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AMC 10 · 2000–2024

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Every problem since 2000, read and tagged by hand — topic, technique, difficulty, the one insight that cracks it, and the trap that costs you the point.

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The shape of the test

The shape of the AMC 10, problems 1 to 25Each column is one problem position across all 52 contests, coloured by topic category. Algebra falls from 71% of problem 1 to 12% of problem 25. Geometry grows to 48% at problem 19. Number theory and counting dominate the last five. Mean difficulty rises from 1.0 to 4.6 out of 5.Problem 1: 52 problems, mean difficulty 1.0Problem 2: 52 problems, mean difficulty 1.0Problem 3: 52 problems, mean difficulty 1.2Problem 4: 52 problems, mean difficulty 1.3Problem 5: 52 problems, mean difficulty 1.4Problem 6: 52 problems, mean difficulty 1.8Problem 7: 52 problems, mean difficulty 1.9Problem 8: 52 problems, mean difficulty 2.0Problem 9: 52 problems, mean difficulty 2.0Problem 10: 52 problems, mean difficulty 2.1Problem 11: 52 problems, mean difficulty 2.4Problem 12: 52 problems, mean difficulty 2.3Problem 13: 52 problems, mean difficulty 2.6Problem 14: 52 problems, mean difficulty 2.7Problem 15: 52 problems, mean difficulty 2.8Problem 16: 52 problems, mean difficulty 2.8Problem 17: 52 problems, mean difficulty 3.2Problem 18: 52 problems, mean difficulty 3.3Problem 19: 52 problems, mean difficulty 3.4Problem 20: 52 problems, mean difficulty 3.5Problem 21: 52 problems, mean difficulty 3.6Problem 22: 52 problems, mean difficulty 4.0Problem 23: 52 problems, mean difficulty 4.0Problem 24: 52 problems, mean difficulty 4.2Problem 25: 52 problems, mean difficulty 4.6
1510152025
AlgebraNumber TheoryCounting & ProbabilityGeometryLogic, Statistics & Miscmean difficulty 1.0 → 4.6 (of 5)

Each column is one problem position across all 52 contests. The test is not 25 problems of rising hardness — it is 25 different tests, and the mix under your feet changes as you move right.

See the numbers
#AlgebraNumber TheoryCounting & ProbabilityGeometryLogic, Statistics & MiscMean difficulty
13774131.00
23561641.04
33363821.15
426103941.29
52873951.37
621124871.79
720931821.87
8201341141.96
92111101002.02
1017552142.13
11181071252.38
12127101762.35
13168101442.58
14171181512.71
15161161722.85
16107151732.81
17108122023.15
181011131713.27
199882523.42
2097142203.52
21710122123.62
22313181714.00
2379152014.04
241111121714.19
25616161224.56

45

topics, 5 categories

Every problem carries one primary topic and up to two more, plus 21 technique tags. Filter the bank by any of them.

1, 3, 7, 14

days of review

Every problem you miss lands in an error log and comes back on a schedule until you own it.

6 / 1.5 / 0

scored like the real exam

Timed mock tests of any past contest, with a report on which positions and topics cost you the points.

One problem, the whole method

2018 AMC 10B · Problem 11

Which of the following expressions is never a prime number when pp is a prime number?

  1. A

    p2+16p^2+16

  2. B

    p2+24p^2+24

  3. C

    p2+26p^2+26

  4. D

    p2+46p^2+46

  5. E

    p2+96p^2+96

Key insight

For any prime p other than 3, p^2 is 1 mod 3, so p^2 + 26 is divisible by 3; p = 3 gives 35 = 5*7.

The trap

Testing only p = 2 and p = 3 and picking the first expression that looks composite, without checking the other choices produce a prime for some p.

Full solution, alternatives and common mistakes →

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