# Integrated Math III Online Credit Recovery

In this third-year high school integrated math course, students expand on previous high school math topics including systems of equations and inequalities, polynomials, trigonometry, statistics, and functions. The introduction of complex numbers leads to new adventures in factoring polynomials, solving polynomial equations, and graphing polynomials. Students work with radical and rational expressions and equations and extend their knowledge of exponential functions to inverses and logarithmic functions. They learn about the unit circle and use trigonometric functions to model periodic processes. Geometric topics include three-dimensional visualization, design and optimization, and real-world modeling. Students are introduced to piecewise and logistic functions and perform quadratic and exponential regressions. Finally, students use statistical and probability tools, such as the standard normal distribution, to understand data, and use simulations, experiments, and surveys to make inferences.

Diagnostic tests assess students’ current knowledge and generate individualized study plans, so students can focus on topics that need review.

Semester 1

Unit 1: Systems of Linear Equations and Inequalities

In this unit, students extend solving systems of two linear equations to solving systems of three linear equations and learn how to solve compound inequalities. They also learn how to use equations and inequalities to solve linear programming problems, including problems about maximizing profit and minimizing cost.

• Course Checkpoints

• Foundations

• Solve Systems of Two Linear Equations

• Solve Systems of Three Linear Equations

• Inequalities in One Variable

• Compound Inequalities

• Inequalities in Two Variables

• Systems of Linear Inequalities

• Linear Programming

• Applications of Linear Programming

Unit 2: Radicals and Complex Numbers

In this unit, students cover square roots in more depth than they have before and work with higher roots and rational exponent expressions. Students learn about imaginary numbers, simplify expressions with imaginary numbers, and perform operations with complex numbers.

• Foundations

• Square Roots

• Simplify Radical Expressions

• Fractional Exponents and Higher Roots

• Imaginary Numbers

• Complex Numbers

Unit 3: Polynomials

This unit focuses on polynomials. Students learn several ways to factor polynomials and then factor to solve polynomial equations. They use their knowledge of complex numbers to determine complex solutions to quadratic equations and to factor polynomials over the set of complex numbers.

• Foundations

• Work with Polynomials

• Multiply Polynomials

• Factoring Patterns

• More Factoring Patterns

• Solve Polynomial Equations

• Solve Quadratic Equations

• The Quadratic Formula

• Factor Over the Complex Numbers

Unit 4: Polynomial Functions

Polynomials can be divided in the same way that real numbers can be divided. In this unit, students divide polynomials using long division and synthetic division. They learn long division leads to factoring, finding roots and zeros of polynomial equations and functions, and graphing polynomial functions. It is all brought together when students learn the fundamental theorem of algebra.

• Foundations

• Power Functions

• Polynomial Long Division

• Synthetic Division

• The Polynomial Remainder Theorem

• Factors and Rational Roots

• Graph Polynomial Functions

• The Fundamental Theorem of Algebra

Unit 5: Radical and Rational Expressions

This unit introduces students to the concept of extraneous solutions. Students solve radical equations, simplify rational expressions, perform operations with rational expressions, and solve rational equations.

• Foundations

• Solve Radical Equations 1

• Solve Radical Equations 2

• Rational Expressions

• Multiply and Divide Rational Expressions

• Add and Subtract Rational Expressions

• Simplify Complex Fractions

• Solve Rational Equations

Unit 6: Exponential and Logarithmic Functions

In this unit, students work with exponential functions, learn about inverses, and learn how logarithms arise naturally as inverses of exponential functions. Students graph logarithmic functions and use logarithms to solve mathematical and real-world problems.

• Foundations

• Exponential Growth and Decay

• Graph Exponential Functions

• Inverses

• Logarithms

• Properties of Logarithms

• Use Logarithms to Solve Exponential Equations

• Applications of Exponential Equations

• Graph Logarithmic Functions

Unit 7: Modeling with Geometry

In this unit, students use their visualization skills to determine cross sections and three-dimensional objects formed by rotating two-dimensional shapes. They use distances, surface area, volume, and density to solve many types of real-world problems.

• Foundations

• Cross Sections of Three-Dimensional Objects

• Generate Three-Dimensional Objects

• Geometry on Earth

• Manufacturing: Design and Optimization

• Geometric Modeling

• Density

• Fermi Problems

Semester 2

Unit 1: Radians and Trigonometric Functions

In this unit, students solve problems using right triangle trigonometry. Students then move onto the unit circle, where they learn how to use radian measure to define trigonometric functions that are no longer bound by angles in a triangle.

• Semester 2 Introduction

• Foundations

• Right Triangle Trigonometry

• Applications of Right Triangle Trigonometry

• Radians and Degrees

• Coterminal Angles

• The Unit Circle

• Trigonometric Identities

• Trigonometric Functions of Any Angle

• Inverse Trigonometric Functions

• Applications of Inverse Trigonometric Functions

Unit 2: Graphs of Sinusoidal Functions

Graphs of sine and cosine functions are called sinusoids. In this unit, students see how the graphs of the sine and cosine functions are waves that can be shifted, amplified, and compressed to model many periodic phenomena.

• Foundations

• Sinusoidal Graphs

• Sinusoidal Graphs: Amplitude

• Sinusoidal Graphs: Period

• Sinusoidal Graphs: Vertical Shift

• Sinusoidal Family of Functions

• Create Trigonometric Models

• Interpret Trigonometric Models

• Sketch Trigonometric Models

Unit 3: More Function Types

The focus of this unit is on graphing different types of functions. Students graph rational, radical, and quadratic functions, perform quadratic and exponential regressions, and are introduced to piecewise-defined functions, step functions, and logistic growth functions.

• Foundations

• Reciprocal Power Functions

• Graph Rational Functions

• More Rational Functions

• Radical Functions

• Quadratic Functions

• Quadratic Regression Models

• Exponential Regression Models

• Absolute Value Functions

• Piecewise-Defined Functions

• Step Functions

• Logistic Growth Functions

Unit 4: Using Function Models

In this unit, students solve systems of linear and quadratic equations algebraically and graphically, solve equations by determining intersection points, and determine key features of functions such as where a function is increasing or decreasing. Students compare features of different types of functions and learn how to combine functions.

• Foundations

• Linear and Quadratic Systems

• Intersections of Graphs

• Key Features of Functions

• Compare Models

• Average Rate of Change

• Combine Functions

Unit 5: Probability Distributions

In this unit, students learn about probability distributions, including the binomial distribution and the normal distribution. Students use the normal distribution to analyze and compare data.

• Foundations

• Create Probability Distributions

• Interpret Probability Distributions

• Binomial Distributions

• Continuous Random Variables

• The Normal Distribution

• Standardize Data

• Compare Scores

• The Standard Normal Curve

• Find Standard Scores

Unit 6: Data Gathering and Analysis

Collecting and interpreting samples is the groundwork of statistics. In this unit, students focus on how the sampling process is improved by random selection, and how samples can be used to make estimations and predictions.

• Foundations

• Sample and Population

• Statistics and Parameters

• Simulations

• Margin of Error

• Surveys, Experiments, Studies, and Reports