Written Topics for 2021-2022


  • All symbolic manipulators, including HP's and the TI-Nspire CAS, are prohibited for the freshmen and sophomore levels at all meets.
  • Laptops, PDAs, phones, and other non-calculating devices are not allowed.

Freshmen

  1. Ratios, Proportion and Percent: May include 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. (2018-19)
  2. NO CALCULATOR. Number Bases: May include conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2020-21)
  3. Counting Basics and Simple Probability: May include tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2020-21)
  4. NO CALCULATOR. Number Theory and Divisibility: May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2019-20)

Sophomores

  1. Perimeter, Area, and Surface Area: May include squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem. May include prisms, pyramids, and cylinders. No trigonometry. No spheres. No cones. (2017-18)
  2. NO CALCULATOR. Logic, Sets, and Venn Diagrams: Notation, intersection, unions, subsets, empty set, complements, universal set, cardinality (number of elements) of a set, solution sets, and number of subsets. Should include classic type Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables. (2018-19)
  3. Geometric Probability: 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. (2019-20)
  4. NO CALCULATOR. Advanced Geometry Topics: Restricted to 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. (2017-18)

Juniors

  1. Systems of Linear Equations and Inequalities with Applications: May include absolute value, intersections, area and/or perimeter of a region, corner points, slopes, distances, inconsistent/consistent systems, and independent/dependent systems. (2018-19)
  2. NO CALCULATOR. Polynomials: May include factor, remainder, and rational root theorems; Descartes’ Rule of Signs; upper/lower bounds of roots; coefficient analysis; determining polynomials given various information. (2020-21)
  3. Probability: The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. Does not include binomial distribution nor expected value. (2020-21)
  4. NO CALCULATOR. Logs and Exponentials: May include 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. (2020-21)

Seniors

  1. Triangle Trigonometry with Applications: May include right triangle trigonometry, laws of sines and cosines, area, angles of elevation and depression, compass bearing. The emphasis is not on precalculus trigonometric identities. (2017-18)
  2. NO CALCULATOR. Theory of Equations: Including 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 Pre-Calculus texts. (2019-20)
  3. Probability: May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2019-20)
  4. NO CALCULATOR. Conics: May include locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations. (2020-21)