# Written Topics for 2019-2020

• 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. NO CALCULATOR. Number Bases: Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2018-19)
2. Counting Basics and Simple Probability: Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2018-19)
3. NO CALCULATOR. Number Theory and Divisibility: May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2017-18)
4. Coordinate Geometry: Includes distance, midpoint, slope, parallels, perpendiculars and applications. (2009-10)

### Sophomores

1. NO CALCULATOR. Functions: Linear, quadratic, greatest integer, absolute value, step functions, piecewise, exponential. (1993-94)
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. (2018-19)
3. NO CALCULATOR. Circles: Standard material including arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles. (2010-11)
4. Coordinate Geometry: Includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, and applications, points of concurrency (no circles). (2018-19)

### Juniors

1. NO CALCULATOR. Polynomials: Including factor, remainder, and rational root theorems; coefficient analysis; determining equations given various information. (2001-02)
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. (2018-19)
3. 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. (2017-18)
4. 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 2018-19)

### Seniors

1. 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. (2017-18)
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. (2018-19)
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, and harmonic sequences and series. No calculus. (2015-16)
4. Vectors: (Previously called 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. (2016-17)