Unit
1 
Reasoning
and Proof
Develops student understanding of formal reasoning in geometric,
algebraic, and statistical contexts and of basic principles that
underlie those reasoning strategies. 

Topics
include:
Inductive and deductive reasoning strategies; principles of logical
reasoning—Affirming the Hypothesis and Chaining Implications;
properties of line reflections; relation among angles formed by two
intersecting lines or by two parallel lines and a transversal; rules
for transforming algebraic expressions and equations; design of experiments;
use of data from a randomized experiment to compare two treatments,
sampling distribution constructed using simulation, randomization
test, and statistical significance; inference from sample surveys,
experiments, and observational studies and how randomization relates
to each. 
Unit
2 
Inequalities
and Linear Programming
Develops student ability to reason both algebraically and graphically
to solve inequalities in one and two variables, introduces systems
of inequalities in two variables, and develops a strategy for optimizing
a linear function in two variables within a system of linear constraints
on those variables. 

Topics
include:
Inequalities in one and two variables, number line graphs, interval
notation, systems of linear inequalities, and linear programming. 
Unit
3 
Similarity
and Congruence
Extends student understanding of similarity and congruence and their
ability to use those relations to solve problems and to prove geometric
assertions with and without the use of coordinates. 

Topics
include:
Connections between Law of Cosines, Law of Sines, and sufficient
conditions for similarity and congruence of triangles; connections
between transformations and sufficient conditions for congruence
and similarity of triangles; centers of triangles, applications of
similarity and congruence in realworld contexts; necessary and sufficient
conditions for parallelograms, sufficient conditions for congruence
of parallelograms, and midpoint connector theorems. 
Unit
4 
Samples
and Variation
Develops student ability to use the normal distribution as a model
of variation, introduces students to the binomial distribution and
its use in making inferences about population parameters based on
a random sample, and introduces students to the probability and statistical
inference used in industry for statistical process control. 

Topics
include:
Normal distribution, standardized scores and estimating population
percentages, binomial distributions (shape, expected value, standard
deviation), normal approximation to a binomial distribution, odds,
statistical process control, and the Central Limit Theorem. 
Unit
5 
Polynomial
and Rational Functions
Extends student ability to represent and draw inferences about polynomial
and rational functions using symbolic expressions and manipulations. 

Topics
include:
Definition and properties of polynomials, operations on polynomials;
completing the square, proof of the quadratic formula, solving quadratic
equations (including complex number solutions), vertex form of quadratic
functions; definition and properties of rational functions, operations
on rational expressions. 
Unit
6 
Circles
and Circular Functions
Develops student understanding of properties of special lines, segments,
angles, and arcs in circles and the ability to use those properties
to solve problems; develops student understanding of circular functions
and the ability to use those functions to model periodic change;
and extends student ability to reason deductively in geometric settings. 

Topics
include:
Properties of chords, tangent lines, and central and inscribed angles
and their intercepted arcs; linear and angular velocity; radian measure
of angles; and circular functions as models of periodic change. 
Unit
7 
Recursion
and Iteration
Extends student ability to model, analyze, and solve problems in
situations involving sequential and recursive change. 

Topics
include:
Iteration and recursion as tools to model and solve problems about
sequential change in realworld settings, including compound interest
and population growth; arithmetic, geometric, and other sequences
together with their connections to linear, exponential, and polynomial
functions; arithmetic and geometric series; finite differences; linear
and nonlinear recurrence relations; and function iteration, including
graphical iteration and fixed points. 
Unit
8 
Inverse
Functions
Develops student understanding of inverses of functions with a focus
on logarithmic functions and their use in modeling and analyzing
problem situations and data patterns. 

Topics
include:
Inverses of functions; logarithmic functions and their relation to
exponential functions, properties of logarithms, equation solving
with logarithms; and inverse trigonometric functions and their applications
to solving trigonometric equations. 