AP PreCalculus Course Syllabus - Course Description - Assessment Practices - Essential Questions - Curriculum Framework

Sep 20, 2026

Uploaded by Elsa

AP PreCalculus course syllabus for a full academic year, covering all high school PreCalculus topics alongside advanced Algebra and Geometry concepts. Emphasis is placed on fluent conceptual and procedural understanding, abstract and quantitative reasoning, clear mathematical communication, modeling with mathematics, and evaluating conclusions within defined timelines. Students complete varied assessments including quizzes, complex problem-solving explanations, real-world scenario tasks, and AP exam-style questions. Curriculum is organized into four units: polynomial/rational, exponential/logarithmic, trigonometric/polar, and functions with parameters/vectors/matrices, plus optional enrichment topics and assigned resources and grading weights.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

Course Description

Assessment Practices

Essential Questions

Curriculum Framework

Unit/Topic 1: Polynomial and Rational Functions

Unit/Topic 2: Exponential and Logarithmic Functions

Unit/Topic 3: Trigonometric and Polar Functions

Unit/Topic 4: Functions Involving Parameters, Vectors, and Matrices

Resources

Grading

AP PreCalculus Course Syllabus Course Description In this full year AP PreCalculus course, students explore all high school PreCalculus topics as well as advanced Algebra and Geometry concepts. This class requires students to demonstrate fluent understanding of conceptsand procedures, reason abstractly and quantitatively to solve problems, communicate reasoning, model with mathematics, and evaluate conclusions. As in all advanced level courses, students are expected to complete work according to given timelines so they are prepared to move through the curriculum at the required pace. Students who successfully complete this course will be prepared for Calculus I. In alignment with the skills detailed in the Portrait of the Crusader, students in this course solve problems through innovation, imagination, and self-advocacy, and they seek personal relevance in and ownership of learning to become truly college and career ready. Assessment Practices Throughout the course, teachers strive to include varied assessments, including traditional quizzes and tests to measure discrete skills; problem/solution/explanation opportunities where students solve a complex problem and communicate their reasoning; and real-world scenarios where students define the problem, develop a plan, and solve the problem, adjusting as necessary and communicating their reasoning when required. Students practice answering questions modeled after the AP exam throughout the course. Essential Questions 1. How do we use previous math topics from Algebra and Geometry to discover PreCalculus rules? 2. How do we interpret and analyze real life situations using PreCalculus? 3. How do we integrate technology to support PreCalculus topics ? Curriculum Framework Unit/Topic 1 : Polynomial and Rational Functions ● Define change in tandem and rates of change ● Apply rates of change in Linear and quadratic functions ● Apply polynomial functions and rates of change ● Find complex zeros of polynomial and rational functions ● Examine end behavior of polynomial and rational functions ● Define rational functions and vertical asymptotes ● Define rational functions with holes ● Write equivalent representations of polynomial and rational expressions ● Define transformations of functions ● Apply function model selection and assumption articulation ● Apply function model construction and application Unit/Topic 2 : Exponential and Logarithmic Functions ● Explain change in arithmetic and geometric sequences ● Define exponential functions ● Explain change in linear and exponential functions ● Explore exponential function rules ● Apply exponential function context and data modeling ● Apply competing function model validation ● Define composition of functions ● Define inverse and logarithmic functions ● Explore logarithmic function rules ● Solve exponential and logarithmic equations and inequalities ● Apply logarithmic and function context and data modeling ● Apply semi-log plots Unit/Topic 3 : Trigonometric and Polar Functions ● Define periodic phenomena ● Explore sine, cosine, and tangent functions ● Apply sinusoidal functions ● Define sinusoidal function transformations ● Apply sinusoidal function context and data modeling ● Define inverse trigonometric functions ● Solve trigonometric equations and inequalities ● Graph the secant, cosecant, and cotangent functions ● Define polar coordinates ● Graph polar function ● Explore rates of change in polar functions Enrichment if time permits: Analytic Trigonometry ● Verify trigonometric identities ● Apply sum and difference formulas Unit/Topic 4 : Functions Involving Parameters, Vectors, and Matrices ● Define parametric functions ● Apply parametric functions modeling planar motion ● Apply parametric functions and rates of change ● Define parametrically defined circles and lines ● Explain implicitly defined functions ● Define conic secti

FAQs

What skills are students expected to demonstrate in AP PreCalculus?

Students are expected to show fluent understanding of concepts and procedures, reason abstractly and quantitatively, communicate reasoning, model with mathematics, and evaluate conclusions.

How are students assessed throughout the course?

Assessment includes quizzes and tests, opportunities for solving complex problems with explanations and reasoning communication, and real-world scenarios where students define, plan, solve, and communicate adjustments as needed.

What are the main curriculum units in this syllabus?

The course is organized into four units: polynomial and rational functions; exponential and logarithmic functions; trigonometric and polar functions; and functions involving parameters, vectors, and matrices, with optional enrichment topics.

Sep 20, 2026

Uploaded by Elsa