**Individual Restricted Events**

These events are restricted to students enrolled in the specific course this school year. Some questions may test typical knowledge and skills associated with the specific course.

**Algebra I Restricted **could involve solving problems requiring the application of: simplification and factoring of expressions, solving linear and quadratics equations, operations with radicals, basic inequalities, functions, and graphs of equations and inequalities, and application of algebraic skills in problem solving contexts

**Geometry Restricted** could involve solving problems requiring the application of: constructions, logic, similarity and congruence, geometry of the triangle and other polygons, geometry of the circle, area, perimeter, volume, three-dimensional geometry, transformations, and coordinate geometry.

**Algebra II Restricted** could involve solving problems requiring the application of: absolute value, inequalities, polynomials, systems of equations, arithmetic and geometric sequences, the binomial theorem, matrices, and logarithmic and exponential functions.

**Fourth Year Mathematics Restricted** could involve solving problems requiring the application of topics found in a substantial Trigonometry or Math Analysis course.

**Calculus with Clickers Restricted** could involve solving problems requiring the application of topics found in a substantial Calculus course, including limits, derivatives and integrals. Although a correct solution is paramount for each problem, speed of "clicking in" that correct solution is also required.

**Open Individual Events**

These events are open to any student.

**Algebra** could involve solving problems requiring the application of: real number properties, simplification and factoring of expressions, solving linear and quadratic equations, operations with radicals, basic inequalities, functions, graphs of equations and inequalities, absolute value, polynomials, systems of equations, arithmetic and geometric sequences, the binomial theorem, matrices, and logarithmic and exponential functions, and application of algebraic skills in problem solving contexts.

**Geometry** could involve solving problems requiring the application of constructions, logic, similarity and congruence, geometry of the triangle and other polygons, geometry of the circle, area, perimeter, volume, three-dimensional geometry, transformations, and coordinate geometry. Some questions may test typical knowledge and skills associated with the high school Geometry course.

**Counting and Probability** test could involve solving problems requiring the application of: basic counting techniques, permutations, combinations, independent and mutually exclusive events, probability, conditional probability, odds, and expected value.

**Mathematical Reasoning** could involve solving problems requiring the application of logic, discrete mathematics, number theory, numerical or geometric patterns, ratio and proportion, mathematical induction, inductive and deductive reasoning, and reasoning involving indirect arguments and use of counter examples.

**Team Events**

A team of three or four students may work on the test cooperatively (together or separately, by sharing and discussing quietly) using any team strategy. Only one set of answers will be accepted from the team. Some questions may test typical knowledge and skills associated with the specific course.

**Algebra I Team** is restricted to students enrolled in Algebra I this school year. The test could involve solving problems requiring the application of real number properties, simplification and factoring of expressions, solving linear and quadratic equations, operations with radicals, basic inequalities, functions, graphs of equations and inequalities, and application of algebraic skills in problem solving contexts.

**Geometry Team** is restricted to students enrolled in geometry this school year. The test could involve solving problems requiring the application of constructions, logic, similarity and congruence, geometry of the triangle and other polygons, geometry of the circle, area, perimeter, volume, three-dimensional geometry, transformations, and coordinate geometry.

**Algebra II Team** is restricted to students enrolled in Algebra II this school year. The test could involve solving problems requiring the application of absolute value, inequalities, polynomials, systems of equations, arithmetic and geometric sequences, the binomial theorem matrices, and logarithmic and exponential functions. Some 2uestions may test typical knowledge and skills associated with the high school Algebra II course.

**Fourth Year Mathematics Team** is restricted to students enrolled in mathematics beyond Algebra II this school year. The test could involve solving problems requiring the application of topics found in a substantial Trigonometry or Math Analysis course. Some questions may test typical knowledge and skills associated with high school courses beyond Algebra II.

**Challenging Problems Event**

**Challenging Problems Event**

Two copies of the problems and one answer form will be given to each sponsor at the beginning of the Relays (10AM). The answer form is due by 12 noon. Any team member may contribute to the solution of a problem, but no faculty assistance is allowed. Students may consult books or notes, use calculators, or confer among themselves, but may not consult anyone not on their team. Partial credit may be given on some problems.

**MathMania Event**

Which school has the best problem solvers? This team event pits each school against all others, and occurs on the main floor as students and sponsors watch from the bleachers. This head to head competition will begin one half hour prior to the awards assembly. This is a single elimination contest, so teams survive only so long as they continue to answer questions correctly. The first problem will be given to all competing teams; subsequent questions will only be given to those teams still in competition. The length of time given to answer each question varies and is determined by the monitor of the event. Questions will become more difficult as the contest progresses. The winning team will receive a trophy which stays at that school until the next year's competition. Each school can enter exactly one team of 3 or 4 students in this event. Topics included in these problems will cover the entire high school mathematics curriculum through Fourth Year Mathematics.

**Computer Programming** Event

This event requires students to write or edit existing computer programs to solve problems that are mathematical in nature. Tasks in the past have and will continue to involve varied environments such as games (like Chinese Checkers) or computer robots (using RoboCode). Currently, students are expected to complete these tasks prior to the Pummill Math Relays; then display (or in certain instances compete with) their resulting productions during the Pummills. Specific instructions for each year’s event is found from the Pummill Relays website.

**Submission of Sample Questions**

In order to better match the student's current school mathematics with the goals of the Standards and the background of University event writers, we need your help. We are continuing to ask sponsors and/or teachers from the participating schools to submit at least two questions (with choices and a correct answer indicated) for each event. Variations of these questions may be used during future Relays. These sample questions, on one hand, might indicate your perspective on the range and nature of questions considered consistent with students' current school experiences. On the other hand, sample questions may be submitted with the intent to encourage students and other educators to value mathematical experiences and concepts other than those currently being emphasized.

**Nature of Events**

In an attempt to promote the values and emphases reflected by the NCTM Standards, Missouri’s Show-Me Standards and MAP testing, and now the Common Core State Standards for Mathematics, we are continuing to modify Pummill Relay tests to increase the emphasis on problem solving and application of concepts. This is a gradual process given the multiple choice format required to deal with the large number of participants in a short period of time. Some events may be affected to a greater extent than others. One consequence of these modifications is a decreased emphasis on calculation or manipulation of variables as the primary goal of a problem. And because calculators are allowed on all Pummill tests, calculator-neutral as well as calculator-enhanced problems are being produced for these tests.

**Length of Events**

The length of all events (except MathMania, Computer Programming, and Challenging Problems) remains at 30 minutes.

**Tie-Breaking**

**Tie-Breaking**

There is no penalty for guessing on these tests. Tie-breaking procedures used by graders involve specific problems within each test (determined ahead of time or selected using a random number generator).