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AP Precalculus
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- Course & Exam Description 2-up
- Revision Sheet
- Syllabus Checklist 2-up
- Scheme of Work
- Exam Technique 2-up
- Command Words — A3 poster
- Lesson Plans — one page per topic 2-up
- Class Mark Book
1. Polynomial and Rational Functions 40 files
Handouts
Presentation slides
Exercise walk-through slides
- 1.1 Change in Tandem Past-paper walk-through
- 1.2 Rates of Change Past-paper walk-through
- 1.3 Rates of Change in Linear and Quadratic Functions Past-paper walk-through
- 1.4 Polynomial Functions and Rates of Change
- 1.5 Polynomial Functions and Complex Zeros Past-paper walk-through
- 1.6 Polynomial Functions and End Behavior Past-paper walk-through
- 1.7 Rational Functions and End Behavior
- 1.8 Rational Functions and Zeros
- 1.9 Rational Functions and Vertical Asymptotes
- 1.10 Rational Functions and Holes
- 1.11 Equivalent Representations of Polynomial and Rational Expressions
- 1.12 Transformations of Functions
- 1.13 Function Model Selection and Assumption Articulation Past-paper walk-through
- 1.14 Function Model Construction and Application Past-paper walk-through
Vocabulary
Topic Quizzes
Exercise sheets
- 1.1 Change in Tandem 2-up
- 1.2 Rates of Change 2-up
- 1.3 Rates of Change in Linear and Quadratic Functions 2-up
- 1.4 Polynomial Functions and Rates of Change 2-up
- 1.5 Polynomial Functions and Complex Zeros 2-up
- 1.6 Polynomial Functions and End Behavior 2-up
- 1.7 Rational Functions and End Behavior 2-up
- 1.8 Rational Functions and Zeros 2-up
- 1.9 Rational Functions and Vertical Asymptotes 2-up
- 1.10 Rational Functions and Holes 2-up
- 1.11 Equivalent Representations of Polynomial and Rational Expressions 2-up
- 1.12 Transformations of Functions 2-up
- 1.13 Function Model Selection and Assumption Articulation 2-up
- 1.14 Function Model Construction and Application 2-up
Past Paper Questions
- 1.1 Change in Tandem 2-upAnswers2-up
- 1.2 Rates of Change 2-upAnswers2-up
- 1.3 Rates of Change in Linear and Quadratic Functions 2-upAnswers2-up
- 1.5 Polynomial Functions and Complex Zeros 2-upAnswers2-up
- 1.6 Polynomial Functions and End Behavior 2-upAnswers2-up
- 1.13 Function Model Selection and Assumption Articulation 2-upAnswers2-up
- 1.14 Function Model Construction and Application 2-upAnswers2-up
2. Exponential and Logarithmic Functions 46 files
Presentation slides
Exercise walk-through slides
- 2.1 Change in Arithmetic and Geometric Sequences
- 2.2 Change in Linear and Exponential Functions
- 2.3 Exponential Functions Past-paper walk-through
- 2.4 Exponential Function Manipulation Past-paper walk-through
- 2.5 Exponential Function Context and Data Modeling Past-paper walk-through
- 2.6 Competing Function Model Validation Past-paper walk-through
- 2.7 Composition of Functions Past-paper walk-through
- 2.8 Inverse Functions Past-paper walk-through
- 2.9 Logarithmic Expressions
- 2.10 Inverses of Exponential Functions Past-paper walk-through
- 2.11 Logarithmic Functions Past-paper walk-through
- 2.12 Logarithmic Function Manipulation Past-paper walk-through
- 2.13 Exponential and Logarithmic Equations and Inequalities Past-paper walk-through
- 2.14 Logarithmic Function Context and Data Modeling Past-paper walk-through
- 2.15 Semi-log Plots
Vocabulary
Topic Quizzes
Exercise sheets
- 2.1 Change in Arithmetic and Geometric Sequences 2-up
- 2.2 Change in Linear and Exponential Functions 2-up
- 2.3 Exponential Functions 2-up
- 2.4 Exponential Function Manipulation 2-up
- 2.5 Exponential Function Context and Data Modeling 2-up
- 2.6 Competing Function Model Validation 2-up
- 2.7 Composition of Functions 2-up
- 2.8 Inverse Functions 2-up
- 2.9 Logarithmic Expressions 2-up
- 2.10 Inverses of Exponential Functions 2-up
- 2.11 Logarithmic Functions 2-up
- 2.12 Logarithmic Function Manipulation 2-up
- 2.13 Exponential and Logarithmic Equations and Inequalities 2-up
- 2.14 Logarithmic Function Context and Data Modeling 2-up
- 2.15 Semi-log Plots 2-up
Past Paper Questions
- 2.3 Exponential Functions 2-upAnswers2-up
- 2.4 Exponential Function Manipulation 2-up
- 2.5 Exponential Function Context and Data Modeling 2-up
- 2.6 Competing Function Model Validation 2-upAnswers2-up
- 2.7 Composition of Functions 2-upAnswers2-up
- 2.8 Inverse Functions 2-upAnswers2-up
- 2.10 Inverses of Exponential Functions 2-upAnswers2-up
- 2.11 Logarithmic Functions 2-up
- 2.12 Logarithmic Function Manipulation 2-upAnswers2-up
- 2.13 Exponential and Logarithmic Equations and Inequalities 2-upAnswers2-up
- 2.14 Logarithmic Function Context and Data Modeling 2-upAnswers2-up
3. Trigonometric and Polar Functions 41 files
Handouts
Presentation slides
Exercise walk-through slides
- 3.1 Periodic Phenomena
- 3.2 Sine, Cosine, and Tangent
- 3.3 Sine and Cosine Function Values
- 3.4 Sine and Cosine Function Graphs Past-paper walk-through
- 3.5 Sinusoidal Functions Past-paper walk-through
- 3.6 Sinusoidal Function Transformations Past-paper walk-through
- 3.7 Sinusoidal Function Context and Data Modeling
- 3.8 The Tangent Function
- 3.9 Inverse Trigonometric Functions Past-paper walk-through
- 3.10 Trigonometric Equations and Inequalities Past-paper walk-through
- 3.11 The Secant, Cosecant, and Cotangent Functions
- 3.12 Equivalent Representations of Trigonometric Functions Past-paper walk-through
- 3.13 Trigonometry and Polar Coordinates
- 3.14 Polar Function Graphs
- 3.15 Rates of Change in Polar Functions
Vocabulary
Topic Quizzes
Exercise sheets
- 3.1 Periodic Phenomena 2-up
- 3.2 Sine, Cosine, and Tangent 2-up
- 3.3 Sine and Cosine Function Values 2-up
- 3.4 Sine and Cosine Function Graphs 2-up
- 3.5 Sinusoidal Functions 2-up
- 3.6 Sinusoidal Function Transformations 2-up
- 3.7 Sinusoidal Function Context and Data Modeling 2-up
- 3.8 The Tangent Function 2-up
- 3.9 Inverse Trigonometric Functions 2-up
- 3.10 Trigonometric Equations and Inequalities 2-up
- 3.11 The Secant, Cosecant, and Cotangent Functions 2-up
- 3.12 Equivalent Representations of Trigonometric Functions 2-up
- 3.13 Trigonometry and Polar Coordinates 2-up
- 3.14 Polar Function Graphs 2-up
- 3.15 Rates of Change in Polar Functions 2-up
Past Paper Questions
- 3.4 Sine and Cosine Function Graphs 2-upAnswers2-up
- 3.5 Sinusoidal Functions 2-upAnswers2-up
- 3.6 Sinusoidal Function Transformations 2-upAnswers2-up
- 3.9 Inverse Trigonometric Functions 2-upAnswers2-up
- 3.10 Trigonometric Equations and Inequalities 2-upAnswers2-up
- 3.12 Equivalent Representations of Trigonometric Functions 2-upAnswers2-up
4. Functions Involving Parameters, Vectors, and Matrices 32 files
Presentation slides
Exercise walk-through slides
- 4.1 Parametric Functions
- 4.2 Parametric Functions Modeling Planar Motion
- 4.3 Parametric Functions and Rates of Change
- 4.4 Parametrically Defined Circles and Lines
- 4.5 Implicitly Defined Functions
- 4.6 Conic Sections
- 4.7 Parametrization of Implicitly Defined Functions
- 4.8 Vectors
- 4.9 Vector-Valued Functions
- 4.10 Matrices
- 4.11 The Inverse and Determinant of a Matrix
- 4.12 Linear Transformations and Matrices
- 4.13 Matrices as Functions
- 4.14 Matrices Modeling Contexts
Topic Quizzes
Exercise sheets
- 4.1 Parametric Functions 2-up
- 4.2 Parametric Functions Modeling Planar Motion 2-up
- 4.3 Parametric Functions and Rates of Change 2-up
- 4.4 Parametrically Defined Circles and Lines 2-up
- 4.5 Implicitly Defined Functions 2-up
- 4.6 Conic Sections 2-up
- 4.7 Parametrization of Implicitly Defined Functions 2-up
- 4.8 Vectors 2-up
- 4.9 Vector-Valued Functions 2-up
- 4.10 Matrices 2-up
- 4.11 The Inverse and Determinant of a Matrix 2-up
- 4.12 Linear Transformations and Matrices 2-up
- 4.13 Matrices as Functions 2-up
- 4.14 Matrices Modeling Contexts 2-up
2026 1 files
- 2026 Questions
- AP Precalculus — Question index 2-up
- 1.1 Change in Tandem 2-upAnswers2-up
- 1.2 Rates of Change 2-upAnswers2-up
- 1.3 Rates of Change in Linear and Quadratic Functions 2-upAnswers2-up
- 1.5 Polynomial Functions and Complex Zeros 2-upAnswers2-up
- 1.6 Polynomial Functions and End Behavior 2-upAnswers2-up
- 1.13 Function Model Selection and Assumption Articulation 2-upAnswers2-up
- 1.14 Function Model Construction and Application 2-upAnswers2-up
- 2.3 Exponential Functions 2-upAnswers2-up
- 2.4 Exponential Function Manipulation 2-up
- 2.5 Exponential Function Context and Data Modeling 2-up
- 2.6 Competing Function Model Validation 2-upAnswers2-up
- 2.7 Composition of Functions 2-upAnswers2-up
- 2.8 Inverse Functions 2-upAnswers2-up
- 2.10 Inverses of Exponential Functions 2-upAnswers2-up
- 2.11 Logarithmic Functions 2-up
- 2.12 Logarithmic Function Manipulation 2-upAnswers2-up
- 2.13 Exponential and Logarithmic Equations and Inequalities 2-upAnswers2-up
- 2.14 Logarithmic Function Context and Data Modeling 2-upAnswers2-up
- 3.4 Sine and Cosine Function Graphs 2-upAnswers2-up
- 3.5 Sinusoidal Functions 2-upAnswers2-up
- 3.6 Sinusoidal Function Transformations 2-upAnswers2-up
- 3.9 Inverse Trigonometric Functions 2-upAnswers2-up
- 3.10 Trigonometric Equations and Inequalities 2-upAnswers2-up
- 3.12 Equivalent Representations of Trigonometric Functions 2-upAnswers2-up
Topic quizzes
- 1. Polynomial and Rational Functions 2-up
- 2. Exponential and Logarithmic Functions 2-up
- 3. Trigonometric and Polar Functions 2-up
- 4. Functions Involving Parameters, Vectors, and Matrices 2-up
Unit tests
- 1. Polynomial and Rational Functions 2-upAnswers2-up
- 2. Exponential and Logarithmic Functions 2-upAnswers2-up
- 3. Trigonometric and Polar Functions 2-upAnswers2-up
Mock papers
Course companion
Glossary
Topic handouts
- 1.1 Change in Tandem 2-up
- 1.2 Rates of Change 2-up
- 1.3 Rates of Change in Linear and Quadratic Functions 2-up
- 1.4 Polynomial Functions and Rates of Change 2-up
- 1.5 Polynomial Functions and Complex Zeros 2-up
- 1.6 Polynomial Functions and End Behavior 2-up
- 1.7 Rational Functions and End Behavior 2-up
- 1.8 Rational Functions and Zeros 2-up
- 1.9 Rational Functions and Vertical Asymptotes 2-up
- 1.10 Rational Functions and Holes 2-up
- 1.11 Equivalent Representations of Polynomial and Rational Expressions 2-up
- 1.12 Transformations of Functions 2-up
- 1.13 Function Model Selection and Assumption Articulation 2-up
- 1.14 Function Model Construction and Application 2-up
- 2.1 Change in Arithmetic and Geometric Sequences 2-up
- 2.2 Change in Linear and Exponential Functions 2-up
- 2.3 Exponential Functions 2-up
- 2.4 Exponential Function Manipulation 2-up
- 2.5 Exponential Function Context and Data Modeling 2-up
- 2.6 Competing Function Model Validation 2-up
- 2.7 Composition of Functions 2-up
- 2.8 Inverse Functions 2-up
- 2.9 Logarithmic Expressions 2-up
- 2.10 Inverses of Exponential Functions 2-up
- 2.11 Logarithmic Functions 2-up
- 2.12 Logarithmic Function Manipulation 2-up
- 2.13 Exponential and Logarithmic Equations and Inequalities 2-up
- 2.14 Logarithmic Function Context and Data Modeling 2-up
- 2.15 Semi-log Plots 2-up
- 3.1 Periodic Phenomena 2-up
- 3.2 Sine, Cosine, and Tangent 2-up
- 3.3 Sine and Cosine Function Values 2-up
- 3.4 Sine and Cosine Function Graphs 2-up
- 3.5 Sinusoidal Functions 2-up
- 3.6 Sinusoidal Function Transformations 2-up
- 3.7 Sinusoidal Function Context and Data Modeling 2-up
- 3.8 The Tangent Function 2-up
- 3.9 Inverse Trigonometric Functions 2-up
- 3.10 Trigonometric Equations and Inequalities 2-up
- 3.11 The Secant, Cosecant, and Cotangent Functions 2-up
- 3.12 Equivalent Representations of Trigonometric Functions 2-up
- 3.13 Trigonometry and Polar Coordinates 2-up
- 3.14 Polar Function Graphs 2-up
- 3.15 Rates of Change in Polar Functions 2-up
- 4.1 Parametric Functions 2-up
- 4.2 Parametric Functions Modeling Planar Motion 2-up
- 4.3 Parametric Functions and Rates of Change 2-up
- 4.4 Parametrically Defined Circles and Lines 2-up
- 4.5 Implicitly Defined Functions 2-up
- 4.6 Conic Sections 2-up
- 4.7 Parametrization of Implicitly Defined Functions 2-up
- 4.8 Vectors 2-up
- 4.9 Vector-Valued Functions 2-up
- 4.10 Matrices 2-up
- 4.11 The Inverse and Determinant of a Matrix 2-up
- 4.12 Linear Transformations and Matrices 2-up
- 4.13 Matrices as Functions 2-up
- 4.14 Matrices Modeling Contexts 2-up
Lesson slides
- 1. Polynomial and Rational Functions
- 2. Exponential and Logarithmic Functions
- 3. Trigonometric and Polar Functions
- 4. Functions Involving Parameters, Vectors, and Matrices
Lesson slides
- 1.1 Change in Tandem Past-paper walk-through
- 1.2 Rates of Change Past-paper walk-through
- 1.3 Rates of Change in Linear and Quadratic Functions Past-paper walk-through
- 1.4 Polynomial Functions and Rates of Change
- 1.5 Polynomial Functions and Complex Zeros Past-paper walk-through
- 1.6 Polynomial Functions and End Behavior Past-paper walk-through
- 1.7 Rational Functions and End Behavior
- 1.8 Rational Functions and Zeros
- 1.9 Rational Functions and Vertical Asymptotes
- 1.10 Rational Functions and Holes
- 1.11 Equivalent Representations of Polynomial and Rational Expressions
- 1.12 Transformations of Functions
- 1.13 Function Model Selection and Assumption Articulation Past-paper walk-through
- 1.14 Function Model Construction and Application Past-paper walk-through
- 2.1 Change in Arithmetic and Geometric Sequences
- 2.2 Change in Linear and Exponential Functions
- 2.3 Exponential Functions Past-paper walk-through
- 2.4 Exponential Function Manipulation Past-paper walk-through
- 2.5 Exponential Function Context and Data Modeling Past-paper walk-through
- 2.6 Competing Function Model Validation Past-paper walk-through
- 2.7 Composition of Functions Past-paper walk-through
- 2.8 Inverse Functions Past-paper walk-through
- 2.9 Logarithmic Expressions
- 2.10 Inverses of Exponential Functions Past-paper walk-through
- 2.11 Logarithmic Functions Past-paper walk-through
- 2.12 Logarithmic Function Manipulation Past-paper walk-through
- 2.13 Exponential and Logarithmic Equations and Inequalities Past-paper walk-through
- 2.14 Logarithmic Function Context and Data Modeling Past-paper walk-through
- 2.15 Semi-log Plots
- 3.1 Periodic Phenomena
- 3.2 Sine, Cosine, and Tangent
- 3.3 Sine and Cosine Function Values
- 3.4 Sine and Cosine Function Graphs Past-paper walk-through
- 3.5 Sinusoidal Functions Past-paper walk-through
- 3.6 Sinusoidal Function Transformations Past-paper walk-through
- 3.7 Sinusoidal Function Context and Data Modeling
- 3.8 The Tangent Function
- 3.9 Inverse Trigonometric Functions Past-paper walk-through
- 3.10 Trigonometric Equations and Inequalities Past-paper walk-through
- 3.11 The Secant, Cosecant, and Cotangent Functions
- 3.12 Equivalent Representations of Trigonometric Functions Past-paper walk-through
- 3.13 Trigonometry and Polar Coordinates
- 3.14 Polar Function Graphs
- 3.15 Rates of Change in Polar Functions
- 4.1 Parametric Functions
- 4.2 Parametric Functions Modeling Planar Motion
- 4.3 Parametric Functions and Rates of Change
- 4.4 Parametrically Defined Circles and Lines
- 4.5 Implicitly Defined Functions
- 4.6 Conic Sections
- 4.7 Parametrization of Implicitly Defined Functions
- 4.8 Vectors
- 4.9 Vector-Valued Functions
- 4.10 Matrices
- 4.11 The Inverse and Determinant of a Matrix
- 4.12 Linear Transformations and Matrices
- 4.13 Matrices as Functions
- 4.14 Matrices Modeling Contexts
Vocabulary lists
- 1. Polynomial and Rational Functions 2-up
- 2. Exponential and Logarithmic Functions 2-up
- 3. Trigonometric and Polar Functions 2-up
- 4. Functions Involving Parameters, Vectors, and Matrices
Flashcards
Weekly vocab tests
- Week 1 · Topic 1 · Polynomial and Rational Functions 2-upAnswer key
- Week 2 · Topic 1 · Polynomial and Rational Functions 2-upAnswer key
- Week 3 · Topic 2 · Exponential and Logarithmic Functions 2-upAnswer key
- Week 4 · Topics 2–3 · Exponential and Logarithmic Functions, Trigonometric and Polar Functions 2-upAnswer key
- Week 5 · Topics 1–4 · Polynomial and Rational Functions, Trigonometric and Polar Functions, Functions Involving Parameters, Vectors, and Matrices 2-upAnswer key
Weekly homework
Exercise sheets
- Complete pack — exercise sheets + past papers 2-up
- 1 Polynomial and Rational Functions — Part 1 2-upAnswer key
- 1 Polynomial and Rational Functions — Part 2 2-upAnswer key
- 2 Exponential and Logarithmic Functions — Part 1 2-upAnswer key
- 2 Exponential and Logarithmic Functions — Part 2 2-upAnswer key
- 3 Trigonometric and Polar Functions — Part 1 2-upAnswer key
- 3 Trigonometric and Polar Functions — Part 2 2-upAnswer key
- 4 Functions Involving Parameters, Vectors, and Matrices — Part 1 2-upAnswer key
- 4 Functions Involving Parameters, Vectors, and Matrices — Part 2 2-upAnswer key
Past papers
- 1.1 Change in Tandem Answers2-up
- 1.2 Rates of Change Answers2-up
- 1.3 Rates of Change in Linear and Quadratic Functions Answers2-up
- 1.5 Polynomial Functions and Complex Zeros Answers2-up
- 1.6 Polynomial Functions and End Behavior Answers2-up
- 1.13 Function Model Selection and Assumption Articulation Answers2-up
- 1.14 Function Model Construction and Application Answers2-up
- 2.3 Exponential Functions Answers2-up
- 2.4 Exponential Function Manipulation
- 2.5 Exponential Function Context and Data Modeling
- 2.6 Competing Function Model Validation Answers2-up
- 2.7 Composition of Functions Answers2-up
- 2.8 Inverse Functions Answers2-up
- 2.10 Inverses of Exponential Functions 2-upAnswers2-up
- 2.11 Logarithmic Functions
- 2.12 Logarithmic Function Manipulation Answers2-up
- 2.13 Exponential and Logarithmic Equations and Inequalities Answers2-up
- 2.14 Logarithmic Function Context and Data Modeling 2-upAnswers2-up
- 3.4 Sine and Cosine Function Graphs Answers2-up
- 3.5 Sinusoidal Functions Answers2-up
- 3.6 Sinusoidal Function Transformations Answers2-up
- 3.9 Inverse Trigonometric Functions 2-upAnswers2-up
- 3.10 Trigonometric Equations and Inequalities Answers2-up
- 3.12 Equivalent Representations of Trigonometric Functions Answers2-up
Tips
Answer in sentences, not symbols. The rubric wants "as x increases, f increases at a decreasing rate" — a correct sketch or a correct derivative-like statement in symbols does not replace it.
Work with the graphing calculator you will use in the exam, and know which questions permit it. Fluency with the tool is worth marks; discovering its menus during the exam is not.
Note which parent function each question is really about. Sorting the released questions that way makes the underlying pattern visible far faster than working through papers in order.