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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 full Precalculus syllabus: 8 subjects, 43 chapters and 135 topics, with 401 flashcards written against it.

8Subjects

43Chapters

135Topics

401Flashcards

Precalculus subjects

Precalculus has 8 subjects. Each one is listed below with its chapters in syllabus order; open a subject for every topic and sub-topic inside them.

Functions and Their Graphs

6 chapters · 22 topics · 51 flashcards

Foundations of Functions · 4 topics
Analyzing Graphs of Functions · 5 topics
Library of Parent Functions · 4 topics
Transformations of Functions · 4 topics
Combinations and Composition · 2 topics
Inverse Functions · 3 topics

Polynomial and Rational Functions

7 chapters · 23 topics · 50 flashcards

Quadratic Functions and Models · 3 topics
Higher-Degree Polynomial Functions · 4 topics
Polynomial Division · 3 topics
Zeros of Polynomial Functions · 4 topics
Complex Numbers · 2 topics
Rational Functions · 4 topics
Inequalities · 3 topics

Exponential and Logarithmic Functions

5 chapters · 16 topics · 50 flashcards

Exponential Functions · 3 topics
Logarithmic Functions · 3 topics
Properties of Logarithms · 3 topics
Exponential and Logarithmic Equations · 3 topics
Modeling and Applications · 4 topics

Trigonometry

5 chapters · 15 topics · 50 flashcards

Angles and Their Measure · 3 topics
Right Triangle Trigonometry · 3 topics
Trigonometric Functions of Any Angle · 3 topics
Graphs of Trigonometric Functions · 3 topics
Inverse Trigonometric Functions · 3 topics

Analytic Trigonometry

5 chapters · 14 topics · 50 flashcards

Fundamental Identities · 3 topics
Verifying Trigonometric Identities · 2 topics
Solving Trigonometric Equations · 3 topics
Sum and Difference Formulas · 2 topics
Multiple-Angle and Product-Sum Formulas · 4 topics

Applications of Trigonometry and Vectors

5 chapters · 14 topics · 50 flashcards

Law of Sines · 3 topics
Law of Cosines · 2 topics
Vectors in the Plane · 3 topics
Dot Product · 3 topics
Complex Numbers in Trigonometric Form · 3 topics

Analytic Geometry and Polar Coordinates

4 chapters · 11 topics · 50 flashcards

Conic Sections · 3 topics
Translations and Classification of Conics · 2 topics
Parametric Equations · 3 topics
Polar Coordinates · 3 topics

Systems, Sequences, and an Introduction to Limits

6 chapters · 20 topics · 50 flashcards

Systems of Equations and Inequalities · 3 topics
Matrices and Determinants · 4 topics
Partial Fraction Decomposition · 2 topics
Sequences and Series · 5 topics
Counting and Probability · 2 topics
Introduction to Limits · 4 topics

Precalculus flashcards

401 question-and-answer cards across 8 subject decks, each shown in full on its subject page.

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.

How many chapters and topics are in the Precalculus syllabus?

43 chapters and 135 topics, across 8 subjects. Polynomial and Rational Functions is the largest subject, with 23 topics in 7 chapters.

Are there Precalculus flashcards?

Yes — 401 question-and-answer flashcards in 8 subject decks. Each deck is printed in full on its subject page here, and the same cards are in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.

Mathematics syllabus

Mathematics · full syllabus breakdown

7 subjects · 63 chapters · 351 flashcards Calculus syllabus