This course is designed to build a solid foundation in essential mathematical concepts. It’s perfect for students who need a refresher, are preparing for higher-level math, or want to build confidence for everyday life and professional tasks.
Course Goal
To master the fundamental principles of arithmetic, algebra, and geometry, and apply them to solve real-world problems with confidence.
Course Content
Chapter 1: Foundational Arithmetic
Chapter 2: Algebra I
Chapter 3: Functions and Graphing
Chapter 4: Geometry and Measurement
Module 1.1: Numbers and Operations
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18 Topics
1 Quiz
Introduction to Number Sense & Operations
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Integers
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Fractions
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Decimals
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Percentages
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Order of Operations (PEMDAS/BODMAS)
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Exponents
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Square Roots
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Ratios and Rates
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Proportions
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1. Introduction to Mathematics
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2. Addition and Subtraction of Small Numbers
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3. Multiplication and Division of Small Numbers
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4. Large Whole Numbers: Place Values and Estimating
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5. Negative Numbers
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6. Understanding Exponents and Their Operations
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7. Order of Arithmetic Operations: PEMDAS
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8. Square Roots, Cube Roots, and Other Roots
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Ch 1: Foundational Arithmetic – Module 1.1: Numbers & Operations
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Module 1.2: Fractions, Decimals, Percentages
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9 Topics
1 Quiz
Variables
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Expressions
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Linear Equations
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Simple Inequalities
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Patterns
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1. Understanding Fractions, Improper Fractions, and Mixed Numbers
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2. Decimals: Notation and Operations
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3. Working with Percentages
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4. Converting Between Fractions, Decimals, and Percentages
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Ch 1: Foundational Arithmetic – Module 1.2: Fractions, Decimals, Percentages
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Module 1.3: Advanced Operations and Properties
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9 Topics
1 Quiz
1. Addition and Subtraction of Large Numbers
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2. Multiplication of Large Numbers
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3. Division of Large Numbers: Long Division
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4. The Distributive Property for Arithmetic
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5. Divisibility, Prime Numbers, and Prime Factorization
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6. Least Common Multiple (LCM)
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7. Greatest Common Factor (GCF)
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8. Addition and Subtraction of Fractions
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9. Multiplication and Division of Fractions
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Ch 1: Foundational Arithmetic – Module 1.3: Advanced Operations & Properties
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Module 1.4: Data Analysis
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1 Topic
1 Quiz
1. Analyzing Sets of Data: Range, Mean, Median, and Mode
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Ch 1: Foundational Arithmetic – Module 1.4: Data Analysis
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Module 2.1: Introduction to Algebra
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6 Topics
1 Quiz
1. Introduction to Algebra: Using Variables
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2. Adding and Subtracting Polynomials
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3. Multiplying Binomials by the FOIL Method
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4. Solving Quadratics by Factoring
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5. Solving Quadratics by Completing the Square
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6. Solving Quadratics by Using the Quadratic Formula
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Ch 2: Algebra I – Module 2.1: Introduction to Algebra
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Module 2.2: Polynomials and Quadratics
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6 Topics
1 Quiz
1. Introduction to Polynomials
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2. Adding and Subtracting Polynomials
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3. Multiplying Binomials by the FOIL Method
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4. Solving Quadratics by Factoring
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5. Solving Quadratics by Completing the Square
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6. Solving Quadratics by Using the Quadratic Formula
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Ch 2: Algebra I – Module 2.2: Polynomials & Quadratics
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Module 2.3: Rational Expressions & Advanced Polynomials
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2 Topics
1 Quiz
1. Manipulating Rational Expressions: Simplification and Operations
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2. Solving Higher-Degree Polynomials by Synthetic Division and the Rational Roots Test
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Ch 2: Algebra I – Module 2.3: Rational Expressions & Advanced Polynomials
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Module 3.1: Fundamentals of Functions
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7 Topics
1 Quiz
1. Back to Algebra: What are Functions?
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2. Manipulating Functions Algebraically and Evaluating Composite Functions
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3. Manipulating Functions Algebraically and Evaluating Composite Functions
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4. Graphing Algebraic Functions: Domain and Range, Maxima and Minima
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5. Transforming Algebraic Functions: Shifting, Stretching, and Reflecting
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6. Continuous, Discontinuous, and Piecewise Functions
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7. Inverse Functions
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Ch 3: Functions & Graphing – Module 3.1: Fundamentals of Functions
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Module 3.2: Graphing Lines & Systems
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6 Topics
1 Quiz
1. Graphing in Algebra: Ordered Pairs and the Coordinate Plane
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2. Graphing Lines in Algebra: Understanding Slopes and Y-Intercepts
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3. Graphing Lines in Slope-Intercept Form (y = mx + b)
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4. Graphing Lines in Standard Form (ax + by = c)
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5. Parallel and Perpendicular Lines
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6. Solving Systems of Two Equations and Two Unknowns: Graphing, Substitution, and Elimination
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Ch 3: Functions & Graphing – Module 3.2: Graphing Lines & Systems
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Module 3.3: Special Functions & Conics
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6 Topics
1 Quiz
1. Graphing Higher-Degree Polynomials: The Leading Coefficient Test and Finding Zeros
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2. Graphing Rational Functions and Their Asymptotes
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3. Graphing Conic Sections Part 1: Circles
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4. Graphing Conic Sections Part 2: Ellipses
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5. Graphing Conic Sections Part 3: Parabolas in Standard Form
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6. Graphing Conic Sections Part 4: Hyperbolas
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Ch 3: Functions & Graphing – Module 3.3: Special Functions & Conics
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Module 4.1: Fundamentals of Euclidean Geometry
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6 Topics
1 Quiz
1. Introduction to Geometry: Ancient Greece and the Pythagoreans
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2. Basic Euclidean Geometry: Points, Lines, and Planes
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3. Types of Angles and Angle Relationships
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4. Types of Triangles in Euclidean Geometry
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5. The Pythagorean Theorem
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6. Proving the Pythagorean Theorem
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Ch 4: Geometry & Measurement – Module 4.1: Fundamentals of Euclidean Geometry
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Module 4.2: Triangles & Polygons
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4 Topics
1 Quiz
1. Proving Triangle Congruence and Similarity
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2. Special Lines in Triangles: Bisectors, Medians, and Altitudes
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3. The Triangle Midsegment Theorem
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4. Types of Quadrilaterals and Other Polygons
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Ch 4: Geometry & Measurement – Module 4.2: Triangles & Polygons
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Module 4.3: Area, Volume & 3D Shapes
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5 Topics
1 Quiz
1. Calculating the Perimeter of Polygons
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2. Circles: Radius, Diameter, Chords, Circumference, and Sectors
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3. Calculating the Area of Shapes
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4. Three-Dimensional Shapes Part 1: Types, Calculating Surface Area
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5. Three-Dimensional Shapes Part 2: Calculating Volume
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Ch 4: Geometry & Measurement – Module 4.3: Area, Volume & 3D Shapes
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