Topics and Objectives
1. Factoring Polynomials/Rational Expression Operations
— - Factor second-degree polynomials
— - Factor by grouping
— - Reduce rational expressions to lowest terms
— - Add/subtract/multiply /divide rational expressions
— - Simplify compound fractions
2. Using Graphing Calculators
— - understand screen coordinates
— - use the Trace, Zoom, and Intersect commands
3. Functions
— - Identify functions vs relations in tables, graphs, and equations
— - Use function notations interchangeably and identify the domains and ranges
— - Solve equations and formulas for a variable
— - Identify increasing and decreasing functions
— - find local maxima and minima
— - Define functions piecewise
— - Shift graphs horizontally and vertically
— - Stretch and shrink graphs
— - Reflect graphs in the x and y axis
— - Perform operations on functions
— - Find the composition of two functions
— - Find the inverse of a function
— - Graph the inverse of a function
4. Linear Functions
— - Use slope-intercept and linear combination forms in problem solving
— - Fit a linear model to to a situation or data
— - Explore the graph Ax + By = C
— - Define the slope of a line
5. Quadratic Functions
— - Solve quadratic equations for real and complex solutions using the square root method, factoring and the Quadratic Formula.
— - Fit a quadratic model to data using the graphing calculator.
— - Perform operations with complex numbers and analyze the solutions and x-intercepts of quadratics using the discriminant
— - Use the vertex form of a quadratic function
— - Solve equations involving radicals
— - Solve equations of quadratic type
— - Solve linear and quadratic inequalities
6. Polynomial and Rational Functions
— - Analyze graphs of polynomials
— - Divide polynomials using long and synthetic division
— - Apply the Remainder and Factor theorems
— - Approximate real zeros at turning points
— - Solve polynomial inequalities
— - Find vertical and horizontal asymptotes of Rational functions
— - Draw the graph of a Rational function
— - Solve Rational inequalities
— - Find factors of polynomials with real coefficients
— - Find rational zeros
— - Model using Direct variation
— - Model using Inverse variation
7. Exponential and Logarithmic Functions
— - Evaluate logarithmic expressions and solve logarithmic equations.
— - Apply properties of logarithms to solving exponential and logarithmic equations and applications.
— - Apply exponential growth and decay models (including continuous growth) to problem solving.
— - Define exponential functions
— - Analyze graphs of exponential functions including Base e
— - Calculate compound interest (including continuous interest)
— - Write an equation that models exponential growth or negative exponential growth
— - Apply the change-of-base formula
— - Solve problems using a logarithmic scale
8. Systems of Equations
— - Solve systems of equations in two variables using graphing, substitution, linear combination.
— - Solve systems of equations in three variables using elimination by addition
9. Basic Formulas of Analytic Geometry
— - Apply basic formulas of Analytic Geometry