Written Topics for 2025-2026

  • 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. Counting Basics and Simple Probability: The emphasis is on organized thinking, not using formulas. Topics: tree type problems, combinations, and permutations. (2024-25)
  2. NO CALCULATOR. Number Theory and Divisibility: Patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2022-23)
  3. NO CALCULATOR. Ratios, Proportion and Percent: Money, simple interest (not compound interest), discounts, unit conversions, percentages of increase or decrease and error, and direct variations. It should not require knowledge of advanced algebra. While questions should not be trivial, they should be approachable to most contestants. (2023-24)
  4. NO CALCULATOR. Quadratics: Domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (2023-24)

Sophomores

  1. 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. (2024-25)
  2. NO CALCULATOR. Similarity: The standard geometric treatment including perimeter, area, and volume relationships, conditions determining similarity, similarity in right triangles and polygons. It may include a few proportion theorems that are not specifically similarity, such as the angle bisector theorem. (2022-23)
  3. NO CALCULATOR. Perimeter, Area, and Surface Area: Squares, triangles, rectangles, circles, and shapes made from these; includes the Pythagorean Theorem. (2023-24)
  4. NO CALCULATOR. Advanced Geometry Topics: Brahmagupta’s formula, point to line distance formula, area of a triangle given vertices, Stewart’s Theorem, Ptolemy’s Theorem, Mass points, inradius and circumradius, Ceva’s Theorem, and Theorem of Menelaus. An understanding of standard high school Geometry topics is assumed. Geometry for Enjoyment and Challenge, Chapter 16, by Richard Rhoad, George Milauskas, and Robert Whipple (2023-24

Juniors

  1. 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. (2024-25; also see old senior contests)
  2. NO CALCULATOR. Triangle Trigonometry with Applications: Right triangle trigonometry, laws of sines and cosines, and of course, word problems. (Senior 2023-24)
  3. NO CALCULATOR. Sequences and Series: Sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, alternating, and harmonic sequences and series. No calculus. (2023-24)
  4. NO CALCULATOR. Logarithms and Exponentials: Domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential and logarithmic growth and decay, and applications. No complex numbers. (2024-25)

Seniors

  1. NO CALCULATOR. Probability: Combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2024-25)
  2. NO CALCULATOR. Trigonometric Equations and Identities: Solving trig equations and simplifying trig expressions using standard formulas (e.i., double-angle, half-angle, sum-to-product, and product-to-sum). (2009-10)
  3. NO CALCULATOR. Theory of Equations: Factor, remainder, and rational root theorems, upper bounds, coefficient analysis, Descartes’ Rule of Signs, synthetic division, complex roots, and determining equations given various info. Possible sources: Advanced Mathematics by Richard G. Brown, or some older precalculus texts. (2023-24)
  4. NO CALCULATOR. Polar Coordinates and Equations: Graphs, systems, and de Moivre’s Theorem. Includes conics and intersections of polar curves that are not simultaneous solutions to the system (“ghost points”). Analytic Geometry, by Gordon Fuller and Dalton Tarwater (6th-7th ed) is a good source. (2023-24)