Calculus is a course that many of us will encounter at some point in our education. For some people, math is their strong suit, and calculus, while challenging, is interesting and even fun to work through. For the rest of us, calculus can seem really daunting and difficult to approach, especially if math is not your favorite or is particularly difficult. Taking AP Calculus in high school can be a beneficial step for not only earning credit in college but for having a solid foundation in the field of mathematics. To help you navigate taking an AP Calculus course in high school, here are some tips and tricks to make the process a bit smoother.
Choosing which AP Calculus course to take
If you are good at math, have some prior knowledge of calculus, and enjoy a rigorous course load, Calculus BC might be for you. The course is more fast paced than that of AB, but covers all the same topics. AB has a total of 8 units. In addition to these 8, BC will cover two more units and some extra topics within units 6-8. On the other hand, if you feel steady ground with math 3, Algebra ll, or precalculus and want to ease into Calculus a bit, AB might be a better option. AB does not go as in depth as BC, which results in it being a slower paced course. If you want to take BC at some point, taking AB beforehand can be helpful in building a solid foundation in calculus. Regardless of what you choose, it would be benifical to talk to teachers and other students who have taken the course before to see what will best fit your skill level.
Taking an AP Calculus course comes with a set of underlying expectations:
- Be willing to spend extra time making sure you understand concepts. As the year starts, its important to be careful and make sure you understand basic concepts first before trying to attempt a big scary math problem. Some terms you will become familiar with include limits, derivatives, and integrals. These are some of the most fundamental concepts of calculus, and making sure that you have a strong understanding with the basics will help you greatly.
- Go into the course with good base knowledge in topics like trigonometry, logarithms, and functions. These topics learned in previous classes tend to pop up randomly throughout the year, so better familiarize yourself with them now than later. For example, the Unit Circle will be your best friend. Even if you don’t have it memorized right now, you will be doing lots of trigonometry (at least at the basic level) that it will be naturally engraved in your brain.
- Practice, practice, practice. Make sure that you know how to solve different types of problems within the same concept. Have study sessions with your friends, do practice problems on Khan Academy, find past FRQs, do anything you can to keep up with the content and be confident in solving. Before going to class the next day, it might also be helpful to review the last concept learned to see the connection between them.
It is important to keep these expectations in mind throughout the course, as the concepts build on each other and get progressively difficult.
Tips and Tricks
Now that we’ve covered some of the basics to know, lets move on to some more specific tips and tricks.
- Know how to apply concepts and understand the differences between them. MVT, IVT, and EVT will all be necessary when you have to explain why you got an answer for a test, or for an FRQ.
- The first topic covered in the course is limits. By the time the end of the course rolls around, limits may get lost in the many other concepts floating in your head. Please try to remember them, they are the basic grounds of calculus and show up on the AP exam.
- I would not worry too much about the derivatives/integrals of sec, cosec, and cot. They do pop up every now and then so it is good to know them, but they aren’t the most important thing in comparison to everything else you will learn.
- Get a graphing calculator at the beginning of the year and learn how to use it alongside lessons. I recommend a Texas Instruments TI-84, though any other graphing calculator is fine (just make sure it’s permitted on the AP exam).
- All the things necessary for you to know how to do on the calculator are not too hard to learn. Your teachers will generally explain them to you, but there are great videos online that show you everything you need to know.
- In terms of online calculators, a great one is Desmos. It’s also also really fun/easy to use. Please use it if your graphing calculator is charging and you are practicing problems (only on Calculator permitted ones, of course).
- While calculators can be really helpful, make sure you are not relying on them (especially on problems which calculators will not be permitted for). Use them on a regular basis, but don’t forget how to solve problems without it!
Utilize your resources!
- If your teacher hasn’t already provided resources like helpful websites practice problems, or an exam prep book, seek those things out as soon as possible. Past AP exams, timed FRQs, and multiple choice exams online are super beneficial and can give you a feel for what you still need to work on to be successful. Even right now, they can be helpful when you want to see practice questions from just a specific unit.
- If I had the chance, I would probably add an AP Calculus prep book to my Amazon cart. I recommend that you do it right now! Getting one at the beginning of the year will probably be a good idea. While it is possible to rely solely on online resources, having a prep book helps practice be more accessible. Ask your teacher or former AP Calc students which brand they recommend; I think the Princeton Review is always a good one.
- Borrowing an old prep book can be helpful too! Depending on the year, the AP exam format could be different, but there are still practice problems and the same concepts are covered.
Good habits to fall into!
- Pace your studying! Do not try to overstudy the morning before, let alone even the night before. Review, but don’t try to cram any concepts (chances are they probably aren’t going to stick anyways). Instead, start reviewing for an exam in small bits (ex. one lesson a day) a week before.
- Generally, there is still a bit of content a little before the test, but you don’t really need to review it unless you are stuck (it's still fresh in your brain so leave it till the end!).
- Go back through your homework from the unit and see if there was a certain type of problem you struggled with. Go to your teacher’s office hours or ask your friends if they understood what you didn’t.
- Find patterns in problems! There are certain kinds of problems and different ways to solve them. Know how to recognize these different types, so that you aren’t solving them wrong. This will also help you solve problems more effiiently
- A great way to collaborate with your peers and friends is to work through problems by pretending to explain it to them. This will help solidify the concept in your own terms, and might help your peers understand it better too.
- Finish your work on time. You don’t want to be regretting not finishing an assignment at the end of the semester when you are at a borderline grade. That small homework assignment could potentially change your grade, so don’t put yourself in a position where you get the bad side of the situation.
Being completely transparent, AP Calculus is a difficult course. There will be some times where you feel mastery with the content, and other times where you won’t. Despite this, I believe with effort and an efficient work ethic, you can be successful in this course. Good luck taking this course, and have fun!