Course syllabus
AP® Precalculus
A High Bluff Academy course, authorized through the College Board's AP Course Audit.
AP® Precalculus is a course about functions as models of change. The College Board's framework covers polynomial, rational, exponential, logarithmic, trigonometric, and polar functions, and, in Unit 4, parametric, implicitly defined, and vector-valued functions and matrices. Each family of functions is used to model how quantities change together.
The College Board designed AP Precalculus to prepare students for college-level calculus and to give a grounding for other mathematics and science courses. Because it may be a student's last high school mathematics course, the College Board also structured it as a coherent capstone in its own right.
The College Board describes AP Precalculus as the equivalent of a first-semester college precalculus course.
The College Board's AP Precalculus framework has four units. Units 1, 2, and 3 cover what colleges and universities typically expect for college credit or placement, and they are assessed on the AP Exam. Unit 4 covers additional topics that schools may include, and it is not assessed on the AP Exam.
High Bluff Academy's course includes all four units.
Course identification
- Course title
- AP Precalculus
- Subject area
- Mathematics
- AP authorization
- Authorized through the College Board's AP Course Audit
- Framework
- College Board, AP Precalculus Course and Exam Description, effective fall 2026
- Length
- Two semesters of credit; the calendar length depends on the format
- Prerequisites
- The recommended preparation below; High Bluff Academy may ask for placement testing
- Term
- Set at enrollment
Credit and accreditation
- School of record
- High Bluff Academy
- CEEB code
- 053036
- AP Exam
- Given at High Bluff Academy, an official College Board testing site
- Accreditation
- Accrediting Commission for Schools, Western Association of Schools and Colleges (ACS WASC)
- Credits
- 10 credits: 5 for each semester
- Grading
- A letter grade for each semester, recorded on the High Bluff Academy transcript
- Transcript title
- AP Precalculus, with the AP designation
High Bluff Academy is a private, college-preparatory school in Rancho Santa Fe, California. It offers coursework leading to a high school diploma and grants that diploma. The course is authorized through the College Board's AP Course Audit, which permits High Bluff Academy to use the AP designation for the course on student transcripts. One enrollment covers both semesters: a student earns 5 credits for each semester passed and 10 credits for the full course. A semester is passed with a grade of D or better.
How the course is offered
High Bluff Academy offers AP Precalculus in person as a group class, one-on-one with a teacher, and online, with a High Bluff Academy teacher as the teacher of record. The course framework, the credit, and the transcript record are the same in every format. Availability of each format may vary with enrollment and demand.
Recommended preparation
The College Board recommends that students begin the course with the topics of the Algebra 1, Geometry, and Algebra 2 sequence behind them.
Proficiency in
- Linear and quadratic functions: manipulating them algebraically, and solving the related equations and inequalities
- Adding and multiplying polynomials, factoring quadratic trinomials, and using the quadratic formula
- Solving right-triangle problems with trigonometry
- Solving systems of equations in two and three variables
Familiarity with
- Piecewise-defined functions
- Exponential functions and the rules for exponents
- Radicals, such as square roots and cube roots
- Complex numbers
- Communicating and reasoning with graphical, numerical, analytical, and verbal representations of functions
High Bluff Academy may ask for an unofficial transcript and placement testing before a student enrolls in a mathematics course.
Units and topics
Unit 1
Polynomial and Rational Functions
Assessed on the AP Exam
How quantities change together and how rates of change are measured, then polynomial and rational functions: zeros, including complex zeros, end behavior, vertical asymptotes and holes, equivalent forms, and transformations. The unit closes by selecting, building, and applying function models.
- 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
Unit 2
Exponential and Logarithmic Functions
Assessed on the AP Exam
Arithmetic and geometric sequences alongside linear and exponential change, then exponential functions, composition and inverse functions, logarithmic expressions and functions, exponential and logarithmic equations and inequalities, modeling data and validating competing models, and semi-log plots.
- 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
Unit 3
Trigonometric and Polar Functions
Assessed on the AP Exam
Periodic phenomena and the sine, cosine, and tangent functions, sinusoidal functions, their transformations, and sinusoidal models of data, inverse trigonometric functions, trigonometric equations and inequalities, the secant, cosecant, and cotangent functions, equivalent trigonometric forms, and polar coordinates, polar graphs, and rates of change in polar functions.
- 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
Unit 4
Functions Involving Parameters, Vectors, and Matrices
Not assessed on the AP Exam
Parametric functions and planar motion, implicitly defined functions and conic sections, vectors and vector-valued functions, and matrices: inverses and determinants, linear transformations, and matrices as functions and as models of contexts.
- 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
Mathematical practices
The College Board organizes the skills of AP Precalculus into three mathematical practices, which it expects students to build throughout the course.
Practice 1
Procedural and Symbolic Fluency
Working with functions, equations, and expressions algebraically.
- 1.ASolve equations and inequalities given in analytical form, with and without technology.
- 1.BRewrite functions, equations, and expressions in analytically equivalent forms suited to a mathematical or applied context.
- 1.CBuild new functions through transformations, composition, inverses, or regression to model contexts, criteria, or data, with and without technology.
Practice 2
Multiple Representations
Translating mathematical information from one representation to another.
- 2.ARead information from graphical, numerical, analytical, and verbal representations to answer a question or build a model, with and without technology.
- 2.BProduce equivalent graphical, numerical, analytical, and verbal representations of a function suited to a mathematical or applied context, with and without technology.
Practice 3
Communication and Reasoning
Communicating with precise language and giving reasons for conclusions.
- 3.ADescribe the characteristics of a function as precisely as its representation and the available tools allow.
- 3.BApply numerical results in a mathematical or applied context.
- 3.CSupport conclusions or choices with logical reasoning or appropriate data.
Function modeling runs through the framework: students select a model from stated criteria or from data, build it, state the assumptions behind it, and check it against competing models (topics such as 1.13, 1.14, 2.5, 2.6, 2.14, and 3.7).
The course gives students opportunities to develop all three practices, including choosing, constructing, and defending function models.
Assessment and grading
Each semester grade is built from the categories below, which carry the weights High Bluff Academy usually uses. Every format includes a midterm examination and a final examination each semester.
| Category | Weight | What it covers |
|---|---|---|
| Homework | 40% | Homework assigned during the semester |
| Tests | 40% | Tests during the semester, including the midterm examination |
| Final examination | 20% | The examination at the end of the semester |
Academic integrity
Work submitted for a grade must be the student's own. Tests and exams are taken under the conditions the teacher sets, including whether a calculator is allowed, and the College Board's rules apply on the AP Exam.
Graphing calculator
The College Board treats a graphing calculator as an integral part of AP Precalculus, and one is required on two parts of the AP Exam. It also expects technology to support, not replace, symbolic work by hand.
The College Board expects students to practice using a graphing calculator to perform calculations, graph functions and read their graphs, make tables of values, find real zeros, points of intersection, and maximum and minimum values, solve equations in one variable numerically, fit regression models and plot their residuals, and perform matrix operations.
Every student has individual access to a graphing calculator for coursework, and the web or app version of the Desmos graphing calculator is one way to have it. A handheld calculator from the College Board's approved list is optional; a student who plans to use one on the AP Exam should practice with it during the year.
During the school year, the College Board allows the web or app version of the Desmos graphing calculator in place of, or alongside, a handheld calculator, and it says the Desmos graphing calculator has the capabilities expected for the AP Precalculus Exam. On the AP Exam, the Desmos calculator must be the one built into the testing app; the web or app version cannot be used.
The AP Exam
The AP Precalculus Exam assesses Units 1, 2, and 3. It lasts 2 hours and 55 minutes and has two sections.
| Part | Questions | Time | Share of score | Calculator |
|---|---|---|---|---|
| Section I, Part A: multiple choice | 29 | 65 minutes | 43.75% | Not permitted |
| Section I, Part B: multiple choice | 13 | 40 minutes | 18.75% | Graphing calculator required |
| Section II, Part A: free response | 2 | 35 minutes | 18.75% | Graphing calculator required |
| Section II, Part B: free response | 2 | 35 minutes | 18.75% | Not permitted |
| Section I | 42 | 105 minutes | 62.5% | |
| Section II | 4 | 70 minutes | 37.5% | |
| Exam total | 46 | 175 minutes | 100% |
On the exam, a Desmos graphing calculator is built into the testing app for the calculator parts, and students may also bring up to two handheld graphing calculators from the College Board's approved list. Calculators should be set to radian mode.
Each free-response question is scored out of 6 points, and two of the four set the mathematics in a real-world modeling context. Students answer the multiple-choice questions and read the free-response questions in the College Board's digital testing app, and they handwrite their free-response answers in a paper booklet.
Scores are reported on a scale of 1 to 5. This is the exam format in effect from the May 2027 exam. The AP Exam is given in schools in May.
High Bluff Academy is an official College Board testing site, and students enrolled in the course can take the AP Exam there.
A student who takes the AP Exam at a school other than the one where they take the course, or who takes the exam without taking the course, gets a join code from the AP coordinator at the school where they will test and joins an exam-only section there.
Materials and technology
- Graphing calculator
- The Desmos graphing calculator on the web or as an app, or a handheld model from the College Board's approved list
- Course framework
- apcentral.collegeboard.org/courses/ap-precalculus