This page hosts automatically created pdf versions of the content on the Math Educational Resources. We hope that these pdf versions help you for your studies.

Should you need more help, check out the hints and video lecture on the Math Educational Resources .

If you’re not quite ready to simulate a full exam, we suggest you thoroughly and slowly work through each problem. To check if your answer is correct, without spoiling the full solution, check out the pdf with the final answers only.

When you feel reasonably confident, simulate a full exam and grade your solutions. A pdf with the full solutions is at the bottom of this page.

Resist the temptation to read any of the solutions before completing each question by yourself first! We recommend you follow the guide below.

Exam Simulation: When you’ve studied enough that you feel reasonably confident, print the raw exam (link below) without looking at any of the questions right away. Find a quiet space, such as the library, and set a timer for the real length of the exam (usually 2.5 hours). Write the exam as though it is the real deal.

Reflect on your writing: Generally, reflect on how you wrote the exam. For example, if you were to write it again, what would you do differently? What would you do the same? In what order did you write your solutions? What did you do when you got stuck?

Grade your exam: Use the full solutions pdf to grade your exam. Use the point values as shown in the original exam.

Reflect on your solutions: Now that you have graded the exam, reflect again on your solutions. How did your solutions compare with our solutions? What can you learn from your mistakes?