# Written Topics for 2022-2023

• 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. Basic Statistics: Measures of central tendency (mean, median, and mode), histograms, box-and-whisker plots, stem and leaf plots, range, interquartile range (IQR), potential outliers. No variance. No standard deviation. No comparison of sample and population means. (Resource: Sections 1.3 and 2.1-2.5 in the text OpenStax: https://openstax.org/details/books/introductory-statistics). (2020-21)
2. Counting Basics and Simple Probability: Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas. (2021-22)
3. NO CALCULATOR. Number Bases: Including conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2021-22)
4. NO CALCULATOR. Number Theory and Divisibility: May include patterns (such as trailing zeros), factors, primes, divisibility rules, unique factorization, LCM, GCD, and their relationships. (2021-22)

### Sophomores

1. Quadratic Functions: Includes domain, ranges, inverse, composition, quadratic formula, graphs of quadratic functions, max and min values, and applications. (So 2004-05, Fr 2016-17, Fr 2017-18)
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. (2021-22)
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. (2020-21)
4. 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. (2020-21)

### Juniors

1. Algebraic Coordinate Geometry Including Circles: Includes distance, midpoint, slope, parallel, perpendicular, equations of lines, simple area and perimeter, applications, and equations of circles. Coordinates are included. No trig. (2017-18)
2. Probability: The standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. Does not include binomial distribution nor expected value. (2021-22)
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. (2020-21)
4. NO CALCULATOR. Conics: Including locus definitions, eccentricity, directrix, and area of an ellipse. No parametrics, no polar, and no rotations. (Jr 1979-80, Sr 2021-22)

### Seniors

1. Applications of Matrices and Markov Chains: includes solving large systems of equations, using matrix inverses and using transition matrices (aka Markov Chains). Does not include geometric transformations. (Jr 2014-15, Sr 2007-08). Source: "Finite Mathematics for Managerial, Life, and Social Sciences", Tan, Sections 9.1-9.3. ISBN: 978-1285464657. Reportedly this is the ICTM orals source from 2018. Includes: regular Markov chain, steady-state distribution vector, absorbing states.
2. Probability: May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2021-22)
3. NO CALCULATOR. Linear Diophantine Equations: May include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems. (2018-19)
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, alternating, and harmonic sequences and series. No calculus. (2020-21)