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
Jun 5 - Nov 13
7:30 - 9:00
PM ET
Jun 5 - Nov 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
$630 (~$29/week)
$692 w/books
$630 (~$29/week)
With Books $692
ENROLL
Monday
Jun 20 - Dec 12
7:30 - 9:00
PM ET
Jun 20 - Dec 12
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
$630 (~$29/week)
$692 w/books
$630 (~$29/week)
With Books $692
ENROLL
Thursday
Jul 7 - Dec 8
7:30 - 9:00
PM ET
Jul 7 - Dec 8
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
$630 (~$29/week)
$692 w/books
$630 (~$29/week)
With Books $692
ENROLL
Wednesday
Aug 3 - Jan 18
7:30 - 9:00
PM ET
Aug 3 - Jan 18
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
$630 (~$29/week)
$692 w/books
$630 (~$29/week)
With Books $692
ENROLL
Sunday
Aug 21 - Feb 12
7:30 - 9:00
PM ET
Aug 21 - Feb 12
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
$630 (~$29/week)
$692 w/books
$630 (~$29/week)
With Books $692
ENROLL
Friday
Sep 2 - Feb 17
7:30 - 9:00
PM ET
Sep 2 - Feb 17
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
$630 (~$29/week)
$692 w/books
$630 (~$29/week)
With Books $692
ENROLL
Wednesday
Sep 28 - Mar 15
7:30 - 9:00
PM ET
Sep 28 - Mar 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
$630 (~$29/week)
$692 w/books
$630 (~$29/week)
With Books $692
ENROLL
Sunday
Nov 13 - Apr 30
7:30 - 9:00
PM ET
Nov 13 - Apr 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
$630 (~$29/week)
$692 w/books
$630 (~$29/week)
With Books $692
ENROLL
Tuesday
Dec 13 - May 23
7:30 - 9:00
PM ET
Dec 13 - May 23
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
$630 (~$29/week)
$692 w/books
$630 (~$29/week)
With Books $692
ENROLL

AoPS Holidays

There are no classes May 28‐30, July 2‐4, September 3‐5, October 31, November 21‐27, and December 21‐January 3.

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 Exponential Form
Lesson 12 Roots of Unity
Lesson 13 Geometry Using Complex Numbers
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.

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

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