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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? SYLLABUS  

Schedule

Sunday
Sep 29 - Mar 16
7:30 - 9:00
PM ET
Sep 29 - Mar 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
$670 (~$31/lesson)
$732 w/books
$670 (~$31/lesson)
With Books $732
CLOSED
Sunday
Nov 10 - Apr 27
7:30 - 9:00
PM ET
Nov 10 - Apr 27
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
$670 (~$31/lesson)
$732 w/books
$670 (~$31/lesson)
With Books $732
ENROLL
2 spots left
Tuesday
Dec 10 - May 20
7:30 - 9:00
PM ET
Dec 10 - May 20
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
$670 (~$31/lesson)
$732 w/books
$670 (~$31/lesson)
With Books $732
ENROLL
Wednesday
Jan 8 - Jun 4
7:30 - 9:00
PM ET
Jan 8 - Jun 4
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
$670 (~$31/lesson)
$732 w/books
$670 (~$31/lesson)
With Books $732
ENROLL
Tuesday
Feb 25 - Jul 22
7:30 - 9:00
PM ET
Feb 25 - Jul 22
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
$670 (~$31/lesson)
$732 w/books
$670 (~$31/lesson)
With Books $732
ENROLL
Sunday
Mar 16 - Aug 24
7:30 - 9:00
PM ET
Mar 16 - Aug 24
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
$670 (~$31/lesson)
$732 w/books
$670 (~$31/lesson)
With Books $732
ENROLL
Wednesday
Apr 9 - Sep 3
7:30 - 9:00
PM ET
Apr 9 - Sep 3
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
$670 (~$31/lesson)
$732 w/books
$670 (~$31/lesson)
With Books $732
ENROLL

AoPS Holidays

There are no classes November 25 ‐ December 1, December 21 ‐ January 3, May 24 ‐ 26, July 4 ‐ 6, August 29 ‐ September 1, and October 31, 2025.

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

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

Overall a fantastic course! The instructors were very responsive and personable. Absolutely fantastic.