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Learn Competition Math

Problem-solving techniques for contests, beyond what school covers.

Free to start. Built from a single prompt. No credit card.

Competition math is problem solving under time pressure, using school-level knowledge in unusual, clever ways. Contests in the United States include MATHCOUNTS for middle school, the AMC 8, AMC 10 and AMC 12, and the AIME for top AMC scorers. Problems draw on four areas: algebra, geometry, number theory and counting with probability. Calculus is not needed, but creativity is. Success comes less from new facts than from techniques like casework, complementary counting, symmetry, modular arithmetic and working backwards, plus lots of practice with past problems. Learnr builds a competition math course for your level and teaches techniques in short interactive lessons.

How to learn Competition Math, step by step

Learn the contest formats first. The AMC 10 and 12 each have 25 multiple-choice questions in 75 minutes, and the AIME has 15 questions with integer answers from 0 to 999. Knowing the format shapes how you practice.
Build each of the four core areas. Work through algebra, geometry, number theory and counting in turn. Books from the Art of Problem Solving series are widely used for this, though any rigorous problem source works.
Collect techniques, not just answers. After each problem, write the key idea in a notebook: complementary counting, a clever substitution, an auxiliary line. Reviewing that notebook turns single solutions into reusable tools.
Practice past problems by difficulty. Past AMC and AIME problems are freely available online. Work in difficulty bands, such as problems 10 to 15 on the AMC 10, until you solve most of them, then move up.
Struggle before reading solutions. Give a hard problem 20 to 30 minutes before looking. Then read the solution, close it, and rewrite it yourself. The struggle is what builds contest instinct.
Keep a daily problem habit and timed mocks. Solve a few problems every day, with a Learnr streak if it helps, and take a full timed practice test every couple of weeks to build pacing and stamina.

What you'll learn

Use modular arithmetic, divisibility and prime factorization in contest problems
Solve counting and probability problems with casework and complements
Apply geometry tools like similar triangles, power of a point and area ratios
Manipulate algebraic expressions with factoring tricks and Vieta's formulas
Manage time and choose which problems to attempt on a timed contest

What's inside your Competition Math course

A sample path Learnr builds for Competition Math. Your real course adapts to your goal and level.

1. Problem-solving strategies and contest formats
2. Number theory: divisibility, primes and modular arithmetic
3. Counting and probability
4. Algebra: factoring, functions and Vieta's formulas
5. Geometry: triangles, circles and area
6. Timed practice and reviewing mistakes

How long does it take to learn Competition Math?

A strong school math student can become competitive at the AMC 8 or MATHCOUNTS level within a few months of weekly practice. Qualifying for the AIME usually takes one to several years of steady problem solving, depending on starting level and hours per week.

What you need before you start

Solid algebra and geometry at your grade level. Younger students can start with pre-algebra skills; the contest techniques themselves are taught along the way.

Common mistakes to avoid

Reading the solution after two minutes of trying. Without real struggle, you remember the answer but not the way of thinking that found it.
Practicing only problems you can already solve. Most growth comes from problems a little beyond your current level.
Ignoring timing until contest day. Mix untimed deep work with regular timed sets so pacing and problem selection feel familiar.

How Learnr builds your course

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Learn and level up

Move through bite-sized lessons and interactive practice, earning XP and keeping your streak.

Competition Math questions, answered

Do I need calculus for math competitions?

No. Contests like MATHCOUNTS, the AMC and the AIME avoid calculus and focus on algebra, geometry, number theory and counting used in creative ways.

Is Learnr affiliated with these contests?

No. Learnr is an independent learning app and is not connected to MATHCOUNTS, the Mathematical Association of America, which runs the AMC and AIME, or any other contest organizer.