As of October 2024, I’ve been a TA for five first-year calculus courses at UBC. Students often ask me, “How do I succeed in this class?” or more frequently, “How do I pass this class?” Here’s my advice.
1: Make a Spreadsheet
Keep a list of questions you struggled with and write down what you learned from them. I use a spreadsheet that looks like this:
| Question | Concept | Notes |
|---|---|---|
| WW00, Q1 | FTC | Use the chain rule to differentiate. |
| … | … | … |
Color-code the questions: green if you understand everything, yellow if you’re a little confused, or red if you’re completely lost. Include only the questions you get wrong. This technique is a lifesaver during exam season, providing a personalized list of challenging questions for you to study from. Additionally, reading through the “Notes” column before an exam helps recall the techniques you’ve learned throughout the course.
2: Don’t Forget the Basics
With the fast pace of math courses, its easy to assume that you don’t have time to review previous material. But I think this is a terrible mindset. Calculus exams are unforgiving, and you will do poorly if you don’t have a solid understanding of precalculus. I highly encourage everyone who thinks they have gaps in their foundational knowledge to review the following topics:
- Exponent laws
- Logarithm rules
- Finding intercepts and asymptotes
- Function composition and inverse functions
- Trigonometric functions and the unit circle
It shouldn’t take you more than a couple hours to go over these concepts, and doing so and it will make the rest of your semester so much easier.
3: Put the Calculator Away
If you came from the Canadian high school system, you were probably allowed a calculator for your precalculus classes. However, calculators are not allowed in the first-year calculus courses at UBC (and most upper-year math courses). Some students live in denial of this policy and continue using a calculator whenever possible throughout the semester. Unsurprisingly, these people later lose marks on exams due to computation errors. To minimize the chances of these silly mistakes, I think its best to avoid using a calculator while doing practice problems. Mental math isn’t fun, but it is necessary for success in calculus. One exception to this rule is the written assignments in MATH 100/101, which often require laborious calculations. You should still try to solve these problems with pencil and paper, but definitely check your answers with a calculator.
4: Embrace the Struggle
If you don’t have an exam soon, it’s okay to struggle with practice questions. You often learn more this way than by asking a friend or going to office hours. Trying new ideas and getting things wrong deepens your understanding of the material. When you finally get the right answer, you’ll understand not just how to solve the problem, but why the solution works. Spending an hour on a difficult problem can be more productive than doing ten easier problems in the same period. Of course, if you’ve exhausted every idea you have, it’s time to get help.
5: Practice Being Fast
If you have an exam soon, you should practice doing problems quickly. I’ve found that math exams have more restrictive time limits than exams in other departments, especially on midterms. The all-too-common experience of “I remembered how to solve the problem after the test!” is ultimately a problem of being too slow. Find out how long the test is, find out how many questions there are, and ensure you can work fast enough.
When taking the test, tackle the easiest problems first. If you’re well-prepared, you’ll get through these quickly, leaving you with more time for the harder problems. On final exams, I like to take a bathroom break at the halfway point—it helps me refocus. When checking your work, try doing the problems in reverse. For example, if a question asks you to evaluate an integral, check that the derivative of your answer is the original function. It isn’t always straightforward, but try to have a mindset of verifying rather than redoing.
Conclusion
First-year calculus courses at UBC are challenging for everyone, even math majors. I know someone who has taken over fifteen math courses at UBC and still says the MATH 101 final was the hardest exam they’ve ever written. Luckily, there are many resources available for students. Sign up for Piazza, go to office hours, and discuss the material with your friends. Success in these classes is not impossible—thousands of students score above 80% in MATH 1XX every year. I believe that you can be one of them. Good luck!