Math HS I - Algebra II / Intro to Pre-Calculus (Virtual)

Our Math HS I (Advanced Algebra II / Introduction to Pre-Calculus) course is a rigorous course designed for students who are ready to move beyond Algebra I and dive into the deeper and more complex world of advanced mathematics. Building on the foundation established in earlier courses, this class blends advanced Algebra II with a wide range of Pre-Calculus topics to prepare students for future coursework in Calculus, physics, engineering, and beyond.

Students will develop fluency with exponential and logarithmic functions, strengthen their trigonometry skills, and explore key concepts in analytical geometry, vectors, and matrices. The course also introduces students to the fundamental principles of calculus, such as limits, continuity, basic differentiation, and integration—providing a head start on AP or college-level courses.

Through a mix of problem-solving, graphing, and real-world applications, students will build both the conceptual understanding and technical skills necessary for success in advanced math.

Math HS I Topics:

Logarithms and Exponentials

1. Meaning of Logarithms
2. Properties of Logarithms
3. Solving Exponential and Logarithmic Equations
4. Exponential Equations with Logarithms and Writing Logs in Terms of Others
5. Discrete and Continuous Exponential Growth and Decay
6. Graphing Exponential Functions
7. Graphing Logarithmic Functions

Trigonometry

1. Right Triangle Trigonometry and Evaluating Ratios
2. Angles and Angle Measure
3. Coterminal Angles and Reference Angles
4. Unit Circle
5. Exact Trigonometric Values of Special Angles
6. Law of Sines
7. Law of Cosines
8. Graphing Trigonometric Functions $$y=sin⁡x and $$y=cos⁡x
9. Graphing Trigonometric Functions $$y=tan⁡x and $$y=cot⁡x
10. Solving Trigonometric Equations
11. Advanced Topics in Trigonometry

Polynomial and Rational Functions

1. Dividing Polynomials
2. Graphing Polynomial Functions
3. Rational Functions and Their Graphs

Analytical Geometry

1. Conic Sections (Parabolas, Circles, Ellipses, Hyperbolas)
2. Parametric Equations
3. Polar Coordinates and Graphs

Vectors and Their Applications

1. Vector Operations
2. Dot Product and Cross Product
3. Applications in Physics and Engineering

Sequences and Series

1. Arithmetic Sequences and Series
2. Geometric Sequences and Series
3. Sigma Notation
4. Convergence and Divergence
5. Binomial Theorem

Limits and Continuity

1. Understanding Limits
2. Evaluating Limits
3. Continuity and Discontinuities

Introduction to Calculus Concepts

1. Basic Differentiation
2. Basic Integration
3. Area Under a Curve

Complex Numbers

1. Operations with Complex Numbers
2. Polar Form of Complex Numbers
3. De Moivre’s Theorem

Matrices and Determinants

1. Matrix Operations
2. Inverses and Determinants
3. Solving Systems of Equations Using Matrices
4. Applications of Matrices

Enrollment Guidelines:

• Returning AlphaMinds students who have successfully completed our Math MS IV class during the previous school year.

• New Students are admitted by assessment. To request an assessment, please email us at [email protected].