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Code Scholars Tutoring · AP Precalculus

AP Precalculus Course Outline

Unit order, topic placement, and exam weightings follow the current College Board framework. Every topic listed below is an official course topic; the surrounding explanation is written by Code Scholars.

4 units58 topics

The detailed notes are discussed during the course with worked examples, guided practice, and time for questions. Lesson order and pacing can follow the student’s school syllabus.

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Unit 1: Polynomial and Rational FunctionsExam assessed, 30 to 40 percent of the multiple-choice section. The unit opens with how two quantities change together and builds toward choosing and defending a function model. Rate of change, end behavior, and the difference between a hole and an asymptote all trace back to reading a function rather than manipulating it.14 topics

  • 1.1Change in Tandem

    MCQ Sample

  • 1.2Rates of Change

    FRQ Sample

  • 1.3Rates of Change in Linear and Quadratic Functions

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  • 1.4Polynomial Functions and Rates of Change

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  • 1.5Polynomial Functions and Complex Zeros

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  • 1.6Polynomial Functions and End Behavior

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  • 1.7Rational Functions and End Behavior

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  • 1.8Rational Functions and Zeros

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  • 1.9Rational Functions and Vertical Asymptotes

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  • 1.10Rational Functions and Holes

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  • 1.11Equivalent Representations of Polynomial and Rational Expressions

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  • 1.12Transformations of Functions

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  • 1.13Function Model Selection and Assumption Articulation

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  • 1.14Function Model Construction and Application

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Unit 2: Exponential and Logarithmic FunctionsExam assessed, 25 to 40 percent of the multiple-choice section. The organizing idea is proportional change: what it looks like in a sequence, in a function, in a table, and on a semi-log plot. Logarithms arrive as the inverse that makes those relationships solvable rather than as a separate set of rules.15 topics
Unit 3: Trigonometric and Polar FunctionsExam assessed, 30 to 35 percent of the multiple-choice section. Periodic behavior is introduced as something to model before it is something to compute, so amplitude, period, and shifts are read as facts about a situation. Polar functions close the unit by describing position with distance and direction instead of coordinates.15 topics
Unit 4: Functions Involving Parameters, Vectors, and Matrices — additional course content, not assessed on the AP ExamCollege Board includes this unit in the course and assigns it no exam weighting, so nothing here appears on the AP Exam. It is still taught: parametric motion, vectors, and matrices are exactly the ideas that reappear in calculus, physics, linear algebra, and computer graphics. Students preparing only for the exam can treat it as optional; students continuing in mathematics should not.14 topics

Independently developed by Code Scholars Tutoring. Lesson order and pacing can be adapted to the student’s school syllabus.

AP® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this material.