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Worksheets

Downloadable problem sets and solutions — from beginner to olympiad level.

Showing 40 worksheets

Homework
Beginner
Homework Set 14: Mental Math

March 6, 2026

Homework problems that cover mental math, a niche yet useful skill for various competitions.

Geometry
Homework
Intermediate
Homework Set 15: Rigid Transformations

April 12, 2026

Homework problems on rigid transformations — reflections, rotations, and translations — and their applications to competition geometry.

Algebra
Problem Set
Intermediate
Problem Set 16: Logarithms

April 10, 2026

Practice problems on logarithms covering log identities, change of base, and exponential-to-log conversion for competition settings.

Geometry
Problem Set
Intermediate
Problem Set 15: Coordinate Geometry

March 27, 2026

Coordinate geometry problems on minimum path lengths, reflections across lines, and shortest-distance constructions on the Cartesian plane.

Mixed
Problem Set
Beginner
Problem Set 14: Mental Math

March 6, 2026

Mental math techniques including the nearest-multiple-of-10 method for rapid multiplication, useful for timed competition rounds.

Geometry
Homework
Intermediate
Homework Set 13: Ptolemy's Theorem

February 27, 2026

Homework problems that cover Ptolemy's theorem, a rather fundamental theorem in algebra concerning cyclic quadrilaterals.

Geometry
Problem Set
Intermediate
Problem Set 13: Ptolemy's Theorem

February 27, 2026

Problem set applying Ptolemy's Theorem to cyclic quadrilaterals and regular polygons to find diagonal and side lengths.

Combinatorics
Homework
Intermediate
Homework Set 12: Stars and Bars

February 20, 2026

Homework problems on Stars and Bars, one of the most common ways to solve combinatorics problems.

Combinatorics
Problem Set
Intermediate
Problem Set 12: Stars and Bars

February 20, 2026

Counting problems solved using the Stars and Bars technique, covering distributions of identical objects into distinct bins.

Number Theory
Homework
Beginner
Homework Set 11: Bases

February 13, 2026

Learn the basics of bases, which can be used to simplify a lot of difficult problems into much easier ones.

Geometry
Homework
Advanced
Homework Set 10: Nine-point Circle

February 6, 2026

A comprehensive problem set that takes you through the basics and use cases of the nine-point circle.

Geometry
Problem Set
Advanced
Problem Set 10: Triangle Centers

February 6, 2026

Problems on triangle centers — incenter, circumcenter, and nine-point circle — using both coordinate and classical geometric approaches.

Algebra
Homework
Intermediate
Homework Set 9: Invariants

February 5, 2026

Homework set on invariants, often used to quickly find patterns and answers in seemingly complex or unsolvable problems.

Algebra
Problem Set
Intermediate
Problem Set 9: Invariants

January 23, 2026

Problems on mathematical invariants — quantities preserved under repeated operations — used to prove impossibility results and find closed-form answers.

Number Theory
Homework
Beginner
Homework Set 8: Modular Arithmetic

January 18, 2026

Learn about and solve questions on modular arithmetic and Euler's totient theorem.

Number Theory
Problem Set
Intermediate
Problem Set 8: Fermat's Little Theorem

January 16, 2026

Problems applying Fermat's Little Theorem and Euler's totient function to compute large modular exponentiations efficiently.

Combinatorics
Homework
Beginner
Homework Set 7: Pascal's Triangle

January 9, 2026

Homework set with problems on Pascal's triangle, a powerful tool in combinatorics, algebra.

Combinatorics
Problem Set
Beginner
Problem Set 7: Pascal's Triangle

January 9, 2026

Problems exploring Pascal's Triangle, binomial coefficients, and their symmetry properties and applications to counting.

Algebra
Homework
Beginner
Homework Set 6: Complex Numbers

November 14, 2025

Homework set with problems on complex numbers, often necessary for understanding the solutions to many different problems.

Algebra
Problem Set
Intermediate
Problem Set 6: Complex Numbers

November 14, 2025

Problem set on complex number arithmetic, modulus, conjugates, and their applications in competition problems.

Algebra
Homework
Intermediate
Homework Set 5: Geometric Series

November 7, 2025

Learn about various use cases of the geometric series and its summations.

Algebra
Problem Set
Intermediate
Problem Set 5: Geometric Series

November 7, 2025

Problems on geometric series including finding common ratios, evaluating infinite sums, and applying the series formula to word problems.

Algebra
Problem Set
Intermediate
Problem Set 4: Induction

October 31, 2025

Proof by induction problems establishing base cases and inductive steps to prove divisibility results, closed-form formulas, and inequalities.

Algebra
Homework
Intermediate
Homework Set 4: Induction

October 30, 2025

Discover how to prove various different problems using the method of induction, often necessary in proof-based competitions.

Number Theory
Homework
Beginner
Homework Set 3: Nim

October 17, 2025

Learn the basics of game theory through the game of Nim and finding winning strategies.

Combinatorics
Problem Set
Beginner
Problem Set 3: Game Theory

October 16, 2025

Game theory problems based on Nim-style coin removal games, practicing the analysis of winning and losing positions under optimal play.

Algebra
Homework
Beginner
Homework Set 2: Factorials

September 26, 2025

Homework set with problems on factorials and their prime factorizations.

Number Theory
Problem Set
Beginner
Problem Set 2: Factorials

September 26, 2025

Problems on factorials, trailing zeros, and finding the largest prime power dividing n! using Legendre's formula.

Algebra
Homework
Intermediate
Homework Set 1: Simon's Favorite Factoring Trick

September 19, 2025

Homework set with problems on Simon's Favorite Factoring Trick, one of the tools used to solve Diophantine equations.

Algebra
Problem Set
Beginner
Problem Set 1: Simon's Favorite Factoring Trick

September 19, 2025

Introduction to Simon's Favorite Factoring Trick for factoring and solving integer equations of the form xy + ax + by + c = 0.

Mixed
Problem Set
Intermediate
Trial Set: Mixed Review

August 29, 2025

Kickoff problem set covering a mixed range of competition topics including geometric series, number theory, and combinatorics.

Combinatorics
Problem Set
Beginner
Problem Set 16: Expected Value

April 4, 2025

Problems on expected value and basic probability including dice outcomes, investment scenarios, and real-world applications.

Geometry
Problem Set
Beginner
Problem Set 15: Coordinate Geometry

March 21, 2025

Coordinate geometry problems covering perpendicular bisectors, parallelogram coordinates, and point relationships on the Cartesian plane.

Number Theory
Problem Set
Beginner
Problem Set 14: Number Bases

February 28, 2025

Problems on converting between number bases and working with base representations, including large numbers in non-decimal bases.

Number Theory
Problem Set
Beginner
Problem Set 13: Prime Numbers

February 21, 2025

Problems on prime numbers including finding primes with specific sum or product properties.

Number Theory
Problem Set
Beginner
Problem Set 12: Divisibility Rules

February 14, 2025

Problems proving and applying divisibility rules for integers 1–10, with applications to checking divisibility of large numbers.

Number Theory
Problem Set
Intermediate
Problem Set 11: Diophantine Equations

January 31, 2025

Problems on linear Diophantine equations, determining when integer solutions exist and finding them using the extended Euclidean algorithm.

Number Theory
Problem Set
Intermediate
Problem Set 10: Euler's Totient Theorem

January 24, 2025

Problems applying Euler's totient function to compute modular exponentiations and find totient values, including cases where the base and modulus are not coprime.

Number Theory
Problem Set
Beginner
Problem Set 9: Modular Arithmetic

January 17, 2025

Introduction to modular arithmetic through clock problems, last-digit computations, and finding patterns in powers of integers.

Number Theory
Problem Set
Beginner
Problem Set 8: GCD and LCM

January 10, 2025

Problems on greatest common divisors and least common multiples, including the GCD-LCM product identity and sum minimization.

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