This collection of American Mathematics Competitions (AMC) problems is student curated. It is intended as an information and learning resource beyond the classroom, to help high school students apply age-appropriate formulas to Comp Math when developing problem-solving skills.

TAS student Roy Park has made a service-learning contribution to the Math community by organizing AMC materials by topic. This is significant: Comp Maths are typically chronologically organized by year and can be daunting for younger learners to find by topic. Roy's topical organization makes the resource more accessible for high school students and for learners focused on specific areas. Additionally, by providing explanations, supports high school learners understand process, not just solutions.

The collection is designed so that it can grow from contributions by other students in the Math and Data Science Team.

Original competition materials are attributed to the Mathematical Association of America (MAA).

Curated Comp Math Collection

Recognizing Patterns Using the Difference-of-Squares Identity

Problem Solving Approach

This practice problem demonstrates how recognizing a familiar algebraic identity can simplify calculations. Rather than expanding expressions individually, students identify a difference-of-squares pattern and apply it to reach the solution efficiently.

Simulated Practice Problem

Evaluate:

Worked Solution

Using the difference-of-squares identity:

Problem-Solving Note: Recognizing the difference-of-squares pattern eliminates the need to calculate two large squares.

Student Contributor

Sim Simulator Algebraica

AMC Source

Original practice problem; not from an AMC competition

Key Concepts / Formulas

Difference of squares; algebraic identities

Suggested Learning Level

Grades 8–10; introductory algebra

Keywords

Algebra, difference of squares, identities, simplification

Original Source Reference

AI Simulation, Original simulated example. Not AMC Material

Math Topic

Algebra

Problem-Solving Method

Pattern Recognition

Resource Type

Problem and Solution

AMC Level

AMC 8

Publication Date

2026

Download

amc_-_prototype_-_algebra.pdf

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Finding the Area of a Right Triangle

Problem Solving Approach

This practice problem illustrates how the Pythagorean theorem can be used to determine an unknown side length before calculating the area of a right triangle.

Problem-Solving Note: The key is recognizing that the missing side must be calculated before applying the area formula.

Student Contributor

Sim Simulator Geometrica

AMC Source

AI simulated prototype. Not an AMC Source

Key Concepts / Formulas

Pythagorean theorem; triangle area

Suggested Learning Level

Grade 8, right triangles

Keywords

Geometry, triangles, Pythagorean theorem, area

Original Source Reference

AI Simulation

Math Topic

Geometry

Problem-Solving Method

Geometric Reasoning

Resource Type

Problem and Solution

AMC Level

AMC 8

Publication Date

2026

Download

trump_foreign_policy_analysis.pdf

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Counting Outcomes Using Combinations

Problem Solving Approach

This practice problem introduces combinations as a method for counting selections when order does not matter. Students learn to distinguish between selecting objects and arranging them.

Practice Problem

A mathematics club has 8 members.

How many different groups of 3 students can be selected to represent the club?

Worked Solution

Since the order of selection does not matter, use combinations:

Problem-Solving Note: The important distinction is that selecting students does not involve arranging them in a particular order.

Student Contributor

Sim Simulator Otherica

AMC Source

AI Generated Content for Simulation

Key Concepts / Formulas

Combinations; factorials; counting

Suggested Learning Level

Grades 9–10; introductory combinatorics

Keywords

Combinatorics, counting, combinations, factorials

Original Source Reference

Simulation

Math Topic

Other

Problem-Solving Method

Logical Reasoning

Resource Type

Worked Example

AMC Level

AMC 10

Publication Date

2026

Download

amc-prototype-other_topic.pdf

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