# MMT Topics Covered ## Contest Structure

#### ALGEBRA

• Systems of equations
• Vieta’s
• Binomial Theorem
• Simon’s Favorite Factoring Trick
• Ratios
• (Infinite) Geometric Series
• Arithmetic Series
• Sum/Difference of Powers
• Rate/Time
• Floor/Ceiling
• Absolute Value
• Substitution (Nested Roots/Repeated Fractions)
• Mean, Median, Mode, Range
• Telescoping

#### COMBINATORICS

• Sticks and Stones
• Permutation/Combination
• Properties of Inclusion Exclusion for three or less sets
• Basic Geometric Probability
• Conditional Probability
• Expected Values
• Complementary Counting
• Recursion
• Bijections
• Casework
• Pigeonhole Principle
• Double-counting
• Basic Invariants

#### GEOMETRY

• Area Formulas
• Volume Formulas
• Shoelace Formula
• Pythagorean Theorem
• Distance Formula
• Similar Triangles
• Angle Chasing
• Power of a Point
• Basic Mass Points
• Heron’s Formula
• Pick’s Theorem
• Surface Area for Pyramids, Prisms, and Cones
• Arcs and Sectors
• Angle Bisector Theorem
• Internal/External Angles

#### NUMBER THEORY

• Fermat’s Little Theorem
• Euclidean Algorithm
• Chinese Remainder Theorem
• Divisibility
• Chicken McNugget Theorem
• GCD and LCM
• Number of Factors
• Sum of Factors
• Basic Modular Arithmetic
• Fundamental Theorem of Arithmetic

## Round 1 - Mounting Mayhem (Puzzle Round)

• The Mounting Mayhem Round will consist of some mathematical-based puzzle questions.
• Students have 15 minutes to read the Puzzles
• Students will have 60 minutes to solve as many of them as possible.
• Puzzles can range from logic to number theory to geometry and more. They often require out-of-the-box thinking although all topics can readily be understood and grasped by middle schoolers.
• Harder puzzles will be worth more points, but these puzzles will be longer and/or require more creativity — you must decide what problems to focus your time on to optimize your team score.

## Round 2 - Bucking Bingo

• The “Bingo” Round will consist of 24 questions to be solved in 60 minutes.
• The questions will vary in difficulty, but not necessarily in increasing order — rather the difficult problems will be randomly distributed.
• In this round, each correctly solved question is worth points, but each completed and correct Bingo (each of the problems in a given row, column, or long diagonal are solved and correct) is worth bonus points!
• You are not expected to solve all the questions in this
round within the allotted time. Instead, we encourage
you to strategize how you might use your time to
• The image on the right shows the format of the
Bingo board: ## Round 3 - Gallop Round (Guts)

• The Gallop Round will consist of 27 questions to be solved in 60 minutes.
• The questions will be divided into 9 sets of 3 questions each, and you must submit the answers to one set before accessing the problems for the next. This means you must strategize when to submit each set (incomplete or not) to ensure you get access to as many questions as possible.
• The problems will get progressively more difficult, and later problems will be worth more points.
• Submissions will be scored immediately and a live score of all participating teams will be available during the competition. Prepare for the adrenaline rush!

## Round 4 - Mystery Mare (Pressure Round)

• The Mystery Mare round is exactly that — a mystery!
• Hints about the nature of the round will be revealed as the competition date nears.
• We promise it will be as fun and engaging as the other rounds.