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Content Topics and Essential Learnings
Set Theory
o Apply basic properties of algebra
o Apply basic information regarding the coordinate plane
o Solve linear equations and inequalities
o Write equations of lines
o Solve equations algebraically, graphically, and numerically
Function Composition
o Model and solve equations
o Understand the limitations of the graphics calculator
o Analyze functions graphically
o Find the composition of a function
o Find the inverse of a function
o Use graphical transformations to graph a function
Polynomial
o Write equations of parabolas in vertex form
o Identify power functions and their properties
o Graph transformations of monomial functions
o Divide polynomials
o Use the rational zeros, remainder, and factor theorems
o Do arithmetic with complex numbers
o Use zeros of polynomial functions to write equations and vise versa
o Solve equations with polynomial fractions
Unit Circle
o Convert from degrees to radians and vise versa
o Review basic trigonometric functions and special right triangles
o Use reference triangles to solve problems
o Create and use a unit circle
o Evaluate periodic functions
o Analyzing graphs of sinusoids
o Evaluate inverse trigonometric functions by hand
Logs/Exponentials
o Know the properties of a exponential function
o Apply exponential and logistic functions to real life problems
o Know the properties of a logistic function
o Evaluate log and natural log expressions
o Use arithmetic on logarithms
Conics and Polar Coordinates
o Write equations in standard form for a parabola
o Identify the parts of a parabola
o Write equations in standard form for an ellipse
o Identify the parts of an ellipse
o Write equations in standard form for a hyperbola
o Identify the parts of a hyperbola
o Graph polar coordinates
o Convert from rectangular to polar and vise versa
o Graph polar coordinates
o Analyze polar graphs
Introduction to Limits
o Find limits of equations graphically and algebraically
o Understand how to apply the properties of limits
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