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Precalculus Syllabus

Bridges algebra and calculus through the study of functions, trigonometry, sequences, and analytic geometry to prepare students for higher mathematics.. The complete Precalculus outline — 8 subjects, 43 chapters and 135 topics — laid out so you can see exactly what has to be covered and tick each item off as you go.

8Subjects

43Chapters

135Topics

0Sub-topics

401Flashcards

~100hEst. first pass

Precalculus subjects

Each subject below has its own page with the full chapter → topic → sub-topic tree and a set of real exam-style flashcards.

Functions and Their Graphs

6 chapters · 22 topics

~15h first pass · 51 flashcards Polynomial and Rational Functions

7 chapters · 23 topics

~15h first pass · 50 flashcards Exponential and Logarithmic Functions

5 chapters · 16 topics

~10h first pass · 50 flashcards Trigonometry

5 chapters · 15 topics

~10h first pass · 50 flashcards Analytic Trigonometry

5 chapters · 14 topics

~10h first pass · 50 flashcards Applications of Trigonometry and Vectors

5 chapters · 14 topics

~10h first pass · 50 flashcards Analytic Geometry and Polar Coordinates

4 chapters · 11 topics

~8h first pass · 50 flashcards Systems, Sequences, and an Introduction to Limits

6 chapters · 20 topics

~15h first pass · 50 flashcards

Precalculus flashcard decks

401 question-and-answer cards across 8 decks, written against this syllabus. Preview any deck free.

How to work through the Precalculus syllabus

The outline on this page is arranged the way the syllabus itself is: subject, then chapter, then topic, then sub-topic. That last level is what most study plans skip, and it is where coverage actually goes wrong — a chapter marked "done" often has three sub-topics inside it that were never touched.

Weight your plan accordingly: Polynomial and Rational Functions carries 23 topics while Analytic Geometry and Polar Coordinates carries 11. Giving both the same number of weeks is the most common planning mistake for Precalculus.

The ~100 hour estimate above is a first pass only: roughly 45 minutes per topic plus 12 minutes per sub-topic. Revision cycles, past papers and mocks sit on top of that number.

Precalculus syllabus FAQ

What subjects are in the Precalculus syllabus?

Precalculus covers 8 subjects: Functions and Their Graphs, Polynomial and Rational Functions, Exponential and Logarithmic Functions, Trigonometry, Analytic Trigonometry, Applications of Trigonometry and Vectors, Analytic Geometry and Polar Coordinates and Systems, Sequences, and an Introduction to Limits. Together they contain 43 chapters and 135 named topics.

How much do you have to study for Precalculus?

The full Precalculus outline breaks down into 43 chapters, 135 topics and 0 sub-topics. Polynomial and Rational Functions is the largest single subject with 23 topics across 7 chapters.

How long does it take to cover the whole Precalculus syllabus?

Roughly 100 hours for one full pass. That estimate allows about 45 minutes per topic plus 12 minutes per sub-topic, so it is first-pass coverage — revision, past papers and mock tests sit on top of it. At 3 hours a day that is about 5 weeks.

Are there Precalculus flashcards?

Yes — 401 question-and-answer flashcards across 8 decks, one per subject, written against this syllabus. A sample of every deck is readable on this site for free, and the complete decks are in the Examius app.

Is this Precalculus syllabus free to use?

Yes. Every page here is free to read, and importing the Precalculus syllabus into the Examius app to tick off topics as you finish them is free too. No account is needed to start.

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