Standards for Teaching and Learning

AII.N.2: Simplify numerical expressions with powers and roots, including fractional and negative exponents.

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

Operations with Radical Expressions

AII.N.3: Know the representation of complex numbers (e.g., a + bi where a and b are real numbers) and the procedures for adding, multiplying, and inverting complex numbers. Understand the associative, commutative, and identity properties for complex arithmetic.

AII.P.1: Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative and recursive patterns such as Fibonacci Numbers and Pascal's Triangle.

Arithmetic Sequences

Finding Patterns

Geometric Sequences

AII.P.2: Identify arithmetic and geometric sequences and finite arithmetic and geometric series. Use the properties of such sequences and series to solve problems, including finding the formula for the general term and the sum, recursively and explicitly.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

AII.P.3: Understand functional notation, evaluate a function at a specified point in its domain, and perform operations on functions with emphasis on the domain and range.

Addition and Subtraction of Functions

Function Machines 1 (Functions and Tables)

Function Machines 3 (Functions and Problem Solving)

AII.P.4: Understand exponential and logarithmic functions and their basic arithmetic properties, including change of base and formulas for exponential of a sum and logarithm of a product.

Compound Interest

Exponential Functions

AII.P.5: Given algebraic, numeric, and/or graphical representations, recognize functions as polynomial, rational, logarithmic, or exponential, and describe their behavior.

Compound Interest

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Quadratics in Factored Form

Rational Functions

AII.P.6: Find solutions to radical equations; find solutions to quadratic equations (with real coefficients and real or complex roots) graphically, by factoring, by completing the square, or by using the quadratic formula.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Operations with Radical Expressions

Quadratics in Factored Form

Quadratics in Polynomial Form

Radical Functions

Roots of a Quadratic

AII.P.7: Solve a variety of equations and inequalities using algebraic, graphical, and numerical methods, including the quadratic formula. Include polynomial, exponential, and logarithmic functions, expressions involving the absolute values, and simple rational expressions.

Absolute Value with Linear Functions

Compound Interest

Exponential Functions

Polynomials and Linear Factors

Quadratics in Factored Form

AII.P.9: Use symbolic, numeric, and graphical methods to solve systems of equations and/or inequalities involving algebraic, exponential, and logarithmic expressions. Describe the relationships among the methods.

Linear Programming

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

AII.P.10: Solve everyday problems that can be modeled using polynomial, rational, exponential, logarithmic, and step functions; absolute values; and square roots. Apply appropriate graphical, tabular, or symbolic methods to the solution. Include compound interest, exponential growth and decay, and direct and inverse variation problems.

Compound Interest

Introduction to Exponential Functions

AII.P.11: Recognize translations and scale changes of a given function f(x) resulting from substitutions for the various parameters a, b, c, and d in y = af(b(x + c/b)) + d. In particular, describe qualitatively the effect of such changes on polynomial, rational, exponential, and logarithmic functions.

Introduction to Exponential Functions

Rational Functions

Zap It! Game

AII.G.3: Relate geometric and algebraic representations of lines and simple curves.

AII.D.1: Select an appropriate graphical representation for a set of data and use appropriate statistics (e.g., quartile or percentile distribution) to communicate information about the data, including box plots.

AII.D.2: Use combinatorics (e.g., fundamental counting principle, permutations, and combinations) to solve problems, including computing geometric probabilities and probabilities of compound events.

Binomial Probabilities

Permutations and Combinations

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.