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## AP®︎/College Calculus AB

# 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.

## Welcome to the journey of calculus!

## 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 parenthesis, x, squared, plus, 2, x, plus, 3, right parenthesis, plus, left parenthesis, 3, x, squared, minus, 3, x, right parenthesis, equals, 4, x, squared, minus, x, plus, 3
- Multiplying and Factoring: left parenthesis, x, plus, 2, right parenthesis, left parenthesis, 3, x, minus, 5, right parenthesis, \Leftrightarrow, 3, x, squared, plus, x, minus, 10

- Adding: left parenthesis, x, squared, plus, 2, x, plus, 3, right parenthesis, plus, left parenthesis, 3, x, squared, minus, 3, x, right parenthesis, equals, 4, x, squared, minus, x, plus, 3
- Know how to solve simple linear equations.
- For example, 2, x, plus, 3, equals, 5, x, minus, 7

- Know how to solve quadratic equations, such as 2, x, squared, plus, 3, x, minus, 5, equals, 0
- Know the properties of exponents.
- x, squared, y, squared, equals, left parenthesis, x, y, right parenthesis, squared
- left parenthesis, 2, start superscript, x, end superscript, right parenthesis, left parenthesis, 2, start superscript, y, end superscript, right parenthesis, equals, 2, start superscript, x, plus, y, end superscript

- x, squared, y, squared, equals, left parenthesis, x, y, right parenthesis, squared
- Know how certain expressions are secretly exponentials in disguise
- Reciprocals: For example, start fraction, 1, divided by, x, end fraction, equals, x, start superscript, minus, 1, end superscript
- Roots: For example, square root of, x, end square root, equals, x, start superscript, 1, slash, 2, end superscript

- Reciprocals: For example, start fraction, 1, divided by, x, end fraction, equals, x, start superscript, minus, 1, end superscript
- Know what logarithms are, as well as their properties.
- y, equals, 2, start superscript, x, end superscript says the same thing as log, start base, 2, end base, left parenthesis, y, right parenthesis, equals, x.
- log, left parenthesis, x, right parenthesis, plus, log, left parenthesis, y, right parenthesis, equals, log, left parenthesis, x, y, right parenthesis.
- log, left parenthesis, a, start superscript, x, end superscript, right parenthesis, equals, x, log, left parenthesis, a, right parenthesis.

- y, equals, 2, start superscript, x, end superscript says the same thing as log, start base, 2, end base, left parenthesis, y, right parenthesis, equals, x.

#### 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 how to represent a function with a graph.
- Know the graphs of various elementary functions.
- Linear functions
- Quadratic functions
- Have at least a loose idea for what the graph of an n, start superscript, start text, t, h, end text, end superscript degree polynomial might look like.
- Exponentials
- Logarithms

- Linear functions
- Know how to manipulate functions.
- It's also helpful to be familiar with function terminology

## Geometry

- Know how to compute the area of simple shapes.

## Trigonometry

- Be comfortable with each of the basic trigonometry functions: sine, left parenthesis, x, right parenthesis, cosine, left parenthesis, x, right parenthesis and tangent, left parenthesis, x, right parenthesis
- Know what each one represents.
- Know the values of these functions when x takes on one of the following values: 0, start fraction, pi, divided by, 6, end fraction, start fraction, pi, divided by, 4, end fraction, start fraction, pi, divided by, 3, end fraction, start fraction, pi, divided by, 2, end fraction.
- Know what the graph of each of these functions looks like.

- Know what each one represents.

## 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?(29 votes)
- 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"(21 votes)

- 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.(5 votes)
- Hey, it is very possible to do that, and if you have an interest in math, you should definitely do it! Just make sure you have a strong precalc foundation before you start ap calc.(8 votes)

- Do we also need to learn logarithm before learning Calculus?(3 votes)
- Yes, the logarithm is very important in Calculus.(13 votes)

- 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(8 votes) - What is the difference between Precalculus for BC and Precalculus for AB?(4 votes)
- 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(8 votes)

- 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?(5 votes)
- You can purchase textbooks online, or borrow one from a library. I would suggest purchasing a book in which you could practice problems, besides just reading about.(3 votes)

- Which calculator would be a good choice for AP Calculus BC?(2 votes)
- A TI-84 or a similar model graphing calculator should work.(9 votes)

- 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!(4 votes)
- I would recommend only taking Brief Calculus. You will have more time to focus on the math and learn it really well.

Sometimes difficult things in math just take extra time to work out and understand, so often having adequate time is what makes math manageable/fun instead of stressful.

Hope this helps! Good luck with your classes :)(4 votes)

- 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(1 vote)
- The most important topics are algebra topics, such as factoring polynomials, simplifying expressions, solving equations & inequalities, polynomial functions, rational functions, exponential functions, logarithmic functions, trigonometric functions, and inverse trigonometric functions.

The next most important topics are geometry & measurement topics, such as Pythagorean theorem, perimeter, area, surface area, volume, similar triangles, and right triangle trigonometry.

When you join calculus, you will learn the concept of a limit. The concept of a limit will lead to the concepts of the derivative (think of the slope of a curve at a point on the curve) and the integral (think of the area under a curve but above the x-axis). Furthermore, you will learn that the processes of taking the derivative and taking the integral are essentially inverses of each other (Fundamental Theorem of Calculus)!(8 votes)

- What's the difference between pre-calculus and get ready to calculus?(3 votes)
- Pre-calculus is the collection of topics you study before learning calculus. In high school, you might spend a year studying pre-calculus. In college, it can be one semester or two quarters.

Get Ready for AP Calculus is a resource you can use to review topics that will help you do well in calculus. For instance, before you start learning about limits, you can go over the get ready section on limits to review.

Alot of the videos and exercises are the same as in the pre-calculus section - what makes the get ready section different is that everything is organized around what you will be learning in calculus.(2 votes)