Free practice
Math Competition Practice Problems by Contest and Grade
19 free sets of math competition practice problems for grades 1–8, one for each contest and grade: Math Kangaroo, Noetic, MOEMS, CML and AMC 8. Every problem is original and comes with a full solution, and every set is also a printable PDF by email.
Prep guides by contest: Math Kangaroo Noetic MOEMS CML AMC 8
On this page · 5 sections
Free math contest problems by grade
Find your child's grade, then pick a contest. Each link opens ten practice problems at that contest's level, ramped from warm-ups to the hardest kind, with every answer explained. Read them on the page, or ask for the printable PDF there.
Grade 1
| Grade | Math Kangaroo | Noetic | MOEMS | CML | AMC 8 |
|---|---|---|---|---|---|
| 1 | · | · | · | · | |
| 2 | · | · | |||
| 3 | · | · | |||
| 4 | · | ||||
| 5 | · | ||||
| 6 | |||||
| 7 | · | ||||
| 8 | · |
A set that spans two grades, such as Math Kangaroo Grades 3–4, appears in both rows. MOEMS Division E covers grades 4–6 and Division M covers grades 6–8, so a 6th grader can use either.
Free full-length AMC 8 practice test
For grades 6–8
A complete mock AMC 8, with every answer explained
- 25 original questions in the real 25-question, 40-minute, A–E format
- An answer key to score it, then every solution worked out
- Ready to print for a timed practice run
Practice problems by contest
Each contest's practice page collects all of its free sets in one place, with how the contest works and where to go next.
Math Kangaroo
Grades 1–2 · Grades 3–4 · Grades 5–6 · Grades 7–8
Math Kangaroo practice problems →
Noetic Learning Math Contest
Grade 2 · Grade 3 · Grade 4 · Grade 5 · Grade 6
Noetic practice problems →
MOEMS (Math Olympiads)
Division E · Division M
MOEMS practice problems →
Continental Math League
Grade 2 · Grade 3 · Grade 4 · Grade 5 · Grade 6 · Grade 7 · Grade 8
CML practice problems →
AMC 8
Grades 6–8
AMC 8 practice problems →
Which contest fits your child?
The contests differ in format, timing and how they are entered. Our guide to choosing the right math competition for your child compares them in a few minutes. For a list by grade, see the best math competitions for 2nd graders , 3rd graders , 4th graders , 5th graders , 6th graders and 7th and 8th graders .
Math competition practice: common questions
Are these math competition practice problems free?
Yes. All 19 practice sets on this page are free to read online with no sign-up. Each set is ten problems with a full solution for every one, and each is also a free printable PDF that we email to you.
Are these real past contest questions?
No. Every problem is original, written in the style and difficulty of the contest and grade it is for. That means a child who has already seen the official past papers still gets fresh practice. Our Math Kangaroo and CML practice pages also point to where the official sample papers are.
Which practice set should my child start with?
Start with the set for the contest your child is entering, at their own grade. If they have not picked a contest yet, try the set for their grade from two different contests and see which style they enjoy more. Our guide on choosing a math competition walks through the options by grade.
How should my child use a practice set?
Have them work all ten problems on paper in one sitting, writing down an answer for each. Then go through the solutions together, including the common wrong answer explained for each problem. The problems that went wrong show what to practice next.
What grades are covered?
Grades 1 through 8. Math Kangaroo has a set for each two-grade band, Noetic and CML have one set per grade, MOEMS has one set per division, and AMC 8 has a ten-problem set plus a full-length practice test for grades 6–8.
All problems on this page and the pages it links to are original, written in the style and difficulty of each contest.
This guide is not affiliated with or endorsed by Math Kangaroo USA or Kangourou sans Frontières. “Math Kangaroo” is a trademark of its respective owners.
This guide is not affiliated with or endorsed by Noetic Learning. “Noetic Learning Math Contest” is a trademark of its respective owners.
This guide is not affiliated with or endorsed by Math Olympiads for Elementary and Middle Schools (MOEMS®). “MOEMS” is a trademark of its respective owners.
This guide is not affiliated with or endorsed by Continental Mathematics League. “Continental Mathematics League” is a trademark of its respective owners.
This guide is not affiliated with or endorsed by the Mathematical Association of America (MAA) or the American Mathematics Competitions. “AMC 8” is a trademark of its respective owners.