# Integrated Math I

Integrated Math I is a fully accredited, Common Core-aligned course that builds on the foundations developed in Prealgebra. Upon completing the course, students will build a solid base for success in Integrated Math II and beyond.

## Content

In this course, students broaden their understanding of equations and inequalities, delivering into one-variable equations with unknown coefficients, two-variable linear equations and inequalities, systems of equations, and nonlinear equations. They will learn how to apply their knowledge to model a variety of situations. Students will also deepen their understanding of units and discover how to think of them algebraically and use them to solve problems.

This course marks the beginning of students' journey into 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 specific function types, namely exponential, absolute value, and piecewise functions, creating a solid foundation for analyzing more advanced functions in future courses.

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.

Building upon their prior understanding of sequences, students will learn to work with formal sequence notation, delve into recursive sequences, and master arithmetic sequences.

This course also introduces various critical geometric concepts. Students will become adept at performing geometric transformations in the coordinate plane and will be able to describe their functional representations. In addition, they will study essential geometric principles, such as the Pythagorean theorem, special right triangles, circles, and the distance formula.

Lastly, students will learn the fundamentals of linear correlation, emphasizing the important distinction between correlation and causation.

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.

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 of systems 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.
• 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.
• Understand formal sequence notation, recursive and arithmetic sequences, and applications.
• Perform geometric transformations in the coordinate plane, such as translations, rotations, reflections, and composite transformations, and describe and work with their functional representations.
• Gain an in-depth understanding of fundamental geometric concepts such as triangle congruence, the Pythagorean theorem, special right triangles, the area and circumference of a circle, and the distance formula in two dimensions.
• Plot data on a scatter plot, describe the (linear) correlation between two data sets, approximate a trend line and interpret the coefficients. Distinguish between correlation and causation.
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
28 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. 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. Calculating the Intersection of Two Lines 2.7.8. Modeling Number Problems Using Systems of Linear Equations 2.7.9. Modeling Coin Problems Using Systems of Linear Equations 2.7.10. Solving Systems of Nonlinear Equations Using Graphs 2.7.11. Approximating Solutions to Systems of Linear Equations 2.7.12. 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. 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.
9 topics
 4.11.1. Writing Radical Expressions Using Fractional Exponents 4.11.2. The Square Root of a Perfect Square With Algebraic Expressions 4.11.3. The Square Root of a Perfect Square With Domain Restrictions 4.11.4. The Cube Root of a Perfect Cube With Algebraic Expressions 4.11.5. Simplifying Square Root Expressions Using the Product Rule 4.11.6. Combining Radical Expressions Using the Product Rule 4.11.7. Simplifying Square Root Expressions Using the Quotient Rule 4.11.8. Evaluating Algebraic Radical Expressions 4.11.9. Adding and Subtracting Radical Expressions
5.
Rational Expressions & Equations
8 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 5.12.4. Splitting Rational Expressions Into Separate Terms
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
13 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
7.
Absolute Value
6 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. Absolute Value Inequalities
8.
Exponential Functions
21 topics
8.16. Rules of Exponents
 8.16.1. The Product Rule for Exponents With Algebraic Expressions 8.16.2. The Quotient Rule for Exponents With Algebraic Expressions 8.16.3. The Power Rule for Exponents With Algebraic Expressions 8.16.4. The Power of Product Rule With Algebraic Expressions 8.16.5. The Power of Quotient Rule With Algebraic Expressions 8.16.6. Combining the Rules of Exponents With Algebraic Expressions
8.17. Exponential Expressions and Equations
 8.17.1. Solving Exponential Equations with Integer Solutions 8.17.2. Solving Exponential Equations with Fractional Solutions 8.17.3. Creating Exponential Growth Expressions 8.17.4. Creating Exponential Decay Expressions
8.18. Exponential Functions
 8.18.1. Exponential Functions 8.18.2. Modeling Exponential Growth With Functions 8.18.3. Interpreting Exponential Growth 8.18.4. Solving Exponential Growth Problems 8.18.5. Modeling Exponential Decay With Functions 8.18.6. Interpreting Exponential Decay 8.18.7. Solving Exponential Decay Problems 8.18.8. Linear vs. Exponential Growth and Decay 8.18.9. Linear vs. Exponential Growth and Decay Models 8.18.10. Graphing Exponential Growth Functions 8.18.11. Graphing Exponential Decay Functions
9.
Polynomials
19 topics
9.19. Polynomials
 9.19.1. Introduction to Polynomials 9.19.2. The Degree of a Polynomial 9.19.3. Simplifying Polynomials 9.19.4. The Distributive Law for Polynomials 9.19.5. Adding and Subtracting Polynomials 9.19.6. Monomials, Binomials and Trinomials 9.19.7. Multiplying Binomials 9.19.8. Multiplying Polynomials 9.19.9. Squaring Binomials 9.19.10. Expanding Binomials Using Pascal's Triangle 9.19.11. The Difference of Squares Formula
9.20. Factoring Polynomials
 9.20.1. The Greatest Common Factor of Two Monomials 9.20.2. Factoring Simple Polynomials Using Greatest Common Factors 9.20.3. Factoring Perfect Square Trinomials 9.20.4. Factoring Perfect Square Trinomials With Leading Coefficients 9.20.5. Factoring Differences of Squares 9.20.6. Factoring Trinomials 9.20.7. Factoring Trinomials Using Common Factors 9.20.8. Factoring Trinomials With Leading Coefficients
10.
Sequences
12 topics
10.21. Introduction to Sequences
 10.21.1. Introduction to Sequences 10.21.2. Recursive Sequences 10.21.3. Fibonacci Sequences
10.22. Arithmetic Sequences
 10.22.1. Arithmetic Sequences 10.22.2. Recursive Formulas for Arithmetic Sequences 10.22.3. The Nth Term of an Arithmetic Sequence 10.22.4. Translating Between Explicit and Recursive Formulas for Arithmetic Sequences 10.22.5. Finding the Common Difference of an Arithmetic Sequence Given Two Terms 10.22.6. Finding the Nth Term of an Arithmetic Sequence Given Two Terms 10.22.7. Determining Indexes of Terms in Arithmetic Sequences 10.22.8. Solving for Variables in Arithmetic Sequences 10.22.9. Modeling With Arithmetic Sequences
11.
Transformations
16 topics
11.23. Geometric Transformations
 11.23.1. Translations of Geometric Figures 11.23.2. Rotations of Geometric Figures 11.23.3. Rotating Objects in the Coordinate Plane Using Functions 11.23.4. Reflections of Geometric Figures in the Cartesian Plane 11.23.5. Reflections of Figures Across Arbitrary Lines 11.23.6. Dilations of Geometric Figures 11.23.7. Dilations of Figures in the Coordinate Plane 11.23.8. Stretches of Geometric Figures 11.23.9. Combining Stretches of Geometric Figures 11.23.10. Combining Geometric Transformations 11.23.11. Reflective Symmetry 11.23.12. Rotational Symmetry
11.24. Congruence
 11.24.1. Rigid Motions and Congruence 11.24.2. The Angle-Side-Angle (ASA) Criterion for Congruent Triangles 11.24.3. The Side-Angle-Side (SAS) Criterion for Congruent Triangles 11.24.4. The Side-Side-Side (SSS) Criterion for Congruent Triangles
12.
Geometry
26 topics
12.25. Right Triangles
 12.25.1. The Pythagorean Theorem 12.25.2. The 45-45-90 Triangle 12.25.3. The 30-60-90 Triangle 12.25.4. The Area of a 45-45-90 Triangle 12.25.5. The Area of a 30-60-90 Triangle 12.25.6. The Area of an Equilateral Triangle 12.25.7. Diagonals of Squares
12.26. Circles
 12.26.1. Introduction to Circles 12.26.2. Arcs, Segments, and Sectors of Circles 12.26.3. The Circumference of a Circle 12.26.4. Areas of Circles 12.26.5. Central Angles and Arcs 12.26.6. Calculating Arc Lengths of Circular Sectors Using Angles in Degrees 12.26.7. Calculating Areas of Circular Sectors Using Angles in Degrees 12.26.8. Further Calculating Areas of Sectors Using Angles in Degrees 12.26.9. Problem Solving With Circles
12.27. Coordinate Geometry
 12.27.1. Parallel Lines in the Coordinate Plane 12.27.2. Finding the Equation of a Parallel Line 12.27.3. Perpendicular Lines in the Coordinate Plane 12.27.4. Finding Equations of Perpendicular Lines 12.27.5. Midpoints in the Coordinate Plane 12.27.6. The Distance Formula 12.27.7. The Shortest Distance Between a Point and a Line 12.27.8. Calculating Perimeters of Shapes in the Coordinate Plane 12.27.9. Calculating Areas of Rectangles in the Coordinate Plane 12.27.10. Calculating Areas of Triangles and Quadrilaterals in the Coordinate Plane
13.
Statistics
6 topics
13.28. Correlation
 13.28.1. Scatter Plots 13.28.2. Trend Lines 13.28.3. Making Predictions Using Trend Lines 13.28.4. Interpreting Coefficients of Trend Lines 13.28.5. Linear Correlation 13.28.6. Correlation vs. Causation