CEMC study guide
CEMC · Work through your exam, one topic at a time.
CEMC refers to the mathematics contests and assessments written by the Centre for Education in Mathematics and Computing at the University of Waterloo. Students in elementary through high school take them to measure their problem-solving ability against a widely used Canadian standard, and strong results are often cited in scholarship and enrichment applications. The CEMC study guide has 6 sections and about 1,603 words.
01Algebra and Functions
A candidate should be fluent with manipulating expressions (factoring, expanding, completing the square), solving linear and quadratic equations and inequalities, and understanding functions as rules with domain, range, composition, and inverses. Know the shapes and key features of linear, quadratic, polynomial, exponential, logarithmic, and absolute-value graphs, and how transformations (shifts, stretches, reflections) act on them.
279 words, about 1 min02Geometry and Trigonometry
Master triangle geometry (similarity, congruence, Pythagorean theorem, area formulas), circle properties (inscribed angles, tangents, chords, sector area and arc length), coordinate geometry (distance, midpoint, slope, equations of lines and circles), and solid geometry (surface area and volume of prisms, cylinders, cones, spheres). In trigonometry, know the unit circle, radian-degree conversion, exact values at standard angles, the sine and cosine laws, and basic identities such as sin^2 + cos^2 = 1.
267 words, about 1 min03Number Theory and Discrete Mathematics
Be comfortable with divisibility, primes and prime factorization, greatest common divisor and least common multiple, modular arithmetic, and base representation. Know the division algorithm, the Euclidean algorithm, and how gcd and lcm relate: gcd(a,b) lcm(a,b) = a b for positive integers.
248 words, about 1 min04Sequences, Series, and Limits
Recognize arithmetic and geometric sequences, write closed forms for the nth term and partial sums, and handle telescoping sums and simple recurrences. Understand convergence of infinite geometric series ( r < 1) and the meaning of a limit informally: what value a sequence or function approaches.
277 words, about 1 min05Combinatorics and Probability
Distinguish permutations (order matters) from combinations (order does not), apply the multiplication and addition principles, and use complementary counting when direct counting is messy. In probability, know sample spaces, equally likely outcomes, independent events (P(A and B) = P(A)P(B)), mutually exclusive events (P(A or B) = P(A) + P(B)), and conditional probability.
247 words, about 1 min06Problem Solving and Mathematical Reasoning
This domain rewards strategy over memorization. Develop the habits of reading a problem twice, restating it in your own words, identifying what is given and what is asked, and choosing a representation (equation, diagram, table, small cases).
285 words, about 1 min