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AMC 8 Practice
Free AMC 8 Practice Problems — with Answer Key
Print a set of AMC 8-style practice problems below — number theory (divisors, remainders, factorials), counting (permutations and combinations), and probability — each with a complete answer key. Every set is generated fresh, so your student always has new problems to work. No account required.
AMC 8 Practice Problems
Percent of a number
1.What is 40% of 200?
2.What is 60% of 200?
3.What is 15% of 40?
Counting divisors
4.How many positive divisors does 8232 have?
5.How many positive divisors does 7875 have?
6.How many positive divisors does 3675 have?
Remainders of powers
7.What is the remainder when 639 is divided by 5?
8.What is the remainder when 744 is divided by 11?
9.What is the remainder when 936 is divided by 5?
Units digit of a sum of powers
10.What is the units digit of 638 + 841?
11.What is the units digit of 254 + 434?
12.What is the units digit of 943 + 347?
Trailing zeros of a factorial
13.How many trailing zeros does 86! (86 factorial) end in?
14.How many trailing zeros does 84! (84 factorial) end in?
Permutations
15.In how many ways can 2 runners out of 8 finish in the first 2 places (order matters)?
16.In how many ways can 3 runners out of 5 finish in the first 3 places (order matters)?
17.In how many ways can 3 runners out of 7 finish in the first 3 places (order matters)?
Combinations
18.A team of 4 is chosen from 11 players (order does not matter). How many different teams are possible?
19.A team of 7 is chosen from 9 players (order does not matter). How many different teams are possible?
20.A team of 2 is chosen from 6 players (order does not matter). How many different teams are possible?
Probability with two dice
21.Two fair six-sided dice are rolled. What is the probability that the sum is 8? (Give a fraction in lowest terms.)
22.Two fair six-sided dice are rolled. What is the probability that the sum is 4? (Give a fraction in lowest terms.)
23.Two fair six-sided dice are rolled. What is the probability that the sum is 7? (Give a fraction in lowest terms.)
Answer Key
1.80
2.120
3.6
4.32
5.24
6.18
7.1
8.3
9.1
10.4
11.0
12.6
13.20
14.19
15.56
16.60
17.210
18.330
19.36
20.15
21.5/36
22.1/12
23.1/6
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Frequently asked questions
Are these AMC 8 problems free?
Yes — view, print, and share every set for free, with no account and no signup.
Do they come with an answer key?
Every set includes a full answer key at the bottom of the page.
Are these the real, official AMC 8 problems?
No — these are original AMC 8-style practice problems in the same topics and format (number theory, counting, probability), so your student can practice the skills the AMC 8 tests without reusing copyrighted past exams.
Can I get a new set of problems?
Yes — click “Generate a new sheet” for a fresh set with a matching answer key.
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