High School Competition Practice Worksheets & Problems

High school competition math modeled on the AMC 10 and AMC 12, in two tiers over a shared foundation. The AMC 10 tier covers equations and systems, sequences and series, inequalities, plane geometry, circles and coordinate geometry, number theory, and counting; the AMC 12 tier adds logarithms, complex numbers, trigonometry, advanced polynomials and Vieta, and functional equations. Every problem is auto-generated with a complete step-by-step solution.

What High School Competition covers

AMC 10 Tier (Grades 8-10)

Algebra: Equations and Systems

• Linear Equations and Systems
• Quadratic Equations and the Discriminant
• Vieta's Relations: Sum and Product of Roots
• Exponential Equations and Systems
• Word Problems: Two-Resource and Mixture

Sequences, Series and Progressions

• Arithmetic Sequences and Series
• Geometric Sequences and Series
• Term from a Partial-Sum Formula
• Comparing Two Series: Equal Sums and Ratios
• Recursive Sequences

Inequalities and Absolute Value

• Quadratic and Rational Inequalities
• Absolute Value Equations and Inequalities
• Sign and Ordering Deductions
• AM-GM and Optimization
• Floor, Ceiling and the Greatest-Integer Function

Exponents, Radicals and Logarithms

• Laws of Exponents and Rational Exponents
• Simplifying and Denesting Radicals
• Introduction to Logarithms
• Change of Base and Log Combinations

Ratios, Rates, Proportions and Work

• Ratio, Proportion and Variation
• Rate, Time and Distance
• Work and Combined Rates
• Percent and Profit/Loss Applications
• Averages and Basic Statistics

Plane Geometry: Angles, Triangles and Polygons

• Angle Chasing and Triangle Angles
• Polygon Angles and Angles in Arithmetic Progression
• Pythagorean Theorem and Special Triangles
• Perimeter, Area and Equal-Perimeter Comparisons

Circles, Area and Coordinate Geometry

• Circle Angles, Chords and Tangents
• Two-Circle Configurations
• Coordinate Geometry: Lines and Distance
• Area on the Coordinate Plane
• Ellipses and Conic Sections
• Transformations on the Coordinate Plane

Number Theory and Counting

• Divisibility and Remainders
• Number Bases and Cross-Base Reversal
• Counting and Basic Probability
• Logic, Sets and Syllogisms
• Digit and Cryptarithm Puzzles
• Clock and Calendar Arithmetic

Solid Geometry and Volume

• Volume and Surface Area of Prisms and Cubes
• Volume and Surface Area of Cylinders
• Volume and Surface Area of Pyramids and Cones
• Volume and Surface Area of Spheres
• Inscribed, Composite Solids and Nets

Functions

• Function Notation and Evaluation
• Composition of Functions
• Inverse Functions
• Domain, Range and Piecewise Functions
• Custom-Defined Operations

AMC 12 Tier (Grades 10-12)

Advanced Algebra: Polynomials, Vieta and Functional Equations

• Polynomial Roots and Advanced Vieta
• Partial-Fraction Decomposition
• Cubic and Higher-Degree Roots (Roots in AP)
• Functional Equations

Logarithms, Exponentials and Complex Numbers

• Advanced Logarithmic Equations
• Exponential Growth and Log Applications
• Complex Numbers and Roots of Unity

Trigonometry

• Right-Triangle and Unit-Circle Trigonometry
• Law of Sines and Law of Cosines
• Trigonometric Identities and Equations

Advanced Geometry: Similarity, Cevians and Power of a Point

• Similar Triangles and Medians
• Cevians: Mass Points, Ceva and Menelaus
• Power of a Point and Cyclic Quadrilaterals
• Advanced Area Ratios and Equal-Area Divisions

Advanced Number Theory, Combinatorics and Probability

• Modular Arithmetic and Advanced Divisibility
• Advanced Counting
• Probability and Expected Value
• Diophantine Equations
• Geometric Probability
• Binomial Theorem and Expansion

Sample High School Competition problems

A few auto-generated examples — every worksheet you make is a fresh set, with complete step-by-step solutions.

Generating sample problems…

More math practice

• Pre-Algebra practice Grades 6–7
• Algebra 1 practice Grades 8–9 · High School
• Geometry practice High School
• Elementary Math practice Grades 4–5
• Competition Math practice Grades 4–8 · Contest
• Printable workbooks →
• Common Core standards coverage →