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Curriculum
- 6 Sections
- 51 Lessons
- 10 Weeks
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- 🧠 UNIT 1: Polynomial and Rational FunctionsThis unit develops strong command over polynomial and rational functions through algebraic manipulation, graphical behavior, and contextual interpretation. Students learn how structure affects shape, end behavior, and real-world meaning.9
- 1.1Understanding Polynomial Functions
- 1.2Polynomial Function Graphs & End Behavior
- 1.3Zeros, Multiplicity, and Graphical Behavior
- 1.4Transformations of Polynomial Functions
- 1.5Rational Functions & Asymptotes
- 1.6Holes, Intercepts, and Discontinuities
- 1.7Solving Polynomial & Rational Equations
- 1.8Modeling with Polynomial & Rational Functions
- 1.9Unit 1 AP-Style Practice & Concept Review
- 📈 UNIT 2: Exponential and Logarithmic FunctionsStudents build a deep understanding of trigonometric functions using the unit circle, graphs, and identities. The unit also introduces polar coordinates and their connection to periodic motion.9
- 2.1Introduction to Exponential Function
- 2.2Exponential Growth & Decay Models
- 2.3Graphical and Algebraic Properties of Exponentials
- 2.4Introduction to Logarithmic Functions
- 2.5Logarithmic Laws & Properties
- 2.6Solving Exponential & Logarithmic Equations
- 2.7Inverse Functions: Exponential ↔ Logarithmic
- 2.8Real-World Modeling with Logs & Exponentials
- 2.9Unit 2 AP-Style Practice & Strategy Session
- 🔁 UNIT 3: Trigonometric and Polar FunctionsThis unit strengthens higher-level reasoning through functions with parameters, matrix operations, and vector representation. Students learn to analyze how changing parameters affects outcomes—an essential AP skill.9
- 4.1Angles, Radians & the Unit Circle
- 4.2Sine, Cosine, and Tangent Functions
- 4.3Graphs of Trigonometric Functions
- 4.4Amplitude, Period & Phase Shifts
- 4.5Trigonometric Identities & Equations
- 4.6Inverse Trigonometric Functions
- 4.7Modeling Periodic Phenomena
- 4.8Introduction to Polar Coordinates
- 4.9Unit 3 AP-Style Practice & Mixed Review
- 🔄 UNIT 4: Functions Involving Parameters, Vectors & MatricesThis unit strengthens higher-level reasoning through functions with parameters, matrix operations, and vector representation. Students learn to analyze how changing parameters affects outcomes—an essential AP skill.9
- 5.1Function Composition & Inverses
- 5.2Functions with Parameters
- 5.3Understanding Vectors in the Plane
- 5.4Vector Operations & Applications
- 5.5Matrices & Matrix Operations
- 5.6Solving Systems Using Matrices
- 5.7Modeling with Vectors & Matrices
- 5.8Interpreting Results in Context
- 5.9Unit 4 AP-Style Practice & Concept Integration
- 🧩 UNIT 5: Modeling, Multiple Representations & Mathematical ReasoningThis unit integrates all previous concepts and emphasizes justification, interpretation, and communication. Students learn to move seamlessly between representations and explain reasoning clearly—crucial for AP free-response success.9
- 6.1Multiple Representations of Functions
- 6.2Interpreting Graphs and Tables
- 6.3Mathematical Modeling Strategies
- 6.4Selecting Appropriate Function Models
- 6.5Error Analysis & Reasonableness
- 6.6Writing Mathematical Justifications
- 6.7Mixed Function Comparisons
- 6.8AP Free-Response Style Questions
- 6.9Unit 5 Cumulative Review
- 📝 FINAL EXAM PREPARATION MODULEA focused module designed to maximize AP exam performance through targeted practice, strategy, and time management.6
Multiple Representations of Functions
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