I: Students will use the language and operations of algebra to evaluate, analyze and solve problems.

I.2: Analyze the behavior of sequences and series.

I.2.b: Represent sequences and series using various notations.

Arithmetic Sequences
Geometric Sequences

I.2.c: Identify arithmetic and geometric sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

I.2.d: Discover and justify the formula for a finite arithmetic series.

Arithmetic Sequences
Arithmetic and Geometric Sequences

I.2.e: Discover and justify the formulas for finite and infinite geometric series.

Geometric Sequences

II: Students will understand and represent functions and analyze function behavior.

II.1: Analyze and solve problems using polynomial functions.

II.1.d: Understand the relationships among the solutions of a polynomial equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial.

Polynomials and Linear Factors

II.1.e: Write an equation with given solutions.

Solving Equations on the Number Line

II.2: Model and graph functions and transformations of functions.

II.2.a: Model real-world relationships with functions.

Linear Functions

II.2.b: Graph rational, piece-wise, power, exponential, and logarithmic functions.

Absolute Value with Linear Functions
Compound Interest
Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Logarithmic Functions
Rational Functions

II.2.c: Identify the effects of changing the parameter a in y = af (x), y = f (ax), y = f (x − a) , and y = f (x) + a , given the graph of y = f (x).

Translating and Scaling Functions
Zap It! Game

II.3: Analyze the behavior of functions.

II.3.a: Identify the domain, range, and other attributes of families of functions and their inverses.

Graphs of Polynomial Functions
Logarithmic Functions
Radical Functions

II.3.c: Identify and analyze continuity, end behavior, asymptotes, symmetry (odd and even functions), and limits, and connect these concepts to graphs of functions.

Exponential Functions
General Form of a Rational Function
Logarithmic Functions

III: Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.

III.1: Solve problems using trigonometry.

III.1.a: Define the six trigonometric functions using the unit circle.

Cosine Function
Sine Function
Tangent Function

III.1.b: Prove trigonometric identities using definitions, the Pythagorean Theorem, or other relationships.

Simplifying Trigonometric Expressions

III.1.c: Simplify trigonometric expressions and solve trigonometric equations using identities.

Sum and Difference Identities for Sine and Cosine

III.1.e: Construct the graphs of the trigonometric functions and their inverses, and describe their behavior, including periodicity and amplitude.

Cosine Function
Sine Function
Tangent Function

III.2: Graph curves using polar and parametric equations.

III.2.b: Represent complex numbers in rectangular and polar form, and convert between rectangular and polar form.

Points in the Complex Plane

III.2.d: Multiply complex numbers in polar form and use DeMoivre?s Theorem to find roots of complex numbers.

Points in the Complex Plane

III.3: Solve problems involving the geometric properties of conic sections.

III.3.a: Write equations of conic sections in standard form.

Circles
Ellipses
Hyperbolas
Parabolas

III.3.c: Solve real-world applications of conic sections.

Circles

IV: Students will understand concepts from probability and statistics and apply statistical methods to solve problems.

IV.1: Compute probabilities for discrete distributions and use sampling distributions to calculate approximate probabilities.

IV.1.a: Obtain sample spaces and probability distributions for simple discrete random variables.

Polling: City

IV.1.b: Compute binomial probabilities using Pascal?s Triangle and the Binomial Theorem.

Binomial Probabilities

IV.1.e: Calculate parameters of sampling distributions for the sample average, sum, and proportion.

Polling: City
Populations and Samples

IV.1.f: Calculate probabilities in real problems using sampling distributions.

Polling: City

IV.2: Analyze bivariate data using linear regression methods.

IV.2.b: Compute predictions of y-values for given x-values using a regression equation, and recognize the limitations of such predictions.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines