AP Precalculus

Last updated

Advanced Placement (AP) Precalculus (also known as AP Precalc) is an Advanced Placement precalculus course and examination, offered by the College Board, in development since 2021 [1] and announced in May 2022. [2] The course debuted in the fall of 2023, with the first exam session taking place in May 2024. The course and examination are designed to teach and assess precalculus concepts, as a foundation for a wide variety of STEM fields and careers, and are not solely designed as preparation for future mathematics courses such as AP Calculus AB/BC. [3]

Contents

Purpose

According to the College Board,

Offering a college-level precalculus course in high school will give students a new and valuable option for improving math readiness and staying on track for college. [4]

AP Precalculus centers on functions modeling dynamic phenomena. This research-based exploration of functions is designed to better prepare students for college-level calculus and provide grounding for other mathematics and science courses. In this course, students study a broad spectrum of function types that are foundational for careers in mathematics, physics, biology, health science, social science, and data science. Furthermore, as AP Precalculus may be the last mathematics course of a student's secondary education, the course is structured to provide a coherent capstone experience and is not exclusively focused on preparation for future courses. [3]

Topic outline

Unit 1: Polynomial and Rational Functions (6–6.5 weeks)

#Topic TitleRecommended Instructional Periods
1.1Change in Tandem2
1.2Rates of Change2
1.3Rates of Change in Linear and Quadratic Functions2
1.4Polynomial Functions and Rates of Change2
1.5Polynomial Functions and Complex Zeros2
1.6Polynomial Functions and End Behavior1
1.7Rational Functions and End Behavior2
1.8Rational Functions and Zeros1
1.9Rational Functions and Vertical Asymptotes1
1.10Rational Functions and Holes1
1.11Equivalent Representations of Polynomial and Rational Expressions2
1.12Transformations of Functions2
1.13Function Model Selection and Assumption Articulation2
1.14Function Model Construction and Application2

Unit 2: Exponential and Logarithmic Functions (6–6.5 weeks)

#Topic TitleRecommended Instructional Periods
2.1Change in Arithmetic and Geometric Sequences2
2.2Change in Linear and Exponential Functions2
2.3Exponential Functions1
2.4Exponential Function Manipulation2
2.5Exponential Function Context and Data Modeling2
2.6Competing Function Model Validation2
2.7Composition of Functions2
2.8Inverse Functions2
2.9Logarithmic Expressions1
2.10Inverses of Exponential Functions2
2.11Logarithmic Functions1
2.12Logarithmic Function Manipulation2
2.13Exponential and Logarithmic Equations and Inequalities3
2.14Logarithmic Function Context and Data Modeling2
2.15Semi-log Plots2

Unit 3: Trigonometric and Polar Functions (7–7.5 weeks)

#Topic TitleRecommended Instructional Periods
3.1Periodic Phenomena2
3.2Sine, Cosine, and Tangent2
3.3Sine and Cosine Function Values2
3.4Sine and Cosine Function Graphs2
3.5Sinusoidal Functions2
3.6Sinusoidal Function Transformations2
3.7Sinusoidal Function Context and Data Modeling2
3.8The Tangent Function2
3.9Inverse Trigonometric Functions2
3.10Trigonometric Equations and Inequalities3
3.11The Secant, Cosecant, and Cotangent Functions2
3.12Equivalent Representations of Trigonometric Functions2
3.13Trigonometry and Polar Coordinates2
3.14Polar Function Graphs2
3.15Rates of Change in Polar Functions2

Unit 4: Functions Involving Parameters, Vectors, and Matrices (7–7.5 weeks)

#Topic TitleRecommended Instructional Periods
4.1Parametric Functions2
4.2Parametric Functions Modeling Planar Motion2
4.3Parametric Functions and Rates of Change2
4.4Parametrically Defined Circles and Lines2
4.5Implicitly Defined Functions2
4.6Conic Sections3
4.7Parametrization of Implicitly Defined Functions2
4.8Vectors3
4.9Vector-Valued Functions1
4.10Matrices2
4.11The Inverse and Determinant of a Matrix2
4.12Linear Transformations and Matrices1
4.13Matrices as Functions3
4.14Matrices Modeling Contexts3

Note that Unit 4 will not be tested on the AP Precalculus exam. [5]

Exam

The exam is composed of 2 sections, each with 2 different types of questions.

Section I consists of 40 multiple choice questions. 28 do not allow the use of a calculator, while the last 12 do allow a calculator. The non-calculator section is worth 43.75% of the exam score, while the calculator section is worth 18.75%. [5]

Section II of the Exam includes 4 free response questions, with 2 not allowing a calculator and 2 allowing use of a calculator. Section II is worth 37.5% of the exam score, with the non-calculator and calculator sections weighed equally. [5]

AP Precalculus exams will be scored on the standard 1–5 AP scale, with 5 signifying that the student is "extremely well qualified" for equivalent college credit and 1 signifying "no recommendation." [3]

The 2025 AP Precalculus exam is set to take place on Tuesday, May 13, 2025 at 8AM local time. [6]

Score distribution

All information comes from the official College Board website. [7]

Score20242025
525.9%28%
423.9%26%
325.9%27%
214.6%11%
19.8%8%
% of scores 3 or higher75.6%81%
Mean3.42
Standard deviation1.28
Number of students184,394

See also

References

  1. "MAA Blog: Thoughts on AP Precalculus". MATH VALUES. Archived from the original on 2022-05-22. Retrieved 2022-05-26.
  2. "New AP Precalculus Course Will Expand Access to STEM Majors and Careers – Newsroom". newsroom.collegeboard.org. Archived from the original on 2022-05-22. Retrieved 2022-05-26.
  3. 1 2 3 College Board, "AP® Precalculus Proposed Course Framework Archived 2022-05-16 at the Wayback Machine ", 2022. Accessed 26 May 2022.
  4. "AP Precalculus – AP Central | College Board". AP Central. 2022-04-29. Archived from the original on 2022-05-22. Retrieved 2022-05-26.
  5. 1 2 3 "AP Precalculus Course Framework – AP Central | College Board". Archived from the original on 2022-09-10. Retrieved 2022-09-10.
  6. "AP Precalculus – AP Students | College Board". apstudents.collegeboard.org. Archived from the original on 2025-01-27. Retrieved 2025-01-27.
  7. "Past AP Precalculus Score Distributions". College Board. College Board . Retrieved 2025-05-03.