Mathematical Practices
Can also be used as Embedded Common Formative Assessments
Embedded Files
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.
Solve equations & inequalities represented analytically, with and without technology.
Express functions, equations, or expressions in analytically equivalent forms that are useful in a given mathematical or applied context.
Construct new functions using transformations, compositions, inverses, or regressions, that may be useful in modeling contexts, criteria, or data, with and without technology.
Identify information from graphical, numerical, analytical, and verbal representations to answer a question or construct a model, with and without technology.
Construct equivalent graphical, numerical, analytical, and verbal representations of functions that are useful in a given mathematical or applied context, with and without technology.
Describe the characteristics of a function with varying levels of precision, depending on the function representation and available mathematical tools.
Apply numerical results in a given mathematical or applied context.
Support conclusions or choices with a logical rationale or appropriate data.
Building Mathematical Practices in Unit 1
Polynomial & Rational Functions
Throughout the course, students should practice communicating mathematics and developing notational fluency—and that practice should begin in Unit 1. Students should use precise language such as, “On the closed interval 0 to 1, as the value of x increases, the value of y increases then decreases.” To the fullest extent possible, students should work on functions presented in contextual scenarios such as graphs showing distance vs. time, tables showing velocity vs. time, or scenarios involving volume vs. time. In these contexts, students should use clear language when referring to variables and functions, including units of measure as appropriate. For example, when considering a problem of filling a pool with water, a student may write, “The input values of the function V are times in minutes, and the output values are volumes in cubic meters. The average rate of change of the function V over the time interval t equals 2 minutes to t equals 5 minutes is 0.4 cubic meters per minute.” Practicing communicating with precise language can help students clarify their thinking and make important connections while revealing misconceptions.
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 1 and embed them into instruction as formative assessments.
The latter, FRQs, is one way to bring in the Mathematical Practices.
For other forms of assessment, check out the Assessment tab!
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