The 2021 Canadian Open Mathematics Challenge — Oct 28/29

## Practice Questions:

Practice for the COMC using the following past exam questions:

## Topics to study:

Most of the problems on this year's COMC will be based on the mathematics curriculum taught in secondary schools and CÉGEPs. Some questions require a degree of understanding beyond the curriculum. Potential topics include:

- Probability
- Euclidean and analytic geometry
- Trigonometry, including functions, graphs and identities
- Exponential and logarithmic functions
- Functional notation
- Systems of equations
- Polynomials, including relationships involving the roots of quadratic and cubic equations
- The remainder theorem
- Sequences and series
- Simple counting problems
- The binomial theorem
- Elementary number theory, including tests for divisibility, number of divisors, and simple Diophantine equations

## Problem of the Week:

Beginning in the first week of September, we will post a sample problem to familiarize you with the kinds of questions you might find on a COMC exam. The solution is posted the following week when the next problem is posted. See our Problem of the Week page.

## Other resources:

*Crux Mathematicorum*: This is the CMS's flagship problem solving periodical. Each issue contains articles on problems and problem solving as well as original problems and problems from mathematics competitions and Olympiads from around the world. The journal is interactive in the sense that the published solutions to the problem sets all come from the readership. Crux is designed for students and hobbyists who are keen to sharpen their skills with other national and international level problem solvers. You can check out the main Crux web site and the archive. All volumes are free to the public.

*A Taste of Mathematics*
is a booklet series published by the Canadian Mathematical Society. They are designed as enrichment materials for high school students with an interest in and aptitude for mathematics. Some booklets in the series also cover the materials useful for mathematical competitions at national and international levels. The following volumes are all available for ordering through our online store, by mail or by phone:

- Mathematical Olympiads' Correspondence Program (1995-96) by Edward J. Barbeau.
- Algebra Intermediate Methods by Bruce L.R. Shawyer.
- Problems for Mathematics Leagues by Peter I. Booth, John McLoughlin and Bruce L.R. Shawyer.
- Inequalities by Edward J. Barbeau and Bruce L.R. Shawyer.
- Combinatorial Explorations by Richard Hoshino and John McLoughlin.
- More Problems for Mathematics Leagues by Peter I. Booth, John McLoughlin and Bruce L.R. Shawyer.
- Problems of the Week by Jim Totten.
- Problems for Mathematics Leagues III by Peter I. Booth, John McLoughlin and Bruce L.R. Shawyer.
- The CAUT Problems by Edward Barbeau.
- Modular Arithmetic by Naoki Sato.
- Problems for Junior Mathematics Leagues by Bruce L.R. Shawyer & Bruce B. Watson.
- Transformational Geometry by Edward Barbeau.
- Quadratics and Complex Numbers by Edward J. Barbeau.
- Sequences and Series by Margo Kondratieva with Justin Rowsell.
- Géométrie plane, avec des nombres par Michel Bataille.
- Recurrence Relations by Iliya Bluskov.

*The Math Olympian*: A Novel by Richard Hoshino. Richard Hoshino was a member of the Canadian Team to the International Math Olympiad in Mumbai India (1996) and won a silver medal. His book tells the story of Bethany's road to the International Mathematical Olympiad. Through persistence, perseverance, and the support of innovative mentors who inspired her with a love of learning, Bethany confronts challenges and develops the creativity and confidence to reach her potential. In training to become a world champion mathelete, Bethany discovers the heart of mathematics. This book not only describes her journey, but details the different approaches that can be undertaken to solve an array of mathematical problems. A great read for students interested or participating in mathematics competitions. Copies can be obtained from Friesenpress and Amazon
.

To report errors or omissions for this page, please contact us at comc@cms.math.ca.