. When reviewing past exams, perform the problems yourself as if it were the actual test instead of just skimming the questions. No matter how comfortable you feel with the material, taking an exam is stressful. If you don’t know exactly what you are doing, odds are you won’t figure it out during the exam. It will be easy to identify on the previous exams which problems are the difficult ones. They are the ones you read and think “Hmm, I suppose they covered some other topics on the syllabus last year.” Trust me, nine out of ten times that problem will show up on your test.
But don’t despair. Due to the difficulty in writing questions and the unique characteristics tough problems need to have, there are usually no more than 4-5 problem types you need to learn from these previous tests. In fact, if the past exam history is long enough, you’ll see the professor will cycle through them every few years. Master these four or five and you’ve mastered the exam. Don’t be afraid to spend hours on a single hard problem until you can produce the solution easily. If the solution key does not provide an answer, go to a TA or scour the internet until you find one.
“No matter how comfortable you feel with the material, taking an exam is stressful. If you don’t know exactly what you are doing, odds are you won’t figure it out during the exam.”
Conclusion
Being able to perform difficult problems correctly is almost always the difference between a top mark and an average one. Difficult problems often account for 20-30% of the exam and very few students will attempt them, not to mention get them correct. If you can answer them well, it’s like getting 20 to 30 points of extra credit, which matters a lot when the average grade is 40%.
Have a tip to study for a math exam? Feel free to email us at [email protected].
Feel like your already a math master? Take a look at our article on writing essays.
