Precalculus Online Math Course
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Precalculus

Introduction and evaluation of trigonometric functions, trigonometric identities, geometry with trigonometry, parametric equations, special coordinate systems, complex numbers, exponential form of complex numbers, De Moivre's Theorem, roots of unity, geometry with complex numbers, two-dimensional and three-dimensional vectors and matrices, determinants, dot and cross product, applications of vectors and matrices to geometry.

22 weeks

Diagnostics

ARE YOU READY? DO YOU NEED THIS?

Documents

SYLLABUS
22 weeks ARE YOU READY? DO YOU NEED THIS?  

Schedule

Monday
Oct 14 - Mar 30
7:30 - 9:00
PM ET
Oct 14 - Mar 30
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$545
$602 w/books
$545
With Books $602
ENROLL
Friday
Dec 6 - May 15
7:30 - 9:00
PM ET
Dec 6 - May 15
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$545
$602 w/books
$545
With Books $602
ENROLL
Monday
Jan 27 - Jun 29
7:30 - 9:00
PM ET
Jan 27 - Jun 29
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$570
$627 w/books
$570
With Books $627
ENROLL
Thursday
Mar 19 - Aug 13
7:30 - 9:00
PM ET
Mar 19 - Aug 13
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$570
$627 w/books
$570
With Books $627
ENROLL
Wednesday
Apr 22 - Sep 16
7:30 - 9:00
PM ET
Apr 22 - Sep 16
7:30 - 9:00 PM Eastern
6:30 - 8:00 PM Central
5:30 - 7:00 PM Mountain
4:30 - 6:00 PM Pacific
Click here to see more time zones
$570
$627 w/books
$570
With Books $627
ENROLL
Summer 2020This course will be offered in Summer 2020. Click here to join our mailing list to be notified when the course schedule is available.

AoPS Holidays

There are no classes November 25–December 1, December 21–January 3, May 23–25, July 3–5, and September 5–7.

Who Should Take?

This class typically follows our Intermediate Algebra course. Students should have completed an honors Algebra 2 or an equivalent course before considering this class. Students who have already taken a standard trigonometry or precalculus class should not simply assume this class is too easy for them. Instead, they should take the diagnostic test above to determine if this class is appropriate for them. Similarly, a student who has completed an honors Algebra 2 course should consider taking our Intermediate Algebra class prior to taking our Precalculus class. Our Intermediate Algebra class includes the non-trigonometric topics of a typical precalculus class, plus a great many interesting topics left out of most standard curricula.

Lessons

Lesson 1 Basic Trigonometry
Lesson 2 Graphing Trig and Inverse Trig Functions
Lesson 3 Trigonometric Identities I
Lesson 4 Trigonometric Identities II
Lesson 5 Law of Cosines and Law of Sines
Lesson 6 More Geometry with Trigonometry
Lesson 7 Parametric Equations
Lesson 8 Polar, Cylindrical, and Spherical Coordinates
Lesson 9 Introduction to Complex Numbers and the Complex Plane
Lesson 10 Trigonometry and Complex Numbers
Lesson 11 Roots of Unity
Lesson 12 Geometry Using Complex Numbers I
Lesson 13 Geometry Using Complex Numbers II: Roots of Unity
Lesson 14 Vectors in Two Dimensions
Lesson 15 Vectors and Matrices in Two Dimensions
Lesson 16 Matrices in Two Dimensions
Lesson 17 Matrices in Two Dimensions II
Lesson 18 Determinants of 2x2 Matrices and Introduction to 3D Vectors
Lesson 19 Matrices in Three Dimensions
Lesson 20 Lines and Planes in Three Dimensions
Lesson 21 Cross Product and Determinant
Lesson 22 Applications of Vectors to Euclidean Geometry

Required Textbook

Precalculus
By Richard Rusczyk

A comprehensive textbook covering precalculus topics. Specific topics covered include trigonometry, complex numbers, vectors, and matrices. Includes many problems from the AIME and USAMO competitions.

I have loved all the Art of Problem Solving courses that I've taken in the past, and this one was no exception. The instructor was very knowledgeable and fun to work with, and I learned many new concepts every week. It is a great privilege to take these classes; Art of Problem Solving has truly changed my life.

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