Algebra 101

This unit introduces the fundamental building blocks of algebra, including variables, expressions, order of operations, and properties of real numbers. Students learn to simplify expressions and develop a strong foundation for solving equations and understanding mathematical relationships.

Students learn techniques to solve linear and multi-step equations, including those with variables on both sides. This unit also covers inequalities, compound inequalities, and absolute value equations, preparing students to model and solve real-world problems algebraically.

This unit covers graphing points on the coordinate plane, understanding the concept of a function, and interpreting function notation. Students learn to graph linear equations and inequalities, explore slope concepts, and begin analyzing the relationship between algebraic and graphical representations.

Students explore methods for solving systems of equations, including graphing, substitution, and elimination. The unit emphasizes problem-solving and applications, introducing systems of inequalities and real-world scenarios that require algebraic modeling.

This unit introduces polynomials, their operations, and factoring techniques. Students learn to add, subtract, multiply, and divide polynomials, apply special product rules, and factor trinomials and other special cases, building skills to solve quadratic equations efficiently.

Students study quadratic functions and equations, exploring their graphs, vertex, and axis of symmetry. Techniques for solving quadratics, including factoring, completing the square, and the quadratic formula, are covered, along with an introduction to complex numbers and transformations of quadratic functions.

This unit focuses on higher-degree polynomials, their graphs, end behavior, and turning points. Students learn the Remainder and Factor Theorems, synthetic division, and the Fundamental Theorem of Algebra, preparing them to analyze and solve more complex polynomial equations.

Students simplify, multiply, divide, add, and subtract rational expressions. The unit covers solving rational equations, identifying extraneous solutions, and graphing rational functions, including asymptotes and intercepts, with applications to real-world algebraic problems.

This unit explores radicals and rational exponents, teaching students to simplify and perform operations with radicals. Students solve radical equations and graph radical functions, deepening their understanding of algebraic relationships involving roots and fractional exponents.

Students apply the laws of exponents, explore exponential functions, and model growth and decay. The unit introduces logarithms, their properties, and solving exponential and logarithmic equations, highlighting applications in science, finance, and real-world problem solving.

This unit covers arithmetic and geometric sequences and series, including infinite geometric series. Students learn formulas for sums, explore patterns, and apply the Binomial Theorem to expand powers of binomials, connecting algebraic concepts to broader mathematical structures.

Students study circles, parabolas, ellipses, and hyperbolas, analyzing their equations and key features. Applications of conic sections in geometry and real-world contexts are emphasized, bridging algebraic manipulation and geometric visualization.

This unit examines both linear and nonlinear systems of equations and inequalities. Students solve these systems algebraically and graphically, apply problem-solving strategies, and explore mixed and advanced real-world scenarios requiring algebraic reasoning.

Students explore basic probability, counting principles, and combinatorics. Descriptive statistics, probability distributions, and expected values are covered, enabling students to interpret data, make predictions, and connect algebraic reasoning with statistical concepts.

Introduces fundamental trigonometric concepts, including angles, the unit circle, and trigonometric functions. Students learn to graph functions, solve basic trigonometric equations, and apply identities to solve problems, preparing for advanced algebraic and pre-calculus studies.

This unit covers the Law of Sines and Cosines, sum/difference formulas, double and half-angle identities, and advanced trigonometric equations. Students apply these concepts to real-world and mathematical problems, strengthening algebraic reasoning and pre-calculus readiness.