Free middle school competition math practice
Mathyessy is a free contest math practice site for middle schoolers preparing for MATHCOUNTS, the AMC 8 and similar competitions. Every page below explains a topic and works through problems step by step. Each one links to a matching practice set in the app with instant feedback, adaptive difficulty and mistake review. No account is needed.
Algebra
62 practice sets in the app · 11 worked problem pages
One-variable linear equations practiceSolving a linear equation means undoing what was done to x, in reverse order, while keeping both sides balanced.Algebra word problems practiceThe hard part of a word problem is the translation. Once it is an equation, the algebra is quick.Systems of equations practiceTwo unknowns need two equations. Contest problems often reward finding what is asked without solving for each variable.Ratio practice problemsA ratio compares quantities. Most ratio problems become easy once you find the size of one 'part'.Percent practice problemsPercent means 'per hundred'. Turning percents into multipliers makes discounts and percent changes quick.Rate problems practiceDistance, work and production problems all use one idea: amount = rate × time.Arithmetic sequences and series practiceAn arithmetic sequence adds the same amount each time. Two formulas handle almost every contest question.Factoring quadratics practiceTo factor x² + bx + c, find two numbers that multiply to c and add to b.Quadratic formula and discriminant practiceThe quadratic formula solves any quadratic. The discriminant tells you what kind of roots to expect before you solve.Simon's Favorite Factoring Trick practiceAn equation like xy + 3x + 4y = 24 looks stuck, until you add one number to both sides and it factors.Exponent laws practiceA few exponent rules cover almost everything: same base means add, subtract or multiply the exponents.
Geometry
20 practice sets in the app · 10 worked problem pages
Pythagorean theorem practice problemsFind missing sides of right triangles, spot Pythagorean triples and uncover the hidden right triangles that contest problems love.Special right triangles: 45-45-90 and 30-60-90 practiceTwo triangles show up in contest geometry again and again. Learn their side ratios once and you can skip the Pythagorean theorem.Triangle area practice problemsBase times height over two is only the start. Contest problems make you find the height, use a right triangle or reach for Heron's formula.Circle area and circumference practice problemsMost contest circle questions want an answer in terms of π. The real skill is finding the radius.Arc length and sector area practiceA sector is a slice of a circle. Work out what fraction of the circle you have, and the rest is the area or circumference formula.Polygon interior and exterior angle practiceFour short formulas cover almost every polygon angle question in middle school contests.Similar triangles and scale factor practiceSimilar figures have the same shape at different sizes. Know how lengths, areas and volumes scale and these problems become one-liners.Triangle inequality practice problemsCan three lengths make a triangle? One rule decides, and contest problems ask you to count how many lengths work.Prism and cube volume practiceEvery prism follows one rule: the area of the base times the height.Surface area practice problemsSurface area is the total area of every face. Picture unfolding the solid flat and add up the pieces.
Counting & Probability
20 practice sets in the app · 9 worked problem pages
Permutations practice problemsPermutations count arrangements where order matters: lineups, rankings, codes and seatings.Combinations practice problemsCombinations count selections where order does not matter: committees, teams, toppings and hands of cards.Probability practice problemsProbability is counting twice: once for the outcomes you want and once for all possible outcomes.Complementary counting practiceWhen the cases you want are messy, count the ones you don't want and subtract.Casework counting practiceBreak a hard count into a few easy ones. The key is choosing cases that don't overlap and don't miss anything.Expected value practice problemsExpected value is the long-run average: what a game pays per play if you played it many, many times.Stars and bars practice problemsHow many ways can you share identical candies among kids? Stars and bars turns it into a single combination.Pigeonhole principle practice'How many must you pick to guarantee…?' Imagine the unluckiest possible picks, then add one.Grid path counting practiceA shortest path on a grid is just a word made of R's and U's. Counting paths means counting those words.
Number Theory
20 practice sets in the app · 9 worked problem pages
Divisibility rules practiceDivisibility rules let you test huge numbers in seconds, and they are the key to missing-digit puzzles.Prime factorization practiceBreaking a number into primes is the first step for divisors, GCD, LCM, perfect squares and factorial problems.Greatest common divisor (GCD) practiceThe GCD is the biggest number that divides both. Prime factorizations and the Euclidean algorithm find it fast.Least common multiple (LCM) practiceTwo bells, two buses, two blinking lights: when do they line up again? That's the LCM.Counting divisors practiceHow many factors does 360 have? You don't need to list them. Factor it into primes and multiply.Modular arithmetic practiceModular arithmetic is arithmetic with remainders. It turns giant calculations into small ones.Units digit and cycles practiceWhat is the last digit of 7²⁰²⁶? Only the last digits matter, and they repeat in short cycles.Number bases practiceBase 10 uses place values 1, 10, 100… Other bases work the same way with different place values.Trailing zeros in factorials practiceEach trailing zero comes from a factor of 10 = 2 × 5. In a factorial, the 5s are the bottleneck.