Mathematical Practices

Can also be used as Embedded Common Formative Assessments

AP Precalculus centers on functions modeling dynamic phenomena. Research indicates that deep understanding of functions and their graphs as embodying dynamic covariation of quantities best supports student preparation for calculus.

AP Precalculus Mathematical Practices

Click the skill for Questions to Ask Students & Sample Activities.

Skill 1.A

Solve equations & inequalities represented analytically, with and without technology.

Skill 1.B

Express functions, equations, or expressions in analytically equivalent forms that are useful in a given mathematical or applied context.

Skill 1.C

Construct new functions using transformations, compositions, inverses, or regressions, that may be useful in modeling contexts, criteria, or data, with and without technology.

Skill 2.A

Identify information from graphical, numerical, analytical, and verbal representations to answer a question or construct a model, with and without technology.

Skill 2.B

Construct equivalent graphical, numerical, analytical, and verbal representations of functions that are useful in a given mathematical or applied context, with and without technology.

Skill 3.A

Describe the characteristics of a function with varying levels of precision, depending on the function representation and available mathematical tools.

Skill 3.B

Apply numerical results in a given mathematical or applied context.

Skill 3.C

Support conclusions or choices with a logical rationale or appropriate data.

Building Mathematical Practices in Unit 3

Trigonometric & Polar Functions

Students should have multiple experiences transitioning among, and communicating about, the various representations of trigonometric functions, especially sinusoidal functions. It is important that, in addition to solving trigonometric equations and finding equivalent trigonometric expressions, students build sinusoidal models with and without technology and practice constructing different representations. As students transition to thinking in the polar plane, they will refine their communications related to characteristics of functions. The more casual language that students may have adopted such as “goes up” and “goes down” will need to be replaced with more careful language that addresses a function’s behavior related to angles and radii.

See AP Classroom for more information.

Mathematical Practices & the AP Exam

Look in AP Classroom for Multiple Choice Questions (MCQ) & Free-Response Question (FRQ) progress checks

for Unit 3 and embed them into instruction as formative assessments.

The latter, FRQs, is one way to bring in the Mathematical Practices.