Three Tips for Studying For Your Calculus Midterm

With midterm season fast approaching, many students taking first year calculus are still coming to grips with the volume of content that has already been presented in the course, and are wondering what portions they should focus on when preparing for their midterm. With this in mind, here are three tips to help guide your studying as you prepare for your upcoming exam:

The two main things that have likely been covered to date in the course are limits, and differentiation techniques. There is a fair bit of theory that has been presented, but at the end of the day, your midterm is likely to focus on solving questions, so make sure you get lots of practice solving limits and finding derivatives of different types of functions. In particular, ensure that you are comfortable with using the limit definition of the derivative to find derivatives of functions, as this is a key outcome of the first half of the course, and will likely be tested.

Beyond simply solving limits and derivatives, there are two problem types that often come up on first year calculus midterms. This first is to “find the equation of the tangent line of a function at a particular point”, and “using the intermediate value theorem, show that f(x) = 0 has at least 1 solution on the interval (a,b).” The second half of the course offers more interesting application questions as students get into optimization and related rates questions, but at this stage, these are two classic application problems that students will want to be comfortable with, as one or both is likely to be included on your midterm.

Often times, similar questions from those asked in assignments are asked again on midterm exams. Assignments are also a great indication of what your professor wants to focus on in the course, so take the time to go through the assignments that you have completed so far, as they should be a good indication of what will be asked on the midterm. If time permits, I would even re-solve as many assignment questions as you can, as this will likely be good practice in preparation for the exam.