# Algebra I

Algebra I is a fully accredited, Common Core-aligned course that builds on the foundations developed in Prealgebra. Upon completing the course, students will create a solid base for success in subsequent courses such as Geometry, Algebra II, and beyond.

## Content

In this course, students will significantly broaden their understanding of equations and inequalities. This includes delving into one-variable equations and inequalities with unknown coefficients, two-variable linear equations and inequalities, and systems of equations and inequalities. Students will acquire the skills necessary to apply this knowledge in modeling a variety of real-world situations.

Students will deepen their comprehension of units of measurement. They will learn to approach units from an algebraic perspective and master the art of using unit manipulations to solve problems.

This course sees the introduction of functions into the student's mathematical journey. Here, they will explore fundamental concepts such as domain, range, roots, extrema, end behavior, and inverse functions. Armed with this knowledge, students will delve into the study of specific function types - including exponential, absolute value, and piecewise functions - establishing a solid foundation for analyzing more advanced functions in subsequent courses.

Students will learn to perform arithmetic operations with rational and radical expressions and solve simple rational and radical equations.

For the first time, students will encounter polynomials. They will become proficient in terminology associated with one-variable polynomials and master fundamental polynomial operations such as addition, subtraction, multiplication, and factoring.

Students will master solving, graphing, and interpreting quadratic equations and functions. They will become adept at using various techniques for analyzing quadratics, including factoring, completing the square, and applying the quadratic formula. Real-world applications, including vertical motion and profit function analysis, are tackled within these units.

In the final unit, students will explore the world of sequences. They will dive deeply into arithmetic and geometric sequences and learn to identify, model, and apply sequences in various situations.

Upon successful completion of this course, students will have mastered the following:
• Master linear equations, including cases with one or multiple unknown coefficients, and apply their skills to real-world problems involving consecutive integers, speed, distance, time, work, and mixtures.
• Become proficient in solving linear inequalities. They will apply interval notation to describe solutions, find unions and intersections of intervals, solve systems of inequalities, graph solutions to inequalities, and model situations using inequalities.
• Develop proficiency in two-variable linear equations, including point-slope form, standard form, and master procedures for determining properties of straight lines. They will also describe how parallel and perpendicular lines in the coordinate plane are related.
• Gain mastery in solving two-variable systems of linear equations using substitution and elimination. This includes cases with fractional and decimal coefficients, systems with no solutions, and many solutions. Students will relate solutions to the intersection of two lines and apply their understanding to modeling situations. Furthermore, students will begin to develop an understanding of systems of nonlinear equations.
• Solve simple square root, cube root, and higher-root equations and identify cases with no real solutions.
• Gain a deeper understanding of units and their applications, including unit conversions using algebraic techniques and working with direct and inverse variation.
• Explore radical and rational expressions, and develop the ability to manipulate and solve equations involving these concepts.
• Begin their journey into functions. Students will also be introduced to key concepts such as various representations of functions, the vertical line test, domain, range, global extrema, end-behavior, increasing and decreasing functions, function arithmetic (including function composition), and inverse functions.
• Master the rules of absolute value, solving simple absolute value equations and inequalities, and plotting and analyzing absolute value functions.
• Develop a strong foundation in exponential equations and functions, including manipulating expressions, solving equations, graphing exponential functions, and exponential growth and decay applications.
• Become proficient in working with polynomials, including simplifying, adding, subtracting, multiplying, and factoring polynomials.
• Solve quadratic equations using various methods, including applying the zero product rule, completing the square and the quadratic formula.
• Graph and analyze quadratic functions, calculate the axis of symmetry using various methods and find intersections of lines and quadratic functions.
• Model real-world situations using quadratic functions, including vertical motion, revenue, cost, and profit functions.
• Understand formal sequence notation, recursive, arithmetic, geometric sequences, and applications.
1.
Equations & Inequalities
24 topics
1.1. Linear Equations
 1.1.1. Solving Linear Equations With Unknown Coefficients 1.1.2. Solving Linear Equations With Unknown Coefficients by Factoring 1.1.3. Solving Linear Inequalities With Unknown Parameters 1.1.4. Solving Many-Variable Equations
1.2. Modeling With Linear Equations
 1.2.1. Interpreting Linear Expressions 1.2.2. Modeling With Linear Equations 1.2.3. Consecutive Integer Problems 1.2.4. Speed, Distance, Time Problems 1.2.5. Further Speed, Distance, Time Problems 1.2.6. Modeling Work Problems 1.2.7. Modeling Mixture Problems
1.3. Linear Inequalities
 1.3.1. Solving Compound Inequalities 1.3.2. Interval Notation 1.3.3. Unbounded Intervals 1.3.4. Unions of Intervals 1.3.5. Intersections of Intervals 1.3.6. Compound OR Inequalities 1.3.7. Compound AND Inequalities 1.3.8. Introduction to Modeling With Inequalities 1.3.9. Modeling With One-Step Inequalities 1.3.10. Modeling With Two-Step Inequalities
1.4. Nonlinear Equations
 1.4.1. Solving Equations Using the Square Root Method 1.4.2. Solving Equations With Odd Exponents Using the Nth Root Method 1.4.3. Solving Equations With Even Exponents Using the Nth Root Method
2.
Two-Variable Equations & Inequalities
30 topics
2.5. Graphs of Linear Equations
 2.5.1. Equations of Lines in Slope-Intercept Form 2.5.2. Finding Properties of Lines Given in Slope-Intercept Form 2.5.3. Equations of Lines in Point-Slope Form 2.5.4. Equations of Lines in Standard Form 2.5.5. Determining Properties of Lines Given in Standard Form 2.5.6. Parallel Lines in the Coordinate Plane
2.6. Modeling With Two-Variable Linear Equations
 2.6.1. Modeling With Linear Equations in Two Variables 2.6.2. Further Modeling With Linear Equations in Two Variables 2.6.3. Analyzing and Interpreting Graphs of Linear Equations 2.6.4. Distance-Time Graphs 2.6.5. Calculating Acceleration From a Speed-Time Graph 2.6.6. Calculating Distance From a Speed-Time Graph
2.7. Systems of Equations
 2.7.1. Introduction to the Elimination Method 2.7.2. Solving Systems of Linear Equations Using Elimination: One Transformation 2.7.3. Solving Systems of Linear Equations Using Elimination: Two Transformations 2.7.4. Systems of Linear Equations With Fractional Coefficients 2.7.5. Systems of Linear Equations With Decimal Coefficients 2.7.6. Systems of Equations With No Solutions and Infinitely Many Solutions 2.7.7. Consistency and Dependency in Linear Systems 2.7.8. Calculating the Intersection of Two Lines 2.7.9. Modeling Number Problems Using Systems of Linear Equations 2.7.10. Modeling Coin Problems Using Systems of Linear Equations 2.7.11. Solving Systems of Nonlinear Equations Using Graphs 2.7.12. Approximating Solutions to Systems of Linear Equations 2.7.13. Approximating Solutions to Systems of Nonlinear Equations
2.8. Two-Variable Linear Inequalities
 2.8.1. Graphing Strict Two-Variable Linear Inequalities 2.8.2. Graphing Non-Strict Two-Variable Linear Inequalities 2.8.3. Further Graphing of Two-Variable Linear Inequalities 2.8.4. Solving Systems of Linear Inequalities 2.8.5. Modeling With Two-Variable Linear Inequalities
3.
Units
13 topics
3.9. Working With Units
 3.9.1. Unit Conversions Using Base Units of Mass 3.9.2. Two-Step Unit Conversions 3.9.3. Unit Conversions Using Base Units of Length 3.9.4. Unit Conversions Using Units of Time 3.9.5. Converting Units of Area to Smaller Units 3.9.6. Converting Units of Area to Larger Units 3.9.7. Determining Units in Formulas 3.9.8. Selecting Units for Rates of Change 3.9.9. Converting Between Mixed Units 3.9.10. Degrees of Accuracy
3.10. Direct and Inverse Variation
 3.10.1. Inverse Variation 3.10.2. Modeling with Direct Variation 3.10.3. Modeling With Inverse Variation
4.
11 topics
 4.11.1. The Square Root of a Perfect Square With Algebraic Expressions 4.11.2. The Square Root of a Perfect Square With Domain Restrictions 4.11.3. The Cube Root of a Perfect Cube With Algebraic Expressions 4.11.4. Simplifying Square Root Expressions Using the Product Rule 4.11.5. Combining Radical Expressions Using the Product Rule 4.11.6. Simplifying Square Root Expressions Using the Quotient Rule 4.11.7. Evaluating Algebraic Radical Expressions 4.11.8. Adding and Subtracting Radical Expressions 4.11.9. Rationalizing Denominators of Algebraic Expressions 4.11.10. Rationalizing Denominators With Two Terms 4.11.11. Solving Radical Equations
5.
Rational Expressions & Equations
7 topics
5.12. Rational Expressions
 5.12.1. Equivalent Expressions With Fractions 5.12.2. Simplifying Rational Expressions 5.12.3. Simplifying Rational Expressions by Factoring
5.13. Rational Equations
 5.13.1. Solving Rational Equations Containing One Fractional Term 5.13.2. Solving Rational Equations Using Cross-Multiplication 5.13.3. Solving Rational Equations Containing Binomials Using Cross-Multiplication 5.13.4. Solving Rational Equations Using the Flip Method
6.
Functions
17 topics
6.14. Functions
 6.14.1. Introduction to Functions 6.14.2. Visual Representations of Functions 6.14.3. Graphs of Functions 6.14.4. The Domain of a Function 6.14.5. The Vertical Line Test 6.14.6. Global Extrema of Functions 6.14.7. End Behavior of Functions 6.14.8. The Range of a Function 6.14.9. The Range of a Function: Advanced Cases 6.14.10. The Roots of a Function 6.14.11. Increasing and Decreasing Functions 6.14.12. Piecewise Functions 6.14.13. Modeling With Linear Functions 6.14.14. The Arithmetic of Functions 6.14.15. Function Composition 6.14.16. Describing Function Composition 6.14.17. Introduction to Inverse Functions
7.
Absolute Value
14 topics
7.15. Absolute Value Expressions, Equations & Inequalities
 7.15.1. Absolute Value Expressions 7.15.2. Rules of Absolute Value 7.15.3. Further Rules of Absolute Value 7.15.4. Absolute Value Equations 7.15.5. Further Absolute Value Equations 7.15.6. Equations Connecting Absolute Value and Linear Functions 7.15.7. Absolute Value Equations With Extraneous Solutions 7.15.8. Absolute Value Inequalities
7.16. Absolute Value Functions
 7.16.1. Absolute Value Graphs 7.16.2. Vertical Reflections of Absolute Value Graphs 7.16.3. Stretches of Absolute Value Graphs 7.16.4. Combining Transformations of Absolute Value Graphs 7.16.5. Domain and Range of Absolute Value Functions 7.16.6. Roots of Absolute Value Functions
8.
Exponential Functions
22 topics
8.17. Rules of Exponents
 8.17.1. Writing Radical Expressions Using Fractional Exponents 8.17.2. The Product Rule for Exponents With Algebraic Expressions 8.17.3. The Quotient Rule for Exponents With Algebraic Expressions 8.17.4. The Power Rule for Exponents With Algebraic Expressions 8.17.5. The Power of Product Rule With Algebraic Expressions 8.17.6. The Power of Quotient Rule With Algebraic Expressions 8.17.7. Combining the Rules of Exponents With Algebraic Expressions
8.18. Exponential Expressions & Equations
 8.18.1. Solving Exponential Equations 8.18.2. Solving Exponential Equations with Fractional Solutions 8.18.3. Creating Exponential Growth Expressions 8.18.4. Creating Exponential Decay Expressions
8.19. Exponential Functions
 8.19.1. Exponential Functions 8.19.2. Modeling Exponential Growth With Functions 8.19.3. Interpreting Exponential Growth 8.19.4. Solving Exponential Growth Problems 8.19.5. Modeling Exponential Decay With Functions 8.19.6. Interpreting Exponential Decay 8.19.7. Solving Exponential Decay Problems 8.19.8. Linear vs. Exponential Growth and Decay 8.19.9. Linear vs. Exponential Growth and Decay Models 8.19.10. Graphing Exponential Growth Functions 8.19.11. Graphing Exponential Decay Functions
9.
Polynomials
20 topics
9.20. Polynomials
 9.20.1. Introduction to Polynomials 9.20.2. The Degree of a Polynomial 9.20.3. Simplifying Polynomials 9.20.4. The Distributive Law for Polynomials 9.20.5. Adding and Subtracting Polynomials 9.20.6. Monomials, Binomials and Trinomials 9.20.7. Multiplying Binomials 9.20.8. Multiplying Polynomials 9.20.9. Squaring Binomials 9.20.10. Expanding Binomials Using Pascal's Triangle 9.20.11. The Difference of Squares Formula
9.21. Factoring Polynomials
 9.21.1. The Greatest Common Factor of Two Monomials 9.21.2. Factoring Simple Polynomials Using Greatest Common Factors 9.21.3. Factoring Perfect Square Trinomials 9.21.4. Factoring Perfect Square Trinomials With Leading Coefficients 9.21.5. Factoring Differences of Squares 9.21.6. Factoring Trinomials 9.21.7. Factoring Trinomials Using Common Factors 9.21.8. Factoring Trinomials With Leading Coefficients 9.21.9. Further Factoring Trinomials With Leading Coefficients
10.
33 topics
 10.23.1. Graphing Elementary Quadratic Functions 10.23.2. Vertical Reflections of Quadratic Functions 10.23.3. Graphs of General Quadratic Functions 10.23.4. Roots of Quadratic Functions 10.23.5. The Discriminant of a Quadratic Function 10.23.6. The Axis of Symmetry of a Parabola 10.23.7. The Average of the Roots Formula 10.23.8. The Vertex Form of a Parabola 10.23.9. Writing the Equation of a Parabola in Vertex Form 10.23.10. Domain and Range of Quadratic Functions 10.23.11. Finding Intersections of Lines and Quadratic Functions
 10.24.1. Modeling Downwards Vertical Motion 10.24.2. Modeling Upwards Vertical Motion 10.24.3. Vertical Motion 10.24.4. Revenue, Cost, and Profit Functions 10.24.5. Constructing Revenue, Cost, and Profit Functions 10.24.6. Maximizing Profit and Break-Even Points
11.
Sequences
18 topics
11.25. Introduction to Sequences
 11.25.1. Introduction to Sequences 11.25.2. Recursive Sequences 11.25.3. Fibonacci Sequences
11.26. Arithmetic Sequences
 11.26.1. Arithmetic Sequences 11.26.2. Recursive Formulas for Arithmetic Sequences 11.26.3. The Nth Term of an Arithmetic Sequence 11.26.4. Translating Between Explicit and Recursive Formulas for Arithmetic Sequences 11.26.5. Finding the Common Difference of an Arithmetic Sequence 11.26.6. Finding the Nth Term of an Arithmetic Sequence Given Two Terms 11.26.7. Determining Indexes of Terms in Arithmetic Sequences 11.26.8. Solving for Variables in Arithmetic Sequences 11.26.9. Modeling With Arithmetic Sequences
11.27. Geometric Sequences
 11.27.1. Introduction to Geometric Sequences 11.27.2. The Recursive Formula for a Geometric Sequence 11.27.3. The Nth Term of a Geometric Sequence 11.27.4. Translating Between Explicit and Recursive Formulas for Geometric Sequences 11.27.5. Finding the Common Ratio of a Geometric Sequence Given Two Terms 11.27.6. Determining Indexes of Terms in Geometric Sequences
12.
Bivariate Statistics
6 topics
12.28. Correlation & Regression
 12.28.1. Scatter Plots 12.28.2. Trend Lines 12.28.3. Making Predictions Using Trend Lines 12.28.4. Interpreting Trend Line Coefficients 12.28.5. Linear Correlation 12.28.6. Selecting a Regression Model