AP Precalculus

AP Precalculus is a course designed to prepare students for college-level calculus and other STEM courses. The curriculum is focused on four main units, each building on the last to develop a strong understanding of algebraic, functional, and trigonometric concepts. The course emphasizes a four-pillar approach: representing functions in multiple ways (symbolically, numerically, graphically, and verbally), applying mathematical reasoning, using technology appropriately, and communicating mathematical ideas.

Key Course Units

Unit 1: Polynomial and Rational Functions

This unit delves into the behavior and characteristics of polynomial and rational functions. Students learn to analyze graphs, identify key features like intercepts and asymptotes, and solve equations and inequalities involving these functions. They also model real-world situations with polynomial and rational functions.

Unit 2: Exponential and Logarithmic Functions

Students explore the relationships between exponential and logarithmic functions, including how they are inverses of each other. They apply properties of exponents and logarithms to solve equations, analyze graphs, and model phenomena such as population growth and radioactive decay.

Unit 3: Trigonometric and Polar Functions

This unit expands on previous knowledge of trigonometry. Students learn about the unit circle, trigonometric identities, and the graphs of trigonometric functions, including their amplitude, period, and phase shift. They also explore polar coordinates and their relationship to the Cartesian coordinate system, which is essential for understanding more advanced topics in calculus.

Unit 4: Functions Involving Parameters, Vectors, and Matrices

The final unit introduces new ways to represent functions and solve problems. Students work with parametric equations to describe motion and other dynamic relationships. They also learn about vectors and matrices and how to perform operations with them to solve systems of equations and analyze geometric transformations.

The AP Precalculus exam given in May is a three-hour exam that tests students' understanding of functions and their applications, as well as their ability to apply mathematical reasoning and communicate their findings. It is a hybrid digital exam, where multiple-choice questions are answered and free-response questions are viewed in the Bluebook app, but the free-response answers are handwritten in a paper booklet.

The exam is scored on a scale of 1 to 5, with 5 being the highest. A score of 3 is generally considered a passing score, and many colleges grant credit for scores of 3 or higher, although some top universities may only accept a 4 or 5. The raw scores from both sections are combined into a composite score, which is then converted to the final AP score.