# Written Topics for 2016-2017

• 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. (2015-16)
2. Counting Basics and Simple Probability: Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2015-16)
3. NO CALCULATOR. Quadratics: Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (2012-13)
4. NO CALCULATOR. Number Bases: Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (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). (2012-13)
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. (2015-16)
3. 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. (2014-15)
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 by Rhoad, Milauskas, and Whipple, Chapter 16. (2015-16)

### Juniors

1. Algebraic Coordinate Geometry (Including Circles): Includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, applications, and standard circle material including power theorems, arcs, angles, area, inscribed and circumscribed polygons, sectors and segments, and equations of circles. Coordinates are included. No trig. (2012-13)
2. 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. (2015-16)
3. 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. (2014-15)
4. NO CALCULATOR. Sequences and Series: Including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus. (2015-16)

### Seniors

1. Triangle Trigonometry with Applications: Including right triangle trigonometry, laws of sines and cosines, and of course, word problems. (2015-16)
2. 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. (2015-16)
3. NO CALCULATOR. Diophantine Equations: May include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems. (2014-15)
4. NO CALCULATOR. Vector Analytic Graphing: Includes two dimensional vector applications, two and three dimensional vectors, equations of lines and planes in space, scalar, inner and cross products, perpendicularly and parallels. distance between lines, points and planes. (No calculus) (2014-15) 