## Pre-Algebra

Total Units: 16

Two new number concepts are introduced: the integers and the rational numbers. Students learn the difference between a number and a variable, and how to solve simple equations with one variable. Students will gain further practice with decimals and percent, and solve problems involving simple and compound interest. Simple polynomials are introduced, which students will learn to add, subtract, and use the distributive property to multiply.

### Whole Numbers

- 1.1 Introduction to Whole Numbers
- 1.2 Place Value of Whole Numbers
- 1.3 Rounding Whole Numbers
- 1.4 Roman Numerals
- 1.5 Patterns

### Integers

- 2.1 Introduction to Integers
- 2.2 Integers & Absolute Value
- 2.3 Graphing Integers on a Number Line
- 2.4 Comparing & Ordering Integers
- 2.5 Adding Integers
- 2.6 Subtracting Integers
- 2.7 Multiplying Integers
- 2.8 Dividing Integers

### Variables and Expressions

- 3.1 Introduction to Variables & Expressions
- 3.2 Writing Expressions
- 3.3 Evaluating Expressions
- 3.4 Order of Operations
- 3.5 Equivalent Expressions
- 3.6 Evaluating Expressions using Substitution
- 3.7 Properties of Real Numbers
- 3.8 Like Terms
- 3.9 Distributive Property

### Rational Numbers

- 4.1 Introduction to Rational Numbers
- 4.2 Divisibility
- 4.3 Factors & Multiples
- 4.4 Prime Numbers
- 4.5 Prime Factors
- 4.6 Exponents
- 4.7 Greatest Common Factor
- 4.8 Least Common Multiple

### Fractions

- 5.1 Introduction to Fractions
- 5.2 Equivalent Fractions & Simplifying
- 5.3 Mixed Numbers & Improper Fractions
- 5.4 Multiplying Fractions
- 5.5 Reciprocals
- 5.6 Fractions - Relating Multiplication & Division
- 5.7 Fractions - Cancelling to Simplify Multiplication
- 5.8 Adding & Subtracting with Like Denominators
- 5.9 Comparing Fractions
- 5.10 Adding & Subtracting with Unlike Denominators

### Equations

- 6.1 Introduction to Equations
- 6.2 Problem Solving with Equations
- 6.3 Solving Equations Using Addition & Subtraction
- 6.4 Solving Equations Using Multiplication & Division
- 6.5 Solving Equations Using Reciprocals
- 6.6 Solving Multi-Step Equations with Variables on Both Sides
- 6.7 Solving Multi-Step Equations with Fractions
- 6.8 Writing Equations

### Inequalities

- 7.1 Introduction to Inequalities
- 7.2 Graphing Inequalities on a Number Line
- 7.3 Adding & Subtracting Inequalities
- 7.4 Multiplying & Dividing Inequalities
- 7.5 Conjunctions & Disjunctions
- 7.6 Solving Inequalities

### The Coordinate Plane

- 8.1 Introduction to the Coordinate Plane
- 8.2 Graphing a Coordinate Point
- 8.3 Using a Table of Values
- 8.4 First Differences
- 8.5 X and Y Intercepts & Standard Form
- 8.6 Classifying Slope
- 8.7 Calculating Slope
- 8.8 Slope-Intercept Form
- 8.9 Graphing Inequalities
- 8.10 Changing Forms: Standard to Slope

### Decimals

- 9.1 Introduction to Decimals
- 9.2 Decimals and Estimation
- 9.3 Decimals to Fractions
- 9.4 Fractions to Decimals
- 9.5 Scientific Notation
- 9.6 Repeating & Terminating Decimals

### Percent

- 10.1 Introduction to Percent
- 10.2 Decimals and Percent
- 10.3 Finding Percent of a Number
- 10.4 Simple Interest
- 10.5 Compound Interest
- 10.6 Discount Solving Percent Equations
- 10.7 Percent of Change

### Polynomials

- 11.1 Introduction to Polynomials
- 11.2 Adding Polynomials
- 11.3 Subtracting Polynomials
- 11.4 Multiplying Polynomials
- 11.5 Common Factoring

### Triangles

- 12.1 Introduction to Triangles
- 12.2 Triangle Classifications
- 12.3 Square Roots
- 12.4 Pythagorean Theorem

### 2D Geometry

- 13.1 Introduction to 2D Geometry
- 13.2 Parallel & Perpendicular Lines
- 13.3 Classifying Polygons
- 13.4 Interior Angles of Polygons
- 13.5 Exterior Angles of Polygons
- 13.6 Perimeter
- 13.7 Area
- 13.8 Circumference of a circle
- 13.9 Area of a Circle
- 13.10 Area of Irregular Shapes
- 13.11 Perimeter of Irregular Shapes

### 3D Geometry

- 14.1 Introduction to 3D Geometry
- 14.2 Surface Area of a Rectangular Prism
- 14.3 Surface Area of Pyramids
- 14.4 Surface Area of Cylinders
- 14.5 Volume of Rectangular Prisms
- 14.6 Volume of Cylinders & Triangular Prisms
- 14.7 Volume of Pyramids & Cones
- 14.8 Volume and Surface Area of a Sphere

### Analyzing Data

- 15.1 Introduction to Analyzing Data
- 15.2 Line Graphs and Pictographs
- 15.3 Bar Graphs
- 15.4 Stem-and-Leaf Plots
- 15.5 Measures of Central Tendency Part I
- 15.6 Measures of Central Tendency Part II
- 15.7 Box-and-Whisker Plots
- 15.8 Circle Graphs

### Probability and Statistics

- 16.1 Introduction to Probability & Statistics
- 16.2 Ratio and Proportion
- 16.3 Unit Rate and Proportion
- 16.4 Simple Probability
- 16.5 Independent Events
- 16.6 Dependent Events
- 16.7 Fundamental Counting Principle

## Algebra I

Total Units: 12

It expands on material introduced in Pre-Algebra while introducing functions, systems of linear equations and trigonometry. The primary goal of Algebra I is for students to develop beyond understanding rudimentary mathematical operations to comprehend more abstract algebraic ideas.

### Equations

- 1.1 Introduction to Equations
- 1.2 Solving Equations - Adding & Subtracting
- 1.3 Solving Equations - Multiplying & Dividing
- 1.4 Two Step Equations
- 1.5 Multistep & Distributive Part I
- 1.6 Multistep & Distributive Part II
- 1.7 Equations with Multiple Variables
- 1.8 Solving Percent Equations
- 1.9 More Applications

### Linear Functions

- 2.1 Introduction to Linear Functions
- 2.2 Graphing Coordinate Point
- 2.3 Relations and Linear Functions Pt I
- 2.4 Relations and Linear Functions Pt II
- 2.5 Direct Variation
- 2.6 Slope & Rate of Change
- 2.7 Calculating Slope
- 2.8 Slope-Intercept Form
- 2.9 X and Y Intercepts & Standard Form
- 2.10 Calculate Slope using dydx and Intercepts
- 2.11 Equation of a Line
- 2.12 Special Lines
- 2.13 Cost vs Time Functions
- 2.14 Distance vs Time

### Inequalities & Absolute Value Functions

- 3.1 Introduction to Inequalities & Absolute Value Functions
- 3.2 Writing Solution Sets
- 3.3 Graphing 1D
- 3.4 Solving Multistep
- 3.5 Compound Inequalities
- 3.6 Solving Compound Inequalities
- 3.7 Inequalities in 2D
- 3.8 Absolute Value
- 3.9 Graphing Absolute Value Functions

### Exponential Functions

- 4.1 Introduction to Exponents
- 4.2 The Product Property
- 4.3 The Quotient Property
- 4.4 Zero and Negative Exponents
- 4.5 Fractional Exponents
- 4.6 Power of a Power Property
- 4.7 Power of a Product Property
- 4.8 Power of a Fraction
- 4.9 Order of Operations with Exponents – Numeric
- 4.10 Simplifying Algebraic Expressions with Exponents
- 4.11 Scientific Notation Part I
- 4.12 Scientific Notation Part II
- 4.13 Scientific Notation Part III
- 4.14 Exponential Decay
- 4.15 Exponential Growth

### Polynomials

- 5.1 Introduction to Inequalities
- 5.2 Adding Polynomials
- 5.3 Subtracting Polynomials
- 5.4 Adding & Subtracting Polynomials With More Than One Variable
- 5.5 Multiplying Polynomials
- 5.6 Common Factoring
- 5.7 Factoring Polynomials Using The GCF
- 5.8 Factoring Perfect Square Trinomials
- 5.9 Factoring Difference Of Squares
- 5.10 Factoring Trinomials
- 5.11 Solving Equations Using Factoring
- 5.12 Graphing The Cubic Function

### Quadratic Functions

- 6.1 Introduction To Quadratic Functions
- 6.2 Graphing Quadratic Functions
- 6.3 Graphing Quadratic Function - Vertex Form
- 6.4 Solving Equations with Square Roots
- 6.5 Solving by Completing the Square
- 6.6 Converting Quadratic Functions Into Vertex Form Using Completing the Square
- 6.7 The Quadratic Formula
- 6.8 Graphing Quadratic Inequalities
- 6.9 Applications Of Quadratics

### Rational Functions

- 7.1 Introduction to Rational Functions
- 7.2 Simplifying Rational Expressions
- 7.3 Adding & Subtracting Rational Expressions
- 7.4 Multiplying Rational Expressions
- 7.5 Dividing Rational Expressions
- 7.6 Graph of a Rational Function

### Radical Functions

- 8.1 Introduction to Radical Functions
- 8.2 Prime Factors
- 8.3 Square Roots
- 8.4 Simplifying Radicals – Numerical
- 8.5 Simplifying Radicals – Algebraic
- 8.6 Adding & Subtracting Radicals
- 8.7 Multiplying Radicals
- 8.8 Dividing Radicals
- 8.9 Solving Radical Equations
- 8.10 Graphing Radical Functions

### Transformations

- 9.1 Introduction to Transformations
- 9.2 Domain of Parent Functions
- 9.3 Range of Parent Functions
- 9.4 Translations
- 9.5 Reflections
- 9.6 Vertical Stretches & Compressions
- 9.7 Horizontal Stretches & Compressions
- 9.8 Summary on Transformations
- 9.9 Multiple Transformations

### Systems of Equations & Inequalities

- 10.1 Introduction to Systems of Linear Equations & Inequalities
- 10.2 Graphing Systems of Linear Equations
- 10.3 Graphing Inequalities
- 10.4 Graphing Systems of Inequalities
- 10.5 Evaluating Expressions using Substitution
- 10.6 Solving a System of Equations by Substitution
- 10.7 Solving Systems of Equations by Elimination
- 10.8 Identifying Types of Systems using Equations
- 10.9 Writing an Equation
- 10.10 Applications of Systems of Equations & Inequations

### Trigonometry

- 11.1 Introduction to Trigonometry
- 11.2 Sine Ratio
- 11.3 Cosine Ration
- 11.4 Tangent Ratio

### Probability

- 12.1 Introduction to Probability
- 12.2 Simple Probability
- 12.3 Fundamental Counting Principle
- 12.4 Independent Events
- 12.5 Dependent Events
- 12.6 Compound Probability
- 12.7 Experimental & Theoretical Probability
- 12.8 Set Theory & Venn Diagrams
- 12.9 Set Theory - Intersection and Union

## Algebra II

Total Units: 15

Emphasis on functions returns as the functional families learned in Algebra I are studied in more detail. Algebra II expands on quadratic, polynomial, exponential, radical and rational functions and introduces logarithmic functions. Students learn how to use and operate on complex numbers so that complex solutions of quadratic and polynomial functions can be considered. This course focuses on more abstract and theoretical concepts, allowing students to improve their critical thought processes. The primary goal of this course is for students to own a strong understanding of all types of functions and prepare them for Pre-Calculus.

### Review of Equations & Exponents

- 1.1 Introduction to Equations
- 1.2 Multistep & Distributive Part I
- 1.3 Multistep & Distributive Part II
- 1.4 Equations with Multiple Variables
- 1.5 Slope & Rate of Change
- 1.6 Calculating Slope Using a Graph
- 1.7 Calculate Slope Using dydx & Intercepts
- 1.8 Slope-Intercept Form
- 1.9 Equation of a Line
- 1.10 Introduction to Exponents
- 1.11 The Product Property
- 1.12 The Quotient Property
- 1.13 Zero and Negative Exponents
- 1.14 Fractional Exponents
- 1.15 Power of a Power Property
- 1.16 Power of a Product Property
- 1.17 Power of a Fraction
- 1.18 Simplifying Algebraic Expressions with Exponents

### Systems of Linear Equations & Inequalities

- 2.1 Intro to Systems of Linear Equations & Inequalities
- 2.2 Solving a System of Equations by Substitution
- 2.3 Solving a System of Equations by Elimination
- 2.4 Graphing Systems of Linear Equations
- 2.5 Graphing Systems of Inequalities
- 2.6 Linear Programming

### Polynomial Functions

- 3.1 Introduction to Polynomials
- 3.2 Adding & Subtracting Polynomials
- 3.3 Multiplying Polynomials
- 3.4 Dividing Polynomials Using Long Division
- 3.5 Dividing Polynomials Using Synthetic Division
- 3.6 Remainder Theorem
- 3.7 Factor Theorem
- 3.8 Factoring Polynomials Using the GCF
- 3.9 Factoring Using Difference of Squares
- 3.10 Factoring Perfect Square Trinomials
- 3.11 Factoring Trinomials
- 3.12 Factoring Using Sums or Difference of Cubes
- 3.13 Solving Equations Using Factoring

### Functions

- 4.1 Introduction to Functions
- 4.2 Function Notation & Evaluation
- 4.3 Domain of a Function & Interval Notation
- 4.4 Range of a Function & Interval Notation
- 4.5 Adding & Subtracting Functions
- 4.6 Multiplying & Dividing Functions
- 4.7 Composition of Functions
- 4.8 Inverse Functions
- 4.9 Composition and Inverse
- 4.10 Piecewise Functions
- 4.11 Step Functions

### Complex Numbers

- 5.1 Introduction to Imaginary & Complex Numbers
- 5.2 Adding & Subtracting Complex Numbers
- 5.3 Multiplying Complex Numbers
- 5.4 Complex Conjugates
- 5.5 Dividing Complex Numbers
- 5.6 Absolute Value & Complex Numbers

### Polynomial Functions Solving & Graphing

- 6.1 Finding a Polynomial Given the Roots
- 6.2 Location Principle & Multiplicity of Zeros
- 6.3 Rational Root Theorem
- 6.4 The Quadratic Formula
- 6.5 The Complex Conjugate Root Theorem
- 6.6 Fundamental Theorem of Algebra & Descartes Rule of Signs
- 6.7 Graphing Polynomials

### Quadratic Functions

- 7.1 Introduction to Quadratic Functions
- 7.2 Graphing Quadratic Functions in Vertex Form
- 7.3 Solving Quadratics with Square Roots
- 7.4 Solving Quadratics with Completing the Square
- 7.5 Converting Quadratic Function to Vertex Form using Completing the Square
- 7.6 Graphing Quadratic Inequalities
- 7.7 Applications of Quadratics

### Exponential & Logarithmic Functions

- 8.1 Intro to Exponential & Logarithmic Properties
- 8.2 Exponential Growth
- 8.3 Exponential Decay
- 8.4 Logarithmic Functions
- 8.5 Evaluating Logarithmic Functions
- 8.6 Product Property of Logarithms
- 8.7 Quotient Property of Logarithms
- 8.8 Power Property of Logarithms
- 8.9 Exponential-Logarithmic Inverse Properties
- 8.10 Application of Logarithms
- 8.11 The Natural Exponential Function
- 8.12 The Natural Logarithm
- 8.13 Solving Logarithmic Equations

### Exponential & Logarithmic Functions

- 9.1 Introduction to Rational Functions
- 9.2 Direct Variation
- 9.3 Inverse Variation
- 9.4 Joint & Combined Variation
- 9.5 Simplifying Rational Expressions
- 9.6 Adding & Subtracting Rational Expressions
- 9.7 Multiplying Rational Expressions
- 9.8 Dividing Rational Expressions
- 9.9 Complex Fractions
- 9.10 Solving Rational Equations
- 9.11 Graph of a Rational Function
- 9.12 Graph of a Rational Function Continued

### Radical Functions

- 10.1 Introduction to Radical Functions
- 10.2 Simplifying Radicals - Numerical
- 10.3 Simplifying Radicals - Algebraic
- 10.4 Multiplying Radicals
- 10.5 Dividing Radicals
- 10.6 Adding & Subtracting Radicals
- 10.7 Solving Radical Equations
- 10.8 Graphing Radical Functions

### Conic Sections

- 11.1 Introduction to Conic Sections
- 11.2 Distance & Midpoint Formulas
- 11.3 Parabolas Part I
- 11.4 Parabolas Part II
- 11.5 Circles Part I
- 11.6 Circles Part II
- 11.7 Ellipses Part I
- 11.8 Ellipses Part II
- 11.9 Hyperbolas Part I
- 11.10 Hyperbolas Part II
- 11.11 Solving Non Linear Systems

### Statistics & Probability

- 12.1 Introduction to Statistics
- 12.2 Independent & Dependent Events
- 12.3 Measures of Central Tendency
- 12.4 Hisotgrams & Circle Graphs
- 12.5 Stem & Leaf Plots
- 12.6 Box & Whisker Plots
- 12.7 Scatter Plots
- 12.8 Permutations
- 12.9 Combinations
- 12.10 Measures of Dispersion

### Series & Patterns

- 13.1 Introduction to Series & Patterns
- 13.2 Sequences & Series
- 13.3 Arithmetic Sequences
- 13.4 Arithmetic Series
- 13.5 Geometric Sequences
- 13.6 Finite Geometric Series
- 13.7 Infinite Geometric Series
- 13.8 Pascal's Triangle
- 13.9 Binomial Theorem

### Trigonometry

- 14.1 Introduction to Trigonometric Functions
- 14.2 Finding an Unknown Angle
- 14.3 Reciprocal Ratios
- 14.4 Sine Law
- 14.5 Cosine Law
- 14.6 Angles in Standard Position
- 14.7 Special Triangles & Exact Values

### Matrices

- 15.1 Introduction to Matrices
- 15.2 Basic Matrix Operations
- 15.3 Matrix Multiplication
- 15.4 Determinant of a Matrix
- 15.5 Inverse of a Matrix