Unit
1 
Functions,
Equations, and Systems
Reviews and extends student ability to recognize, describe, and use
functional relationships among quantitative variables, with special
emphasis on relationships that involve two or more independent variables. 

Topics
include:
Direct and inverse variation and joint variation; power functions;
linear equations in standard form; and systems of two linear equations
with two variables, including solution by graphing, substitution,
and elimination. 
Unit
2 
Matrix
Methods
Develops student understanding of matrices and ability to use matrices
to model and solve problems in a variety of realworld and mathematical
settings. 

Topics
include:
Constructing and interpreting matrices, matrix addition, scalar multiplication,
matrix multiplication, powers of matrices, inverse matrices, comparing
algebraic properties of matrices to those of real numbers, and using
matrices to solve systems of equations. 
Unit
3 
Coordinate
Methods
Develops student understanding of coordinate methods for representing
and analyzing properties of geometric shapes, for describing geometric
change, and for producing animations. 

Topics
include:
Representing twodimensional figures and modeling situations with
coordinates, including computergenerated graphics; distance in the
coordinate plane, midpoint of a segment, and slope; coordinate and
matrix models of rigid transformations (translations, rotations,
and line reflections), of size transformations, and of similarity
transformations; animation effects. 
Unit
4 
Regression
and Correlation
Develops student ability to describe how two quantitative variables
on a scatterplot are related, including fitting a function to the
data and the use of correlation to measure the strength of a linear
association between the two variables. 

Topics
include:
Construct and interpret scatterplots; compute and interpret a linear
model including slope and intercept, residuals, and the correlation
coefficient; sum of squared errors; influential points; and distinguish
between correlation and causation. 
Unit
5 
Nonlinear
Functions and Equations
Introduces function notation, reviews and extends student ability
to construct and reason with functions that model parabolic shapes
and other quadratic relationships in science and economics, with
special emphasis on formal symbolic reasoning methods, and introduces
common logarithms and algebraic methods for solving exponential equations. 

Topics
include:
Formalization of function concept, notation, domain and range; factoring
and expanding quadratic expressions, solving quadratic equations
by factoring and the quadratic formula, applications to supply and
demand, breakeven analysis; common logarithms and solving exponential
equations using base 10 logarithms. 
Unit
6 
Modeling
and Optimization
Develops student ability in mathematical modeling, optimization,
and problem solving, through study of vertexedge graphs, as students
model and solve problems about networks, paths, and circuits. 

Topics
include:
Mathematical modeling, optimization, algorithmic problem solving,
and using minimum spanning trees, Hamilton paths, the Traveling Salesperson
Problem, critical paths, and the PERT technique to solve network
optimization problems. 
Unit
7 
Trigonometric
Methods
Develops student understanding of trigonometric functions and the
ability to use trigonometric methods to solve triangulation and indirect
measurement problems. 

Topics
include:
Sine, cosine, and tangent functions of measures of angles in standard
position in a coordinate plane and in a right triangle; indirect
measurement; analysis of variablesided triangle mechanisms; derivation
and application of the Law of Sines and Law of Cosines. 
Unit
8 
Probability
Distributions
Develops student understanding of independent events, conditional
probability, and expected value and how to use them to interpret
data and evaluate outcomes of decisions. 

Topics
include:
Twoway frequency tables, Multiplication Rule, independent and dependent
events, conditional probability, probability distributions and their
graphs, waitingtime (or geometric) distributions, and expected value
for games of chance and for applications such as insurance. 