Competition Math Precalculus

Ages 13–18 | Grades 8–12

Math
Sunday · 5:00 PM to 7:00 PM
An accelerated review of precalculus, built around vectors and matrices.
The class meets on Sundays from 5:00 PM to 7:00 PM, August 16 – December 13, 2026.

Accelerated Precalculus Review: Vectors, Matrices, and Coordinate Systems

• Textbook: Precalculus (Art of Problem Solving) by Richard Rusczyk.
• Assumes a strong algebra foundation and familiarity with trigonometric functions.
• Topics are sequenced by core idea rather than by dimension — vectors and matrices are introduced much as a first linear algebra course would, starting with vectors in several dimensions and moving to linear transformations and then matrices.
• Prepares students for the foundational math of a calculus sequence.
• Two flexible sessions are held in reserve at the end of the term (see below).

Class Schedule:

August: Functions, Coordinates, and Vectors
S1 (Aug 16): Functions, Inverses, Graphing, and Transformations — Ch. 1
S2 (Aug 23): Parameterization, Polar Coordinates, and 3D Coordinates — 5.1–5.3
S3 (Aug 30): Vectors and the Dot Product — 9.1, 9.2

September: Vectors in Space (no class Sep 6, Labor Day weekend)
S1 (Sep 13): Projections and 3D Vectors — 9.4, 11.1
S2 (Sep 20): Lines, Linear Dependence, and Planes, Part 1 — 9.3, 12.1
S3 (Sep 27): Lines and Planes, Part 2; the Cross Product — 12.2, 12.3

October: Matrices and Determinants
S1 (Oct 4): Matrices, Matrix Multiplication, and Matrices as Transformations — 10.1–10.3
S2 (Oct 11): Matrices in Higher Dimensions; the Determinant — 11.2, 10.4
S3 (Oct 18): Determinants in Higher Dimensions — 10.5, 11.3, 12.4
S4 (Oct 25): Matrix Inversions — 10.6, 12.5

November: Linear Systems, Vector Geometry, and Complex Numbers (no class Nov 29, Thanksgiving)
S1 (Nov 1): m × n Matrices and Linear Systems — 11.4
S2 (Nov 8): Vector Geometry — Ch. 13
S3 (Nov 15): Complex Numbers — Ch. 6–8 (selections)
S4 (Nov 22): Cumulative Review

December: Flexible Sessions
S1 (Dec 6): Optional — Targeted trigonometry review: unit circle fluency, graphs and transformations of the trigonometric functions, the Pythagorean and angle-sum identities, and the inverse trigonometric functions with their domain restrictions — Ch. 2–4 (selections)
S2 (Dec 13): Optional — Complex numbers continued: polar form and De Moivre's theorem, roots of unity, and multiplication by a complex number as a rotation and scaling of the plane — Ch. 6–8 (continued)

If the class needs more time on trigonometry earlier in the term, the schedule may shift to accommodate additional review. That decision is made during the course.