Honors Algebra 2: Polynomials and Complex Numbers

By the end of this course, learners will be able to analyze, graph, and transform polynomial functions, apply techniques such as factoring, division, and the Remainder and Factor Theorems to solve higher-order equations, and use the Fundamental Theorem of Algebra to understand the complete set of polynomial solutions. They will also develop fluency with complex numbers, performing arithmetic operations, representing them in both algebraic and geometric forms, and applying them to solve equations that have no real solutions. As the second course in the three-part Honors Algebra 2 specialization, this class moves beyond routine algebraic skills to build deep mathematical reasoning. Students will see how polynomials and complex numbers provide the foundation for modern algebra, engineering, and physics, while practicing advanced problem-solving strategies that encourage both precision and creativity. What makes this course unique is its balance of rigor and accessibility. Learners progress through challenging concepts with step-by-step guidance, visual explanations, and real-world applications that demonstrate why these topics matter. Completing this course prepares students not only to excel in advanced high school mathematics but also to transition confidently into college-level coursework.

This is the third course in the Honors Algebra 2 sequence. By the end of this course, students will be able to analyze, interpret, and apply advanced families of functions, including exponential, logarithmic, radical, and inverse functions. Learners will develop fluency in evaluating and graphing these functions, solving equations that involve them, and applying their properties to real-world models and predictions. Along the way, students will deepen their understanding of how different function types connect, building a stronger algebraic foundation for future courses in precalculus, calculus, and beyond.

This course is designed not only to strengthen core problem-solving skills but also to highlight the power of mathematics as a tool for describing patterns and solving practical problems. What makes this course unique is its balance between theory and application: students gain a clear understanding of the underlying algebraic rules while also engaging with meaningful contexts such as growth and decay, investment modeling, and data analysis. By completing this course, learners will be prepared to tackle higher-level mathematics with confidence and insight.

Honors Algebra 2: Sequences, Series, Trigonometry, & Probability is the fourth part of a four-part specialization, an engaging, application-focused course that explores how algebra connects to patterns, prediction, and data-driven decision-making. Designed for high school students, college-prep learners, and adult learners refreshing their skills, this course is aligned with the Common Core State Standards and is ideal for independent study through Coursera.

You’ll begin by analyzing sequences and series, uncovering the structure of arithmetic and geometric patterns and using them to model real-world phenomena like interest growth and population trends. The course then transitions to trigonometry, starting with the fundamental relationships in right triangles. You will master the core trigonometric ratios of sine, cosine, and tangent and their reciprocals. Building on this foundation, you’ll explore key trigonometric identities and use them to simplify complex expressions and solve equations. This understanding culminates in exploring trigonometric functions on the unit circle, revealing them as powerful tools for describing periodic behavior—essential in science, engineering, and even music and design. From there, you’ll shift into introductory probability and statistics, learning how to quantify uncertainty, interpret two-way tables, and distinguish between theoretical and experimental results. In the data analysis portion, you’ll evaluate datasets, calculate measures of central tendency and variability, and draw informed conclusions—skills essential in today’s data-driven world. Whether you're interested in STEM, business, or simply making sense of the information around you, this course provides a deep yet accessible look at how algebra helps you describe, analyze, and predict the world around you. With interactive learning and a clear, concept-driven approach, you'll build a strong foundation for future math courses and practical applications alike.