AP PreCalculus - Study Guides, Flashcards, AP-style Practice & Mock Exams
Prepare for the test with our complete AP PreCalculus exam prep, which organizes the entire curriculum into clear units and topics. From polynomial functions to polar coordinates, you can solidify your understanding using our extensive practice materials and get ready to demonstrate your knowledge on exam day.
Course Overview
This course explores the properties and applications of polynomial, rational, exponential, logarithmic, trigonometric, and polar functions. Students will develop proficiency in modeling real-world phenomena and analyzing function behavior, including rates of change. A key focus is preparation for the AP exam format, which requires strategic problem-solving across distinct non-calculator vs calculator sections. Mastery of the official calculator policy is essential, as is the ability to construct clear, logical arguments for the free-response questions. The curriculum also introduces foundational concepts such as parametric equations, vectors, and recursion, providing a comprehensive bridge to calculus-level studies.
The course is structured for systematic preparation across four units. Students should progress by mastering each topic sequentially, using the AP-style quizzes as immediate progress checks. These assessments help identify areas requiring targeted review before attempting the comprehensive Unit Exams. This cyclical process of learning and evaluation builds the foundation needed to tackle the full-length mock exams, which simulate the official testing environment. With over 1900 practice questions available, students have ample opportunity to refine their pacing and problem-solving strategies for all sections of the exam.
Units & Topics
Unit 1: Polynomial and Rational Functions
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We will explore how polynomial and rational functions model real-world scenarios by analyzing their rates of change, key features, and behavior using foundational concepts of limits.
- 1.0Unit Overview
- 1.1Change in Tandem
- 1.2Rates of Change
- 1.3Rates of Change in Linear and Quadratic Functions
- 1.4Polynomial Functions and Rates of Change
- 1.5Polynomial Functions and Complex Zeros
- 1.6Polynomial Functions and End Behavior
- 1.7Rational Functions and End Behavior
- 1.8Rational Functions and Zeros
- 1.9Rational Functions and Vertical Asymptotes
- 1.10Rational Functions and Holes
- 1.11Equivalent Representations of Polynomial and Rational Expressions
- 1.12Transformations of Functions
- 1.13Function Model Selection and Assumption Articulation
- 1.14Function Model Construction and Application
- 1.15Unit Exam
Unit 2: Exponential and Logarithmic Functions
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This unit connects discrete sequences to continuous functions, exploring the inverse relationship between exponential and logarithmic models through transformations, equations, and regression.
- 2.0Unit Overview
- 2.1Change in Arithmetic and Geometric Sequences
- 2.2Change in Linear and Exponential Functions
- 2.3Exponential Functions
- 2.4Exponential Function Manipulation
- 2.5Exponential Function Context and Data Modeling
- 2.6Competing Function Model Validation
- 2.7Composition of Functions
- 2.8Inverse Functions
- 2.9Logarithmic Expressions
- 2.10Inverses of Exponential Functions
- 2.11Logarithmic Functions
- 2.12Logarithmic Function Manipulation
- 2.13Exponential and Logarithmic Equations and Inequalities
- 2.14Logarithmic Function Context and Data Modeling
- 2.15Semi-log Plots
- 2.16Unit Exam
Unit 3: Trigonometric and Polar Functions
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We will analyze the properties and graphs of circular functions, apply them to model data, and extend these concepts to polar coordinates, preparing for derivatives.
- 3.0Unit Overview
- 3.1Periodic Phenomena
- 3.2Sine, Cosine, and Tangent
- 3.3Sine and Cosine Function Values
- 3.4Sine and Cosine Function Graphs
- 3.5Sinusoidal Functions
- 3.6Sinusoidal Function Transformations
- 3.7Sinusoidal Function Context and Data Modeling
- 3.8The Tangent Function
- 3.9Inverse Trigonometric Functions
- 3.10Trigonometric Equations and Inequalities
- 3.11The Secant, Cosecant, and Cotangent Functions
- 3.12Equivalent Representations of Trigonometric Functions
- 3.13Trigonometry and Polar Coordinates
- 3.14Polar Function Graphs
- 3.15Rates of Change in Polar Functions
- 3.16Unit Exam
Unit 4: Functions Involving Parameters, Vectors, and Matrices
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We will model motion and transformations using parametric equations, vectors, and matrices, introducing the concept of limits to analyze rates of change.
- 4.0Unit Overview
- 4.1Parametric Functions
- 4.2Parametric Functions Modeling Planar Motion
- 4.3Parametric Functions and Rates of Change
- 4.4Parametrically Defined Circles and Lines
- 4.5Implicitly Defined Functions
- 4.6Conic Sections
- 4.7Parametrization of Implicitly Defined Functions
- 4.8Vectors
- 4.9Vector-Valued Functions
- 4.10Matrices
- 4.11The Inverse and Determinant of a Matrix
- 4.12Linear Transformations and Matrices
- 4.13Matrices as Functions
- 4.14Matrices Modeling Contexts
- 4.15Unit Exam
Frequently Asked Questions
What is the format of the AP Precalculus exam?
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The exam has two sections: a 120-minute Multiple-Choice Question (MCQ) section and a 60-minute Free-Response Question (FRQ) section. Both sections are divided into two parts: one where a graphing calculator is permitted and one where it is not. This structure tests both your conceptual understanding and your computational fluency.
Is a calculator allowed on the AP Precalculus exam?
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Yes, a graphing calculator is required for designated portions of the exam. Both the MCQ and FRQ sections have calculator-active and non-calculator parts. You must be proficient in using your calculator for tasks like graphing functions and finding zeros, as well as solving problems algebraically without it.
What major topics are covered in AP Precalculus?
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The course covers four major units that build a deep understanding of function families. You will master polynomial, rational, exponential, and logarithmic functions before moving on to trigonometric and polar functions. The curriculum also introduces concepts involving vectors, matrices, and parametric equations to prepare you for calculus.
How should I use this platform to study for the exam?
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We recommend a sequential approach over approximately 39 hours for best results. Work through the units and their 58 topics, using the AP-style quizzes to check comprehension. Solidify your learning with unit exams, and then gauge your overall readiness by taking our full-length mock exams under timed conditions.
What are the Free-Response Questions (FRQs) like?
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The FRQs require you to provide detailed, step-by-step solutions with written justifications. These multi-part questions often synthesize concepts, asking you to model a real-world scenario with trigonometric functions or analyze the behavior of rational functions using their algebraic properties and limits.
How is the AP Precalculus exam scored?
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Your final score is a composite of the MCQ and FRQ sections, which is then scaled to the 1–5 range. The MCQ section assesses a broad range of content knowledge, while the FRQs evaluate your ability to apply multiple skills, justify your reasoning, and communicate your mathematical understanding clearly.
What skills are tested in the non-calculator sections?
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The non-calculator sections test your conceptual understanding and symbolic fluency. You must demonstrate mastery of core skills like solving logarithmic equations, applying trigonometric identities, and determining the end behavior of polynomial functions without technological aid. Strong foundational algebra skills are critical for success here.
What key mathematical skills does this course develop?
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This course develops your procedural and symbolic fluency with complex functions. Key skills include moving between multiple representations of functions (algebraic, graphical, numerical, and verbal), justifying mathematical reasoning, and applying appropriate rules to model dynamic phenomena using functions like exponential and trigonometric expressions.
Are there any formula sheets provided on the exam?
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No, there is no formula sheet provided on the AP Precalculus exam. You are expected to have memorized key formulas and identities, such as trigonometric identities, properties of logarithms, and formulas for sequences and series. Our 1951 flashcards are a great tool for memorizing this essential information.
How can I best prepare for the exam's timing?
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Practicing under timed conditions is the best way to prepare for the exam's pacing. With over 1946 practice questions and 3 full-length mock exams, you can simulate the pressure of the 3-hour test. This helps you build stamina and learn to efficiently allocate your time between the calculator and non-calculator sections.
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