A1.1: Solving Problems

A1.1.A: Select and justify functions and equations to model and solve problems.

Solving Equations on the Number Line

A1.1.B: Solve problems that can be represented by linear functions, equations, and inequalities.

Compound Interest
Linear Inequalities in Two Variables
Solving Equations by Graphing Each Side

A1.1.C: Solve problems that can be represented by a system of two linear equations or inequalities.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

A1.1.E: Solve problems that can be represented by exponential functions and equations.

Compound Interest
Exponential Functions
Introduction to Exponential Functions

A1.2: Numbers, expressions, and operations

A1.2.A: Know the relationship between real numbers and the number line, and compare and order real numbers with and without the number line.

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

A1.2.B: Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables.

Solving Algebraic Equations I
Solving Equations by Graphing Each Side
Solving Equations on the Number Line

A1.2.C: Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions.

Exponents and Power Rules

A1.2.F: Add, subtract, multiply, and divide polynomials.

Addition and Subtraction of Functions
Addition of Polynomials
Dividing Polynomials Using Synthetic Division
Modeling the Factorization of x²+bx+c

A1.3: Characteristics and behaviors of functions

A1.3.A: Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables.

Introduction to Functions

A1.3.B: Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations.

Function Machines 1 (Functions and Tables)
Linear Functions

A1.4: Linear functions, equations, and inequalities

A1.4.A: Write and solve linear equations and inequalities in one variable.

Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

A1.4.B: Write and graph an equation for a line given the slope and the yintercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations.

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

A1.4.C: Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

A1.4.D: Write and solve systems of two linear equations and inequalities in two variables.

Linear Programming
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

A1.4.E: Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent.

Absolute Value with Linear Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions

A1.5: Quadratic functions and equations

A1.5.B: Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation.

Addition and Subtraction of Functions
Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic
Translating and Scaling Functions
Zap It! Game

A1.5.C: Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers.

Modeling the Factorization of x²+bx+c

A1.5.D: Solve quadratic equations that have real roots by completing the square and by using the quadratic formula.

Quadratics in Factored Form
Roots of a Quadratic

A1.6: Data and distributions

A1.6.B: Make valid inferences and draw conclusions based on data.

Box-and-Whisker Plots
Polling: City

A1.6.D: Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions.

Solving Using Trend Lines

A1.6.E: Describe the correlation of data in scatterplots in terms of strong or weak and positive or negative.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

A1.7: Additional Key Content

A1.7.A: Sketch the graph for an exponential function of the form y = abn where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.

Compound Interest

A1.7.B: Find and approximate solutions to exponential equations.

Exponential Functions

A1.7.C: Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A1.7.D: Solve an equation involving several variables by expressing one variable in terms of the others.

Solving Formulas for any Variable