Mathematics III

Model and solve with expressions, equations, inequalities, and functions.  

Rewrite polynomial expressions to prove identities and theorems.  

Apply properties of complex numbers to quadratic solutions and polynomial identities.

Analyze polynomial functions, apply the remainder theorem, and identify zeros and factorizations in real and complex forms.  

Apply geometric concepts to solve real-world and mathematical problems.  

Solve polynomial, radical, and rational equations by using graphs, tables, and algebraic techniques.  

Find and verify inverse functions.  

Model relationships and data with functions, and use the models to make predictions and interpret results.  

Interpret the key features of polynomial, radical, and rational functions using multiple representations.

Understand the inverse relationship between exponential and logarithmic functions, and apply this relationship to rewrite and interpret expressions and equations.  

Solve exponential and logarithmic equations by using graphs, tables, and algebraic techniques.  

Interpret the key features of exponential and logarithmic functions using multiple representations.  

Create and transform graphs of exponential and logarithmic functions.  Analyze and model with piecewise functions.  

Combine and compare functions in multiple representations.  

Create and solve systems of equations and inequalities using graphic and algebraic techniques.  

Prove the laws of sines and cosines.  Connect the ideas of radian measure and arc length to the trigonometric origins of the unit circle while proving and applying the Pythagorean identity.  

Create and transform graphs of trigonometric functions. 

Interpret the key features of trigonometric functions, and apply those features to model real-world periodic phenomena.  

Compare statistical models with experimental and observational data.