Written Topics for 2017-2018


  • 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, 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. (2016-17)
  2. NO CALCULATOR. Number Theory and Divisibility: May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2015-16)
  3. Counting Basics and Simple Probability: Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2016-17)
  4. NO CALCULATOR. Quadratics: Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (2016-17)

Sophomores

  1. Perimeter, Area, and Surface Area: Including squares, triangles, rectangles, circles, and shapes made from these, including the Pythagorean Theorem. (2015-16)
  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. (2014-15)
  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. (2016-17)
  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. A good reference would be Geometry for Enjoyment and Challenge by Rhoad, Milauskas, and Whipple, Chapter 16. (2016-17)

Juniors

  1. Algebraic Coordinate Geometry including Circles: Standard material including power theorems, arcs, angles, area, inscribed and circumscribed polygons, sectors and segments, and equations of circles. Coordinates are included. No trig. (2016-17)
  2. NO CALCULATOR. Rational Functions: Including domain and range, discontinuities, vertical, horizontal, and oblique asymptotes, and roots. (2014-15)
  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. (2016-17)
  4. NO CALCULATOR. Logs and Exponents: May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential logarithmic growth and decay, and applications. No complex numbers. (2015-16)

Seniors

  1. Triangle Trigonometry with Applications: Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (2016-17)
  2. NO CALCULATOR. Parametric Equations: Slopes, equations of lines, simple conics (no rotations), intersection points, position (applications), translating between rectangular and parametric equations. A good reference is Analytic Geometry, by Gordon Fuller and Dalton Tarwater; Addison Wesley. Chapter 7 (5th Ed), or Chapter 8 (6th and 7th Ed). (NEW)
  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. (2016-17)
  4. 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. (2014-15)