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