AII.N: Number Sense and Operations Indicators

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.

Points in the Complex Plane

AII.P: Patterns, Relations, and Algebra Indicators

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

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 x²+bx+c
Operations with Radical Expressions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex 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: Geometry Indicators

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

Slope

AII.D: Data Analysis, Statistics, and Probability Indicators

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.

Box-and-Whisker 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