Math 20A: Calculus 1 Handouts

Review Handouts

Graphs of Basic Functions You Should Know Download Graphs of Basic Functions You Should Know

Graphing is pretty important in the calculus sequence and only gets more important after Calculus 1. Here are at least some graphs of basic functions you should be able to draw without much work. 

Trigonometry Summary Sheet Download Trigonometry Summary Sheet

Here's a trigonometry reference sheet. The most important on these is the first quadrant of the unit circle (once you know those, you get the rest for free, so just memorize the first quadrant), the right angle trigonometry for sine, cosine, and tangent, and the Fundamental Identities. For those Fundamental Identities, know $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$, $\sec(\theta)=\frac{1}{\cos(\theta)}$, $\csc(\theta)=\frac{1}{\sin(\theta)}$, and $\cot(\theta) = \frac{1}{\tan(\theta)}$, as well as the Pythagorean Identity, $\sin^2 \theta + \cos^2 \theta = 1$. I would not memorize the last two Pythagorean identities, as you can derive them from the sine and cosine one. All you need to do is either divide by $\cos^2 \theta$ or $\sin^2 \theta$ to get the other two.

The Addition and Subtraction formulas are definitely useful on occasion. I would advise you to not memorize them, but do remember they exist. The $\sin(2x)$ double angle identity comes up a lot, as do the half angle identities, so those may be worth permanently remembering. You'll see those half angle identities in Calculus 2 a lot.

Calculus Handouts

Limit Summary Sheet Download Limit Summary Sheet

This sheet talks about the definition of limits, limit laws, a brief look into solving limits, continuity and an example, and the Squeeze Theorem and Intermediate Value Theorem.

Solving Limits Algebraically (2.3) Download Solving Limits Algebraically (2.3)

This sheet shows examples of the four techniques you use in 2.3 to solve limits algebraically, along with how to deal with c/0 forms.

Derivative Summary Sheet Download Derivative Summary Sheet 

This summary sheet for derivatives talks about the definition of the derivative, notation, what the derivative means, the derivative rules you will need, as well as examples for implicit and logarithmic differentiation.

Chapter 4 Summary Sheet: Mins and Maxes & Graphing Download Chapter 4 Summary Sheet: Mins and Maxes & Graphing

This summary sheet covers a variety of content in chapter 4, such as the definitions of local and absolute minima and maxima, how to find those, the shapes of graphs, the steps to graph a curve, and when to use f, f', and f''.

L'Hospital's Rule Guide (4.4) Download L'Hospital's Rule Guide (4.4)

This sheet guides you through the main types of L'Hospital's Rule problems, as well as when you cannot use L'Hospital's Rule.

Integration Summary Sheet Download Integration Summary Sheet

This sheet has properties of integrals, the table of indefinite integrals, and the Fundamental Theorem of Calculus, and a quick u-sub example. 

This sheet is one you will use in Chapter 7 in Calculus 2 (which covers integration much moreso than this class), so don't mind integration by parts and the back side for now! 

U-Substitution Guide (5.5) Download U-Substitution Guide (5.5)

This sheet is a more in-depth guide to u-subs, with a variety of examples.