In all of our competition programs, we hold steadfast to one goal: we want each one of them to be an educational activity, one which enriches students’ experiences in their classrooms. Therefore, we tailor our problems to most province's and territory's’ elementary, middle, and high school mathematics curriculum. Furthermore, through our competitions, we hope to develop all participants' mathematical thinking. However, we do encourage a balance of topics in our problems, rather than focusing on Pre-Calculus or Algebraic techniques only. Therefore, possible mathematical topics in our problems include:
Topic | Math Stars Competition Series | Team Challenges Program | Young Years Program | Online Competitions* | Mock Math Challengers |
Computations with basic operations | ✔ | ✔ | |||
Computational shortcuts | ✔ | ✔ | ✔ | ✔ | ✔ |
Pictorial & symbolic number representations | ✔ | ✔ | |||
Measurement & units | ✔ | ✔ | ✔ | ✔ | |
Fractions, percentages, decimals | ✔ | ✔ | ✔ | ✔ | ✔ |
Irrational numbers | ✔ | ✔ | ✔ | ✔ | |
Estimation skills | ✔ | ✔ | ✔ | ||
Scientific notation & number representations | ✔ | ✔ | ✔ | ✔ | |
Exponents & powers | ✔ | ✔ | ✔ | ✔ | ✔ |
Simplifying expressions | ✔ | ✔ | ✔ | ✔ | ✔ |
GCD & LCM | ✔ | ✔ | ✔ | ✔ | ✔ |
Real life applications of grade-appropriate material | ✔ | ✔ | ✔ | ✔ | ✔ |
Working with variables & unknowns | ✔ | ✔ | ✔ | ✔ | ✔ |
Topic | Math Stars Competition Series | Team Challenges Program | Young Years Program | Online Competitions* | Mock Math Challengers |
Linear equations | ✔ | ✔ | ✔ | ✔ | ✔ |
Quadratic equations | ✔ | ✔ | ✔ | ✔ | |
Advanced equations (above degree 2) | ✔ | ✔ | |||
Linear inequalities | ✔ | ✔ | ✔ | ✔ | ✔ |
Advanced Inequalities (degree 2 and above) | ✔ | ✔ | |||
Systems of equations | ✔ | ✔ | ✔ | ✔ | |
Absolute value, radical, and rational equations | ✔ | ✔ | ✔ | ||
Patterning & equation writing | ✔ | ✔ | ✔ | ||
Algebraic manipulations (including polynomials) | ✔ | ✔ | ✔ | ||
Functions & Relations | ✔ | ✔ | ✔ | ✔ | ✔ |
Graphing | ✔ | ✔ | ✔ | ✔ | |
Word problems (rates/ratios, real-life applications, logic) | ✔ | ✔ | ✔ | ✔ | ✔ |
Logarithms & exponents | ✔ | ✔ | |||
Sequences & series | ✔ | ✔ | ✔ | ✔ | |
Algebraic techniques in trigonometry | ✔ | ✔ | |||
Transformations in Cartesian plane | ✔ | ✔ | ✔ | ✔ | ✔ |
Topic | Math Stars Competition Series | Team Challenges Program | Young Years Program | Online Competitions* | Mock Math Challengers |
Identifying shapes & solids | ✔ | ✔ | |||
Geometric constructions | ✔ | ✔ | ✔ | ||
Area & perimeter of 2D figures | ✔ | ✔ | ✔ | ✔ | ✔ |
Special Triangles ( & triangles) | ✔ | ✔ | ✔ | ✔ | |
Advanced triangle properties (medians, angle bisectors, perpendicular bisectors...etc.) | ✔ | ✔ | ✔ | ||
Circle Geometry (more advanced than basic areas/circumference) | ✔ | ✔ | ✔ | ✔ | |
Properties of special quadrilaterals & other polygons | ✔ | ✔ | ✔ | ✔ | ✔ |
Volume & surface area of standard 3D figures | ✔ | ✔ | ✔ | ✔ | ✔ |
Volume & surface area of irregular 3D figures | ✔ | ✔ | |||
Similar & congruent triangles/figures | ✔ | ✔ | ✔ | ✔ | ✔ |
Angles | ✔ | ✔ | ✔ | ✔ | ✔ |
Pythagorean theorem | ✔ | ✔ | ✔ | ✔ | ✔ |
Coordinate systems | ✔ | ✔ | ✔ | ||
Equation of lines (slopes, intercepts, intersections...etc.) | ✔ | ✔ | ✔ | ✔ | |
Distance between points in 2D & 3D | ✔ | ✔ | ✔ | ✔ | |
Areas in 2D plane | ✔ | ✔ | ✔ | ✔ | |
Volumes in 3D plane | ✔ | ✔ | ✔ | ||
Lattice points & midpoints | ✔ | ✔ | ✔ | ✔ | |
Transformations & Locus | ✔ | ✔ | ✔ | ✔ | |
Trigonometry in geometry | ✔ | ✔ |
Topic | Math Stars Competition Series | Team Challenges Program | Young Years Program | Online Competitions* | Mock Math Challengers |
Divisibility rules | ✔ | ✔ | ✔ | ✔ | ✔ |
Primes & composites (including prime factorization) | ✔ | ✔ | ✔ | ✔ | ✔ |
Properties of GCD & LCM | ✔ | ✔ | ✔ | ✔ | |
Modular arithmetic (remainders, congruences...etc.) | ✔ | ✔ | ✔ | ✔ | |
Pigeonhole principle | ✔ | ✔ | ✔ | ✔ | ✔ |
Recursion | ✔ | ✔ | ✔ | ✔ | |
Number bases | ✔ | ✔ | ✔ | ✔ | |
Diophantine equations | ✔ | ✔ | ✔ | ||
Factors & multiples | ✔ | ✔ | ✔ | ✔ | ✔ |
Parity arguments | ✔ | ✔ | |||
Invariants & monovariants | ✔ | ✔ | |||
Number puzzles | ✔ | ✔ | ✔ | ✔ | |
Number patterns (for younger students) | ✔ | ✔ | ✔ |
Topic | Math Stars Competition Series | Team Challenges Program | Young Years Program | Online Competitions* | Mock Math Challengers |
Listing & basic counting principles | ✔ | ✔ | ✔ | ✔ | |
Probability terminology | ✔ | ✔ | ✔ | ||
Experimental probability | ✔ | ✔ | ✔ | ||
Permutations & combinations | ✔ | ✔ | ✔ | ✔ | ✔ |
Constructive counting | ✔ | ✔ | ✔ | ✔ | |
Over-counting & complementary counting | ✔ | ✔ | ✔ | ✔ | |
Case-working | ✔ | ✔ | ✔ | ✔ | ✔ |
Basic probability | ✔ | ✔ | ✔ | ✔ | ✔ |
Advanced probability laws (geometric, conditional, De Morgan's laws...etc.) | ✔ | ✔ | |||
Partitions & recursion | ✔ | ✔ | ✔ | ||
Basic graph theory | ✔ | ✔ | ✔ | ✔ | |
Basic set theory | ✔ | ✔ | ✔ | ✔ | ✔ |
Expected value | ✔ | ✔ | ✔ | ||
Distributions | ✔ | ✔ | ✔ | ||
Venn diagrams | ✔ | ✔ | ✔ | ✔ | ✔ |
Combinatorial Theorems (binomial, hockey-stick, Vandermonde...etc.) | ✔ | ✔ | |||
Basic Markov processes | ✔ | ✔ | |||
Correspondences (one-to-one, one-to-many, many-to-one) | ✔ | ✔ | ✔ | ✔ |
Topic | Math Stars Competition Series | Team Challenges Program | Young Years Program | Online Competitions* | Mock Math Challengers |
Central tendency (mode, mean/average, median) | ✔ | ✔ | ✔ | ✔ | ✔ |
Basic measures of spread (range, inter-quartile range) | ✔ | ✔ | ✔ | ✔ | |
Advanced statistical measures (variance, standard deviation, correlation...etc.) | ✔ | ✔ | |||
Representations of data & types of graphs | ✔ | ✔ | ✔ | ||
Financial literacy | ✔ | ✔ | ✔ | ✔ | ✔ |
Statistics terminology | ✔ | ✔ | ✔ | ||
Basic statistical analysis | ✔ | ✔ | ✔ | ||
Math games | ✔ | ✔ | ✔ | ✔ | |
Geometric dissections | ✔ | ✔ | ✔ | ||
Advanced inequalities (AM-GM, Cauchy-Schwartz...etc.) | ✔ | ✔ | |||
Basic math techniques in physics | ✔ | ✔ |
Note that we also test mathematical rigor & full-solution-writing skills in the Math Stars Competition Series and Team Challenges Program competition programs. Being a generic skill, we chose not to include it in the table above. Furthermore, note that many of the topics above are very broad in nature (e.g. computational shortcuts) and thus consists of subtopics of widely different difficulty, so a competition aimed at younger students (e.g. Young Years Program) would therefore test easier subtopics than a competition aimed at older students (e.g. Team Challenges Program). Finally, note that our Online Competitions may be designed in various different ways, be it a Math Stars National Championship competition or a Daily/Weekly Challenges competition, so the concepts they cover depend on the intended audience of each particular online competition. Thus, even though in the tables above, it is indicated that every concept can be tested in our online competitions, any particular online competition will only test an appropriate subset of these concepts, tailored to the presumed skills of the intended contestants.
Clearly, there are a diverse range of topics that can be covered by the CSSMA competition programs. These topics range in difficulty from elementary school level to even post-secondary level. Therefore, for our competitions, we are not only trying students' academic performance in class, but also help them acquire the knowledge and skills that they may need to pursue their mathematical interests even further. However, we do have a set of topics which we will do every effort to avoid in all of our Competition Programs:
- Calculus & analysis (limits, derivatives, integrals...etc.)
- Advanced functional equations
- Concurrency, collinearity, homothety, inversion, isometry, projective geometry, combinatorial geometry
- Advanced complex numbers & barycentric/trillinear coordinates
- Theoretical number theory (quadratic reciprocity, Pell's equations, prime fields...etc.)
- Generating functions, advanced graph theory, Stirling/Catalan numbers
- Vectors, matrices & linear algebra
- Advanced set theory, group theory, and equivalence relations
- Conic sections (other than circles and basic parabolas/hyperbolas)
- Advanced statistical testing and probability models (Poisson, Geometric, Normal, Student’s-t...etc.)
- Any other post-secondary topics not outlined above
The question is now, how do we make our problems? Being a student run organization, high school and university students are our main problem writers and test solvers. We try to tailor our contest to the prescribed mathematics curriculum of most provinces/territories. This involves the following steps:
- Problem writers draft up a bank of possible problems of approximately the difficulty that we are looking for in our contests. Every problem writer attends a workshop to learn about the desired difficulty levels of the problems of the contest in question and then are expected to reproduce the desired difficulties in their problems. Every problem writer is taught the differences between a problem requiring the usage of a calculator and a problem that doesn’t. Problems that don’t require the use of a calculator allow us to test computational ingenuity and other mental math techniques, while problems that require a calculator allow us to test deeper mathematical reasoning skills.
- Problem test solvers align the problems precisely with specific learning outcomes, which in many cases, is part of a province/territory’s curriculum. We ensure a diversity of different areas of mathematics in our contests so that as few areas of mathematics outlined in the first few tabs on this page are left out as possible. We also align our problems with specific learning outcomes so that the first problem(s) of the contests are below or at the appropriate grade levels tested, the middle problems are at the current grade levels, and the harder problems are higher than the current grade levels. In the case for Math Stars Regional competitions and Young Years Program competitions, one can expect a distribution of about 1/3 of the problems to fall into the “easy” category, 1/2 of the problems to fall into the “medium” category, and 1/6 of the problems to fall into the “hard” category. In the case of all other competitions (with the exception of the Math Stars National Championship), one can expect a distribution of about 1/3 of the problems to fall into the “easy” category, 1/3 of the problems to fall into the “medium” category, and 1/3 of the problems to fall into the “hard” category. In the case of the Math Stars National Championship, one can expect a distribution of about 1/8 of the problems to fall into the “easy” category, 1/2 of the problems to fall into the “medium” category, and 3/8 of the problems to fall into the “hard” category. These figures are approximate and are likely to change from year to year.
- Every problem has a specific number of prescribed learning outcomes that it intends to test. Full solutions are then written up keeping these prescribed learning outcomes in mind. All problems are at least double test solved to ensure their mathematical correctness and curricular accuracy.
- We usually generate a problem bank that has at least four times the number of problem we actually need. This helps us ensure that the best problems appear on our contests and also serves as a way for us to prepare worksheets and extra free resources on our website for coaches.
- For some contests which we have a sample population available, we do our best to trial out our contest ahead of time on the sample population to standardize our contest as well as to make sure that our contests are of the intended difficulty.
Although it would be ideal for us to have a 100% accuracy rate, issues sometimes arise in our problem making and test solving processes. We apologize sincerely for any mistakes that may remain undetected despite our rigorous test solving procedures. Errata includes incorrect answers/solutions and confusing problems. When an errata is discovered during a contest, for the sake of fairness, we generally continue without stopping and make a decision on what to do with the error after the contests have been collected (unless the error is blatantly distracting, in which case we ensure that all competitors have fair access to any decision that we make on the matter during the competition). The marking team and the competition administration team may decide to throw out bad problems, change accepted answers, or do anything else it deems is appropriate to help resolve the situation. Coaches are made aware of the errata and its resolution as soon as possible as well. If an errata is found in the question booklets/solution manual, we will revise those booklets/manuals before handing them out to coaches and students at the end of the competition.
In the event that our contests are too difficult, we need to hear back from students and coaches as soon as possible. We certainly do not want to scare students away with impossibly hard math problems, so we apologize sincerely if our contests have caused your students some grief. After processing all the relevant data, we will modify future contests to make them more appropriate difficulty wise. We appreciate all feedback: in fact, we encourage all students and coaches to fill out the short feedback form that every competition program has available on our website---we generally send out the link to this form to coaches and/or competitors via email after each competition they participate in.