Hello there! I’m Shelby, a math PhD student at University of Illinois – Chicago. For my first post, I’d like to share some tips I’ve gathered on acing preliminary exams and master’s exams.
Not every math PhD program has preliminary exams (aka written qualifiers) and/or master’s exams. But for the programs that do, these exams can seem daunting to first and second year students. Both prelims and master’s exams are long in duration (varies by program, but around 3 hours from my knowledge) and span the topics of multiple courses. They require endurance, mental agility, and a thorough understanding of the test topics.
Prior to grad school, I did not have experience with exams of this nature. Of course I had experience taking 3 hour final exams for a single course, but I had no experience with preparing for an equally long exam that tests my mastery in multiple graduate-level courses. I sought preparation advice from more experienced graduate students and professors and also learned through trial and error. Here are some tips that I’ve found effective in preparing for these types of exams.
1.) Make a study plan several weeks (if not more) prior to your exam date. Include topics you need to review on which days. Check off the days as you complete the study assignments as this will help to motivate you and build a sense of accomplishment. A long-term plan like this will guide you through a steady and thorough review of the material, ensuring that you do not resort to cramming at the last minute.
2.) Prioritize prelim/master’s exam courses as you take them. Don’t take shortcuts in these courses as your success on the prelims and master’s exams depend on a deep understanding of these topics. Stay organized in these courses and make an effort to take excellent notes so you can study from them when preparing for your exam.
3.) Schedule full-length, timed practice exams. This is a particularly useful tip for those who are not naturally great test takers. Schedule mock exams for yourself in the exam setting. For example, if your exam is 3 hours long in a quiet room, schedule a 3 hour block where you will go to a quiet room and do a full length practice exam (without your notes!). This will get you comfortable with the exam setting. The practice under timed pressure will also train you to think on your feet, which you’ll need on the exam.
4.) Find a study group to meet with regularly at least several weeks prior to the exam. Studying math with a group of classmates is always fun and it has many benefits for prelim/master’s exam preparation. Discussing concepts with a study group can help you to absorb concepts more deeply. Talking out loud about your understanding can also highlight weak areas in your understanding; it is better to determine your weak areas of knowledge sooner rather than later. You can also use this as an opportunity to learn from others – perhaps a classmate is strong where you are weak and vice versa. Solving new practice problems together also gives you practice with thinking on your feet but in a stress-free setting.
5.) Complete all learning of exam topics at least a couple of weeks before the exam. This means that, ideally, two weeks prior to the exam, you should not be learning a required concept or topic for the first time. The two weeks prior to the exam should be reserved for practice and review. This two week period of reinforcement and practice will help to solidify the concepts in your brain, releasing your potential for mental agility on test day.
I hope you find some of this tips helpful! Please feel free to add to these tips by commenting below. It would be interesting to see what approaches others have found effective in preparing for these types of exams.