I: Students will use the language and operations of algebra to evaluate, analyze and solve problems.

I.1: Evaluate, analyze, and solve mathematical situations using algebraic properties and symbols.

I.1.a: Solve and graph first-degree absolute value equations of a single variable.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions

I.1.b: Solve radical equations of a single variable, including those with extraneous roots.

Operations with Radical Expressions
Radical Functions

I.1.c: Solve absolute value and compound inequalities of a single variable.

Absolute Value Equations and Inequalities
Compound Inequalities
Solving Linear Inequalities in One Variable

I.1.e: Simplify algebraic expressions involving negative and rational exponents.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

I.2: Solve systems of equations and inequalities.

I.2.a: Solve systems of linear, absolute value, and quadratic equations algebraically and graphically.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

I.2.b: Graph the solutions of systems of linear, absolute value, and quadratic inequalities on the coordinate plane.

Absolute Value Equations and Inequalities
Linear Inequalities in Two Variables
Systems of Linear Inequalities (Slope-intercept form)

I.2.c: Solve application problems involving systems of equations and inequalities.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

I.3: Represent and compute fluently with complex numbers.

I.3.b: Simplify expressions involving complex numbers and express them in standard form, a + bi.

Points in the Complex Plane

I.4: Model and solve quadratic equations and inequalities.

I.4.a: Model real-world situations using quadratic equations.

Addition and Subtraction of Functions

I.4.c: Solve quadratic equations of a single variable over the set of complex numbers by factoring, completing the square, and using the quadratic formula.

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Roots of a Quadratic

I.4.e: Write a quadratic equation when given the solutions of the equation.

Quadratics in Polynomial Form

II: Students will understand and represent functions and analyze function behavior.

II.1: Represent mathematical situations using relations.

II.1.a: Model real-world relationships with functions.

Determining a Spring Constant

II.1.c: Determine when a relation is a function.

Introduction to Functions
Linear Functions

II.1.d: Determine the domain and range of relations.

Introduction to Functions

II.2: Evaluate and analyze functions.

II.2.c: Add, subtract, multiply, and divide functions.

Addition and Subtraction of Functions

II.2.d: Determine whether or not a function has an inverse, and find the inverse when it exists.

Logarithmic Functions

II.3: Define and graph exponential functions and use them to model problems in mathematical and real-world contexts.

II.3.a: Define exponential functions as functions of the form y = abx ,b > 0,b ?? 1.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

II.3.b: Model problems of growth and decay using exponential functions.

Compound Interest

II.3.c: Graph exponential functions.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

II.4: Define and graph logarithmic functions and use them to solve problems in mathematics and real-world contexts.

II.4.a: Relate logarithmic and exponential functions.

Logarithmic Functions

II.4.d: Solve exponential and logarithmic equations.

Exponential Functions

II.4.e: Graph logarithmic functions.

Logarithmic Functions

II.4.f: Solve problems involving growth and decay.

Compound Interest

III: Students will use algebraic, spatial, and logical reasoning to solve geometry and measurement problems.

III.1: Examine the behavior of functions using coordinate geometry.

III.1.a: Identify the domain and range of the absolute value, quadratic, radical, sine, and cosine functions.

Radical Functions

III.1.b: Graph the absolute value, quadratic, radical, sine, and cosine functions.

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Cosine Function
Exponential Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Roots of a Quadratic
Sine Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Zap It! Game

III.1.c: Graph functions using transformations of parent functions.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

III.1.d: Write an equation of a parabola in the form y = a(x − h)2 + k when given a graph or an equation..

Parabolas

III.2: Determine radian and degree measures for angles.

III.2.a: Convert angle measurements between radians and degrees.

Cosine Function
Sine Function
Tangent Function

III.2.b: Find angle measures in degrees and radians using inverse trigonometric functions, including exact values for special triangles.

Tangent Function

III.3: Determine trigonometric measurements using appropriate techniques, tools, and formulas.

III.3.a: Define the sine, cosine, and tangent functions using the unit circle.

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

III.3.b: Determine the exact values of the sine, cosine, and tangent functions for the special angles of the unit circle using reference angles.

Cosine Function
Sine Function
Tangent Function

IV: Students will understand concepts from probability and statistics and apply statistical methods to solve problems.

IV.1: Apply basic concepts of probability.

IV.1.a: Distinguish between permutations and combinations and identify situations in which each is appropriate.

Permutations and Combinations

IV.1.b: Calculate probabilities using permutations and combinations to count events.

Binomial Probabilities
Permutations and Combinations

IV.1.c: Compute conditional and unconditional probabilities in various ways, including by definitions, the general multiplication rule, and probability trees.

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Permutations and Combinations
Probability Simulations
Theoretical and Experimental Probability

IV.2: Use percentiles and measures of variability to analyze data.

IV.2.a: Compute different measures of spread, including the range, standard deviation, and interquartile range.

Describing Data Using Statistics
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

IV.2.b: Compare the effectiveness of different measures of spread, including the range, standard deviation, and interquartile range in specific situations.

Box-and-Whisker Plots