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# What to know before taking calculus

So you're about to take AP Calculus, eh?  Here's a summary of what you should know going into it.

## What to know before taking Calculus

In some sense, the prerequisite for Calculus is to have an overall comfort with algebra, geometry, and trigonometry. After all, each new topic in math builds on previous topics, which is why mastery at each stage is so important.
However, for those of you who have taken courses in these subjects, but are looking to quickly brush up on the essentials before beginning calculus, this sheet is here to highlight a few of the more crucial skills that you should have going into the course.

## Algebra

#### Manipulating expressions

• Know how to manipulate polynomial expressions.
• Adding: $\left({x}^{2}+2x+3\right)+\left(3{x}^{2}-3x\right)=4{x}^{2}-x+3$
• Multiplying and Factoring: $\left(x+2\right)\left(3x-5\right)⇔3{x}^{2}+x-10$
• Know how to solve simple linear equations.
• For example, $2x+3=5x-7$
• Know how to solve quadratic equations, such as $2{x}^{2}+3x-5=0$
• Know the properties of exponents.
• ${x}^{2}{y}^{2}=\left(xy{\right)}^{2}$
• $\left({2}^{x}\right)\left({2}^{y}\right)={2}^{x+y}$
• Know how certain expressions are secretly exponentials in disguise
• Reciprocals: For example, $\frac{1}{x}={x}^{-1}$
• Roots: For example, $\sqrt{x}={x}^{1/2}$
• Know what logarithms are, as well as their properties.
• $y={2}^{x}$ says the same thing as ${\mathrm{log}}_{2}\left(y\right)=x$.
• $\mathrm{log}\left(x\right)+\mathrm{log}\left(y\right)=\mathrm{log}\left(xy\right)$.
• $\mathrm{log}\left({a}^{x}\right)=x\mathrm{log}\left(a\right)$.

#### Functions

Calculus is all about functions, so it is helpful to be pretty fluent when it comes to thinking about functions, graphing functions, and using the appropriate terminology when talking about functions.

## Know when you need to review

The thing about calculus is that it tends to pull examples from all sorts of areas in math. While the list above does cover the main things you should be comfortable with before starting a calculus class, you will inevitably come across some example or topic which references another bit of prerequisite knowledge.
In an ideal world, you would know everything about algebra, geometry and trigonometry 100% perfectly. But more realistically, there are a few things you did not learn perfectly the first time. It's totally fine if that happens, but it can sometimes be tricky to recognize when a calculus problem is hard because you don't know the fundamentals (e.g. algebra) or if it's hard because of the new material (i.e. the calculus itself).
Just make sure you are always willing to ask yourself "Do I have a strong feel for the concepts in this problem?" If the answer is no, don't be afraid to temporarily divert your attention away from the calculus material to review the necessary algebra, geometry or trigonometry. Trust me, in the long run, it is always worth taking a step back before moving forward.

## Interview with Ben Eater

Although this is not directly about calculus preparation, we think this interview Sal did with one of our engineers, Ben Eater, serves as a telling example of why prerequisite knowledge is so important in the context of Calculus.

## Want to join the conversation?

• Is it possible to take an advanced calculus class (e.g. AP Calculus AB) without taking pre-calculus? I've taken Algebra I, II, Geometry, Trigonometry, and Math Analysis. Or is math analysis essentially pre-calculus? • I just finished what my school would consider "pre-calculus" in Algebra II. In addition to algebra, in my class, we incorporated Trigonometry and Analysis concepts, and I have already began taking calculus without any actual "pre-calculus" class. I am not struggling, and I believe you will be fine, if you're okay with the rigor of an advanced class. Since the classes you have taken seem to cover all of the previous knowledge required for calculus, I would say that you are going to do fine if you decide to take an advanced calculus class. It is possible then, at least in my school and state, to take it without "pre-calculus"
• Is it possible to take AP Calculus AB as a 10th grader while still getting an A year round? I'm currently in ninth grade and taking Algebra 2, while also taking Geometry online. I'm not sure if I should take AP Calc because I play sports after school and I'm already going to be taking AP World and AP Physics next year for sure. I've just been debating it constantly because the due date to sign up for the Pre cal class is in less than 2 weeks. So if I did decide yes, then I'd take pre calc over the summer and ap calc during the 10th-grade year. For reference, I've gotten 95-100s on every math course I've taken. • Do we also need to learn logarithm before learning Calculus? • What is the difference between Precalculus for BC and Precalculus for AB? • Pre-calculus is a prerequisite for both types of calculus. Calculus AB covers the first semester of calculus only (Calculus I) Calculus BC covers the first two semesters or a whole year of calculus (Calculus I and II courses combined) All of the topics covered in Calculus AB are also found in BC
• would you recommend I take ap calc ab without taking pre-calc? I did some self studying over summer but im worried that it's not enough, obviously if I took pre-calc I would have a whole year more of experience and an actual teacher. But I heard pre-calc is mostly just reviews of algebra and trigs. would it be too hard if I take it without pre-calc? • I'm an adult working full time and have a family. I need to take Brief Calculus at my community college next semester. I'm doing College Algebra right now and it takes A LOT of effort for me to maintain a B average. Would taking a course in addition to Brief Calc be reasonable? I don't want to overwhelm myself. Thanks! • I have less than one month before school starts, i was wondering if i could fully practiced AP Calc by the time my school starts and i just want to complete this course and try get 5 on the exam. How much time should i spend everyday ?
P.S. i have a flexible time • Can I study the Calculus course on Khan Academy and take the AP Calculus AB test? If I need to learn more about Calculus AB and doesn't have an AP Calculus AB class at my school where should I find the materials to learn it? • i am in class 11 and i need to study calculus.what are the important topics i need to brush up before i join the calculus course.i study according to cbse pattern •  