About Course

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