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Known Functions (Review)

- Linear
- Quadratic
- Polynomial
- Rational
- Radical
- Absolute Value
- Step Functions (floor, ceiling, round)
- Exponential
- Logarithmic

Functions (as a concept)

- Domain/Range
- Inverse
- Even/Odd
- Transformations (easy)
- horizontal shift/stretch/reflect
- vertical shift/stretch/reflect

- horizontal shift/stretch/reflect
- Transformations (hard)
- composition, as in y = f(|x|) or y = (f(x))^2, y = f(int(x)) or y = int(f(x)), etc

- composition, as in y = f(|x|) or y = (f(x))^2, y = f(int(x)) or y = int(f(x)), etc
- Idea of multivariable functions - z = f(x, y) or f(t) = (x(t), y(t))

Trigonometry

- Right triangle definitions (for all 6 functions)
- Unit circle definitions (for all 6 functions - degrees and radians)
- Graphing trig functions (focus on sin x, cos x)
- Inverse trig functions
- Solving trig equations
- Pythagorean Identities
- Sum/Difference Identities
- Double Angle Identities
- Law of Sines/Law of Cosines

Vectors/Vector Functions

- Definitions
- Vector arithmetic (add, subtract, mult by scalar, dot product)
- Definition of magnitude, unit vectors
- Angle between vectors (Law of Cosines in vector form)
- Applications (groundspeed, forces)
- Projections (?)
- Vector Functions as parametric equations
- Motion in the plane with constant velocity
- Parametric equations for circles, ellipses, lines
- Finding/describing intersection between parametric graphs

Polar Functions

- Definition of polar coordinates (r, θ)
- Idea of multiple representations for a given polar point
- Converting points from polar to rectangular and rectangular to polar
- Converting (some) functions from polar to rectangular and rectangular to polar
- Polar equations and graphs of circles (centered at origin, or center along an axis)
- Polar equations and graphs of limaçons/cardioids, roses, lines

Complex Numbers

- Add/subtract/multiply/divide
- Represent in trig form x + iy = r(cos θ + i sin θ)
- Multiply/divide numbers in trig form
- Powers of complex numbers in trig form
- Roots of complex numbers in trig form

3D Space

- Drawing points in (x, y, z)
- Distance formula, midpoint formula
- Equation of sphere
- Equation of plane
- Equation of line
- Vectors in space, including cross product

Sequences/Sums review

- Arithmetic sequences and sums
- Geometric sequences and sums

Counting/Probability

- Use of factorial
- Use of permutations
- Distinguishable permutations (?)
- Use of combinations
- Definition of sample space
- Binomial distribution

Calculus Intro

- Informal definition of limit (including the idea that a limit might not exist)
- Evaluate limit by table
- Evaluate limit by graph
- Evaluate limit with algebra
- factor and cancel
- multiply by conjugate
- simplify complex fraction

- factor and cancel
- Formal definition of the derivative
- Evaluate derivatives using the definition
- Shortcut derivative rules
- constant
- constant multiple
- sum/difference
- power

- constant
- Basic applications
- equation of tangent line to graph
- ID horizontal tangents
- position/velocity

- equation of tangent line to graph
- Antiderivatives (using the same rules as derivatives)