Written Topics for 2026-2027

  • Calculators are not allowed on any contest.
  • Smartwatches, phones, laptops, and other non-calculating devices are not allowed.
  • Dates that topics were last used are in parentheses.

Frosh

  1. NO CALCULATOR. Number Bases: May include conversion and computation in different bases (bases from 2 to 16); finding the base given some information. No quadratics. (2024-25)
  2. NO CALCULATOR. Counting Basics and Simple Probability: The emphasis is on organized thinking, not using formulas. Topics: tree type problems, combinations, and permutations. (2025-26)
  3. NO CALCULATOR. Basic Statistics: May include measures of central tendency (mean, median, and mode), box-and-whisker plots, two-way tables, stem and leaf, range. No variance. No standard deviation. May involve solving a 2x2 linear system of equations. (Resource: OpenStax: https://openstax.org/details/books/introductory-statistics). (2024-25)
  4. NO CALCULATOR. Applications of Systems of Linear Equations and Inequalities and Quadratic Equations: Limited to two variables. May include absolute value, domain, range, composition, max and min values, applications, graphs of quadratic functions, quadratic formula, and vocabulary such as consistent, inconsistent, dependent, independent. (2024-25)

Sophomores

  1. NO CALCULATOR. Logic, Sets, and Venn Diagrams: May include notation, intersection, unions, subsets, empty set, complements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables. (2024-25)
  2. NO CALCULATOR. Geometric Probability: Standard treatment of probability problems with continuous variables using ratios of lengths, areas, and volumes. [Note to question writers: Emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry.] UMAP module 660 is a good source, as is HIMAP module 11. (2025-26)
  3. NO CALCULATOR. Circles: Standard material. May include arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles. (2024-25)
  4. NO CALCULATOR. Surface Area and Volume (3D): Surface area and volume of figures made from triangles, quadrilaterals, circles, and other basic 2D shapes; includes the Pythagorean Theorem. (2024-25)

Juniors

  1. NO CALCULATOR. Modular Arithmetic: May include arithmetic operations in different moduli, divisibility, solving simple linear congruences in one or two variables, Fermat’s Little Theorem, Wilson’s Theorem, and Chinese Remainder Theorem. (2024-25)
  2. NO CALCULATOR. Probability: The standard treatment of probability: combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, and expected value. Does not include binomial distribution. (2025-26; also see old senior contests)
  3. NO CALCULATOR. Geometric Transformations Using Matrices on a Plane: In two dimensions. Includes reflections, rotations, translations, dilations, shears, and compositions. Standard treatment using Algebra 2 texts. For shears refer to Mathematics of Matrices, by Phillip Davis. Ginn and Co., 1965, Library of Congress: 64-24818. Pages 125-161, (2007-08 Oral 2; 2018-19 Senior 1; 2019-20 Junior 4)
  4. NO CALCULATOR. Theory of Polynomials: Including factor, remainder, and rational root theorems; Descartes’ Rule of Signs; students should know about formulas for sums and differences of roots and combinations thereof (Vieta's formulas); coefficient analysis; determining equations given various information. (2024-25)

Seniors

  1. NO CALCULATOR. Diophantine Equations: May include linear Diophantine Equations, systems of linear Diophantine Equations, contextual problems, or simple nonlinear Diophantine Equations - no special techniques. (2024-25)
  2. NO CALCULATOR. Probability: Combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2025-26)
  3. NO CALCULATOR. Vectors: (Previously called Vector Analytic Graphing) May include two dimensional vector applications, two and three dimensional vectors, equations of lines and planes in space, scalar (dot) products, cross products, perpendicularity and parallels, distance between points, lines, and planes. No calculus. (2024-25)
  4. NO CALCULATOR. Sequences and Series: Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, alternating, and harmonic sequences and series. No calculus. (2022-23)