This comprehensive Precalculus course bridges the gap between Algebra II and Calculus. Students explore functions, graphs, polynomial and rational expressions, trigonometry, analytic geometry, and introductory limits and derivatives. With real-world modeling, detailed explanations, and a strong emphasis on reasoning and problem-solving, students develop the skills and mindset necessary for higher-level mathematics. The course includes interactive lessons, assessments, and application-based projects aligned with national and AP-level standards.

Key Benefits:

• Builds deep conceptual understanding of algebra, functions, and trigonometry
• Strengthens logical reasoning, graphing, and modeling skills
• Prepares students for AP Calculus and college-level math
• Includes practice with real-world applications and challenging problems
• Supports mastery with quizzes, projects, and visual tools

What You’ll Learn:

Semester A: Core Algebra & Trigonometric Foundations
Functions & Graphs

• Function notation, domain & range

• Piecewise, inverse, and composite functions

• Transformations and behavior analysis

Linear Functions

• Slope, intercepts, modeling with lines

• Scatter plots, regression, and line of best fit

• Systems of linear equations

Polynomial & Rational Functions

• Quadratics, complex numbers, and power functions

• Zeros, factor and remainder theorems

• Rational expressions, asymptotes, and end behavior

Exponential & Logarithmic Functions

• Growth/decay models, compound interest

• Logarithmic properties and equations

• Real-world modeling using exponential/logarithmic data

Trigonometric Functions

• Angles, unit circle, sine/cosine/tangent graphs

• Radian vs degree measures

• Circular motion and applications

Periodic Functions

• Graphing sine, cosine, tangent, secant, cosecant, cotangent

• Phase shifts, amplitude, frequency

• Inverse trig functions and composite expressions

Semester B: Identities, Geometry & Intro to Calculus
Trigonometric Identities & Equations

• Pythagorean, sum/difference, double/half-angle identities

• Solving trig equations and modeling real-life cycles

Advanced Trigonometry & Vectors

• Law of Sines and Cosines

• Polar coordinates and complex numbers in polar form

• Parametric equations and vector operations

Systems, Matrices & Determinants

• Solving linear/nonlinear systems

• Matrix operations and Cramer’s Rule

• Gaussian elimination and inverse matrices

Analytic Geometry

• Parabolas, ellipses, hyperbolas

• Rotated conics and polar graphing of conic sections

Sequences, Probability & Counting

• Arithmetic & geometric sequences/series

• Binomial Theorem

• Permutations, combinations, and basic probability