Algebra
Manipulating expressions
- Know how to manipulate
- Adding: $(x^2 + 2x + 3) + (3x^2 - 3x) = 4x^2 - x + 3$
- Multiplying and Factoring: $(x + 2)(3x - 5) \Leftrightarrow 3x^2 + x - 10$
- Know how to solve simple linear equations
- For example, $2x + 3 = 5x - 72$
- Know how to solve quadratic equations, such as $2x^2 + 3x - 5 = 0$
- 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, $\dfrac{1}{x} = x^{-1}$
- 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 $\log_{2}(y)=x$
- $\log(x) + \log(y) = \log(xy)$
- $\log(a^x) = x\log(a).$
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 what a function is
- Know how to represent a function with a graph.
- Linear functions
- Quadratic functions
- Have at least a loose idea for what the graph of an $n^{\text{th}}$ degree polynomial might look like.
- Exponentials
- Logarithms
- 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.
Know how to compute the volume of simple 3d shapes.
Analytic geometry
Trigonometry
- Be comfortable with each of the basic trigonometry functions: $\sin(x), \cos(x)$ and $\tan(x)$
- Know what each one represents.
- Know the values of these functions when xxx takes on one of the following values: 000, \dfrac{\pi}{6}6πstart fraction, pi, divided by, 6, end fraction, \dfrac{\pi}{4}4πstart fraction, pi, divided by, 4, end fraction, \dfrac{\pi}{3}3πstart fraction, pi, divided by, 3, end fraction, \dfrac{\pi}{2}2πstart fraction, pi, divided by, 2, end fraction.
- Know what the graph of each of these functions looks like.
