PreCalculus Course Outline:
Sequences and Series
 Demonstrate an understanding of recursive formulas
 Represent sequences graphically
 Develop, analyze and apply procedures to describe sequences algebraically
 Develop, analyze and apply procedures to evaluate the sums of series
 Develop proofs of mathematical statements using mathematical induction
 Demonstrate an understanding of the concept of limit in the context of sequences and series
 Demonstrate an understanding of the concepts of convergence and divergence
 Apply convergence in a variety of contexts
 Demonstrate an understanding of how to find the area of a region under a curve
Functions - a new Perspective
 Combine functions using addition, subtraction, and/or multiplication. Interpret and analyze
these combined functions and use their graphs to solve problems.
 Apply transformations to functions
 Find the equations of combined functions from graphs
 Solve polynomial equations and inequalities
 Form, interpret, and analyze composite functions. Use graphs of composite functions to solve
 Interpret slope to find average and instantaneous rate of change
 Find the slope of the tangent to a graph at a point using a derivative
 Compare the graph of a function to the corresponding graph of the slope of the tangent
 Find the equation of a polynomial function from given points and/or intercepts
 Use the power rule to find the derivative of a polynomial function
 Sketch the graph of polynomial functions using intercepts and critical points
 Solve maximum/minimum problems using a derivative
Functions, Part II
 Plot the graphs of the functions in the transformational form and use these functions to model realworld phenomena.
 Identify the zeros, the vertical, horizontal, and oblique asymptotes, and the points of discontinuity of
rational functions, and sketch the graphs of these functions.
 Simplify rational expressions and complex fractions
 Solve problems that involve rational equations
 Analyze the effect of taking the square root of polynomial and rational functions, plot the graphs of
irrational functions, and use these functions to model real world phenomena.
 Analyze the effect of taking the absolute value of polynomial, rational, and irrational functions,
determine the domain and range of these absolute-value functions, and plot their graphs.
 Analyze and plot the graphs of piecewise functions.
 Review exponential and logarithmic functions and use these functions to model real-world
 Determine the value of e, plot the graph of ex, and use this natural exponential function to model
real-world phenomena.
 Analyze and plot the graph of y = ln x, and use this natural logarithmic function to model real-world
 Solve inequalities involving rational expressions and absolute values.
 Express angle measures in terms of arc length
 Model periodic behavior and solve problems using periodic functions
 Identify equivalent trigonometric relations
 Describe transformations of periodic functions to model situations
 Combine trigonometric functions to create models
 Use matrix multiplication to rotate images
 Prove trigonometric identities
 Solve trigonometric equations
 Identify the graphs of the reciprocal trigonometric functions
 Use reciprocal and inverse trigonometric functions and their graphs to solve problems
Complex Numbers
 Explain the connections between real numbers and complex numbers
 Represent complex numbers in a variety of ways
 Construct and examine graphs in the complex and polar planes
 Develop and evaluate mathematical arguments and proofs
 Apply operations on complex numbers in both rectangular and polar forms
 Translate between polar and rectangular representations, and investigate the relationships in the
operations using graphs
 Apply De Moivre's Theorem