AP Precalculus

Course Overview

Our AP Precalculus course is designed to provide students with a comprehensive foundation in advanced mathematical concepts essential for success in calculus and higher-level mathematics. This course bridges the gap between Algebra 2 and AP Calculus, emphasizing deep conceptual understanding, mathematical reasoning, and problem-solving techniques.

AP Precalculus covers polynomial, rational, exponential, logarithmic, and trigonometric functions, along with their applications. Students will develop strong analytical skills through the study of sequences, series, and mathematical modeling. This course prepares students not only for the AP exam but also for success in AP Calculus and college-level mathematics.

What Makes Our Course Special

What You'll Learn

• Master all major function families: polynomial, rational, exponential, logarithmic, and trigonometric
• Develop strong analytical skills for examining function behavior and transformations
• Build expertise in trigonometry including identities, equations, and applications
• Learn sequences, series, and their applications in mathematical modeling
• Practice advanced problem-solving techniques and mathematical reasoning
• Develop skills in mathematical modeling and real-world applications
• Build the foundation necessary for success in AP Calculus
• Master exam strategies for AP Precalculus success

Detailed Course Curriculum

• Unit 1: Polynomial and Rational Functions 12 hours

  Comprehensive study of polynomial and rational functions, their properties, and applications.

  • Polynomial functions: degree, leading coefficient, and end behavior
  • Zeros, factors, and the Fundamental Theorem of Algebra
  • Rational functions: asymptotes, discontinuities, and behavior
  • Function transformations and their effects on graphs
  • Applications and mathematical modeling with polynomial and rational functions

• Unit 2: Exponential and Logarithmic Functions 10 hours

  Exponential and logarithmic functions with applications to growth, decay, and modeling.

  • Exponential functions: properties, graphs, and applications
  • Logarithmic functions and their relationship to exponentials
  • Properties of logarithms and solving exponential equations
  • Applications: compound interest, population growth, radioactive decay
  • Mathematical modeling with exponential and logarithmic functions

• Unit 3: Trigonometric and Polar Functions 15 hours

  Comprehensive trigonometry including functions, identities, and polar coordinates.

  • Unit circle and trigonometric functions
  • Graphs of trigonometric functions and their transformations
  • Trigonometric identities and solving trigonometric equations
  • Applications of trigonometry to real-world problems
  • Introduction to polar coordinates and polar functions

• Unit 4: Functions Involving Parameters, Vectors, and Matrices 10 hours

  Advanced function concepts including parametric equations, vectors, and matrices.

  • Parametric equations and their applications
  • Vector operations and applications
  • Matrix operations and systems of equations
  • Function composition and inverse functions
  • Advanced function analysis and transformations

• Unit 5: Sequences and Series 8 hours

  Arithmetic and geometric sequences and series with applications.

  • Arithmetic sequences and series
  • Geometric sequences and series
  • Convergence and divergence of infinite series
  • Applications of sequences and series
  • Mathematical induction and recursive relationships

• Unit 6: Exam Preparation and Review 5 hours

  Comprehensive review and exam preparation strategies.

  • Review of all major concepts and problem-solving strategies
  • Practice with released AP Precalculus exam questions
  • Time management and exam strategy techniques
  • Final assessment and performance analysis
  • Last-minute review and confidence building

Ready to Master Advanced Mathematics?

AP Precalculus provides the essential mathematical foundation for success in calculus and advanced STEM courses. This course will not only prepare you for the AP exam but also develop the analytical thinking skills and mathematical maturity necessary for continued success in mathematics, science, and engineering.

Students who complete AP Precalculus with strong understanding find themselves well-prepared for the rigor of AP Calculus and college-level mathematics. The course emphasizes both computational skills and conceptual understanding, creating a solid foundation for lifelong mathematical learning.