All About the all new AP PreCalculus Exam

AP Precalculus is designed to serve as both a capstone in high school mathematics and a bridge to college-level calculus. This course emphasizes a deep understanding of functions in various forms and their real-world applications. By focusing on multiple representations—graphical, numerical, analytical, and verbal—students build the foundation necessary for tackling advanced topics in mathematics and science.

Detailed Syllabus Breakdown

The College Board organizes the AP Precalculus content into four units. Three of these units (Units 1, 2, and 3) are assessed on the AP Exam, while Unit 4 offers additional topics for schools that wish to extend the curriculum.

Unit 1: Polynomial and Rational Functions

• Content Highlights:

  • Change in Tandem, Rates of Change, and Function Behavior: Topics include polynomial functions, complex zeros, end behavior, and rational functions with an emphasis on vertical asymptotes, holes, and zeros.

    
    

  • Multiple Representations: Students are encouraged to express functions analytically, graphically, and verbally.

    
    

• Exam Weighting: Approximately 30–40% of the AP Exam covers these topics.

  
  

Unit 2: Exponential and Logarithmic Functions

• Content Highlights:

  • Sequences, Function Manipulation, and Data Modeling: This unit focuses on the behavior of exponential functions, inverse functions, logarithmic expressions, and equations, along with context-based data modeling.

    
    

• Exam Weighting: These topics account for 27–40% of the exam.

  
  

Unit 3: Trigonometric and Polar Functions

• Content Highlights:

  • Periodic Phenomena and Trigonometric Representations: Detailed study of sine, cosine, tangent, and their graphs, as well as polar coordinates and modeling periodic contexts.

    
    

• Exam Weighting: Approximately 30–35% of the AP Exam is dedicated to these topics.

  
  

Unit 4: Functions Involving Parameters, Vectors, and Matrices

• Content Highlights:

  • Extended Topics: Although rich in advanced content such as parametric functions, vector-valued functions, and matrix operations, these topics are not assessed on the AP Exam. They provide a valuable extension for schools following state or local requirements.

    
    

The AP Exam Structure

The exam is a three-hour test divided into two main sections, designed to assess both your procedural fluency and conceptual understanding.

Section I: Multiple-Choice (40 Questions)

• Structure:

  • Part A: 28 questions where no calculator is permitted, testing your ability to work through problems without technological aid.

  • Part B: 12 questions that require a graphing calculator (set in radian mode), with selected items specifically designed to leverage technology.

    
    

• Timing & Weighting:

  • Part A: 80 minutes (43.75% of the exam)

  • Part B: 40 minutes (18.75% of the exam)

    
    

• Content Distribution:

  • General functions, polynomial and rational functions, exponential and logarithmic functions, and trigonometric and polar functions are all represented with respective weightings:

    • General Functions: 15–23%

    • Polynomial & Rational Functions: 20–25%

    • Exponential & Logarithmic Functions: 22–28%

    • Trigonometric & Polar Functions: 30–35%

      
      

Section II: Free-Response (4 Questions)

• Structure:

  • Part A (Graphing Calculator Required): 2 questions focused on function concepts and modeling a non-periodic context.

  • Part B (No Calculator): 2 questions; one models a periodic context and the other tests symbolic manipulations.

    
    

• Timing & Weighting:

  • Each of the four questions is worth six points, and they are scored on an analytic scale.

    
    

• Skill Assessment:

  • The free-response section is further broken down by skill weightings, with tasks assessing:

    • Procedural and Symbolic Fluency: (e.g., solving equations, expressing equivalent forms, constructing new functions)

      
      

    • Multiple Representations: (e.g., interpreting and constructing graphical, numerical, and verbal representations)

      
      

    • Communication and Reasoning: (e.g., describing function characteristics, applying numerical results, and supporting conclusions)

      
      

For example, the scoring breakdown for the free-response tasks details that:

• FRQ 1 emphasizes function concepts, drawing on both procedural skills and communication.

• FRQ 2 and FRQ 3 involve modeling contexts, non-periodic and periodic, respectively, with the latter focusing on trigonometric applications.

• FRQ 4 centers on symbolic manipulations, demanding strong algebraic fluency without technological assistance.

Download the Official AP PreCalculus specification and the sample questions released by the College Board here.

Exam Weighting for Skills

The AP Exam doesn’t just test content; it rigorously assesses three key mathematical practices:

1. Procedural and Symbolic Fluency

   • Weighting Examples:

     • Solving equations and inequalities: 14–17%

     • Expressing equivalent forms: 9–13%

     • Constructing new functions: 15–19%

       
       

2. Multiple Representations

   • Weighting Examples:

     • Identifying information from various representations: 14–17%

     • Constructing equivalent representations: 6–9%

       
       

3. Communication and Reasoning

   • Weighting Examples:

     • Describing function characteristics: 10–14%

     • Applying numerical results: 9–13%

     • Supporting conclusions with logical reasoning: 13%

       
       

These detailed weightings ensure that students are evaluated not only on their computational accuracy but also on their ability to communicate mathematical ideas clearly and logically.

Classroom Resources and Instructional Model

The official AP Precalculus specification also provides educators with:

• Unit Guides: These outline the sequence and pacing of topics, offering suggestions based on a full academic year of 45-minute class periods, five days a week.

  
  

• Progress Checks: Formative assessments (both multiple-choice and free-response) help teachers gauge student understanding and provide immediate feedback.

  
  

• Mathematical Practices Integration: The course emphasizes procedural fluency, the ability to interpret multiple representations, and strong communication skills, all of which are integrated throughout the curriculum.

  
  

This comprehensive framework is designed to not only prepare students for the AP Exam but also to build a deep and versatile understanding of mathematics that extends into college-level coursework.

All About AP PreCalculus

AP Precalculus stands as a rigorous, well-structured course that prepares students for advanced studies by demanding both high-level computational skills and deep conceptual understanding. The precise breakdown of topics into four units, with only Units 1, 2, and 3 being assessed, ensures that students focus on the foundational concepts critical for college placement. Coupled with a carefully designed exam that evaluates multiple skill sets, the course is both challenging and rewarding.

For further details refer to the official College Board document .