# Algebra I

## Content

### Linear Equations

• Create equations that describe relationships between quantities.
• Relate the solutions of two-variable equations and inequalities to graphs in the coordinate plane.
• Set up and solve systems of linear equations in real-world modeling contexts.

### Nonlinear Equations

• Leverage multiplication as a strategy to transform rational equations into linear equations.
• Extend prior knowledge of radicals and solving linear equations to handle cases when the variable is raised to a power.
• Relate absolute value to distance on the number line and apply this understanding to solve absolute value equations and inequalities.

### Polynomials

• Leverage the distributive property and an understanding of like terms to manipulate polynomial expressions.
• Understand the relationship between multiplication and factoring and apply a systematic method to factor trinomials with leading coefficients.
• Leverage factoring and the quadratic formula as complementary techniques for solving quadratic equations and graphing quadratic functions.

### Functions

• Identify, interpret, and build functions that model relationships between two quantities.
• Represent and reason about functions and sequences using formal notation.

### Graphing

• Visualize functions in the coordinate plane by graphing.
• Leverage the coordinate plane as a tool to represent and solve problems involving geometry and data.
• Understand how transformations affect the shape of a function's graph and use this understanding to graph transformed absolute value functions.
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
26 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
2.6. 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. Solving Systems of Two Linear Equations Using Elimination 2.7.2. Systems of Linear Equations With Fractional Coefficients 2.7.3. Systems of Linear Equations With Decimal Coefficients 2.7.4. Systems of Equations With No Solutions and Infinitely Many Solutions 2.7.5. Calculating the Intersection of Two Lines 2.7.6. Modeling Number Problems Using Systems of Linear Equations 2.7.7. Modeling Coin Problems Using Systems of Linear Equations 2.7.8. Solving Systems of Nonlinear Equations Using Graphs 2.7.9. Approximating Solutions to Systems of Linear Equations 2.7.10. 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. Applying the Quotient Rule for Radicals to Algebraic Expressions 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. Composition of Functions 6.14.16. Finding Algebraic Expressions of Composite Functions 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 with Integer Solutions 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
19 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
10.
33 topics