Integrated Math I is a fully accredited, Common Core-aligned course that builds on the foundations developed in Prealgebra. This course deepens students' knowledge of linear equations, inequalities, units, radical and rational expressions, and rational and other nonlinear equations. Students will explore the concept of a function and study exponential, absolute value, and polynomial functions in detail. They will also deepen their understanding of geometry by investigating geometric transformations, right triangles, circles, and coordinate geometry.

Upon completing the course, students will build a solid base for success in Integrated Math II and beyond.

Students broaden their understanding of equations and inequalities by solving one-variable equations with unknown coefficients, two-variable linear equations and inequalities, systems of equations, and nonlinear expressions and equations. They will expand their understanding of units to incorporate algebraic methods and study direct and inverse variation.

This course marks the beginning of students' exploration of the world of functions. They will explore key concepts such as domain, range, roots, extrema, and end behavior. Furthermore, they will apply this newfound knowledge to study exponential, absolute value, and piecewise functions, creating a solid foundation for analyzing more advanced functions in future courses.

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

This course introduces various critical geometric concepts. Students will become adept at performing single and multi-step geometric transformations in the coordinate plane and describing their functional representations. They will also study essential geometric principles, such as the Pythagorean theorem, special right triangles, circles, and the distance formula.

Students will learn how to apply their knowledge to model various contextual situations at multiple points throughout the course.

By the end of this comprehensive course, students will have significantly enhanced their mathematical skills and knowledge, equipping them for more advanced studies in mathematics.

- Solving linear equations and inequalities containing unknown coefficients.
- Using linear equations to model and solve real-world multi-step problems involving speed, distance, time, work, and mixtures.
- Solving compound inequalities and systems of inequalities, graphing their solutions, and modeling situations in context.
- Interval notation, including unbounded intervals and computing unions and intersections of intervals.
- Solving simple polynomial equations using the nth root method.

- Constructing equations of lines in point-slope and standard form and determining properties of lines given in these forms.
- Solving two-variable systems of linear equations using substitution and elimination, including cases with fractional and decimal coefficients.
- Determining when systems of equations have one, none, or infinitely many solutions and correctly applying consistency and dependency terminology.
- Using two-variable systems to model and solve contextual problems.

- Performing unit conversions using algebraic techniques, including two-step conversions and converting between area units.
- Determining units associated with variables in formulas, including rates of change, and working with standard and non-standard units.
- Understanding and applying the concepts of direct and inverse variation, including modeling and solving real-world and mathematical problems.

- Manipulating and simplifying radical expressions using the rules of radicals.
- Simplifying simple rational expressions by factoring.
- Solving simple rational equations using various techniques.

- Interpreting and evaluating functions represented using algebraic notation, mapping diagrams, tables, and graphs.
- Determining whether a given relation is a function, including applying the vertical line test.
- The concepts of domain, range, root, global extrema, and end behavior of functions, and describing these properties for simple functions.
- Identifying the intervals where a function is increasing or decreasing, including the distinction between strict and non-strict increase or decrease.

- Applying the rules of absolute value.
- Solving absolute value equations and inequalities, including cases with extraneous solutions.
- Plotting graphs of shifted, stretched, and reflected absolute value functions.
- Finding the range and roots of an absolute value function.

- Simplifying algebraic expressions using the rules of exponents.
- Solving exponential equations with integer and fractional solutions.
- Constructing expressions and functions that model exponential growth and decay situations given in context.
- Comparing exponential and linear growth and decay.
- Graphing elementary growth and decay functions.

- Defining polynomials, the degree of a polynomial, monomials, binomials, and trinomials.
- Simplifying, adding, subtracting, and multiplying polynomials.
- Calculating a binomial expansion using Pascal's triangle.
- Factoring quadratic polynomials using greatest common factors, perfect squares, difference of squares, and grouping.

- Applying translations, reflections, dilations, stretches, and composite transformations to two-dimensional figures.
- Using functions to represent transformations in the coordinate plane and using them to find the image of an object.
- Applying the Pythagorean Theorem.
- Understanding the special right triangles and using them to calculate areas.
- Calculating areas and circumferences of circles and solving related problems.
- Finding perimeters and areas of circular sectors.
- Applying the distance formula in two dimensions.
- Working with parallel and perpendicular lines in the coordinate plane.

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
29 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. Two-Variable Linear Inequalities

2.7.1. | Graphing Strict Two-Variable Linear Inequalities | |

2.7.2. | Graphing Non-Strict Two-Variable Linear Inequalities | |

2.7.3. | Further Graphing of Two-Variable Linear Inequalities | |

2.7.4. | Solving Systems of Linear Inequalities | |

2.7.5. | Modeling With Two-Variable Linear Inequalities |

2.8. Systems of Equations

2.8.1. | Introduction to the Elimination Method | |

2.8.2. | Solving Systems of Linear Equations Using Elimination: One Transformation | |

2.8.3. | Solving Systems of Linear Equations Using Elimination: Two Transformations | |

2.8.4. | Systems of Linear Equations With Fractional Coefficients | |

2.8.5. | Systems of Linear Equations With Decimal Coefficients | |

2.8.6. | Systems of Equations With No Solutions and Infinitely Many Solutions | |

2.8.7. | Consistency and Dependency in Linear Systems | |

2.8.8. | Calculating the Intersection of Two Lines | |

2.8.9. | Modeling Number Problems Using Systems of Linear Equations | |

2.8.10. | Modeling Coin Problems Using Systems of Linear Equations | |

2.8.11. | Solving Systems of Nonlinear Equations Using Graphs | |

2.8.12. | Approximating Solutions to Systems of Linear Equations | |

2.8.13. | Approximating Solutions to Systems of Nonlinear Equations |

3.

Units
13 topics

3.9. Working With Units

3.9.1. | Unit Conversions Using Base Units of Mass | |

3.9.2. | Unit Conversions Using Base Units of Length | |

3.9.3. | Unit Conversions Using Units of Time | |

3.9.4. | Two-Step Unit Conversions | |

3.9.5. | Converting Units of Area to Smaller Units | |

3.9.6. | Converting Units of Area to Larger Units | |

3.9.7. | Converting Between Mixed Units | |

3.9.8. | Determining Units in Formulas | |

3.9.9. | Selecting Units for Rates of Change | |

3.9.10. | Degrees of Accuracy |

3.10. Direct and Inverse Variation

3.10.1. | Modeling with Direct Variation | |

3.10.2. | Inverse Variation | |

3.10.3. | Modeling With Inverse Variation |

4.

Rationals & Radicals
17 topics

4.11. Rational Expressions

4.11.1. | Equivalent Expressions With Fractions | |

4.11.2. | Simplifying Rational Expressions | |

4.11.3. | Simplifying Rational Expressions by Factoring | |

4.11.4. | Splitting Rational Expressions Into Separate Terms |

4.12. Rational Equations

4.12.1. | Solving Rational Equations Containing One Fractional Term | |

4.12.2. | Solving Rational Equations Using Cross-Multiplication | |

4.12.3. | Solving Rational Equations Containing Binomials Using Cross-Multiplication | |

4.12.4. | Solving Rational Equations Using the Flip Method |

4.13. Radical Expressions

4.13.1. | Writing Radical Expressions Using Fractional Exponents | |

4.13.2. | The Square Root of a Perfect Square With Algebraic Expressions | |

4.13.3. | The Square Root of a Perfect Square With Domain Restrictions | |

4.13.4. | The Cube Root of a Perfect Cube With Algebraic Expressions | |

4.13.5. | Simplifying Square Root Expressions Using the Product Rule | |

4.13.6. | Combining Radical Expressions Using the Product Rule | |

4.13.7. | Simplifying Square Root Expressions Using the Quotient Rule | |

4.13.8. | Evaluating Algebraic Radical Expressions | |

4.13.9. | Adding and Subtracting Radical Expressions |

5.

Functions
13 topics

5.14. Function Essentials

5.14.1. | Introduction to Functions | |

5.14.2. | Visual Representations of Functions | |

5.14.3. | Graphs of Functions | |

5.14.4. | The Domain of a Function | |

5.14.5. | The Vertical Line Test | |

5.14.6. | Global Extrema of Functions | |

5.14.7. | End Behavior of Functions | |

5.14.8. | The Range of a Function | |

5.14.9. | The Range of a Function: Advanced Cases | |

5.14.10. | The Roots of a Function | |

5.14.11. | Increasing and Decreasing Functions | |

5.14.12. | Piecewise Functions | |

5.14.13. | Modeling With Linear Functions |

6.

Absolute Value
14 topics

6.15. Absolute Value Expressions, Equations & Inequalities

6.15.1. | Absolute Value Expressions | |

6.15.2. | Rules of Absolute Value | |

6.15.3. | Further Rules of Absolute Value | |

6.15.4. | Absolute Value Equations | |

6.15.5. | Further Absolute Value Equations | |

6.15.6. | Absolute Value Inequalities |

6.16. Absolute Value Functions

6.16.1. | Absolute Value Graphs | |

6.16.2. | Vertical Reflections of Absolute Value Graphs | |

6.16.3. | Stretches of Absolute Value Graphs | |

6.16.4. | Combining Transformations of Absolute Value Graphs | |

6.16.5. | Domain and Range of Absolute Value Functions | |

6.16.6. | Roots of Absolute Value Functions | |

6.16.7. | Equations Connecting Absolute Value and Linear Functions | |

6.16.8. | Absolute Value Equations With Extraneous Solutions |

7.

Exponents
21 topics

7.17. The Rules of Exponents

7.17.1. | The Product Rule for Exponents With Algebraic Expressions | |

7.17.2. | The Quotient Rule for Exponents With Algebraic Expressions | |

7.17.3. | The Power Rule for Exponents With Algebraic Expressions | |

7.17.4. | The Power of Product Rule With Algebraic Expressions | |

7.17.5. | The Power of Quotient Rule With Algebraic Expressions | |

7.17.6. | Combining the Rules of Exponents With Algebraic Expressions |

7.18. Exponential Expressions, Equations, and Functions

7.18.1. | Solving Exponential Equations | |

7.18.2. | Solving Exponential Equations with Fractional Solutions | |

7.18.3. | Creating Exponential Growth Expressions | |

7.18.4. | Creating Exponential Decay Expressions | |

7.18.5. | Exponential Functions | |

7.18.6. | Modeling Exponential Growth With Functions | |

7.18.7. | Interpreting Exponential Growth | |

7.18.8. | Solving Exponential Growth Problems | |

7.18.9. | Modeling Exponential Decay With Functions | |

7.18.10. | Interpreting Exponential Decay | |

7.18.11. | Solving Exponential Decay Problems | |

7.18.12. | Linear vs. Exponential Growth and Decay | |

7.18.13. | Linear vs. Exponential Growth and Decay Models | |

7.18.14. | Graphing Exponential Growth Functions | |

7.18.15. | Graphing Exponential Decay Functions |

8.

Polynomials
20 topics

8.19. Polynomial Essentials

8.19.1. | Introduction to Polynomials | |

8.19.2. | The Degree of a Polynomial | |

8.19.3. | Simplifying Polynomials | |

8.19.4. | The Distributive Law for Polynomials | |

8.19.5. | Adding and Subtracting Polynomials | |

8.19.6. | Monomials, Binomials and Trinomials | |

8.19.7. | Multiplying Binomials | |

8.19.8. | Multiplying Polynomials | |

8.19.9. | Squaring Binomials | |

8.19.10. | Expanding Binomials Using Pascal's Triangle | |

8.19.11. | The Difference of Squares Formula |

8.20. Factoring Polynomials

8.20.1. | The Greatest Common Factor of Two Monomials | |

8.20.2. | Factoring Simple Polynomials Using Greatest Common Factors | |

8.20.3. | Factoring Perfect Square Trinomials | |

8.20.4. | Factoring Perfect Square Trinomials With Leading Coefficients | |

8.20.5. | Factoring Differences of Squares | |

8.20.6. | Factoring Trinomials | |

8.20.7. | Factoring Trinomials Using Common Factors | |

8.20.8. | Factoring Trinomials With Leading Coefficients | |

8.20.9. | Further Factoring Trinomials With Leading Coefficients |

9.

Geometry
38 topics

9.21. Geometric Transformations

9.21.1. | Translations of Geometric Figures | |

9.21.2. | Rotations of Geometric Figures | |

9.21.3. | Rotating Objects in the Coordinate Plane Using Functions | |

9.21.4. | Reflections of Geometric Figures in the Cartesian Plane | |

9.21.5. | Reflections of Figures Across Arbitrary Lines | |

9.21.6. | Dilations of Geometric Figures | |

9.21.7. | Dilations of Figures in the Coordinate Plane | |

9.21.8. | Stretches of Geometric Figures | |

9.21.9. | Combining Stretches of Geometric Figures | |

9.21.10. | Combining Geometric Transformations | |

9.21.11. | Reflective Symmetry | |

9.21.12. | Rotational Symmetry |

9.22. Right Triangles

9.22.1. | The Pythagorean Theorem | |

9.22.2. | The 45-45-90 Triangle | |

9.22.3. | The 30-60-90 Triangle | |

9.22.4. | The Area of a 45-45-90 Triangle | |

9.22.5. | The Area of a 30-60-90 Triangle | |

9.22.6. | The Area of an Equilateral Triangle | |

9.22.7. | Diagonals of Squares |

9.23. Circles

9.23.1. | Circles | |

9.23.2. | Arcs, Segments, and Sectors of Circles | |

9.23.3. | The Circumference of a Circle | |

9.23.4. | Areas of Circles | |

9.23.5. | Central Angles and Arcs | |

9.23.6. | Calculating Arc Lengths of Circular Sectors | |

9.23.7. | Calculating Areas of Circular Sectors | |

9.23.8. | Further Calculating Areas of Sectors | |

9.23.9. | Problem Solving With Circles |

9.24. Coordinate Geometry

9.24.1. | Parallel Lines in the Coordinate Plane | |

9.24.2. | Finding the Equation of a Parallel Line | |

9.24.3. | Perpendicular Lines in the Coordinate Plane | |

9.24.4. | Finding Equations of Perpendicular Lines | |

9.24.5. | Midpoints in the Coordinate Plane | |

9.24.6. | The Distance Formula | |

9.24.7. | The Shortest Distance Between a Point and a Line | |

9.24.8. | Calculating Perimeters in the Plane | |

9.24.9. | Calculating Areas of Rectangles in the Plane | |

9.24.10. | Calculating Areas of Triangles and Quadrilaterals in the Plane |