Welcome to the Math Education Resources.
Math Education Resources (MER) provides free hints and peer-reviewed solutions to previous math exams administered at the University of British Columbia - grouped by topic and rated by difficulty. Additional learning content is also provided on our topics pages.
You can find us
How to use this resource
When you feel reasonably confident, simulate a full exam and grade your solutions. A link to the full solutions is above .
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.
Should you need more help, check out the hints and video lecture on the Math Educational Resources.
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?
Plan further studying: Use your mock exam grades to help determine which content areas to focus on and plan your study time accordingly. Brush up on the topics that need work:
Re-do related homework and webwork questions.
The Math Exam Resources offers mini video lectures on each topic.
Work through more previous exam questions thoroughly without using anything that you couldn’t use in the real exam. Try to work on each problem until your answer agrees with our final result.
Do as many exam simulations as possible.
Whenever you feel confident enough with a particular topic, move on to topics that need more work. Focus on questions that you find challenging, not on those that are easy for you. Always try to complete each question by yourself first.
Work through problems
How to use the final answer: The final answer is not a substitution for the full solution! The final answer alone will not give you full marks. The final answer is provided so that you can check the correctness of your work without spoiling the full solution.
To answer each question, only use what you could also use in the exam.
If you found an answer, how could you verify that it is correct from your work only? E.g. check if the units make sense, etc. Only then compare with our result.
If your answer is correct: good job! Move on to the next question.
Otherwise, go back to your work and check it for improvements. Is there another approach you could try? If you still can’t get to the right answer, you can check the full solution on the Math Educational Resources.
Reflect on your work: Generally, reflect on how you solved the problem. Don’t just focus on the final answer, but whether your mental process was correct. If you were stuck at any point, what helped you to go forward? What made you confident that your answer was correct? What can you take away from this so that, next time, you can complete a similar question without any help?
Please note that all final answers were extracted automatically from the full solution. It is possible that the final answer shown here is not complete, or it may be missing entirely. In such a case, please notify the MER team. Your feedback helps us improve.