Welcome to the Princeton Mathematics Exam Archive

This is an ongoing project to make the archive of quiz and exam questions from past semesters available to students in a useful way. Working through old exam problems is the best way to prepare for your exams this semester, and a good way to review ideas from prerequisite courses. Most students learn best from examples, and we hope that these examples will be useful in helping you succeed in your math class this semester.

As you work through the old exam problems you will notice that the same ideas appear over and over in slightly different form, and you will gradually acquire a good feeling for the main concepts as well as the technical complications that might arise. As you practice solving problems on your own, you will strengthen your problem solving abilities and gain confidence that you can handle any surprises or twists you might encounter in the actual exams, or in later courses where you need to apply these mathematical skills to solve problems in other disciplines. Even if you do not immediately know how to solve an exam problem, usually you will have an idea of what the first step should be. Don't be afraid to try things that don't immediately work out—these attempts will give you more insight and suggest alternate approaches, or perhaps help you come up with questions to discuss with your instructor in class or in office hours or answer on your own by consulting your class notes or the textbook or your study group. Collaboration and independent study are both important parts of the learning process in university courses, and this archive should give you a context to practice both!

The problems here are sorted by topics and methods, with filters provided to help you search for practice problems suitable for your upcoming exam or quiz. Answers, hints and full solutions, sometimes using several different methods, are provided. Working through the problems under exam conditions should be your goal. Use the provided solutions sparingly and be sure to follow up with your instructor or your friends in the class if the solutions do not make sense to you. We welcome any feedback from you about errors, large or small!