Here is a list of topics/ideas you need to be familiar with for tests. The list may be incomplete; refer to lecture notes for everything.

You can find example problems to work on in the textbook for this course. Highly recommended!

- Exponent laws
- How to add fractions (LCD)
- How to solve quadratics $ax^2 + bx + c = 0$
- When you are allowed to cancel common factors (all $+$ and $-$ encapsulated in parentheses)
- Coordinate plane
- Set and interval notation
- union, intersection, number line techinque to find these
- Polynomial/rational functions
- How to isolate a variable
- the list goes on...

- Definition of a function
- How to evaluate a function, i.e. $f(a + h)$
- How to find domain of a function (exclude two problems)
- Definition of the graph of a function
- How to graph functions by hand (make a table)
- $ax + b$ has shape of a line
- $ax^2 + bx + c$ has shape of a parabola
- Piecewise functions and their graphs
- Vertical line test
- Word problems of the above

- How to $+, -, \times, \div$ functions and their domains
- Physical meaning of adding two functions together
- fixed/variable/total cost, total profit and revenue
- Definition of composition of functions
- How to decompose a composition into two functions
- Word problems (including in a business context) of the above

- Definition of a limit
- When does a limit exist (cannot be not a number or left and right approach disagree)
- Table + graph method to find limit
- Find limit given a graph
- 10 limit laws and how to apply them correctly
- How to deal with indeterminate forms
- How to find limits at infinity for any function, such as rational function
- Word problems (including in a business context) of the above

- Left- and right-handed limits and the fact that limit laws can be used on them
- How to use them to prove a limit exists
- Intuitive definition of continuity
- Mathematical defintiion of continuity (three conditions)
- Properties of continuous functions
- Any polynomial and rational function are continuous on their domains
- Intermediate value theorem and how it can be used to prove a zero (x-intercept) exists
- Left- and right-handed limits

- Mathematical definition of a derivative
- Two meanings of the derivative
- Find derivative of a function with the definition of the derivative
- When a derivative fails to exist

- Derivative of a constant
- Power Rule
- Pulling constant out
- Derivative distributues across addition and subtraction

- When to use each one
- General Power Rule as a shortcut to the chain rule
- How to apply multiple rules in the same problems

- Actual cost vs. marginal cost
- Average cost functions
- Marginal cost and marginal average cost function
- Demand curve and demand equation $p = f(x)$
- Marginal revenue and profit function
- Finding the revenue function given a demand equation
- English interpretations of each marginal
- Elasticity of demand: calculating + interpretation
- Relationship between elasticity and revenue

- How to calculate higher-order derivatives
- position, velocity and acceleration
- Consumer Price Index: meaning of first and second derivative

- How to implicity differentiate
- When to use product, quotient, and chain rule in implicit differentiation
- Using variable relabeling to help you visualize your simplification roadmap
- Related rates problems

- What an increasing/decreasing function is
- Relationship between $f'(x)$ and whether $f(x)$ is increasing/decreasing
- Be able to find increasing/decreasing intervals
- Definition of relative extrema
- First Derivative Test for Relative Extrema

- What concavity means
- Determining intervals of concavity
- Second Derivative Test for Relative Extrema
- Weakness of Second Derivative Test vs. First (for example, at sharp corners second derivative does not exist)
- Signs of $f'(x)$ and $f''(x)$ force a certain graph shape

- What an absolute extrema is and how it is different than relative extrema
- Continuous function + closed interval forces absolute extrema to exist
- Closed interval test for finding absolute extrema
- Second derivative test + concavity for finding absolute extrema

- Be able to translate English into equations and diagrams
- Solve 4.4 type world problems except the equation to find absolute min/max needs to be parsed from the sentence