Written Topics for 2018-2019


  • 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, percents of increase 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. (2017-18)
  2. NO CALCULATOR. Number Bases: Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2016-17)
  3. Counting Basics and Simple Probability: Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2017-18)
  4. NO CALCULATOR. Linear Equations and Inequalities and Quadratic Equations: Includes word problems leading to linear or absolute value equations and inequalities, as well as quadratic equations. No quadratic inequalities. (2014-15)

Sophomores

  1. Coordinate Geometry with Applications: Includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications. No circles. (2016-17)
  2. NO CALCULATOR. Logic, Sets, and Venn Diagrams: Notation, intersection, unions, subsets, empty set, complements, universal set, cardinality 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. (2017-18)
  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. (2017-18)
  4. 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. (2016-17)

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, types of systems. (2015-16)
  2. 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. (2016-17)
  3. Probability: The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value. (2017-18)
  4. NO CALCULATOR. Rational Functions: Including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots. (2017-18)

Seniors

  1. 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 (Oral #2, 2007-8; senior 2013-14)
  2. NO CALCULATOR. Diophantine Equations: May include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems. (2016-17)
  3. Probability: May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes' Theorem, binomial distribution, expected value, and some simple geometric probability. (2017-18)
  4. NO CALCULATOR. Conics: Including locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations. (2013-14)