Free AMC 8 & AMC 10 Practice Contests
25 original competition-style problems with real contest timing, no calculator, and a worked solution for every problem. Then let StudyDib write your contest-prep plan — free, no credit card.
Free AMC 8 and AMC 10 practice problems with worked solutions
Six original competition problems — three at AMC 8 level, three at AMC 10 level. Tap an answer to check it and read the full solution, including the technique to reuse. No account needed.
- Question 1AMC 8 · Number theory
What is the units digit of 3²⁰²⁶?
- Question 2AMC 8 · Counting
How many positive divisors does 60 have?
- Question 3AMC 8 · Probability
Two fair six-sided dice are rolled. What is the probability that the sum is 7?
- Question 4AMC 10 · Counting
How many integers n with 1 ≤ n ≤ 100 are divisible by 3 or by 5?
- Question 5AMC 10 · Algebra
If x + 1/x = 5, what is the value of x² + 1/x²?
- Question 6AMC 10 · Geometry
The line y = 3 intersects the circle x² + y² = 25 at two points. What is the distance between them?
Want more than a sample? A free account unlocks the full timed AMC 8 practice contest with instant scoring, worked explanations for every question, XP and streaks.
Take the full AMC 8 practice contestWhat is the AMC?
The AMC (American Mathematics Competitions) are contests run by the Mathematical Association of America. They reward creative problem solving rather than memorised formulas, and they are the first step on the path to the AIME and the USA Mathematical Olympiad.
The AMC 8 is for students in grade 8 and below: 25 problems in 40 minutes, one point each. The AMC 10 is for grade 10 and below: 25 problems in 75 minutes, scored 6 points for a correct answer, 1.5 for a blank and 0 for a wrong answer, out of 150.
Because a blank is worth more than a wrong guess on the AMC 10, deciding which problems to skip is a real skill. No calculators are allowed on either contest.
| Contest | Who | Problems | Time | Scoring |
|---|---|---|---|---|
| AMC 8 | Grade 8 and below | 25 | 40 min | 1 pt each, out of 25 |
| AMC 10 | Grade 10 and below | 25 | 75 min | 6 / 1.5 / 0, out of 150 |
Build your free AMC study plan
Answer a few quick questions and StudyDib writes a week-by-week plan for you. No account, no card — 3 free plans a day.
Free practice contests
Pick your level. Each contest is timed like the real thing and scored instantly.
AMC 8
25 middle-school competition problems ordered easy to hard: arithmetic, number theory, counting, probability, geometry and logic.
AMC 10
25 harder problems: algebra, functions, sequences, geometry, coordinate geometry, counting and number theory. No trigonometry or calculus.
What the AMC tests
Algebra & sequences
- Clever manipulation instead of long computation
- Systems, ratios, and word-to-equation translation
- Arithmetic and geometric sequences
Contest tip: Look for symmetry and substitution before grinding through algebra.
Counting & probability
- Casework and complementary counting
- Permutations, combinations, and overcounting
- Expected value and simple probability
Contest tip: Count the opposite when the direct count has too many cases.
Number theory
- Divisibility, factors, primes, GCF and LCM
- Remainders and modular thinking
- Digit and base problems
Contest tip: Test small cases and look for a repeating pattern.
Geometry
- Angle chasing and similar triangles
- Area by subtraction and clever decomposition
- Coordinate geometry and circles
Contest tip: Always redraw the figure yourself, to scale, and label everything you know.
How to prepare for the AMC
Learn techniques, not just answers
Work problems untimed first and write full solutions. The AMC rewards a toolbox of methods.
Keep a mistake log
Every missed problem goes in a notebook with the technique you should have used.
Practise problem triage
In timed sets, secure problems 1-15 first. Blanks score more than wrong guesses on the AMC 10.
Build speed on the easy half
Fast, accurate arithmetic on early problems buys you the minutes you need for the hard ones.
AMC FAQ
Train competition math every week
Create a free account to earn XP and streaks as you solve, take timed contests, and climb the weekly leaderboard.
Problems are original practice items modelled on the AMC's published format and difficulty — they are not copies of released contests. AMC is a program of the Mathematical Association of America, which does not endorse Benkyou Academy.