Topics for 2023-24

  • 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.

Use the tabs below to see the topics by grade level for each meet.

  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. (2021-22)
  2. Counting Basics and Simple Probability: Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2022-23)
  3. NO CALCULATOR. Number Bases: Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2022-23)
  4. NO CALCULATOR. Quadratics: Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (2017-18)
  1. Functions: Linear, quadratic, greatest integer, absolute value, step functions, piecewise, exponential. No logarithms. (2019-20)
  2. 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. (2022-23)
  3. NO CALCULATOR. Perimeter, Area, and Surface Area: Including squares, triangles, rectangles, circles, and shapes made from these; includes the Pythagorean Theorem. (2021-22)
  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. (2021-22)
  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. (2021-22)
  2. Probability: The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, and expected value (new to this level; see old senior contests). Does not include binomial distribution. (2022-23)
  3. 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. (2016-17)
  4. NO CALCULATOR. Logarithms 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. (2021-22)
  1. Triangle Trigonometry with Applications: Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (2021-22)
  2. Probability: May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2022-23)
  3. 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 precalculus texts. (2021-22)
  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. (2009-2010)
  1. Divisibility Rules. (NO CALCULATOR IN PREP OR PRESENTATION.) Source: Introduction to Number Theory by Mathew Crawford – the Art of Problem Solving – Chapter 13 -- ISBN: 978-1-934124-12-3
  2. Game Theory. (CALCULATOR ALLOWED IN PREP) Source: For All Practical Purposes – 9th Edition – by COMAP – Chapter 15 – ISBN: 9781429243162.
  3. Continued Fractions. (NO CALCULATOR IN PREP OR PRESENTATION.) Source: Continued Fractions by C.D. Olds – MAA New Mathematical Library – Chapters 1 – 3 – https://bookstore.ams.org/nml-9
  4. Logic and Logic Circuits. Source from ICTM available in Fall 2023.