**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