# How to Survive AP Calculus...

So you’ve decided to take AP Calculus. Or maybe you’re still deciding because you’re wondering “is AP Calculus AB hard?” Either way, if you’re reading this, you’re probably worried about how you’re going to survive—or even better, do well in—the class. Entering the class on day one, we asked ourselves those same questions. But now, as students who scored 5s on the exam and as AP Calculus tutors on Schoolhouse, we have a lot of useful tips and our experiences might help answer some of your questions.

## Why Take AP Calculus?

Maybe you’re wondering “why even bother,” especially considering how hard AP Calculus is. Well, here are some answers:

### College Credit

Let’s start off with the most obvious—college credit. Like any other AP exam, scoring a 3, 4, or 5 (depending on the college) on College Board’s AP exam could earn you credit for courses you would otherwise have to take in college. This could save you money—and time—while also getting you ahead of the typical student.

### Exposure to College-Level Math

A course as hard as AP Calculus will expose you to the rigor of college-level math. If you’re not sure whether or not you want to pursue college-level math, AP Calculus can serve as a guinea pig. While a lot of people wonder why Calculus is so hard, you can use this opportunity to see if advanced math is the right choice for you without having to pay the heavy prices you would have to pay in college. AP Calculus can serve as a deterrent to advanced mathematics or a gateway to it, completely up to you! It’ll also be a smaller classroom environment where you have the opportunity to have a relationship with your teacher rather than being a person in the crowd of a huge lecture hall in an introductory calculus course.

### Applications in STEM

If you plan on taking a physics-related course, or venturing into engineering, just know that Isaac Newton discovered calculus (concurrently and independently of Leibniz) to help him explain phenomena in physics for a reason. Algebra-based physics often assumes a lot of conditions, such as constant acceleration and uniform force or work, that are simply not applicable in “real-world” physics because “real-world” physics is essentially applied calculus. Calculus can help explain and account for real-life phenomena and applications. Additionally, all engineering pathways (and STEM pathways in general) in college require calculus courses and an earlier exposure might be the right decision for you to get ahead of the game or perhaps show that you don’t really want to pursue this career choice. The ability of being able to make these decisions in the safety of high school without the implications of college is one of the best benefits of AP Calculus and advanced-level classes in general.

### Boost College Applications

A college-level math course looks pretty nice on your transcript. As most high school students don’t take AP Calculus because they think it’s too hard, taking and doing well in such a rigorous course can set you apart from the crowd. Taking AP Calculus, if your school offers, it may even be recommended if you’re applying to highly selective schools in the STEM field.

### Prerequisites

Many students usually take precalculus before taking calculus. Some schools may even require it, and for good reason— Is precalculus hard? Well, it mainly lays the mathematical and analytical foundations that will make higher level math easier. However, from personal experience, I took calculus with barely any precalculus knowledge and did well. My entire calculus class, filled with students who only took half of precalculus due to COVID shutting down schools in March 2020, all passed the exam. So if you haven’t taken precalculus or are a bit rusty, don’t worry; while precalculus is generally advised as a prerequisite, it’s possible to do well without it because calculus is worlds beyond algebra and trigonometry. The reason you aren’t solving integrals properly isn’t because you don’t know pre-calculus but because you don’t understand the calculus concepts. That being said, math still tends to build on itself. You will still have to apply some aspects of precalculus or algebra because once you finish the calculus aspect of a problem, you must use algebra or precalculus to finish it. One of the most prevalent ways algebra or precalculus applies to calculus is understanding how to manipulate equations. Looking at how to approach problems from different angles and using clever manipulation techniques (such as the commonly used algebraic technique of rationalizing radicals in the denominator of a fraction) is key for solving calculus problems. The ingenuity and creativity required to excel in calculus is merely achieved through practice and understanding the beauty of the concepts not the tedious pre-calculus.

## General Tips

### Manage Your Time Wisely

This tip can go for any class, but is particularly important for an accelerated course like AP Calculus. It's difficult to gauge the time commitment of this course as it varies with individual effort, time management, and the teacher but calculus does tend to be a more time-consuming class (surprise?). You want to make sure to do your homework and take the time to practice if you really want to do well in the class and pass the exam.

### Understand, Don’t Memorize

Instead of mindless memorizing theorems, try to really understand them. We get it—sometimes reading a theorem with very big words and math terms can make your eyes glaze over or be intimidating, but we promise that if you try to break it down and take it part by part, the complex terms won’t seem so complex anymore. You’ll actually start to understand it, and you’ll remember the theorem much better than you would through rote memorization because you’ll be able to recall the logical flow of the theorem rather than trying to recall what you believe to be arbitrary and without wisdom. And what’s more, you’ll actually understand the concepts. Be sure to also diversify your conceptual understanding so instead of pouring over an old textbook expecting to be enlightened in vain, you could try visualizing the mathematical connections yourself using Desmos' free graphing calculator which is leagues beyond the standard TI-84 Calculator; Desmos can graph and help you visualize the easiest derivatives to the most complex infinite series. There is also a beautifully created Essence of Calculus Playlist by 3Blue1Brown which covers all the major topics in calculus and caters to every type of learner by visually, mathematically, and geometrically explains the concepts to ensure there is no way you’ll remain confused. The Ultimate AP Calculus Review concisely lists every formula, theorem, and identity you’ll need to know in ten pages and is free to use, save, and print! This tip of diversifying your studying methods can go for all subjects outside of just calculus.

### Always Seek Help

You always should seek help because calculus topics, especially, tend to build on each other. For example, limits are the foundation for derivatives which is the foundation of integrals etc, and knowing these topics backwards and forwards will be the key to your success (especially after differential calculus). If a topic seems difficult at first, try to get exposed to it in different ways as mentioned above. They always say there is only one right answer in math, but oftentimes, there are multiple valid ways to get there and the beauty of math is how people get the same answer through different approaches. Take the natural constant e (2.71828…) which can be derived in a multitude of methods from infinite series to interest rates. Some hunting online might help you find the method that works best with you. So of course, take advantage of free online resources such as the aforementioned schoolhouse.world, Desmos, 3Blue1Brown’s Essence of Calculus Playlist, and The Ultimate Key to AP®.

### Read the Questions

Please read the questions thoroughly. Please. This might seem like an obvious piece of advice, but hear us out. Aside from understanding the question and catching keywords like “not”, AP Calculus problems wording can be extremely tricky. Small differences in similar phrasings can make a big difference and make you think AP Calculus AB is hard. As you go through your course, you will learn more about these “key phrases” to look out for, such as “average rate of change” or “average value”, one which involves slope (a precalculus skill) and the other that involves integration (calculus skills needed). Additionally, reading the questions thoroughly, particularly on AP free-response questions, can even give you clues on what the question is looking for. For example, key notations, such as closed intervals of [x] as opposed to open intervals (x), can give you hints on what theorem the question wants you to apply—for example, the Intermediate Value Theorem versus the Mean Value Theorem. If these calculus terms sound alien, don’t worry—you’ll learn about them all. Just remember to always read the questions thoroughly, both for understanding the question itself and for getting clues on how to approach it.

## Conclusion

If we were to give one last tip, it would be - be confident. Seriously. I know I said “rigorous” and “accelerated” multiple times already, but as long as you’re willing to put the work in, and follow the tips above, you should be well on your way to doing well. Calculus seemed so scary for us when we first took it, too. But look, we made it through, and loved it enough to tutor in it! People often say ”why is Calculus so hard,” but that might be due to how “different” it is. When I sat in class on day one, and my teacher told me this course would teach me how to find the slope at a single point, the area under a curvy function, or the volume of a “solid of revolution” with non-straight edges, I looked at her like she was crazy. Calculus was just unlike any math I had taken before, but “different” didn’t necessarily mean “hard.” If anything, the “difficulty” of calculus mirrors the complex nature of our universe which can be discovered through calculus. It might take some adjusting, but once you understand the concepts, it’s a very rewarding subject, one that definitely blew our minds. And if you ever need some help, we and the rest of the Schoolhouse community will always be here to support you!

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