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## About the Course

Do you want to figure out how quickly you’ll reach 10,000 followers on Instagram? In AP Precalculus, you’ll explore concepts such as polynomial and exponential functions that can help you calculate your rise to influencer status, and many more concepts related to functions, logarithms, and trigonometry that can be applied beyond the classroom.

## 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

## See Where AP Can Take You

AP Precalculus can lead to a wide range of careers and college majors