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About the Course
Taking AP Precalculus prepares you for other college-level mathematics and science courses. During the course, you’ll explore everyday situations using mathematical tools and lenses. You’ll also develop an understanding of modeling and functions, and examine scenarios through multiple representations. The course framework outlines content and skills needed for careers in mathematics, physics, biology, health science, social science, and data science.
Skills You'll Learn
Algebraically manipulating functions, equations, and expressions
Translating mathematical information between representations
Communicating with precise language, and providing rationales for conclusions
Equivalency and Prerequisites
College Course Equivalent
A college precalculus course or a college algebra with trigonometry course.
Recommended Prerequisites
You should have successfully completed introductory algebra and geometry courses. In particular, you should be able to demonstrate proficiency with linear functions, polynomial addition and multiplication, factoring quadratic trinomials, using the quadratic formula, solving right triangle problems involving trigonometry, solving linear and quadratic equations and inequalities, algebraic manipulation of linear equations and expressions, and solving systems of equations in two and three variables. You should also be familiar with piecewise-defined functions, exponential functions and rules for exponents, radicals (e.g., square roots, cube roots), and complex numbers.
Exam Date
About the Units
The course content outlined below is organized into commonly taught units of study that provide one possible sequence for the course. Your teacher may choose to organize the course content differently based on local priorities and preferences.
Course Content
Unit 1: Polynomial and Rational Functions
You’ll expand your understanding of polynomial and rational functions through the lenses of modeling and various rates of change.
Topics may include:
- Describing how quantities change with respect to each other
- Describing end behavior of polynomial and rational functions
- Identifying asymptotes of and holes in the graphs of rational functions
- Modeling aspects of scenarios using polynomial and rational functions
- Identifying assumptions and limitations of function models
On The Exam
30%–40% of multiple-choice section score
Unit 2: Exponential and Logarithmic Functions
You’ll deepen your understanding of inverses by exploring the relationship between exponential and logarithmic functions.
Topics may include:
- Relating geometric sequences and exponential functions
- Modeling data sets with exponential functions
- Composing functions and finding inverses
- Modeling scenarios with logarithmic functions
- Validating a function model using a residual plot
On The Exam
27%–40% of multiple-choice section score
Unit 3: Trigonometric and Polar Functions
You’ll model and explore periodic phenomena using transformations of trigonometric functions.
Topics may include:
- Relating right triangle trigonometry to the sine, cosine, and tangent functions
- Modeling data and scenarios with sinusoidal functions
- Using inverse trigonometric functions to solve trigonometric equations
- Graphing functions using polar coordinates
- Describing how angles and radii change with respect to each other in a polar graph
On The Exam
30%–35% of multiple-choice section score
Unit 4: Functions Involving Parameters, Vectors, and Matrices
You’ll expand your understanding of the function concept by exploring a variety of new function types.
Topics may include:
- Describing how quantities change with respect to each other in a parametric function
- Graphing conic sections using implicitly defined functions and parametric functions
- Using vectors to describe motion of an object
- Describing the impact of a transformation matrix on a graphical object
- Modeling change in a context using matrices
On The Exam
Not Assessed on the AP Exam
Credit and Placement
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Course Resources
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AP Precalculus can lead to a wide range of careers and college majors