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Algebra 2

High School

This course helps students deepen their algebraic understanding and apply it to real-world problems. Through guided lessons, problem sets, and visualizations, learners will practice everything from polynomial operations to trigonometric modeling. Designed for high school learners, it balances conceptual understanding with application and prepares students for standardized exams and higher-level math courses.

In this course, you will:

Explore polynomial arithmetic, division, and factorization.
Work with complex numbers and graph them on the complex plane.
Use rational exponents and radicals to rewrite expressions.
Build and analyze exponential, logarithmic, and trigonometric models.
Solve advanced equations, including rational, radical, and systems of equations.
Apply transformations to different functions and model real-life contexts.

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Unit 1: Polynomial Arithmetic 6 Lessons | Total 240 min

1. 1: Introduction to Polynomials 40 min

2. 2: Adding Polynomials 40 min

3. 3: Subtracting Polynomials 40 min

4. 4: Multiplying Monomials by Polynomials 40 min

5. 5: Multiplying Binomials & Special Products 40 min

6. 6: Applications of Polynomial Arithmetic 40 min

Unit 2: Complex Numbers 5 Lessons | Total 200 min

1. 1: Introduction to Imaginary Numbers 40 min

2. 2: Arithmetic with Complex Numbers 40 min

3. 3: Complex Conjugates & Division 40 min

4. 4: The Complex Plane & Graphical Representation 40 min

5. 5: Solving Quadratics with Complex Roots 40 min

Unit 3: Polynomial Factorization 7 Lessons | Total 280 min

1. 1: Greatest Common Factor (GCF) of Polynomials 40 min

2. 2: Factoring by Grouping 40 min

3. 3: Factoring Quadratics (ax² + bx + c) 40 min

4. 4: Special Products (Difference of Squares, Perfect Squares) 40 min

5. 4: Special Products (Difference of Squares, Perfect Squares) 40 min

6. 5: Factoring Higher Degree Polynomials 40 min

7. 6: Applications of Factoring in Problem-Solving 40 min

Unit 4: Polynomial Division 5 Lessons | Total 200 min

1. 1: Dividing Polynomials by Monomials 40 min

2. 2: Long Division of Polynomials 40 min

3. 3: Synthetic Division Method 40 min

4. 4: Remainder Theorem & Factor Theorem 40 min

5. 5: Applications of Polynomial Division 40 min

Unit 5: Polynomial Graphs 5 Lessons | Total 200 min

1. 1: Zeros of Polynomials 40 min

2. 2: Multiplicity of Roots & Their Effects 40 min

3. 3: End Behavior of Polynomials 40 min

4. 4: Intervals of Increase/Decrease & Turning Points 40 min

5. 5: Sketching Polynomial Graphs 40 min

Unit 6: Rational Exponents & Radicals 6 Lessons | Total 240 min

1. 1: Defining Rational Exponents 40 min

2. 2: Converting Between Exponents & Radicals 40 min

3. 3: Simplifying Radical Expressions 40 min

4. 4: Operations with Radicals (Add, Subtract, Multiply, Divide) 40 min

5. 5: Rationalizing Denominators 40 min

6. 6: Applications of Radical Functions 40 min

Unit 7: Exponential Models 5 Lessons | Total 200 min

1. 1: Review of Exponential Functions 40 min

2. 2: Exponential Growth Models 40 min

3. 3: Exponential Decay Models 40 min

4. 4: Compound Interest & Financial Applications 40 min

5. 5: Half-Life Problems & Population Growth 40 min

Unit 8: Logarithms 5 Lessons | Total 200 min

1. 1: Introduction to Logarithms 40 min

2. 2: Laws of Logarithms 40 min

3. 3: Change of Base Formula 40 min

4. 4: Solving Exponential Equations with Logarithms 40 min

5. 5: Applications of Logarithmic Models 40 min

Unit 9: Transformations of Functions 5 Lessons | Total 200 min

1. 1: Shifts (Vertical & Horizontal) 40 min

2. 2: Reflections Across Axes 40 min

3. 3: Vertical & Horizontal Stretch/Compression 40 min

4. 4: Symmetry in Functions 40 min

5. 5: Transformations of Square Root, Exponential, and Logarithmic Functions 40 min

Unit 10: Equations 5 Lessons | Total 200 min

1. 1: Rational Equations & Restrictions 40 min

2. 2: Square Root Equations 40 min

3. 3: Cube Root Equations 40 min

4. 4: Extraneous Solutions 40 min

5. 5: Systems of Equations (Substitution, Elimination, Graphing) 40 min

Unit 11: Trigonometry 6 Lessons | Total 240 min

1. 1: Introduction to Trigonometric Functions 40 min

2. 2: Graphs of Sine, Cosine, and Tangent 40 min

3. 3: Amplitude, Period, & Phase Shift 40 min

4. 4: Law of Sines 40 min

5. 5: Law of Cosines 40 min

6. 6: Applications of Trigonometric Models 40 min

Unit 12: Modeling 5 Lessons | Total 200 min

1. 1: Function Combinations & Composition in Modeling 40 min

2. 2: Modeling with Multiple Variables 40 min

3. 3: Interpreting Features of Functions in Context 40 min

4. 4: Real-World Applications (Finance, Science, Engineering) 40 min

5. 5: Capstone Project: Building a Complete Model 40 min

Algebra 2

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