Unit
1 
Families
of Functions
Extends student understanding of linear, exponential, quadratic,
power, and circular functions to model data patterns whose graphs
are transformations of basic patterns; and develops understanding
of operations on functions useful in representing and reasoning about
quantitative relationships. 

Topics
include:
Linear, exponential, quadratic, power, and trigonometric functions;
data modeling; translation, reflection, and stretching of graphs;
and addition, subtraction, multiplication, division, and composition
of functions. 
Unit
2 
Vectors
and Motion
Develops student understanding of twodimensional vectors and their
use in modeling linear, circular, and other nonlinear motion. 

Topics
include:
Concept of vector as a mathematical object used to model situations
defined by magnitude and direction; equality of vectors, scalar multiples,
opposite vectors, sum and difference vectors, dot product of two
vectors, position vectors and coordinates; and parametric equations
for motion along a line and for motion of projectiles and objects
in circular and elliptical orbits. 
Unit
3 
Algebraic
Functions and Equations
Reviews and extends student understanding of properties of polynomial
and rational functions and skills in manipulating algebraic expressions
and solving polynomial and rational equations, and develops student
understanding of complex number representations and operations. 

Topics
include:
Polynomials, polynomial division, factor and remainder theorems,
operations on complex numbers, representation of complex numbers
as vectors, solution of polynomial equations, rational function graphs
and asymptotes, and solution of rational equations and equations
involving radical expressions. 
Unit
4 
Trigonometric
Functions and Equations
Extends student understanding of, and ability to reason with, trigonometric
functions to prove or disprove potential trigonometric identities
and to solve trigonometric equations; develops student ability to
geometrically represent complex numbers and their operations and
to find powers and roots of complex numbers expressed in trigonometric
form. 

Topics
include:
Fundamental trigonometric identities, sum and difference identities,
doubleangle identities; periodic solutions of trigonometric equations;
definitions of secant, cosecant, and cotangent functions; absolute
value and trigonometric form of complex numbers, De Moivre's Theorem,
and roots of complex numbers. 
Unit
5 
Exponential
Functions, Logarithms, and Data Modeling
Extends student understanding of exponential and logarithmic functions
to the case of natural exponential and logarithmic functions, solution
of exponential growth and decay problems, and use of logarithms for
linearization and modeling of data patterns. 

Topics
include:
Exponential functions with rules in the form f(x) = Ae^{kx},
natural logarithm function, linearizing bivariate data and fitting
models using log and loglog transformations. 
Unit
6 
Surfaces
and Cross Sections
Extends student ability to visualize and represent threedimensional
shapes using contours, cross sections, and reliefs, and to visualize
and represent surfaces and conic sections defined by algebraic equations. 

Topics
include:
Using contours to represent threedimensional surfaces and developing
contour maps from data; sketching surfaces from sets of cross sections;
conics as planar sections of right circular cones and as loci of
points in a plane; threedimensional rectangular coordinate system;
sketching surfaces using traces, intercepts and cross sections derived
from algebraicallydefined surfaces; and surfaces of revolution and
cylindrical surfaces. 
Unit
7 
Concepts
of Calculus
Develops student understanding of fundamental calculus ideas through
explorations in a variety of applied problem contexts and their representations
in function tables and graphs. 

Topics
include:
Instantaneous rates of change, linear approximation, area under a
curve, and applications to problems in physics, business, and other
disciplines. 
Unit
8 
Counting
Methods and Induction
Extends student ability to count systematically and solve enumeration
problems in a variety of realworld and mathematical settings, and
develops understanding of, and ability to carry out, proofs by mathematical
induction and by use of the Least Number Principle. 

Topics
include:
Systematic listing, counting trees, the Multiplication Principle
of Counting, the Addition Principle of Counting, combinations, permutations,
selections with repetition; the Binomial Theorem, Pascal’s triangle,
combinatorial reasoning; the General Multiplication Rule for Probability;
proof by mathematical induction; and arguments using proof by contradiction
and the Least Number Principle. 