AII/T.1: The student, given rational, radical, or polynomial expressions, will

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

Operations with Radical Expressions
Simplifying Radical Expressions

AII/T.1.d: factor polynomials completely.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

AII/T.3: The student will perform operations on complex numbers, express the results in simplest form using patterns of the powers of i, and identify field properties that are valid for the complex numbers.

Points in the Complex Plane

AII/T.4: Graphing calculators will be used for solving and for confirming the algebraic solutions. The student will solve, algebraically and graphically,

AII/T.4.a: absolute value equations and inequalities;

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions

AII/T.4.b: quadratic equations over the set of complex numbers;

Points in the Complex Plane

AII/T.4.d: equations containing radical expressions.

Radical Functions

AII/T.6: The student will recognize the general shape of function (absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic) families and will convert between graphic and symbolic forms of functions. A transformational approach to graphing will be employed. Graphing calculators will be used as a tool to investigate the shapes and behaviors of these functions.

Absolute Value with Linear Functions
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Introduction to Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions

AII/T.7: Graphing calculators will be used as a tool to assist in investigation of functions. The student will investigate and analyze functions algebraically and graphically. Key concepts include

AII/T.7.a: domain and range, including limited and discontinuous domains and ranges;

Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Logarithmic Functions
Radical Functions

AII/T.7.b: zeros;

Polynomials and Linear Factors
Roots of a Quadratic

AII/T.7.c: x- and y-intercepts;

Cat and Mouse (Modeling with Linear Systems)
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Roots of a Quadratic
Slope-Intercept Form of a Line

AII/T.7.e: asymptotes;

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

AII/T.7.f: end behavior;

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

AII/T.7.g: inverse of a function; and

Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions

AII/T.7.h: composition of multiple functions.

Function Machines 1 (Functions and Tables)

AII/T.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.

Modeling the Factorization of x²+bx+c
Points, Lines, and Equations
Polynomials and Linear Factors

AII/T.9: The student will collect and analyze data, determine the equation of the curve of best fit, make predictions, and solve real-world problems, using mathematical models. Mathematical models will include polynomial, exponential, and logarithmic functions.

Compound Interest
Introduction to Exponential Functions
Zap It! Game

AII/T.10: The student will identify, create, and solve real-world problems involving inverse variation, joint variation, and a combination of direct and inverse variations.

Direct and Inverse Variation

AII/T.12: The student will compute and distinguish between permutations and combinations and use technology for applications.

Permutations and Combinations

AII/T.13: The student, given a point other than the origin on the terminal side of an angle, will use the definitions of the six trigonometric functions to find the sine, cosine, tangent, cotangent, secant, and cosecant of the angle in standard position. Trigonometric functions defined on the unit circle will be related to trigonometric functions defined in right triangles.

Cosine Function
Sine Function
Tangent Function

AII/T.14: The student, given the value of one trigonometric function, will find the values of the other trigonometric functions, using the definitions and properties of the trigonometric functions.

Sine, Cosine, and Tangent Ratios

AII/T.15: The student will find, without the aid of a calculator, the values of the trigonometric functions of the special angles and their related angles as found in the unit circle. This will include converting angle measures from radians to degrees and vice versa.

Cosine Function
Sine Function
Tangent Function

AII/T.17: The student will verify basic trigonometric identities and make substitutions, using the basic identities.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

AII/T.18: The student, given one of the six trigonometric functions in standard form, will

AII/T.18.b: determine the amplitude, period, phase shift, vertical shift, and asymptotes;

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

AII/T.18.c: sketch the graph of the function by using transformations for at least a two-period interval; and

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

AII/T.18.d: investigate the effect of changing the parameters in a trigonometric function on the graph of the function.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

AII/T.21: The student will identify, create, and solve real-world problems involving triangles. Techniques will include using the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines.

Circles
Distance Formula
Estimating Population Size
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine, Cosine, and Tangent Ratios