# Written Topics for 2024-2025

• All symbolic manipulators, including HP's and the TI-Nspire CAS, are prohibited for the frosh and sophomore levels at all meets.
• Laptops, PDAs, phones, and other non-calculating devices are not allowed.

### Frosh

1. Counting Basics and Simple Probability: The emphasis is on organized thinking, not using formulas. May include tree type problems, combinations, and permutations. (2023-24) (ANY CALCULATOR EVEN CAS.)
2. NO CALCULATOR. Number Bases: May include conversion and computation in different bases (bases from 2 to 16); finding the base given some information. (2023-24)
3. NO CALCULATOR. Basic Statistics: May include measures of central tendency (mean, median, and mode), box-and-whisker plots, two-way tables, stem and leaf, range. No variance. No standard deviation. (Resource: OpenStax: https://openstax.org/details/books/introductory-statistics). (2022-23)
4. NO CALCULATOR. Applications of Systems of Linear Equations and Inequalities and Quadratic Equations: Limited to two variables. May include absolute value, domain, range, composition, max and min values, applications, graphs of quadratic functions, quadratic formula, and vocabulary such as consistent, inconsistent, dependent, independent. (2020-21)

### Sophomores

1. Geometric Probability: Standard treatment of probability problems with continuous variables using ratios of lengths, areas, and volumes. (2023-24) (ANY CALCULATOR EVEN CAS.)
2. NO CALCULATOR. Logic, Sets, and Venn Diagrams: May include notation, intersection, unions, subsets, empty set, complements, universal set, cardinality of a set, solution sets, and number of subsets. Should include classic Venn diagram problems involving how many things are in various intersections. Emphasis for logic is on using logic, not formal vocabulary. No truth tables. (2021-22)
3. NO CALCULATOR. Circles: Standard material. May include arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles. (2022-23)
4. NO CALCULATOR. Right Triangles: All things fun about right triangles. May include Pythagorean Theorem (and triples), altitude to hypotenuse, related circles and centers, special right triangles, right triangle trigonometry. (2013-14) (Similar topic for juniors 2008-09.)

### Juniors

1. 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 in 2023-2024; see old senior contests). Does not include binomial distribution. (2023-24) (ANY CALCULATOR INCLUDING CAS.)
2. 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. (2022-23)
3. 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. (2023-24)
4. NO CALCULATOR. Polynomials: Including factor, remainder, and rational root theorems; Descartes’ Rule of Signs; coefficient analysis; determining equations given various information. (2021-22)

### Seniors

1. Probability: May include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes’ Theorem, binomial distribution, expected value, and geometric probability. (2023-24) (ANY CALCULATOR INCLUDING CAS.)
2. NO CALCULATOR. Linear Diophantine Equations: May include linear Diophantine Equations, systems of linear Diophantine Equations, contextual problems, or simple nonlinear Diophantine Equations. (2022-23)
3. NO CALCULATOR. Vectors: (Previously called Vector Analytic Graphing) May include two dimensional vector applications, two and three dimensional vectors, equations of lines and planes in space, scalar, cross products, perpendicularity and parallels, distance between points, lines, and planes. No calculus. (2019-20)
4. NO CALCULATOR. Conics: May include locus definitions, eccentricity, and directrix. No parametrics, no polar, and no rotations. (2021-22)