Library
AP Precalculus
Study AP Precalculus
Revise a topic
Got a question wrong? Open the notes for that topic.
Teaching this subject? Everything for the classroom in one place →
Downloads
- Course & Exam Description
- Revision Sheet
- Syllabus Checklist
- Scheme of Work
- Exam Technique
- Command Words — A3 poster
- Lesson Plans — one page per topic
- Class Mark Book
1. Polynomial and Rational Functions 40 files
Handouts
Presentation slides
Exercise walk-through slides
- 1.1 Change in Tandem
- 1.2 Rates of Change
- 1.3 Rates of Change in Linear and Quadratic Functions
- 1.4 Polynomial Functions and Rates of Change
- 1.5 Polynomial Functions and Complex Zeros
- 1.6 Polynomial Functions and End Behavior
- 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
- 1.14 Function Model Construction and Application
Vocabulary
Topic Quizzes
Exercise sheets
- 1.1 Change in Tandem
- 1.2 Rates of Change
- 1.3 Rates of Change in Linear and Quadratic Functions
- 1.4 Polynomial Functions and Rates of Change
- 1.5 Polynomial Functions and Complex Zeros
- 1.6 Polynomial Functions and End Behavior
- 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
- 1.14 Function Model Construction and Application
Past Paper Questions
Unit Tests
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
- 2.4 Exponential Function Manipulation
- 2.5 Exponential Function Context and Data Modeling
- 2.6 Competing Function Model Validation
- 2.7 Composition of Functions
- 2.8 Inverse Functions
- 2.9 Logarithmic Expressions
- 2.10 Inverses of Exponential Functions
- 2.11 Logarithmic Functions
- 2.12 Logarithmic Function Manipulation
- 2.13 Exponential and Logarithmic Equations and Inequalities
- 2.14 Logarithmic Function Context and Data Modeling
- 2.15 Semi-log Plots
Vocabulary
Topic Quizzes
Exercise sheets
- 2.1 Change in Arithmetic and Geometric Sequences
- 2.2 Change in Linear and Exponential Functions
- 2.3 Exponential Functions
- 2.4 Exponential Function Manipulation
- 2.5 Exponential Function Context and Data Modeling
- 2.6 Competing Function Model Validation
- 2.7 Composition of Functions
- 2.8 Inverse Functions
- 2.9 Logarithmic Expressions
- 2.10 Inverses of Exponential Functions
- 2.11 Logarithmic Functions
- 2.12 Logarithmic Function Manipulation
- 2.13 Exponential and Logarithmic Equations and Inequalities
- 2.14 Logarithmic Function Context and Data Modeling
- 2.15 Semi-log Plots
Past Paper Questions
- 2.3 Exponential Functions
- 2.4 Exponential Function Manipulation
- 2.5 Exponential Function Context and Data Modeling
- 2.6 Competing Function Model Validation
- 2.7 Composition of Functions
- 2.8 Inverse Functions
- 2.10 Inverses of Exponential Functions
- 2.11 Logarithmic Functions
- 2.12 Logarithmic Function Manipulation
- 2.13 Exponential and Logarithmic Equations and Inequalities
- 2.14 Logarithmic Function Context and Data Modeling
Unit Tests
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
- 3.5 Sinusoidal Functions
- 3.6 Sinusoidal Function Transformations
- 3.7 Sinusoidal Function Context and Data Modeling
- 3.8 The Tangent Function
- 3.9 Inverse Trigonometric Functions
- 3.10 Trigonometric Equations and Inequalities
- 3.11 The Secant, Cosecant, and Cotangent Functions
- 3.12 Equivalent Representations of Trigonometric Functions
- 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
- 3.2 Sine, Cosine, and Tangent
- 3.3 Sine and Cosine Function Values
- 3.4 Sine and Cosine Function Graphs
- 3.5 Sinusoidal Functions
- 3.6 Sinusoidal Function Transformations
- 3.7 Sinusoidal Function Context and Data Modeling
- 3.8 The Tangent Function
- 3.9 Inverse Trigonometric Functions
- 3.10 Trigonometric Equations and Inequalities
- 3.11 The Secant, Cosecant, and Cotangent Functions
- 3.12 Equivalent Representations of Trigonometric Functions
- 3.13 Trigonometry and Polar Coordinates
- 3.14 Polar Function Graphs
- 3.15 Rates of Change in Polar Functions
Past Paper Questions
Unit Tests
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
- 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
- AP Precalculus — Question index
- 1.1 Change in Tandem
- 1.2 Rates of Change
- 1.3 Rates of Change in Linear and Quadratic Functions
- 1.5 Polynomial Functions and Complex Zeros
- 1.6 Polynomial Functions and End Behavior
- 1.13 Function Model Selection and Assumption Articulation
- 1.14 Function Model Construction and Application
- 2.3 Exponential Functions
- 2.4 Exponential Function Manipulation
- 2.5 Exponential Function Context and Data Modeling
- 2.6 Competing Function Model Validation
- 2.7 Composition of Functions
- 2.8 Inverse Functions
- 2.10 Inverses of Exponential Functions
- 2.11 Logarithmic Functions
- 2.12 Logarithmic Function Manipulation
- 2.13 Exponential and Logarithmic Equations and Inequalities
- 2.14 Logarithmic Function Context and Data Modeling
- 3.4 Sine and Cosine Function Graphs
- 3.5 Sinusoidal Functions
- 3.6 Sinusoidal Function Transformations
- 3.9 Inverse Trigonometric Functions
- 3.10 Trigonometric Equations and Inequalities
- 3.12 Equivalent Representations of Trigonometric Functions
Topic quizzes
- 1. Polynomial and Rational Functions
- 2. Exponential and Logarithmic Functions
- 3. Trigonometric and Polar Functions
- 4. Functions Involving Parameters, Vectors, and Matrices
Unit tests
- 1. Polynomial and Rational Functions
- 2. Exponential and Logarithmic Functions
- 3. Trigonometric and Polar Functions
Mock papers
Course companion
Glossary
Topic handouts
- 1.1 Change in Tandem
- 1.2 Rates of Change
- 1.3 Rates of Change in Linear and Quadratic Functions
- 1.4 Polynomial Functions and Rates of Change
- 1.5 Polynomial Functions and Complex Zeros
- 1.6 Polynomial Functions and End Behavior
- 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
- 1.14 Function Model Construction and Application
- 2.1 Change in Arithmetic and Geometric Sequences
- 2.2 Change in Linear and Exponential Functions
- 2.3 Exponential Functions
- 2.4 Exponential Function Manipulation
- 2.5 Exponential Function Context and Data Modeling
- 2.6 Competing Function Model Validation
- 2.7 Composition of Functions
- 2.8 Inverse Functions
- 2.9 Logarithmic Expressions
- 2.10 Inverses of Exponential Functions
- 2.11 Logarithmic Functions
- 2.12 Logarithmic Function Manipulation
- 2.13 Exponential and Logarithmic Equations and Inequalities
- 2.14 Logarithmic Function Context and Data Modeling
- 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
- 3.5 Sinusoidal Functions
- 3.6 Sinusoidal Function Transformations
- 3.7 Sinusoidal Function Context and Data Modeling
- 3.8 The Tangent Function
- 3.9 Inverse Trigonometric Functions
- 3.10 Trigonometric Equations and Inequalities
- 3.11 The Secant, Cosecant, and Cotangent Functions
- 3.12 Equivalent Representations of Trigonometric Functions
- 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
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
- 1.2 Rates of Change
- 1.3 Rates of Change in Linear and Quadratic Functions
- 1.4 Polynomial Functions and Rates of Change
- 1.5 Polynomial Functions and Complex Zeros
- 1.6 Polynomial Functions and End Behavior
- 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
- 1.14 Function Model Construction and Application
- 2.1 Change in Arithmetic and Geometric Sequences
- 2.2 Change in Linear and Exponential Functions
- 2.3 Exponential Functions
- 2.4 Exponential Function Manipulation
- 2.5 Exponential Function Context and Data Modeling
- 2.6 Competing Function Model Validation
- 2.7 Composition of Functions
- 2.8 Inverse Functions
- 2.9 Logarithmic Expressions
- 2.10 Inverses of Exponential Functions
- 2.11 Logarithmic Functions
- 2.12 Logarithmic Function Manipulation
- 2.13 Exponential and Logarithmic Equations and Inequalities
- 2.14 Logarithmic Function Context and Data Modeling
- 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
- 3.5 Sinusoidal Functions
- 3.6 Sinusoidal Function Transformations
- 3.7 Sinusoidal Function Context and Data Modeling
- 3.8 The Tangent Function
- 3.9 Inverse Trigonometric Functions
- 3.10 Trigonometric Equations and Inequalities
- 3.11 The Secant, Cosecant, and Cotangent Functions
- 3.12 Equivalent Representations of Trigonometric Functions
- 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. Exponential and Logarithmic Functions
- 3. Trigonometric and Polar Functions
- 4. Functions Involving Parameters, Vectors, and Matrices
Flashcards
Weekly vocab tests
- Week 1 · Topic 1 · Polynomial and Rational Functions
- Week 2 · Topic 1 · Polynomial and Rational Functions
- Week 3 · Topic 2 · Exponential and Logarithmic Functions
- Week 4 · Topics 2–3 · Exponential and Logarithmic Functions, Trigonometric and Polar Functions
- Week 5 · Topics 1–4 · Polynomial and Rational Functions, Trigonometric and Polar Functions, Functions Involving Parameters, Vectors, and Matrices
Weekly homework
Exercise sheets
- Complete pack — exercise sheets + past papers
- 1 Polynomial and Rational Functions — Part 1
- 1 Polynomial and Rational Functions — Part 2
- 2 Exponential and Logarithmic Functions — Part 1
- 2 Exponential and Logarithmic Functions — Part 2
- 3 Trigonometric and Polar Functions — Part 1
- 3 Trigonometric and Polar Functions — Part 2
- 4 Functions Involving Parameters, Vectors, and Matrices — Part 1
- 4 Functions Involving Parameters, Vectors, and Matrices — Part 2
Past papers
- 1.1 Change in Tandem
- 1.2 Rates of Change
- 1.3 Rates of Change in Linear and Quadratic Functions
- 1.5 Polynomial Functions and Complex Zeros
- 1.6 Polynomial Functions and End Behavior
- 1.13 Function Model Selection and Assumption Articulation
- 1.14 Function Model Construction and Application
- 2.3 Exponential Functions
- 2.4 Exponential Function Manipulation
- 2.5 Exponential Function Context and Data Modeling
- 2.6 Competing Function Model Validation
- 2.7 Composition of Functions
- 2.8 Inverse Functions
- 2.10 Inverses of Exponential Functions
- 2.11 Logarithmic Functions
- 2.12 Logarithmic Function Manipulation
- 2.13 Exponential and Logarithmic Equations and Inequalities
- 2.14 Logarithmic Function Context and Data Modeling
- 3.4 Sine and Cosine Function Graphs
- 3.5 Sinusoidal Functions
- 3.6 Sinusoidal Function Transformations
- 3.9 Inverse Trigonometric Functions
- 3.10 Trigonometric Equations and Inequalities
- 3.12 Equivalent Representations of Trigonometric Functions
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.