IM3.1: Students solve inequalities, quadratic equations, and systems of equations. They graph polynomial, rational, algebraic, and piece-wise defined functions. They graph and write the equations of conic sections and compute with and factor polynomials and algebraic fractions. They solve problems involving exponential and logarithmic expressions, as well as define and use arithmetic and geometric sequences and series.

IM3.1.1: Solve combined linear inequalities.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

IM3.1.2: Use a graph to find the solution set of a pair of linear inequalities in two variables.

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

IM3.1.3: Find a common monomial factor in a polynomial.

Factoring Special Products

IM3.1.4: Factor the difference of two squares and other quadratics.

Factoring Special Products
Modeling the Factorization of x²+bx+c
Quadratics in Factored Form

IM3.1.7: Solve quadratic equations by factoring.

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

IM3.1.9: Complete the square to solve quadratic equations.

Roots of a Quadratic

IM3.1.10: Derive the quadratic formula by completing the square.

Roots of a Quadratic

IM3.1.11: Solve equations that contain radical expressions.

Operations with Radical Expressions

IM3.1.12: Recognize and graph various types of functions, including polynomials, rational, and algebraic functions.

General Form of a Rational Function
Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Rational Functions

IM3.1.14: Understand composition of functions and combine functions by composition.

Function Machines 1 (Functions and Tables)

IM3.1.15: Graph relations and functions with and without graphing technology.

Absolute Value with Linear Functions
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Point-Slope Form of a Line
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions
Standard Form of a Line

IM3.1.17: Solve an inequality by examining the graph.

Absolute Value Equations and Inequalities
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Quadratic Inequalities
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

IM3.1.18: Graph functions defined piece-wise.

Absolute Value with Linear Functions

IM3.1.19: Graph absolute value equations and inequalities.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Compound Inequalities

IM3.1.20: Use substitution, elimination, and matrices to solve systems of two or three equations in two or three variables.

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

IM3.1.21: Use system of equations and inequalities to solve word problems.

Linear Programming
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

IM3.1.22: Define complex numbers and perform basic operations with them.

Points in the Complex Plane
Roots of a Quadratic

IM3.1.23: Understand how real and complex numbers are related, including plotting complex numbers as points in the plane.

Points in the Complex Plane

IM3.1.24: Solve quadratic equations in the complex number system.

Points in the Complex Plane
Roots of a Quadratic

IM3.1.25: Solve word problems using quadratic equations.

Addition and Subtraction of Functions

IM3.1.26: Solve equations that contain radical expressions.

Operations with Radical Expressions
Radical Functions

IM3.1.28: Write the equations of conic sections (circle, ellipse, parabola, and hyperbola).

Circles
Ellipses
Hyperbolas
Parabolas

IM3.1.29: Graph conic sections.

Circles
Ellipses
Hyperbolas

IM3.1.31: Divide polynomials by others of lower degree.

Dividing Polynomials Using Synthetic Division

IM3.1.32: Factor polynomials completely and solve polynomial equations by factoring.

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

IM3.1.37: Understand and use negative and fractional exponents.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

IM3.1.40: Solve equations involving algebraic fractions.

Solving Algebraic Equations II

IM3.1.42: Solve problems of direct, inverse, and joint variation.

Determining a Spring Constant
Direct and Inverse Variation

IM3.1.45: Solve logarithmic and exponential equations and inequalities.

Exponential Functions

IM3.1.50: Define arithmetic and geometric sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

IM3.1.51: Find specified terms of arithmetic and geometric sequences.

Arithmetic Sequences
Geometric Sequences

IM3.2: Students describe and use parallel and perpendicular lines. They use coordinate geometry and prove that triangles are congruent or similar. They find the equation of a circle in the coordinate plane and describe and use properties of solids.

IM3.2.1: Understand and use the relationships between special pairs of angles formed by parallel lines and transversals.

Constructing Congruent Segments and Angles
Triangle Angle Sum

IM3.2.2: Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.

Point-Slope Form of a Line
Points, Lines, and Equations

IM3.2.3: Use properties of congruent and similar polygons to solve problems.

Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

IM3.2.5: Describe, classify, and understand relationships among quadrilaterals square, rectangles, rhombus, parallelogram, trapezoid, and kite.

Classifying Quadrilaterals

IM3.2.9: Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.

Beam to Moon (Ratios and Proportions)
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles

IM3.2.15: Find and use measures of sides, volumes of solids, and surface areas of solids. Relate these measures to each other using formulas.

Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders

IM3.3: Students design and interpret surveys, use sampling distributions, and understand standard deviation.

IM3.3.1: Understand and apply basic ideas related to the design and interpretation of surveys, such as background information, random sampling, and bias.

Polling: City
Polling: Neighborhood

IM3.3.2: Construct simulated sampling distributions of sample proportions and use sampling distributions to identify which proportions are likely to be found in a sample of a given size.

Polling: City
Populations and Samples

IM3.3.3: Construct and interpret margin of error and confidence intervals for population proportions.

Polling: City
Polling: Neighborhood

IM3.3.4: Understand the standard deviation as a measure of variability in a distribution.

Real-Time Histogram

IM3.5: Students use iteration and recursion to solve problems.

IM3.5.1: Use iteration and recursion as tools to represent, analyze, and solve problems involving sequential change.

Arithmetic Sequences
Geometric Sequences

IM3.7: Students use a variety of strategies to solve problems and develop and evaluate mathematical arguments and proofs.

IM3.7.1: Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously.

Solving Linear Systems (Standard Form)

IM3.7.4: Identify the hypothesis and conclusion in a logical deduction.

Biconditional Statements
Conditional Statements

IM3.7.5: Use counterexamples to show that statements are false, recognizing that a single counterexample is sufficient to prove a general statement false.

Conditional Statements

IM3.7.6: Use properties of number systems and the order of operations to justify the steps of simplifying functions and solving equations.

Solving Algebraic Equations II
Solving Equations on the Number Line

IM3.7.7: Identify and give examples of undefined terms, axioms, and theorems, and inductive and deductive proof.

Investigating Angle Theorems
Isosceles and Equilateral Triangles
Parallel, Intersecting, and Skew Lines

IM3.7.8: Construct logical arguments, judge their validity, and give counterexamples to disprove statements.

Biconditional Statements
Conditional Statements