## High School Courses: Mathematics

## Advanced Algebra with Financial Applications

### Description

This course walks students through the information needed to make the best decisions with money. Advanced Algebra with Financial Applications is an advanced course incorporating real-world applications, collaboration, and calculations using technology. Students learn the formulas used to determine account balances, monthly payments, total costs, and more. They examine budgeting, spending, saving, investment, and retirement. Students explore mortgages and other debt structures and how to make good decisions about borrowing money. This knowledge will propel students into the future with a good foundation on how to handle finances.

**Pre-Requisites:** Algebra II recommended

**Credits:** 1.0

**Estimated Completion Time:** 2 segments/32-36 weeks

### Major Topics and Concepts

#### Segment I

##### Savings

- Linear Growth
- Exponential Growth
- Compound Interest
- Growth and Decay

##### Spending

- Data Representations
- Linear Representations
- Income Tax
- Deferment
- Purchasing Costs

##### Debt

- APR
- Finance Charges
- Cash or Credit
- Credit Scores and Reports
- Cash Management
- Budgeting
- Pay It Off

#### Segment II

##### Mortgage

- Fixed Rate
- Adjustable Rate
- Balloon
- Comparing Options
- Points
- Additional Fees
- Total Cost

##### Investments

- Pre-Writing
- Future Value
- Present Value
- Purchasing Stocks
- Stocks and Bonds
- Portfolios

##### Retirement

- Financial Goals
- Plans
- Insurance
- Net Worth

## Algebra I

### Description

Algebra I is the foundation—the skills acquired in this course contain the basic knowledge needed for all future high school math courses. The material covered in this course is important, but everyone can do it. Anyone can have a good time solving the hundreds of real-world problems algebra can help answer. Each module in this course is presented in a step-by-step way right on the computer screen. Hands-on labs make the numbers, graphs, and equations more real. The content in this course is tied to real-world applications like sports, travel, business, and health. This course is designed to give students the skills and strategies to solve all kinds of mathematical problems. Students will also acquire the confidence needed to handle everything high school math has in store for them.

**Pre-Requisites:** Middle School Grade 7 Mathematics Advanced or Pre-Algebra

**Credits:** 1.0

**Estimated Completion Time:** 2 segments/ 32-36 weeks

### Major Topics and Concepts

#### Segment 1

##### Module 01: Algebra Foundations

- Numerical Operations
- Algebraic Expressions
- Units and Graphs
- Descriptive Modeling and Accuracy
- Translations
- Algebraic Properties and Equations

##### Module 02: Equations and Inequalities

- One-Variable Equations
- Two-Variable Equations
- Absolute Value Equations
- Inequalities
- Compound Inequalities
- Literal Equations

##### Module 03: Linear Functions

- Relations and Functions
- Function Notation and Graphs
- Linear Functions
- Linear Models
- Writing Linear Functions
- Horizontal and Vertical Lines

##### Module 04: Exponential Functions

- Properties of Exponents
- Operations with Radicals
- Exponential Functions and Models
- Graphing Exponential Functions
- Sequences
- Exploring Linear and Exponential Growth

##### Module 05: Systems of Equations

- Solving Systems of Equations Graphically
- Solving Systems of Equations Algebraically
- Solving Systems of Equations Approximately
- Two-Variable Linear Inequalities
- Systems of Linear Inequalities

#### Segment 2

##### Module 06: Statistics

- Representing Data
- Comparing Data Sets
- Data Sets and Outliers
- Two-Way Frequency Tables
- Scatter Plots and Line of Best Fit
- Correlation and Causation

##### Module 07: Polynomials

- Introduction to Polynomials
- Addition and Subtraction of Polynomials
- Multiplication of Monomials
- Division of Monomials
- Multiplication of Polynomials
- Special Products
- Division of Polynomials
- Function Operations

##### Module 08: Factoring

- Greatest Common Factor
- Factoring By Grouping
- Factoring Trinomials
- Perfect Square Trinomials
- Difference of Perfect Squares
- Polynomial Functions

##### Module 09: Quadratic Functions

- Quadratic Models
- Quadratics and Completing the Square
- Quadratics and the Quadratic Formula
- Applications of Quadratic Functions
- Exploring Non-Linear Systems and Growth

## Algebra I for Credit Recovery

### Description

Algebra I is the foundation—the skills acquired in this course contain the basic knowledge needed for all future high school math courses. The material covered in this course is important, but everyone can do it. Anyone can have a good time solving the hundreds of real-world problems algebra can help answer. Each module in this course is presented in a step-by-step way right on the computer screen. Hands-on labs make the numbers, graphs, and equations more real. The content in this course is tied to real-world applications like sports, travel, business, and health. This course is designed to give students the skills and strategies to solve all kinds of mathematical problems. Students will also acquire the confidence needed to handle everything high school math has in store for them.

**Pre-Requisites:** Student has previously completed Algebra I without achieving a passing grade.

**Credits:** 1.0

**Estimated Completion Time:** 10 weeks per segment

### Major Topics and Concepts

#### Segment 1

##### Module 01: Algebra Foundations

- Numerical Operations
- Algebraic Expressions
- Units and Graphs
- Descriptive Modeling and Accuracy
- Translations
- Algebraic Properties and Equations

##### Module 02: Equations and Inequalities

- One-Variable Equations
- Two-Variable Equations
- Absolute Value Equations
- Inequalities
- Compound Inequalities
- Literal Equations

##### Module 03: Linear Functions

- Relations and Functions
- Function Notation and Graphs
- Linear Functions
- Linear Models
- Writing Linear Functions
- Horizontal and Vertical Lines

##### Module 04: Exponential Functions

- Properties of Exponents
- Operations with Radicals
- Exponential Functions and Models
- Graphing Exponential Functions
- Sequences
- Exploring Linear and Exponential Growth

##### Module 05: Systems of Equations

- Solving Systems of Equations Graphically
- Solving Systems of Equations Algebraically
- Solving Systems of Equations Approximately
- Two-Variable Linear Inequalities
- Systems of Linear Inequalities

**Segment 2**

##### Module 06: Statistics

- Representing Data
- Comparing Data Sets
- Data Sets and Outliers
- Two-Way Frequency Tables
- Scatter Plots and Line of Best Fit
- Correlation and Causation

##### Module 07: Polynomials

- Introduction to Polynomials
- Addition and Subtraction of Polynomials
- Multiplication of Monomials
- Division of Monomials
- Multiplication of Polynomials
- Special Products
- Division of Polynomials
- Function Operations

##### Module 08: Factoring

- Greatest Common Factor
- Factoring By Grouping
- Factoring Trinomials
- Perfect Square Trinomials
- Difference of Perfect Squares
- Polynomial Functions

##### Module 09: Quadratic Functions

- Quadratic Models
- Quadratics and Completing the Square
- Quadratics and the Quadratic Formula
- Applications of Quadratic Functions
- Exploring Non-Linear Systems and Growth

## Algebra IA

### Description

Algebra and the world around you. You may not know it, but algebra is behind the scenes of just about everything. How long will it take to get to school? What does it mean to be average in height? What percentage of your time do you spend studying or watching TV? There are ways to measure and calculate everything from the amount of water in a glass, to the amount of glass needed to build a skyscraper. This course will review some of the fundamental math skills you learned in middle school, and then get you up to speed on the basic concepts of algebra. Each module takes you step-by-step into the world of integers, equations, graphs and data analysis. You’ll work at your own pace until the numbers come out right. This course connects algebra to the real world. It also demystifies algebra, making it easier to understand and master. The goal is to create a foundation in math that will stay with you throughout high school.

**Pre-Requisites:** Student should be in 9th grade or higher. Course is part of a two-year sequence with Algebra IB.

**Credits:** 1.0

**Estimated Completion Time:** 2 segments / 32-36 weeks

### Major Topics and Concepts

#### Segment 1

- Grouping Numbers (real, rational, irrational, integers, whole, counting)
- Properties (commutative, associative, identity, distributive)
- Order of Operations {PEMDAS)
- Absolute Value
- Squares & Square Roots (exponents/radicals)
- Exponents (negative exponents, fractional exponents, 0 power)
- Rounding Decimals (ones, tenths, hundredths, thousandths)
- Estimating (using strategies for estimation)
- Scientific Notation (standard form to scientific notation & vice versa)
- Graphs (identifying line, bar, scatterplot and circle graph properties)
- Data Tables (creating and interpreting)
- Charts & Diagrams (stem & leaf plots/tree diagram interpretation)
- Circle & Line Graphs (interpreting data from graphs)
- Central Tendencies & Correlation Lab
- Ratios/Fractions/Percents
- Integers & Adding
- Positive & Negative Integers (adding)
- Positive & Negative Integers (subtracting)
- Computing with Integers
- Multiplying Integers
- Dividing Integers
- Combining Like Terms (variables and integers)
- Distributing
- Distributing and Combining Like Terms
- One Step Equations
- One & Two Step Equations
- Equations with Variables on Both Sides
- Multi-step Equations
- Special Equations (x = all real numbers & no solution)
- Absolute Value Equations
- English to Algebra (translating word problems)
- English to Algebra (solving equations from word problems)
- Evaluating Expressions
- Formulas (perimeter, area of polygons & circles)
- Measurement Conversions

#### Segment 2

- Distance = Rate x Time (Lab)
- Surface Area & Volume (Lab)
- Integer Review
- Solving Inequalities
- Graphing Inequalities on Number Line
- Ohms Lab (inequalities and scientific notation)
- Percent/Fraction Review
- Functions
- Prime Factorization
- Simple Factoring
- Simplifying Radicals
- Simplifying Exponents
- Standard Form vs. Slope-Intercept Form Equations
- Finding the Slope
- Changing Standard Form to Slope-Intercept Form
- Graphing Linear Equations (x- and y-intercepts method)
- Graphing Linear Equations (slope-intercept method)
- Solving Systems of Equations (addition method)
- Solving Systems of Equations (substitution method)
- Solving Systems of Equations (graphing method)
- Point-Slope Formula
- Horizontal & Vertical Lines

## Algebra IB

### Description

It’s time to finish what you started. In Algebra IA, you learned that algebra is an efficient way to solve some real-world problems. You also acquired the power to do a lot of the important basic work. Now, after a quick review, you’ll be ready to tackle Algebra IB. This course works like the last one. You’ll get step-by-step instructions with all the numbers, equations, and graphs on the screen right in front of you. You’ll also have plenty of time to practice and plenty of opportunities to ask your teacher for help. Along with learning new algebraic strategies and properties, you’ll learn data analysis concepts and techniques. You’ll also see how algebra connects with other high school subjects like geometry, statistics, and biology. Together, Algebra IA and IB will meet your Algebra I requirement. These courses will also give you a powerful tool for understanding how the world works, and how to make it work for you.

**Pre-Requisites:** Algebra IA

**Credits:** 1.0

**Estimated Completion Time:** 2 segments / 32-36 weeks

### Major Topics and Concepts

#### Segment 1

- Exponents and Order of Operations
- Variables, Expressions, and Equations
- Properties of Real Numbers, the Real Number System, and Absolute Value
- Writing and Solving Linear Equations
- Using Formulas and Literal Equations
- Solving Absolute Value Equations
- Independent and Dependent Variables
- Functions, Domain and Range
- Representing Relationships, Function Notation, and Function Rules
- Evaluating and Interpreting a Function
- Formulas
- Patterns of Change and Slopes and Rate of Change
- Horizontal and Vertical Lines
- Slope-Intercept, Standard, and Point-Slope Forms of a Linear Equations
- Scatter Plots from Data
- Absolute Value Functions
- Identifying Special Lines
- Solving Systems of Equations by Graphing
- Solving Systems of Equation using Substitution, Elimination, and Multiplication
- Applications of Linear Systems
- Graphing Linear Inequalities and Graphing Systems of Linear Inequalities
- Adding and Subtracting Polynomials
- Laws of Exponents
- Multiplying a Polynomial with a Monomial
- Multiplying Polynomials and Specials Products
- Polynomial Division
- Scientific Notation

#### Segment 2

- Factoring Polynomials (Greatest Common Factor, Difference of Squares, Perfect Square Trinomials, Factoring by Grouping, and Factoring Trinomials of the Types x2 + bx + c and ax2 + bx + c)
- Solving Quadratic Equations by Factoring
- Quadratic Functions and Quadratic Graphs
- The Quadratic Formula and Using the Discriminant
- Exponential Functions and Exponential Growth and Decay
- Simplifying Rational Expressions
- Adding, Subtracting, Multiplying, and Dividing Rational Expressions
- Solving Equations with Rational Expressions and Applications Using Rational Expressions
- Simplifying Radical Expressions
- Adding, Subtracting, Multiplying, and Dividing Radical Expressions
- Solving Equations with Radical Expressions
- The Pythagorean Theorem
- The Distance and Midpoint Formulas
- Probability
- Measures of Central Tendency (Mean, Median, and Mode)
- Statistical Graphs

## Algebra II

### Description

This course allows students to learn while having fun. Interactive examples help guide students’ journey through customized feedback and praise. Mathematical concepts are applied to everyday occurrences such as earthquakes, stadium seating, and purchasing movie tickets. Students investigate the effects of an equation on its graph through the use of technology. Students have opportunities to work with their peers on specific lessons. Algebra II is an advanced course using hands-on activities, applications, group interactions, and the latest technology.

**Pre-Requisites:** Algebra 1

**Credits:** 1.0

**Estimated Completion Time:** 2 segments / 32-36 weeks

### Major Topics and Concepts

#### Segment I Concepts

##### Module 1

- Algebra 1 Review
- Introduction to Functions
- Graphing Linear Equations and Inequalities
- Writing the Equation of a Line
- Comparing Functions

##### Module 2

- Rational Exponents
- Properties of Rational Exponents
- Solving Radical Equations
- Complex Numbers
- Operations of Complex Numbers

##### Module 3

- Review of Polynomials
- Polynomial Operations
- Greatest Common Factors and Special Products
- Factoring by Grouping
- Sum and Difference of Cubes
- Graphing Quadratics
- Completing the Square
- Solving Quadratic Equations
- Solving Quadratic Equations with Complex Solutions
- Investigating Quadratics

##### Module 4

- Polynomial Long Division
- Polynomial Synthetic Division
- Theorems of Algebra
- Rational Root Theorem
- Solving Polynomial Equations
- Graphing Polynomial Equations
- Polynomial Identities and Proofs

##### Module 5

- Simplifying Rational Expressions
- Multiplying and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Simplifying Complex Fractions
- Discontinuities of Rational Expressions
- Asymptotes of Rational Functions
- Solving Rational Equations
- Applications of Rational Equations

#### Segment II Concepts

##### Module 6

- Solving Systems of Equations Algebraically
- Solving Systems of Non-Linear Equations
- Graphing Systems of Linear Equations
- Graphing Systems of Non-Linear Equations

##### Module 7

- Exponential Functions
- Logarithmic Functions
- Properties of Logarithms
- Solving Exponential Equations with Unequal Bases
- Graphing Exponential Functions
- Graphing Logarithmic Functions
- Exponential and Logarithmic Functions

##### Module 8

- Arithmetic Sequences
- Arithmetic Series
- Geometric Sequences
- Geometric Series
- Sigma Notation
- Infinite, Convergent, and Divergent Series
- Graphing Series

##### Module 9

- Events and Outcomes in a Sample Space
- Independent Probabilities
- Conditional Probability
- Normal Distribution
- Models of Populations
- Using Surveys
- Using Experiments

##### Module 10

- Introduction to the Unit Circle
- Unit Circle and the Coordinate Plane
- Trigonometric Functions with Periodic Phenomena
- Pythagoras, Trigonometry, and Quadrants
- Functions of All Types

## Algebra II for Credit Recovery

### Description

This course allows students to learn while having fun. Interactive examples help guide students’ journeys through customized feedback and praise. Mathematical concepts are applied to everyday occurrences such as earthquakes, stadium seating, and purchasing movie tickets. Students investigate the effects of an equation on its graph through the use of technology. Students have opportunities to work with their peers on specific lessons.

**Pre-Requisites:** Student has previously completed Algebra II without achieving a passing grade.

**Credits:** 1.0

**Estimated Completion Time:** 10 weeks per segment

### Major Topics and Concepts

#### Segment I Concepts

##### Module 1

- Algebra 1 Review
- Introduction to Functions
- Graphing Linear Equations and Inequalities
- Writing the Equation of a Line
- Comparing Functions

##### Module 2

- Rational Exponents
- Properties of Rational Exponents
- Solving Radical Equations
- Complex Numbers
- Operations of Complex Numbers
- Review of Polynomials
- Polynomial Operations

##### Module 3

- Greatest Common Factors and Special Products
- Factoring by Grouping
- Sum and Difference of Cubes
- Graphing Quadratics
- Completing the Square
- Solving Quadratic Equations
- Solving Quadratic Equations with Complex Solutions
- Investigating Quadratics

##### Module 4

- Polynomial Long Division
- Polynomial Synthetic Division
- Theorems of Algebra
- Rational Root Theorem
- Solving Polynomial Equations
- Graphing Polynomial Equations
- Polynomial Identities and Proofs

##### Module 5

- Simplifying Rational Expressions
- Multiplying and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Simplifying Complex Fractions
- Discontinuities of Rational Expressions
- Asymptotes of Rational Functions
- Solving Rational Equations
- Applications of Rational Equations

##### Module 6

- Solving Systems of Equations Algebraically
- Solving Systems of Non-Linear Equations
- Graphing Systems of Linear Equations
- Graphing Systems of Non-Linear Equations

##### Module 7

- Exponential Functions
- Logarithmic Functions
- Properties of Logarithms
- Solving Exponential Equations with Unequal Bases
- Graphing Exponential Functions
- Graphing Logarithmic Functions
- Exponential and Logarithmic Functions

##### Module 8

- Arithmetic Sequences
- Arithmetic Series
- Geometric Sequences
- Geometric Series
- Sigma Notation
- Infinite, Convergent, and Divergent Series
- Graphing Series

##### Module 9

- Events and Outcomes in a Sample Space
- Independent Probabilities
- Conditional Probability
- Normal Distribution
- Models of Populations
- Using Surveys
- Using Experiments

##### Module 10

- Introduction to the Unit Circle
- Unit Circle and the Coordinate Plane
- Trigonometric Functions with Periodic Phenomena
- Pythagoras, Trigonometry, and Quadrants
- Functions of All Types

## Algebra Readiness

### Description

Algebra Readiness is a self-guided mini-course designed to assess your preparedness for Algebra, and to help raise your pre-algebra competencies as needed. Although this is a NON-CREDIT course, taking it will increase the likelihood of your future success in Algebra I.

### Major Topics and Concepts

#### Review topics including the following:

- Prime Factorization
- Least Common Multiples and Greatest Common Factors
- Introduction to Fractions
- Multiplying and Dividing Fractions
- Adding and Subtracting Fractions
- Decimals
- Perfects
- Converting Fractions, Decimals, and Percents
- Exponents
- Square Roots
- Integers
- Order of Operations
- Absolute Value
- One-Step Linear Equations
- Ratios, Rates, and Proportions
- Plotting Coordinates

## Calculus

### Description

Walk in the footsteps of Newton and Leibnitz! An interactive text and graphing software combine with the exciting online course delivery to make Calculus an adventure. This course includes a study of limits, continuity, differentiation, and integration of algebraic, trigonometric and transcendental functions, and the applications of derivatives and integrals.

**Pre-Requisites:** Algebra I, Geometry, Algebra II, Pre-Calculus or Trigonometry/Analytical Geometry.

**Credits:** 1.0

**Estimated Completion Time:** 2 Semesters

### Major Topics and Concepts

#### Module 0: Preparation for Calculus Suggested Pace: 2 weeks

##### Topics

- Understanding the properties of real numbers and the number line
- Using the Cartesian coordinate system to graph functions
- Comparing relative magnitudes of functions – contrasting exponential, logarithmic and polynomial growth

##### Content

- Orientation to course
- Real numbers and the real number line
- Cartesian plane
- Graphs and models
- Linear models and rates of change
- Functions and their graphs

##### Major Assignments and Assessments

- Problem Sets
- Entry Quiz
- Oral Review: Discussion about using Calculator zoom features to examine a graph in a good viewing window and calculator operations to find the zeros of a graph and the point of intersection of two graphs
- Quiz – Functions, Graphs, and Rates of Change

#### Module 1: Limits and Continuity Suggested Pace: 2 weeks

##### Topics

- Intuitive understanding of limit process
- Calculating limits using algebraic methods
- Estimating limits using tables of data
- Estimating limits using graphs
- Understanding asymptotes graphically
- Describing asymptotic behavior in terms of limits involving infinity
- Intuitive understanding of continuity
- Understanding continuity in terms of limits
- Understanding graphs of continuous or non-continuous functions geometrically

##### Content

- Preview of calculus
- Finding limits graphically and numerically
- Evaluating limits analytically
- Continuity and one-sided limits
- Infinite limits

##### Major Assignments and Assessments

- Problems sets
- Quiz – Calculating Limits
- Oral Review: Discussion about using the Calculator to experiment and produce a table of values to examine a function and estimate a limit as x approaches a point and as x grows without bound. Discussion about the limitation of a graphing calculator to show discontinuities in functions and the value of using a calculator to support conclusions found analytically.
- Elluminate Session: Discussion about conditions of continuity.
- Test – Limits and Continuity

#### Module 2: Differentiation Suggested Pace: 5 weeks

**Topics**

- Derivative defined as the limit of the difference quotient
- Graphic, numeric and analytic interpretations of the derivative
- Knowledge of derivatives of power and trigonometric functions
- Basic rules for the derivatives of sums, products, and quotients of functions
- Derivative interpreted as instantaneous rate of change
- Continuity and differentiability
- Slope of curve at a point
- Tangent line to a curve at a point
- Local linear approximation
- Instantaneous rate of change as the limit of average rate of change
- Approximate rate of change from graphs and tables of values
- Chain rule and implicit differentiation
- Equations involving derivatives and problems using their verbal descriptions
- Modeling rates of change and solving related rates problems

##### Content

- The derivative and the tangent line problem
- Basic differentiation rules and rates of change
- The product and quotient rules
- The chain rule
- Implicit differentiation
- Related rates

##### Major Assignments and Assessments

- Problem sets
- Quiz – Definition and computation of derivatives
- Oral Review: Discussion about using a calculator to find the value of a derivative at a point, and how to graph the derived function using a calculator. Discussion about the limitations of the calculator to find the numerical derivative (for example, f ‘(0) for f (x) = |x|).
- Test – Differentiation

#### Module 3: Applications of Differentiation Suggested Pace: 6 weeks

##### Topics

- Corresponding characteristics of graphs of f and f’
- Relationship between the increasing and decreasing behavior of f and the sign of f’
- Corresponding characteristics of graphs of f, f’, and f’’
- Relationship between the concavity of f and the sign of f’
- Points of inflection as places where concavity changes
- Mean Value Theorem and geometric consequences
- Analysis of curves including monotonicity and concavity
- Optimization – absolute and relative extrema
- Equations involving derivatives and problems using their verbal descriptions

##### Content

- Extrema on an interval
- Rolle’s Theorem and the Mean Value Theorem
- Increasing and decreasing functions
- Concavity and the second derivative test
- Limits at infinity
- Curve sketching
- Optimization
- Differentials

##### Major Assignments and Assessments

- Problem sets
- Quiz – Extrema and Concavity
- Oral Review: Discussion about using the calculator to find the critical values of a function by examining the graph of the function and the graph of the function’s derivative.
- Test – Applications of Derivatives
- Semester Exam

#### Module 4: Integration Suggested Pace: 4 weeks

##### Topics

- Definite integral as a limit of Riemann sums
- Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval:
- Basic properties of definite integrals
- Use of the Fundamental Theorem of Calculus to evaluate definite integrals
- Use of the Fundamental Theorem of Calculus to represent a particular antiderivative, and the analytical and graphical analysis of functions so defined
- Find antiderivatives including the use of substitution
- Finding specific antiderivatives using initial conditions, including applications to motion along a line
- Use of Riemann sums and trapezoidal sums to approximate definite integrals of functions represented algebraically, graphically and by tables of values

##### Content

- Antiderivatives and Indefinite Integration
- Area
- Riemann sums and definite integrals
- The Fundamental Theorem of Calculus
- Integration by substitution
- Numerical integration
- Application of definite integrals including area, volume, position/velocity/acceleration and accumulation functions
- The Integral as a function

##### Major Assignments and Assessments

- Problem Sets
- Quiz – Integration and Area
- Quiz – The Fundamental Theorem of Calculus
- Oral Review: Discussion about using the calculator to estimate the value of a definite integral and to support solutions derived analytically.
- Test – Integration

#### Module 5: Transcendental Functions Suggested Pace: 3 weeks

##### Topics

- Use of implicit differentiation in finding the derivative of the inverse of a function
- Geometric interpretation of differential equations via slope fields
- Relationship between slope fields and solution curves for differential equations
- Knowledge of derivatives of exponential, logarithmic, and inverse trigonometric functions
- Basic properties of definite integrals
- Use of the Fundamental Theorem of Calculus to evaluate definite integrals
- Find antiderivatives including the use of substitution
- Application of integrals

##### Content

- The natural logarithmic function and differentiation
- The natural logarithmic function and integration
- Inverse functions including the relationship between the derivative of a function and its inverse at a point
- Exponential functions
- Bases other than e and applications
- Inverse trigonometric functions and differentiation
- Inverse trigonometric functions and integration

##### Major Assignments and Assessments

- Problem Sets
- Quiz – – Natural Logarithmic Functions and Exponential Functions
- Oral Review: Examine the limitations of the graphing calculator in graphing Natural Log functions. Students are required to verbally express the concepts related to the derivatives and integrals of exponential, logarithmic, and inverse trigonometric functions.
- Test: Transcendental Functions

#### Module 6: Differential Equations and Slope Fields: Suggested Pace: 3 weeks

##### Topics

- Differential equations: growth and decay
- Differential equations: separation of variables
- Slope fields

##### Content

- Solving separable differential equations and using them in modeling
- Geometric interpretation of differential equations via slope fields
- Relationship between slope fields and solution curves for differential equations

##### Major Assignments and Assessments

- Problem Sets
- Oral Review: Examine the limitations of the graphing calculator in graphing Natural Log functions. Students are required to verbally express the concepts related to the derivatives and integrals of exponential, logarithmic, and inverse trigonometric functions.
- Test: Differential Equations and Slope Fields

#### Module 7: Applications of Integration Suggested Pace: 3 weeks

##### Topics

- Application of integrals – area and volume

##### Content

- Area of a region between two curves
- Volume

##### Major Assignments and Assessments

- Problem Sets
- Oral Review – Discuss setup on a graphing calculator to find volumes for functions that cannot be integrated by hand. Students are required to be able to explain how the calculator is used to assist with the integration portion of solving a volume problem.
- Students have opportunity to demonstrate their solutions to other members of the class as well as the teacher using the whiteboard, application sharing of MathType and Graphmatica solutions, and the audio feature during this session.
- Test – Applications of Integration

#### Module 8: Integration Techniques and L’Hopital’s Rule Suggested Pace: 2 weeks

##### Topics

- Techniques of Integration
- Techniques for using Differentiation to find Limits

##### Content

- Basic rules of integration
- Indeterminate forms and L’Hopital’s Rule

##### Major Assignments and Assessments

- Problem Sets
- Oral Review – Students must verbally demonstrate the ability to use a calculator generated table to show limiting values of functions and comparative rates of growth of functions.
- Test – Integration Techniques

## Geometry

### Description

Geometry is everywhere, not just in pyramids. Engineers use geometry to build highways and bridges. Artists use geometry to create perspective in their paintings, and mapmakers help travelers find things using the points located on a geometric grid. Throughout this course, students travel a mathematical highway illuminated by spatial relationships, reasoning, connections, and problem-solving.

**Pre-Requisites:** Algebra I

**Credits:** 1.0

**Estimated Completion Time:** 2 segments / 32-36 weeks

### Major Topics and Concepts

#### Segment 1

##### Module 1

- Points, lines, and planes
- Constructions of segments, angles, lines, inscribed triangles, squares, and hexagons
- Introduction to Proofs

##### Module 2

- Translations
- Reflections
- Rotations
- Rigid Motions and Congruence

##### Module 3

- Line and Angle Proofs
- Triangle Proofs
- Parallelogram Proofs

##### Module 4

- Dilations
- Similar Polygons
- Similar Triangles

##### Module 5

- Triangle Congruence and Similarity
- Application of Congruence and Similarity
- Honors Extension Activity

##### Segment 2

##### Module 6

- Using the Coordinates
- Slope
- Coordinate Applications

##### Module 7

- Solving Right Triangles
- Trigonometric Ratios
- Applying Trigonometric Ratios

##### Module 8

- Formulas
- Applications of Volume
- Density
- 3-D Figures

##### Module 9

- Properties of Circles
- Inscribed and Circumscribed Circles
- Applications of Circles

## Geometry for Credit Recovery

### Description

Geometry is everywhere, not just in pyramids. Engineers use geometry to build highways and bridges. Artists use geometry to create perspective in their paintings, and mapmakers help travelers find things using the points located on a geometric grid. Throughout this course, students travel a mathematical highway illuminated by spatial relationships, reasoning, connections, and problem-solving.

### Major Topics and Concepts

##### Segment 1 Topics:

##### MODULE 1:

- Basics of Geometry
- Basic Constructions
- Constructing with Parallel and Perpendicular Lines
- Introduction to Proofs

##### MODULE 2:

- Translations
- Reflections
- Rotations
- Rigid Motion and Congruence

##### MODULE 3:

- Line and Angle Proofs
- Triangle Proofs
- Indirect Proofs

##### MODULE 4:

- Dilations
- Similar Polygons
- Similar Triangles

##### MODULE 5:

- Triangle Congruence and Similarity
- Applications of Congruency and Similarity

##### Segment 2 Topics

##### MODULE 6:

- Using the Coordinates
- Slope
- Coordinate Applications

##### MODULE 7:

- Solving Right Triangles
- Applications of Trigonometric Ratios
- Applying Trigonometric Ratios

##### MODULE 8:

- Formulas
- Applications of Volume
- Density
- 3-D Figures

##### MODULE 9:

- Properties of a Circle
- Inscribed and Circumscribed Circles
- Applications of Circles

## Integrated Mathematics I

### Description

Integrated Mathematics I is the foundation—the skills acquired in this course contain the basic knowledge needed for all future high school math courses. The material covered in this course is important, and everyone can do it. Everyone can have a good time solving the hundreds of real-world problems algebra can help answer. Course activities make the numbers, graphs, and equations more real. The content in this course is tied to real-world applications like sports, travel, business, and health. This course is designed to give students the skills and strategies to solve all kinds of mathematical problems. Students will also acquire the confidence needed to handle everything high school math has in store for them. Integrated Mathematics I emphasizes the importance of algebra and geometry in everyday life through hundreds of real-world examples. Assessments are designed to ensure that your understanding goes beyond rote memorization of steps and procedures. Upon successful course completion, students will have a strong foundation in Integrated Mathematics I and will be prepared for other higher level math courses.

**Pre-Requisites:** None

**Credits:** 1.0

**Estimated Completion Time:** 2 segments / 32-36 weeks

### Major Topics and Concepts

#### Module 01: Algebra Foundations

- Numerical Operations
- Algebraic Expressions
- Units and Graphs
- Descriptive Modeling and Accuracy
- Translations
- Algebraic Properties and Equations

#### Module 02: Equations and Inequalities

- One-Variable Equations
- Two-Variable Equations
- Absolute Value Equations
- Inequalities
- Compound Inequalities
- Literal Equations

#### Module 03: Linear Functions

- Relations and Functions
- Function Notation and Graphs
- Linear Functions
- Linear Models
- Writing Linear Functions
- Horizontal and Vertical Lines

#### Module 04: Exponential Functions

- Properties of Exponents
- Operations with Radicals
- Exponential Functions and Models
- Graphing Exponential Functions
- Sequences
- Exploring Linear and Exponential Growth

#### Module 05: Systems of Equations

- Solving Systems of Equations Graphically
- Solving Systems of Equations Algebraically
- Solving Systems of Equations Approximately
- Two-Variable Linear Inequalities
- Systems of Linear Inequalities

#### Module 06: Statistics

- Representing Data
- Comparing Data Sets
- Data Sets and Outliers
- Two-Way Frequency Tables
- Scatter Plots and Line of Best Fit
- Correlation and Causation

#### Module 07: Polynomials

- Introduction to Polynomials
- Addition and Subtraction of Polynomials
- Multiplication of Monomials
- Division of Monomials
- Multiplication of Polynomials
- Special Products
- Division of Polynomials
- Function Operations

#### Module 08: Factoring

- Greatest Common Factor
- Factoring By Grouping
- Factoring Trinomials
- Perfect Square Trinomials
- Difference of Perfect Squares
- Polynomial Functions

#### Module 09: Quadratic Functions

- Quadratic Models
- Quadratics and Completing the Square
- Quadratics and the Quadratic Formula
- Applications of Quadratic Functions
- Exploring Non-Linear Systems and Growth

#### Module 10: Foundational Geometry

- Basics of Geometry
- Using the Coordinates
- Coordinate Applications
- Formulas
- Applications of Volume

## Integrated Mathematics II

### Description

One day in 2580 B.C.E., a very serious architect stood in a dusty desert with a set of plans. His plans called for creating a structure 480 feet tall, with a square base and triangular sides, using stone blocks weighing two tons each. The Pharaoh wanted the job done right. The better this architect understood geometry, the better his chances were for staying alive. Algebra and geometry are everywhere, not just in pyramids. Engineers use them to build highways and bridges. Artists use them to create perspective in their paintings, and mapmakers help travelers find things using the points located on grids. Throughout this course, students travel a mathematical highway illuminated by spatial relationships, reasoning, connections, and problem-solving.

**Pre-Requisites:** Integrated Mathematics I recommended

**Credits:** 1.0

**Estimated Completion Time:** 2 segments / 32-36 weeks

### Major Topics and Concepts

#### Module 01: Review of Algebra

- Algebra 1 Review
- Introduction to Functions
- Module One Quiz
- Graphing Linear Equations and Inequalities
- Writing the Equation of a Line
- Comparing Functions

#### Module 02: Rational, Complex, and Polynomials

- Rational Exponents
- Properties of Rational Exponents
- Solving Radical Equations
- Complex Numbers
- Operations of Complex Numbers

#### Module 03: Factoring and Quadratics

- Review of Polynomials
- Polynomial Operations
- Greatest Common Factors and Special Products
- Factoring by Grouping
- Sum and Difference of Cubes
- Graphing Quadratics
- Completing the Square
- Solving Quadratic Equations
- Solving Quadratic Equations with Complex Solutions
- Investigating Quadratics

#### Module 04: Systems of Equations and Inequalities

- Solving Systems of Equations Algebraically
- Solving Systems of Nonlinear Equations
- Graphing Systems of Linear Equations
- Graphing Systems of Nonlinear Equations
- Exponential Functions
- Logarithmic Functions

#### Module 05: Statistics

- Events and Outcomes in a Sample Space
- Independent Probability
- Conditional Probability
- Pythagoras, Trigonometry, and Quadrants

#### Module 06: Proofs of Theorems

- Line and Angle Proofs
- Triangle Proofs
- Parallelogram Proofs

#### Module 07: Dilations and Similarity

- Dilations
- Similar Polygons
- Similar Triangles

#### Module 08: Triangle Similarity Proofs

- Triangle Congruence and Similarity
- Using the Coordinates
- Coordinate Applications
- Formulas
- Applications of Volume

#### Module 09: Right Triangles and Trigonometry

- Solving Right Triangles
- Trigonometric Ratios
- Applying Trigonometric Ratios

#### Module 10: Circles

- Properties of a Circle
- Inscribed and Circumscribed Circles
- Applications of Circles

## Integrated Mathematics III

### Description

This course allows students to learn while having fun. Interactive examples help guide students’ journey through customized feedback and praise. Mathematical concepts are applied to everyday occurrences such as earthquakes, stadium seating, and purchasing movie tickets. Students investigate the effects of an equation on its graph through the use of technology. Students have opportunities to work with their peers on specific lessons.

**Pre-Requisites:** Integrated Mathematics I & II

**Credits:** 1.0

**Estimated Completion Time:** 2 segments / 32-36 weeks

### Major Topics and Concepts

#### Module 01: Basics of Geometry

- Points, lines, and planes
- Constructions of segments, angles, lines, inscribed triangles, squares, and hexagons
- Introduction to Proofs

#### Module 02: Transformations and Congruence

- Translations
- Reflections
- Rotations
- Rigid Motions and Congruence

#### Module 03: Coordinate Geometry

- Using the Coordinates
- Slope
- Coordinate Applications

#### Module 04: Volume and Figures

- Formulas
- Applications of Volume
- Density
- 3-D Figures

#### Module 05: Trigonometry

- Introduction to the Unit Circle
- Unit Circle and the Coordinate Plane
- Trigonometric Functions with Periodic Phenomena
- Pythagoras, Trigonometry, and Quadrants

#### Module 06: Dividing and Solving Polynomials

- Polynomial Synthetic Division
- Theorems of Algebra
- Rational Root Theorem
- Solving Polynomial Equations
- Graphing Polynomial Functions
- Polynomial Identities and Proofs

#### Module 07: Rational Expressions

- Simplifying Rational Expressions
- Multiplying and Dividing Rational Expressions
- Adding and Subtracting Rational Expressions
- Simplifying Complex Fractions
- Discontinuities of Rational Expressions
- Asymptotes of Rational Functions
- Solving Rational Equations
- Applications of Rational Equations

#### Module 08: Exponential and Logarithmic Functions

- Exponential Functions
- Logarithmic Functions
- Properties of Logarithms
- Solving Exponential Equations with Unequal Bases
- Graphing Exponential Functions
- Graphing Logarithmic Functions
- Exponential and Logarithmic Functions

#### Module 09: Sequences and Series

- Arithmetic Sequences
- Arithmetic Series
- Geometric Sequences
- Geometric Series
- Sigma Notation
- Infinite, Convergent, and Divergent Series
- Graphing Sequences and Series

#### Module 10: Statistics

- Normal Distribution
- Models of Populations
- Using Surveys
- Using Experiments

## Liberal Arts Math I

### Description

Liberal Arts Mathematics I is a course designed to strengthen mathematical skills for study beyond Algebra I. The course can be used as needed to fit individual district course progression plans and can be taken either before or after Algebra 1. The topics include, but are not limited to, linear equations and inequalities, operations with polynomials, data representation, and analysis, geometric constructions, symmetry, similarity, systems of linear equations and inequalities, functions, quadratic equations, exponential equations, rational equations, radical equations, and graphing equations and functions.

**Pre-Requisites:** Grade 8 Pre-Algebra

**Credits:** 1.0

**Estimated Completion Time:** 2 segments / 32-36 weeks

### Major Topics and Concepts

#### Segment 1

##### Module 1 – Expressions and Equations

- Interpreting Linear Expressions
- Solving Linear Equations
- Solving Linear Inequalities
- Adding and Subtracting Polynomials
- Multiplying Monomials
- Multiplying Polynomials

##### Module 2 – Data and Measurement

- Representing Data
- Comparing Data Sets
- Interpreting Differences in Data Sets
- Using the Normal Distribution
- Converting Units
- Using Measurements

##### Module 3 – Geometry

- Defining Geometric Objects
- Constructing Geometric Objects
- Identifying Symmetry and Transformations
- Proving and Using Similarity
- Solving Problems with Geometry
- Rearranging Formulas
- Using Formulas to Solve Problems

##### Module 4 – Relations and Functions

- Representing Functions
- Using Function Notation
- Identifying Key Features of Linear Functions
- Analyzing Linear Functions
- Analyzing Piecewise Functions

#### Segment 2

##### Module 5 – Linear Functions

- Using Different Forms of Linear Equations
- Writing Linear Equations
- Graphing Linear Equations
- Solving Systems of Linear Equations Graphically
- Solving Systems of Linear Equations Algebraically
- Solving Linear Inequalities

##### Module 6 – Quadratic Functions

- Solving Quadratic Equations
- Interpreting Quadratic Expressions
- Analyzing Quadratic Functions
- Graphing Quadratic Functions

##### Module 7 – Exponential Functions

- Writing Exponential Functions
- Analyzing Exponential Functions
- Graphing Exponential Functions

##### Module 8 – Other Types of Equations

- Solving Radical Equations
- Solving Rational Equations

## Liberal Arts Math II

### Description

Get ready to dive in to Liberal Arts Math II through interactive video-based content. Successful completion of Algebra I and Geometry is required. Additionally, most districts recommend successful completion of Algebra II in their pupil progression plan to fully extend key concepts and prepare you for your mathematical future. The course incorporates the following Standards for Mathematical Practice: Rational Numbers, Seeing Structure in Expressions, Reasoning with Equations and Inequalities, Interpreting Functions, Arithmetic with Polynomials and Rational Expressions, Linear, Quadratic, and Exponential Models, Expressing Geometric Properties with Equations, Conditional Probability and the Rules of Probability, and Making Inferences and Justifying Conclusions.

**Pre-Requisites:** Algebra 1 and Geometry (Algebra 2 is district-dependent, but highly recommended)

**Credits:** 1.0

**Estimated Completion Time:** 2 segments, 32-36 weeks

### Major Topics and Concepts

#### Segment 1

##### Rational Exponents and Complex Numbers

- Rational Exponents
- Properties and Applications of Exponents
- Graphs of Radical Functions
- Complex Numbers

##### Quadratics

- Factoring and Graphing Quadratics
- Completing the Square
- The Quadratic Formula
- Graphing Systems of Equations
- Conics

##### Polynomials and Rational Equations

- The Remainder Theorem
- Solving Polynomials by Factoring
- Sketching Polynomials by Finding Zeros
- Polynomial Identities
- Rational Expressions
- Graphing Rational Functions

##### Exponential and Logarithmic Equations

- Exponential Functions
- Growth and Decay Models
- Transformations
- Solving Equations using Logarithms
- Graphing Exponential and Logarithmic Functions

#### Segment 2

##### Arithmetic and Geometric Sequences and Series

- Arithmetic Sequences
- Geometric Sequences
- Sum of Finite Geometric Series
- Applications of Series

##### Plane Geometry and Trigonometric Graphs

- Perpendicular Lines
- Proofs on the Coordinate Plane
- Proving Theorems Algebraically
- Trigonometric Graphing
- Absolute Value and Piecewise Functions

##### Independent and Conditional Probability

- Introduction to Probability
- Two-way Tables
- Independence vs Dependence
- Conditionality

##### Statistics

- Introduction to Statistics
- Simulations
- Statistical Studies
- Evaluating Reports
- Estimations and Predictions
- Analyzing and Presenting Data

## Pre-Algebra

### Description

Students who love interactive learning will enjoy Pre-Algebra. They experience intrigue and fun when they log in to Pre-Algebra. This hands-on course is full of slideshows, applications, videos, and real-world scenarios. The satisfaction students gain from truly understanding higher level concepts such as functions and systems of equations encourages excitement and joy for learning that they may have never experienced before.

**Pre-Requisites:** Recommended for 8th grade

**Credits:** 1.0

**Estimated Completion Time:** 2 segments/32-36 weeks

### Major Topics and Concepts

#### Module One:

- Real Numbers and ExponentsThe Number Line
- Exponent Rules
- Square and Cube Roots
- Scientific Notation
- Operations with Scientific Notation

#### Module Two:

- Geometric TransformationsTranslations
- Reflections and Rotations
- Congruent Figures
- Similar Figures
- Transversals
- Triangles Angles

#### Module Three:

- Geometric RelationshipsThe Pythagorean Theorem
- Pythagorean Theorem Applications
- The Pythagorean Theorem on the Coordinate Plane
- Volume

#### Module Four:

- FunctionsIntroduction to Functions
- Comparing Functions
- The Linear Function
- Graphs of Functions

#### Module Five:

- Linear RelationshipsGraphs of Proportional Relationships
- Slope-Intercept Form
- Constructing Linear Functions
- Interpreting Linear Models
- Applications of Linear Functions

#### Module Six:

- Patterns of AssociationScatter Plots
- Line of Best Fit
- Interpreting Lines of Best Fit
- Frequency Tables

#### Module Seven:

- Linear EquationsAlgebraic Properties and One-Step Equations
- Two-Step Equations
- Solving Linear Equations
- Equations with Variables on Both Sides
- Equations with Rational Coefficients

#### Module Eight:

- Linear SystemsSystems of Equations
- Solve by Graphing
- Solve by Substitution
- Solve by Elimination
- Applications of Systems

## Pre-Calculus Honors

### Description

Students, as mathematic analysts, will investigate how advanced mathematics concepts can solve problems encountered in operating national parks. The purpose of this course is to study functions and develop the skills necessary for the study of calculus. The Pre-calculus course includes analytical geometry and trigonometry. Pre-calculus is an Honors level course.

**Pre-Requisites:** Algebra I, Algebra II, Geometry

**Credits:** 1.0

**Estimated Completion Time:** 2 segments/32-36 weeks

### Major Topics and Concepts

#### Module 01: Functions and Their Graphs

- Functions and Their Properties
- Graphs of Functions
- Building Functions from Functions
- Inverse Functions
- Graphing Transformations

#### Module 02: Polynomials and Rational Functions

- Quadratic Functions
- Polynomial Functions of Higher Degree
- Real Zeros of Polynomial Functions
- Complex Zeros
- The Fundamental Theorem of Algebra
- Writing about Polynomials
- Rational Functions and Asymptotes
- Graphs of Rational Functions

#### Module 03: Exponential and Logarithmic Functions

- Exponential and Logistic Functions
- Exponential and Logistic Modeling
- Logarithmic Functions and Their Graphs
- Properties of Logarithms
- Equation Solving

#### Module 04: Trigonometric Functions

- Angles and Their Measures
- Trigonometric Functions of Acute Angles
- Trigonometric Functions of Any Angle
- The Unit Circle
- Graphs of Sine and Cosine Functions
- Graphs of Other Trigonometric Functions
- Inverse Trigonometric Functions
- Solving Problems with Trigonometry

#### Module 05: Analytic Trigonometry

- Using Fundamental Identities
- Solving Trigonometric Equations
- Proving Trigonometric Equations
- Sum and Difference Formulas
- Multiple-Angle Formulas

#### Module 06: Additional Topics in Trigonometry

- Law of Sines
- Law of Cosines
- Applying the Law of Sines and Cosines
- Vectors in the Plane
- Dot Products of Vectors
- DeMoivre’s Theorem and nth Roots

#### Module 07: Sequences, Series, and Proof by Induction

- Arithmetic Sequences
- Geometric Sequences
- Series and Summation
- Mathematical Induction

#### Module 08: Topics in Analytical Geometry

- Introduction to Conics: Parabolas
- Ellipses
- Hyperbolas
- Parametric Equations
- Applications of Parametric Equations
- Polar Coordinates
- Graphs of Polar Equations

#### Module 09: Line and Introduction to Calculus

- Introduction to Limits and the Derivative
- Techniques for Evaluating Limits
- Evaluating One-Sided Limits
- Techniques for Evaluating Limits
- Continuity at a Point

## Probability and Statistics Honors

### Description

Probability and Statistics will introduce students to exploring data, sampling, and experimentation by planning and conducting studies, anticipating patterns using probability and simulation, and employing statistical inference to analyze data and draw conclusions.

**Pre-Requisites:** Algebra II

**Credits:** 1.0

**Estimated Completion Time:** 2 segments / 32-36 weeks

### Major Topics and Concepts

#### Segment I Concepts

##### Module 1

- Introduction to Statistics
- Measures of Central Tendency
- Measures of Variation
- Displaying Data

##### Module 2

- Sampling and Surveys
- Experiments
- Correlation Versus Causation

##### Module 3

- Basic Concepts of Probability
- Condition Probability and Two-Way Tables
- The Multiplication and Addition Rule
- Simulations

#### Segment II Concepts

##### Module 4

- Random Variables
- Binomial Probability Distribution
- Geometric Probability Distribution
- Introduction to Normal Probability Distribution

##### Module 5

- Sampling Distributions and Proportions
- Sample Means
- Confidence Intervals for Proportions
- Confidence Intervals for Means

##### Module 6

- Hypothesis Testing- One Proportion
- Hypothesis Testing- One-Sample Mean
- Comparing Two Means

· Scatterplots and Correlation

· Least-Squares Regression