AMC problems by topic
Each of the 2,600 problems in the archive is tagged with the concepts it uses. Those 228 concepts are grouped into 8 areas, so you can practise something as broad as geometry or as specific as the power of a point.
Algebra977 problems
Equations and systems, polynomials and factoring, sequences and series, inequalities, functions, logarithms and complex numbers.
- System of equations119
- Linear equation114
- Arithmetic sequence76
- Quadratic73
- Algebraic manipulation72
- Inequality68
- Logarithm61
- Recursion57
- Vieta's Formulas57
- Factoring54
- Polynomial51
- Complex number49
- Geometric sequence44
- Summation43
- Absolute value42
- Substitution40
- Difference of squares34
- Floor and ceiling functions32
- Custom operation28
- Radical25
- Roots of unity24
- Slope24
- Function21
- Telescoping21
- Ages14
- Completing the square14
- Simon's Favorite Factoring Trick14
- Symmetry (algebra)14
- Binomial theorem9
- Functional equation9
- Fibonacci8
- Mixture7
- Rationalizing denominator7
- Sum and difference of cubes7
- AM-GM Inequality6
- Rational equation6
- Sum of first n squares5
- De Moivre's Theorem4
- Sum of first n odd numbers4
- Calculus3
Geometry893 problems
Triangles and circles, polygons, coordinate geometry, area and similarity, solids, transformations and trigonometry.
- Coordinate geometry124
- Pythagorean Theorem105
- Area decomposition77
- Triangle area77
- Similarity71
- Area ratio60
- Area59
- Equilateral triangle59
- Volume57
- Circle area50
- Tangent circles46
- Regular polygon45
- Special right triangle40
- 3D geometry39
- Circle39
- Cube geometry37
- Trigonometry36
- Transformation35
- Rectangle33
- Right triangle33
- Sector33
- Square (geometry)33
- Isosceles triangle32
- Triangle inequality31
- Tangent line30
- Trigonometric identity30
- Trapezoid28
- Angle chasing27
- Lattice point26
- Law of cosines26
- Distance formula22
- Parabola22
- Sphere21
- Cone20
- Altitude19
- Inscribed angle18
- Angle bisector theorem17
- Chord17
- Angle sum16
- Circumcircle/circumcenter/circumradius16
- Parallel lines16
- Perimeter16
- Midpoint15
- Cyclic quadrilateral14
- Median (geometry)14
- Shoelace formula14
- Arc13
- Incircle/incenter/inradius13
- Power scaling13
- Rhombus13
- Centroid12
- Cylinder12
- Pyramid12
- Surface area12
- Vector12
- Perpendicular bisector11
- Pythagorean Triple11
- Circumference10
- Rectangular prism10
- Congruence8
- Parallelogram8
- Power of a point8
- Heron's Formula7
- Paper folding7
- Ellipse6
- Equiangular polygon6
- Net (3D geometry)6
- Angle bisector5
- Annulus5
- Law of sines5
- Polyhedron5
- Ptolemy's Theorem5
- Reflection (geometry)5
- Kite4
- Radical axis4
- Diagonal3
- Homothety3
- Hyperbola3
Number Theory553 problems
Divisibility and primes, modular arithmetic, digits and number bases, and Diophantine equations.
- Divisibility102
- Digits99
- Modular arithmetic96
- Prime factorization92
- Parity66
- Diophantine Equation58
- Perfect square39
- Prime35
- Factor counting30
- Least common multiple29
- Greatest common divisor28
- Factor21
- Triangular number19
- Units digit14
- Multiple10
- Palindrome10
- Chinese Remainder Theorem9
- Power of 29
- Modular exponentiation7
- Sum of factors7
- Legendre's Formula6
- Continued fraction5
- Perfect power5
- Trailing zeros5
- Multiplicative order4
- Euler's Totient Function3
Combinatorics340 problems
Counting techniques, permutations and combinations, recursion, bijections and graph theory.
- Combinations54
- Counting integers in a range46
- Arrangements with restrictions37
- Multiplication principle37
- Complementary counting29
- Basic counting27
- Graph theory27
- Inclusion-exclusion24
- Permutations21
- Subsets17
- Counting intersections15
- Bijection14
- Double counting10
- Counting pairs9
- Burnside's Lemma8
- Circular arrangements8
- Multiset permutations8
- Stars and bars8
- Combinatorial game7
- Pigeonhole principle7
- Counting shapes in figures6
- Fencepost counting4
- Partitions and compositions4
- Recursive counting4
- Lattice paths3
- Tiling3
- Venn Diagram3
Probability & Statistics325 problems
Basic and conditional probability, expected value, geometric probability, and averages and spread.
- Basic probability92
- Mean90
- Geometric probability47
- Median (data)33
- Dice (probability)32
- Independent events15
- Conditional probability14
- Random walk13
- Recursive probability13
- Mode12
- Complementary probability9
- Expected value9
- Harmonic mean8
- Binomial probability7
- Sampling with/without replacement7
- Geometric distribution4
- Weighted mean4
- Data and graph interpretation3
- Range3
Arithmetic550 problems
Ratios and percentages, rates and speed, unit conversion, exponents, place value and number bases.
Logic57 problems
Logical deduction, counterexamples, cryptarithms and truth-teller puzzles.
Problem-Solving Techniques629 problems
The moves that cut across every subject: casework, symmetry, working backwards, bounding, invariants and small cases.