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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.

## 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:
$({x}^{2}+2x+3)+(3{x}^{2}-3x)=4{x}^{2}-x+3$ - Multiplying and Factoring:
$(x+2)(3x-5)\iff 3{x}^{2}+x-10$

- Multiplying and Factoring:

- Adding:
- Know how to solve simple linear equations.
- For example,
$2x+3=5x-7$

- For example,
- Know how to solve quadratic equations, such as
$2{x}^{2}+3x-5=0$ - Know the properties of exponents.
${x}^{2}{y}^{2}=(xy{)}^{2}$ $({2}^{x})({2}^{y})={2}^{x+y}$

- Know how certain expressions are secretly exponentials in disguise
- Reciprocals: For example,
$\frac{1}{x}}={x}^{-1$ - Roots: For example,
$\sqrt{x}={x}^{1/2}$

- Roots: For example,

- Reciprocals: For example,
- Know what logarithms are, as well as their properties.
says the same thing as$y={2}^{x}$ .${\mathrm{log}}_{2}(y)=x$ .$\mathrm{log}(x)+\mathrm{log}(y)=\mathrm{log}(xy)$ .$\mathrm{log}({a}^{x})=x\mathrm{log}(a)$

#### 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
degree polynomial might look like.${n}^{\text{th}}$ - 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:
,$\mathrm{sin}(x)$ and$\mathrm{cos}(x)$ $\mathrm{tan}(x)$ - Know what each one represents.
- Know the values of these functions when
takes on one of the following values:$x$ ,$0$ ,$\frac{\pi}{6}$ ,$\frac{\pi}{4}$ ,$\frac{\pi}{3}$ .$\frac{\pi}{2}$ - Know what the graph of each of these functions looks like.

- Know the values of these functions when

- 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?(30 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"(24 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.(10 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.(9 votes)

- Do we also need to learn logarithm before learning Calculus?(6 votes)
- Yes, the logarithm is very important in Calculus.(17 votes)

- What is the difference between Precalculus for BC and Precalculus for AB?(6 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(13 votes)

- 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?(6 votes)
- Algebra and trig are arguably the hardest parts of calculus. So, having a solid foundation in them is essential to do well in calc. If you're confident in the skills taught in pre-calc, you can go forward with calc. Otherwise, learning and mastering pre-calc would be a very good investment for calculus.(10 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!(6 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 :)(7 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(9 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?(6 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.(5 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(3 votes)
- 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)!(12 votes)

- Which calculator would be a good choice for AP Calculus BC?(3 votes)
- A TI-84 or a similar model graphing calculator should work.(9 votes)