EO: Expressions and Operations

EO.AII.1: The student will

EO.AII.1.a: add, subtract, multiply, divide, and simplify rational algebraic expressions;

Dividing Exponential Expressions
Solving Algebraic Equations I
Solving Algebraic Equations II

EO.AII.1.b: add, subtract, multiply, divide, and simplify radical expressions containing rational numbers and variables, and expressions containing rational exponents; and

Operations with Radical Expressions
Simplifying Radical Expressions

EO.AII.1.c: factor polynomials completely in one or two variables.

Equivalent Algebraic Expressions II
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

EO.AII.2: The student will perform operations on complex numbers and express the results in simplest form using patterns of the powers of i.

Points in the Complex Plane

EI: Equations and Inequalities

EI.AII.3: The student will solve

EI.AII.3.a: absolute value linear equations and inequalities;

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions

EI.AII.3.b: quadratic equations over the set of complex numbers;

Points in the Complex Plane
Roots of a Quadratic

EI.AII.3.c: equations containing rational algebraic expressions; and

Solving Algebraic Equations II

EI.AII.3.d: equations containing radical expressions.

Radical Functions

F: Functions

F.AII.5: The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve practical problems, including writing the first n terms, determining then nth term, and evaluating summation formulas. Notation will include ∑ and aₙ.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

F.AII.6: For absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic functions, the student will

F.AII.6.a: recognize the general shape of function families; and

Absolute Value with Linear Functions
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Radical Functions
Rational Functions

F.AII.6.b: use knowledge of transformations to convert between equations and the corresponding graphs of functions.

Exponential Functions
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Functions

F.AII.7: The student will investigate and analyze linear, quadratic, absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic function families algebraically and graphically. Key concepts include

F.AII.7.a: domain, range, and continuity;

General Form of a Rational Function
Logarithmic Functions
Radical Functions

F.AII.7.c: extrema;

Absolute Value with Linear Functions
Graphs of Polynomial Functions
Quadratics in Factored Form
Quadratics in Vertex Form
Radical Functions
Zap It! Game

F.AII.7.d: zeros;

Graphs of Polynomial Functions
Logarithmic Functions
Polynomials and Linear Factors
Roots of a Quadratic

F.AII.7.e: intercepts;

Exponential Functions
Graphs of Polynomial Functions
Linear Functions
Points, Lines, and Equations
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Slope-Intercept Form of a Line

F.AII.7.f: values of a function for elements in its domain;

Exponential Functions
General Form of a Rational Function
Logarithmic Functions
Point-Slope Form of a Line
Radical Functions
Slope-Intercept Form of a Line

F.AII.7.g: connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs;

Graphs of Polynomial Functions
Linear Functions

F.AII.7.h: end behavior;

Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Rational Functions

F.AII.7.i: vertical and horizontal asymptotes;

Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Logarithmic Functions
Rational Functions

F.AII.7.j: inverse of a function; and

Logarithmic Functions
Radical Functions

F.AII.8: The student will investigate and describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression.

Polynomials and Linear Factors
Roots of a Quadratic

S: Statistics

S.AII.9: The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of quadratic and exponential functions.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

S.AII.10: The student will represent and solve problems, including practical problems, involving inverse variation, joint variation, and a combination of direct and inverse variations.

Direct and Inverse Variation

S.AII.11: The student will

S.AII.11.a: identify and describe properties of a normal distribution;

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

S.AII.11.c: apply properties of normal distributions to determine probabilities associated with areas under the standard normal curve.

Polling: City

S.AII.12: The student will compute and distinguish between permutations and combinations.

Binomial Probabilities
Permutations and Combinations