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.
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Learning Progression 1: Change in Tandem
Changes in tandem sets the stage for covariation, which is integrated throughout the course. Given a scenario describing covariation, students produce graphical representations. Students begin to understand a graph not as something static but something embodying change. This unit is based on research on best practices in preparation for calculus (see Marilyn Carlson et. al.).
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Learning Progression 2: Rates of Change
Rates of change, rates of change in linear & quadratic functions, and polynomial functions & rates of change.
Include changing rates of change and connection to concavity.
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Learning Progression 3: Polynomial Functions and Complex Zeros
Include non-real roots. Examine complex numbers as zeroes of polynomials and interpretation them.
This progression is not intended to review all the factoring techniques of Algebra .
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Success Criteria: See 1.5.a and/or 1.5.B.
Learning Progression 4: Polynomial & Rational Functions
Limits are not formally defined (saved for Calculus). This is an informal introduction to limits, unbounded behavior and end behavior with limit notation to summarize. The idea of point discontinuity without formalization required to define continuous functions.
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Success Criteria: See 1.7.a, 1.8.A, 1.9.A and/or 1.10.A.
Success Criteria: See 1.7.a, 1.8.A, 1.9.A and/or 1.10.A.
Success Criteria: See 1.7.a, 1.8.A, 1.9.A and/or 1.10.A.
Learning Progression 5: Equivalent Representations of Polynomial and Rational Expressions
This progression includes polynomial long division (synthetic is not included in the Framework nor is it assessed).
This progression also includes the Binomial Theorem .
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Success Criteria: See 1.11.A, 1.11.B and/or 1.11.C.
Learning Progression 6: Transformations of Functions
This progression includes translations (additive) & dilations (multiplicative).
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Learning Progression 7: Modeling
Three types: deterministic, matching criteria, bivariate data. Includes piecewise linear.
Describe assumptions and contextual restrictions for a given model. Apply solutions in a context.
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Success Criteria: See 1.13.A and/or 1.13.B.
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Remember Mathematical Practices!
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and embedded common formative assessments.