First Quarter
I. Introduction to Functions (Previous course)
A. Definitions
B. Domain and range
C. Function notation
D. Types of functions
E. Rates of change
II. Linear Functions (Previous course; Linear Algebra standards 2, 8, 9)
A. Constant rate of change
B. Determining linear functions
C. Geometric properties of linear functions
D. Solving systems of equations
E. Fitting linear functions to data and linear regression
III. Exponential and logarithmic functions (Previous course)
A. Exponential functions and their behavior
B. Graphs of exponential functions
C. Logarithms
D. Using logarithms to solve exponential functions
E. Applications of logarithmic functions
F. Exponential models and e
G. Natural logarithms
H. Fitting curves to data and exponential regression
Second Quarter
I. Transformations of functions (Previous course)
A. Vertical and horizontal shifts of a function’s graph
B. Reflections
C. Vertical stretches
D. Quadratic functions
E. Horizontal stretches
II. Trigonometric Functions (Trigonometry standards 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 19)
A. Introductory applications
B. Angle measurement
C. Trigonometric functions
D. Formulas, specific and general
E. Trigonometric equations and inverses
F. Trigonometric identities
G. Trigonometric models
H. Triangle applications
Third Quarter
I. Composite, inverse and combination functions (Previous course)
A. Composition of functions
B. General inverse functions
C. Combinations of functions
II. Polynomial and rational functions (Mathematical Analysis standards 4, 5, 6)
A. Power functions
B. Polynomial functions
C. Local behavior of polynomial functions
D. Rational functions
E. Local behavior of rational functions
F. End behavior of polynomial and rational functions
III. Trigonometry:Vectors and polar coordinates (Trigonometry standards 7, 15, 16, 17, 19; Mathematical Analysis standards 1, 2, 12)
A. Vectors
B. Components of vectors
C. Applications of vectors
D. The dot product
E. Polar coordinates
IV. Related topics (Trigonometry standards 11, 18, 19; Mathematical Analysis standards 2, 7)
A. Geometric series
B. Parametric equations
C. Implicitly defined curves
D. Complex numbers
E. Applications of trigonometric identities
F. Hyperbolic functions
Fourth Quarter
I. Combinatorics (Probability and Statistics standards 1, 2, 3, 4, 6)
A. Counting principle
B. Multiplication counting principle
C. Permutations
D. Combinations
E. Binomial Theorem and Pascal’s Triangle
F. Applications
II. Limits (Mathematical Analysis standards 3, 8; Calculus standards 1, 2)
A. The limit of a function
B. Definition of limit
C. Continuity
D. Limits at infinity
III. Derivatives (Calculus standard 4)
A. Difference quotients and rates of change
B. The derivative at a point
C. The derivative function
D. Acceleration and deceleration
E. Analyzing graphs
F. Derivatives of functions
IV. Integrals (Calculus standards 13, 14, 15, 16)
A. Introduction
B. Riemann sums
C. The definite integral
D. Properties of definite integrals
E. Area under a curve
F. Definite integrals and volumes
G. The Fundamental Theorem of Calculus