About the AMC 8
The AMC 8 is run by the Mathematical Association of America (MAA). It is open to students in grade 8 or below who are under 15.5 years old on the day of the contest. The format:
| Feature | Details |
|---|---|
| Questions | 25 multiple-choice questions, 5 choices each |
| Time | 40 minutes |
| Scoring | 1 point per correct answer, no penalty for wrong answers, so never leave one blank |
| Calculators | Not allowed |
| When | Usually in January. The MAA lists Jan 21–27, 2027 for the next one |
The problems get harder as you go. The first 10 or so test speed and accuracy, and the last 5 or so need real problem solving in counting, number theory and geometry. Check the MAA's AMC site for registration and the latest rules.
How to prepare for the AMC 8 with Mathyessy
Mathyessy is a free practice site, not an official MAA resource. Its problems are short-answer rather than multiple choice. That is harder than the real test, because you can't work backwards from the choices. The AMC 8 covers the same middle school topics as MATHCOUNTS, so the same practice helps with both.
- Contest Trainer: an adaptive trainer that moves through three stages of increasing difficulty and adjusts to your answers.
- 122 topic sets across algebra, geometry, counting & probability and number theory.
- 60-second speed rounds for quick, accurate answers under time pressure.
- An 8-question diagnostic that points out which topics to work on.
- A 10-question, 15-minute mini mock exam.
- Mistake review, a daily challenge and a leaderboard.
Plan: do the diagnostic, then build up the topics that decide the hard problems: counting & probability, number theory and geometry. Use speed rounds to keep the easy questions fast, so you have time for the hard ones.
AMC 8-style practice problems
These are original Mathyessy problems on typical AMC 8 topics, not official AMC problems.
You need 4 moves right and 4 moves up. How many shortest paths exist?
Show answer and solution
Answer: 70
8 moves in total; choose which 4 are rights: C(8, 4) = 70.
More like this: Grid path counting practice
What is the units digit of 7 to the power 2026?
Show answer and solution
Answer: 9
Powers of 7 end in 7, 9, 3, 1, repeating every 4. 2026 leaves remainder 2 when divided by 4, so the units digit matches 7², which is 9.
More like this: Units digit and cycles practice
A 45-45-90 triangle has legs of length 5. Give the hypotenuse in terms of √2 — enter the number before √2.
Show answer and solution
Answer: 5√2
In a 45-45-90 triangle the hypotenuse is leg × √2, so it is 5√2.
More like this: Special right triangles: 45-45-90 and 30-60-90 practice
A game pays 16 dollars for three heads, 4 dollars for exactly two heads, and 0 otherwise when flipping three coins. What is the expected value in dollars?
Show answer and solution
Answer: $3.50
P(three heads) = 1/8 and P(exactly two heads) = 3/8. E = 16 × 1/8 + 4 × 3/8 = 2 + 1.5 = 3.5.
More like this: Expected value practice problems
How many trailing zeros does 100 factorial have?
Show answer and solution
Answer: 24
⌊100/5⌋ + ⌊100/25⌋ = 20 + 4 = 24. (125 is bigger than 100, so stop.)
More like this: Trailing zeros in factorials practice
A price is raised 25% then discounted 20%. What percent of the original price remains?
Show answer and solution
Answer: 100%
Multiply the multipliers: 1.25 × 0.80 = 1.00. The price ends exactly where it started: 100%.
More like this: Percent practice problems