Our comprehensive, fully accredited, Common Core-aligned Integrated Math II course builds upon the strong foundations acquired in Integrated Math I, delving deeper into algebra, functions, geometry, trigonometry, probability, and statistics. This course will further develop students' mathematical understanding and problem-solving skills, preparing them for success in our Integrated Math III course, the final stepping stone before Calculus.

In this comprehensive course, students will fully master quadratic equations and functions, achieving fluency in the various methods for solving problems that involve quadratics. They will also explore how quadratic functions can be adeptly used in modeling real-world situations. Students will also explore fundamental concepts related to complex numbers.

Building on foundations laid out in Integrated Math I, students will extend their understanding of functions to encompass function arithmetic, composition, periodicity, even and odd functions, and invertible functions. They will be carefully guided through the process of performing graph transformations of functions and will learn to compute inverse functions seamlessly.

As the course progresses, students will enrich their knowledge of exponential functions. This includes a deep dive into logarithms, examining their graphs and properties. Students will learn to solve both exponential and logarithmic equations and further develop their aptitude for modeling scenarios with exponential functions, such as calculating compound interest.

This course aims to broaden studentsâ€™ knowledge to include crucial geometric concepts such as similarity, fundamental circle theorems, conic sections, and solid geometry. Concurrently, students will lay a robust foundation in trigonometry, delving into the unit circle and its pivotal role in extending trigonometric ratios and graphing trigonometric functions.

Finally, students lay solid foundations in probability and combinatorics and build on previous understandings of correlation and regression, further solidifying their skills in these areas.

- Develop a comprehensive understanding of the hierarchical nature of the number system and the role of complex numbers within it.
- Solve quadratic equations using various methods, including applying the zero product rule and 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.
- Further develop their understanding of more general polynomials, including finding the least common factor and least common multiple of two polynomials and describing numerical relationships using polynomial identities.
- Explore and develop a basic comprehension of complex numbers, including addition, subtraction, and multiplication. They will solve quadratic equations with complex roots and understand the cyclic property of the imaginary unit.
- Extend their knowledge of functions to incorporate function composition, describe one-to-one and many-to-one functions, local extrema, periodicity, even and odd functions, and vertical asymptotes of functions.
- Understand the concept of an invertible function, including how graphs of functions and their inverses are related, their domains and ranges, and compute inverses of linear, quadratic, exponential, and logarithmic functions.
- Strengthen their understanding of transformations in the plane to include graph transformations of functions, including vertical and horizontal translations, stretches, and reflections, composite transformations with multiple operations, and absolute value transformations.
- Work with absolute value functions and their associated graphs, describe their properties and further develop their understanding of absolute value equations to more complex cases involving extraneous solutions.
- Further explore exponentials and logarithms, including evaluating logarithms, applying the laws of logarithms, graphing exponential and logarithmic functions, and solving exponential and logarithmic equations.
- Model real-world situations using exponential functions, such as those involving compound interest, including continuously compounded interest.
- Understand geometric sequences, including finding a given geometric sequence's nth term and common ratio, and work with recursive formulas for geometric sequences.
- Utilize sigma notation, calculate the sum of arithmetic series, apply the binomial theorem, and explain how it relates to Pascal's Triangle.
- Solve radical equations, including cases with no real solutions.
- Understand and apply the concept of similarity, including utilizing similarity criteria for triangles, working with areas of similar polygons, and similarity transformations.
- Explore properties of circles, such as inscribed angles, Thales' theorem, and tangent lines.
- Investigate circles and parabolas as conic sections.
- Learn to identify and work with three-dimensional shapes, calculate surface areas and volumes of polyhedra and non-polyhedra, and explore Euler's formula and Platonic solids.
- Develop a strong foundation in trigonometry, including understanding and applying trigonometric ratios, working with radians, and utilizing the unit circle.
- Master graphing and analyzing trigonometric functions, including applying graph transformations and describing their resulting properties.
- Learn the basics of probability and combinatorics, including Venn diagrams, compound events, factorials, permutations, and combinations.
- Analyze data using statistical methods, such as computing a data set's mean, variance, standard deviation, z-scores, and covariance.
- Further explore correlation and regression, including calculating linear correlation coefficients, carrying out linear regression, and analyzing residuals.

1.

Number Systems
10 topics

1.1. The Number System

1.1.1. | The Real Number System | |

1.1.2. | Writing Repeating Decimals as Fractions | |

1.1.3. | Sums and Products of Rational and Irrational Numbers |

1.2. Introduction to Complex Numbers

1.2.1. | Imaginary Numbers | |

1.2.2. | Quadratic Equations with Purely Imaginary Solutions | |

1.2.3. | Complex Numbers | |

1.2.4. | Adding and Subtracting Complex Numbers | |

1.2.5. | Multiplying Complex Numbers | |

1.2.6. | Solving Quadratic Equations With Complex Roots | |

1.2.7. | The Cyclic Property of the Imaginary Unit |

2.

Polynomials
19 topics

2.3. Polynomials

2.3.1. | The Least Common Multiple of Two Monomials | |

2.3.2. | The Least Common Multiple of Two Polynomials | |

2.3.3. | Describing Numerical Relationships Using Polynomial Identities |

2.4. Quadratic Equations

2.4.1. | Introduction to Quadratic Equations | |

2.4.2. | Solving Perfect Square Quadratic Equations | |

2.4.3. | Perfect Square Quadratic Equations with One or No Solutions | |

2.4.4. | The Zero Product Rule for Solving Quadratic Equations | |

2.4.5. | Solving Quadratic Equations Using a Difference of Squares | |

2.4.6. | Solving Quadratic Equations with No Constant Term | |

2.4.7. | Solving Quadratic Equations by Factoring | |

2.4.8. | Solving Quadratic Equations with Leading Coefficients by Factoring | |

2.4.9. | Completing the Square | |

2.4.10. | Completing the Square With Odd Linear Terms | |

2.4.11. | Completing the Square With Leading Coefficients | |

2.4.12. | Solving Quadratic Equations by Completing the Square | |

2.4.13. | Solving Quadratic Equations With Leading Coefficients by Completing the Square | |

2.4.14. | The Quadratic Formula | |

2.4.15. | The Discriminant of a Quadratic Equation | |

2.4.16. | Modeling With Quadratic Equations |

3.

Quadratic Functions
17 topics

3.5. Quadratic Functions

3.5.1. | Graphing Elementary Quadratic Functions | |

3.5.2. | Vertical Reflections of Quadratic Functions | |

3.5.3. | Graphs of General Quadratic Functions | |

3.5.4. | Roots of Quadratic Functions | |

3.5.5. | The Discriminant of a Quadratic Function | |

3.5.6. | The Axis of Symmetry of a Parabola | |

3.5.7. | The Average of the Roots Formula | |

3.5.8. | The Vertex Form of a Parabola | |

3.5.9. | Writing the Equation of a Parabola in Vertex Form | |

3.5.10. | Domain and Range of Quadratic Functions | |

3.5.11. | Finding Intersections of Lines and Quadratic Functions |

3.6. Modeling With Quadratic Functions

3.6.1. | Modeling Downwards Vertical Motion | |

3.6.2. | Modeling Upwards Vertical Motion | |

3.6.3. | Vertical Motion | |

3.6.4. | Revenue, Cost, and Profit Functions | |

3.6.5. | Constructing Revenue, Cost, and Profit Functions | |

3.6.6. | Maximizing Profit and Break-Even Points |

4.

Functions
29 topics

4.7. Functions

4.7.1. | The Arithmetic of Functions | |

4.7.2. | Function Composition | |

4.7.3. | Describing Function Composition | |

4.7.4. | Local Extrema of Functions | |

4.7.5. | One-To-One Functions | |

4.7.6. | Introduction to Inverse Functions | |

4.7.7. | Calculating the Inverse of a Function | |

4.7.8. | Inverses of Quadratic Functions | |

4.7.9. | Graphs of Inverse Functions | |

4.7.10. | Domain and Range of Inverse Functions | |

4.7.11. | Invertible Functions | |

4.7.12. | Plotting X as a Function of Y | |

4.7.13. | Periodic Functions | |

4.7.14. | Even and Odd Functions | |

4.7.15. | Unbounded Behavior of Functions Near a Point | |

4.7.16. | The Average Rate of Change of a Function |

4.8. Graph Transformations of Functions

4.8.1. | Vertical Translations of Functions | |

4.8.2. | Horizontal Translations of Functions | |

4.8.3. | Vertical Stretches of Functions | |

4.8.4. | Horizontal Stretches of Functions | |

4.8.5. | Vertical Reflections of Functions | |

4.8.6. | Horizontal Reflections of Functions | |

4.8.7. | Combining Graph Transformations: Two Operations | |

4.8.8. | Combining Graph Transformations: Three or More Operations | |

4.8.9. | Constructing Functions Using Transformations | |

4.8.10. | Combining Reflections With Other Graph Transformations | |

4.8.11. | Finding Points on Transformed Curves | |

4.8.12. | The Domain and Range of Transformed Functions | |

4.8.13. | Absolute Value Graph Transformations |

5.

Absolute Value Functions
8 topics

5.9. Absolute Value Functions

5.9.1. | Absolute Value Graphs | |

5.9.2. | Vertical Reflections of Absolute Value Graphs | |

5.9.3. | Stretches of Absolute Value Graphs | |

5.9.4. | Combining Transformations of Absolute Value Graphs | |

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

5.9.6. | Roots of Absolute Value Functions | |

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

5.9.8. | Absolute Value Equations With Extraneous Solutions |

6.

Exponentials & Logarithms
34 topics

6.10. Introduction to Logarithms

6.10.1. | Converting From Exponential to Logarithmic Form | |

6.10.2. | Converting From Logarithmic to Exponential Form | |

6.10.3. | Evaluating Logarithms | |

6.10.4. | The Natural Logarithm | |

6.10.5. | The Common Logarithm | |

6.10.6. | Simplifying Logarithmic Expressions |

6.11. The Laws of Logarithms

6.11.1. | The Product Rule for Logarithms | |

6.11.2. | The Quotient Rule for Logarithms | |

6.11.3. | The Power Rule for Logarithms | |

6.11.4. | Combining the Laws of Logarithms | |

6.11.5. | The Change of Base Formula for Logarithms |

6.12. Graphs of Exponential Functions

6.12.1. | Vertical Translations of Exponential Growth Functions | |

6.12.2. | Vertical Translations of Exponential Decay Functions | |

6.12.3. | Interpreting Graphs of Exponential Functions | |

6.12.4. | Combining Graph Transformations of Exponential Functions | |

6.12.5. | Properties of Transformed Exponential Functions |

6.13. Graphs of Logarithmic Functions

6.13.1. | Graphing Logarithmic Functions | |

6.13.2. | Combining Graph Transformations of Logarithmic Functions | |

6.13.3. | Properties of Transformed Logarithmic Functions | |

6.13.4. | Inverses of Exponential and Logarithmic Functions |

6.14. Exponential Equations

6.14.1. | Solving Exponential Equations Using Logarithms | |

6.14.2. | Solving Equations Containing the Exponential Function | |

6.14.3. | Solving Exponential Equations With Different Bases | |

6.14.4. | Solving Exponential Equations With Different Bases Using Logarithms | |

6.14.5. | Solving Exponential Equations Using the Zero-Product Property |

6.15. Logarithmic Equations

6.15.1. | Solving Logarithmic Equations | |

6.15.2. | Solving Logarithmic Equations Containing the Natural Logarithm | |

6.15.3. | Solving Logarithmic Equations Using the Laws of Logarithms | |

6.15.4. | Solving Logarithmic Equations by Combining the Laws of Logarithms | |

6.15.5. | Solving Logarithmic Equations With Logarithms on Both Sides | |

6.15.6. | Solving Logarithmic Equations Using the Zero-Product Property |

6.16. Modeling with Exponential Functions

6.16.1. | Modeling With Compound Interest | |

6.16.2. | Continuously Compounded Interest | |

6.16.3. | Converting Between Exponents |

7.

Sequences & Series
17 topics

7.17. Geometric Sequences

7.17.1. | Introduction to Geometric Sequences | |

7.17.2. | The Recursive Formula for a Geometric Sequence | |

7.17.3. | The Nth Term of a Geometric Sequence | |

7.17.4. | Translating Between Explicit and Recursive Formulas for Geometric Sequences | |

7.17.5. | Finding the Common Ratio of a Geometric Sequence Given Two Terms | |

7.17.6. | Determining Indexes of Terms in Geometric Sequences |

7.18. Arithmetic Series

7.18.1. | Sigma Notation | |

7.18.2. | Properties of Finite Series | |

7.18.3. | Expressing an Arithmetic Series in Sigma Notation | |

7.18.4. | Finding the Sum of an Arithmetic Series | |

7.18.5. | Finding the First Term of an Arithmetic Series | |

7.18.6. | Calculating the Number of Terms in an Arithmetic Series | |

7.18.7. | Modeling With Arithmetic Series |

7.19. The Binomial Theorem

7.19.1. | Pascal's Triangle and the Binomial Coefficients | |

7.19.2. | Expanding a Binomial Using Binomial Coefficients | |

7.19.3. | The Special Case of the Binomial Theorem | |

7.19.4. | Approximating Values Using the Binomial Theorem |

8.

Radical Equations
2 topics

8.20. Radical Equations

8.20.1. | Solving Radical Equations | |

8.20.2. | Solving Advanced Radical Equations |

9.

Geometry
17 topics

9.21. Similarity

9.21.1. | Similarity and Similar Polygons | |

9.21.2. | Side Lengths and Angle Measures of Similar Polygons | |

9.21.3. | Areas of Similar Polygons | |

9.21.4. | Working With Areas of Similar Polygons | |

9.21.5. | Similarity Transformations | |

9.21.6. | The Angle-Angle (AA) Criterion for Similar Triangles | |

9.21.7. | The Side-Side-Side (SSS) Criterion for Similar Triangles | |

9.21.8. | The Side-Angle-Side (SAS) Criterion for Similar Triangles | |

9.21.9. | The Midpoint Theorem | |

9.21.10. | The Triangle Proportionality Theorem |

9.22. Circles

9.22.1. | The Inscribed Angle Theorem | |

9.22.2. | Problem Solving Using the Inscribed Angle Theorem | |

9.22.3. | Thales' Theorem | |

9.22.4. | Angles in Inscribed Right Triangles | |

9.22.5. | Inscribed Quadrilaterals | |

9.22.6. | Tangent Lines to Circles | |

9.22.7. | Circle Similarity |

10.

Conics
15 topics

10.23. Circles as Conic Sections

10.23.1. | The Center and Radius of a Circle in the Coordinate Plane | |

10.23.2. | Equations of Circles Centered at the Origin | |

10.23.3. | Equations of Circles Centered at a General Point | |

10.23.4. | Finding the Center and Radius of a Circle by Completing the Square | |

10.23.5. | Calculating Intercepts of Circles | |

10.23.6. | Intersections of Circles with Lines |

10.24. Parabolas as Conic Sections

10.24.1. | Upward and Downward Opening Parabolas | |

10.24.2. | Left and Right Opening Parabolas | |

10.24.3. | The Vertex of a Parabola | |

10.24.4. | Calculating the Vertex of a Parabola by Completing the Square | |

10.24.5. | The Focus-Directrix Property of a Parabola | |

10.24.6. | Calculating the Focus of a Parabola | |

10.24.7. | Calculating the Directrix of a Parabola | |

10.24.8. | Calculating Intercepts of Parabolas | |

10.24.9. | Intersections of Parabolas With Lines |

11.

Solid Geometry
25 topics

11.25. Introduction to Solid Geometry

11.25.1. | Identifying Three-Dimensional Shapes | |

11.25.2. | Faces, Vertices, and Edges of Polyhedrons | |

11.25.3. | Nets of Polyhedrons | |

11.25.4. | Finding Surface Areas Using Nets | |

11.25.5. | The Distance Formula in Three Dimensions | |

11.25.6. | Euler's Formula for Polyhedra | |

11.25.7. | The Five Platonic Solids |

11.26. Rectangular Solids and Pyramids

11.26.1. | Volumes of Cubes | |

11.26.2. | Surface Areas of Cubes | |

11.26.3. | Face Diagonals of Cubes | |

11.26.4. | Diagonals of Cubes | |

11.26.5. | Volumes of Rectangular Solids | |

11.26.6. | Surface Areas of Rectangular Solids | |

11.26.7. | Diagonals of Rectangular Solids | |

11.26.8. | Volumes of Pyramids | |

11.26.9. | Surface Areas of Pyramids |

11.27. Non-Polyhedrons

11.27.1. | Volumes of Cylinders | |

11.27.2. | Surface Areas of Cylinders | |

11.27.3. | Volumes of Right Cones | |

11.27.4. | Slant Heights of Right Cones | |

11.27.5. | Surface Areas of Right Cones | |

11.27.6. | Volumes of Spheres | |

11.27.7. | Surface Areas of Spheres | |

11.27.8. | Conical Frustums | |

11.27.9. | Volumes of Revolution |

12.

Trigonometry
57 topics

12.28. Introduction to Trigonometry

12.28.1. | Angles and Sides in Right Triangles | |

12.28.2. | The Trigonometric Ratios | |

12.28.3. | Calculating Trigonometric Ratios Using the Pythagorean Theorem | |

12.28.4. | Calculating Side Lengths of Right Triangles Using Trigonometry | |

12.28.5. | Calculating Angles in Right Triangles Using Trigonometry | |

12.28.6. | Modeling With Trigonometry | |

12.28.7. | The Reciprocal Trigonometric Ratios | |

12.28.8. | Trigonometric Ratios in Similar Right Triangles | |

12.28.9. | Trigonometric Functions of Complementary Angles | |

12.28.10. | Special Trigonometric Ratios | |

12.28.11. | Calculating the Area of a Right Triangle Using Trigonometry | |

12.28.12. | Solving Multiple Right Triangles Using Trigonometry |

12.29. Radians

12.29.1. | Introduction to Radians | |

12.29.2. | Calculating Arc Length Using Angles in Radians | |

12.29.3. | Calculating Areas of Sectors Using Angles in Radians | |

12.29.4. | Trigonometric Ratios With Radians |

12.30. The Unit Circle

12.30.1. | Angles in the Coordinate Plane | |

12.30.2. | Negative Angles in the Coordinate Plane | |

12.30.3. | Coterminal Angles | |

12.30.4. | Calculating Reference Angles | |

12.30.5. | Properties of the Unit Circle in the First Quadrant | |

12.30.6. | Extending the Trigonometric Ratios Using the Unit Circle | |

12.30.7. | Extending the Trigonometric Ratios Using Angles in Radians | |

12.30.8. | Extending the Trigonometric Ratios to Negative Angles | |

12.30.9. | Extending the Trigonometric Ratios to Large Angles | |

12.30.10. | Using the Pythagorean Identity in the First Quadrant | |

12.30.11. | Extending the Pythagorean Identity to All Quadrants |

12.31. Special Trigonometric Ratios

12.31.1. | Finding Trigonometric Ratios of Quadrantal Angles | |

12.31.2. | Trigonometric Ratios of Quadrantal Angles Outside the Standard Range | |

12.31.3. | Finding Trigonometric Ratios of Special Angles Using the Unit Circle | |

12.31.4. | Evaluating Trigonometric Expressions | |

12.31.5. | Further Extensions of the Special Trigonometric Ratios |

12.32. Graphing Trigonometric Functions

12.32.1. | Graphing Sine and Cosine | |

12.32.2. | Graphing Tangent and Cotangent | |

12.32.3. | Graphing Secant and Cosecant |

12.33. Properties of Trigonometric Functions

12.33.1. | Describing Properties of the Sine Function | |

12.33.2. | Describing Properties of the Cosine Function | |

12.33.3. | Describing Properties of the Tangent Function | |

12.33.4. | Describing Properties of the Secant Function | |

12.33.5. | Describing Properties of the Cosecant Function | |

12.33.6. | Describing Properties of the Cotangent Function |

12.34. Graph Transformations of Trigonometric Functions

12.34.1. | Vertical Translations of Trigonometric Functions | |

12.34.2. | Vertical Stretches of Trigonometric Functions | |

12.34.3. | Horizontal Translations of Trigonometric Functions | |

12.34.4. | Horizontal Stretches of Trigonometric Functions | |

12.34.5. | Combining Graph Transformations of Sine and Cosine | |

12.34.6. | Graph Transformations of Tangent and Cotangent | |

12.34.7. | Combining Graph Transformations of Tangent and Cotangent | |

12.34.8. | Combining Graph Transformations of Secant and Cosecant | |

12.34.9. | Graphing Reflections of Trigonometric Functions | |

12.34.10. | Graphing Reflections of Trigonometric Functions: Three or More Transformations |

12.35. Properties of Transformed Trigonometric Functions

12.35.1. | Properties of Transformed Sine and Cosine Functions | |

12.35.2. | Finding Zeros and Extrema of Transformed Sine and Cosine Functions | |

12.35.3. | Properties of Transformed Tangent and Cotangent Functions | |

12.35.4. | Properties of Transformed Secant and Cosecant Functions | |

12.35.5. | Interpreting Trigonometric Models | |

12.35.6. | Modeling With Trigonometric Functions |

13.

Probability & Combinatorics
23 topics

13.36. Introduction to Probability

13.36.1. | Sets | |

13.36.2. | Probability From Experimental Data | |

13.36.3. | Sample Spaces and Events in Probability | |

13.36.4. | Single Events in Probability | |

13.36.5. | The Complement of an Event | |

13.36.6. | Venn Diagrams in Probability | |

13.36.7. | Geometric Probability |

13.37. Compound Events in Probability

13.37.1. | The Union of Sets | |

13.37.2. | The Intersection of Sets | |

13.37.3. | Compound Events in Probability From Experimental Data | |

13.37.4. | Computing Probabilities for Compound Events Using Venn Diagrams | |

13.37.5. | Computing Probabilities of Events Containing Complements Using Venn Diagrams | |

13.37.6. | Computing Probabilities for Three Events Using Venn Diagrams | |

13.37.7. | The Addition Law of Probability | |

13.37.8. | Applying the Addition Law With Event Complements | |

13.37.9. | Mutually Exclusive Events |

13.38. Combinatorics

13.38.1. | The Rule of Sum and the Rule of Product | |

13.38.2. | Factorials | |

13.38.3. | Factorials in Variable Expressions | |

13.38.4. | Ordering Objects | |

13.38.5. | Permutations | |

13.38.6. | Combinations | |

13.38.7. | Computing Probabilities Using Combinatorics |

14.

Statistics
8 topics

14.39. Analyzing Data

14.39.1. | Sampling | |

14.39.2. | The Mean of a Data Set | |

14.39.3. | Variance and Standard Deviation | |

14.39.4. | Covariance | |

14.39.5. | The Z-Score |

14.40. Correlation and Regression

14.40.1. | The Linear Correlation Coefficient | |

14.40.2. | Linear Regression | |

14.40.3. | Residuals and Residual Plots |