Grades 2–6 · Free
Continental Math League Practice Problems
Two complete practice meets in the real CML format — 6 problems, 30 minutes — with a worked solution for every question. All original, all free to read, no sign-up needed.
How a CML meet works
Practice is far less stressful when the format isn't a surprise. Here's the shape of a real meet:
Problems per meet
Time limit — 5 minutes a problem
Answers, not multiple choice
Meets a season (3 for grades 2–3)
How to use these
Set a timer for 30 minutes and let your child work through all six problems on paper, writing each answer down plainly. Then go through the solutions together — that second part is where the learning actually happens.
Practice Meet — Grades 2–3
CML gives grades 2 and 3 the same paper, so this meet suits both.
6 problems · 30 minutes · write your answer for each
- 1
How much larger is (8 + 5 + 7) than (30 − 4 − 9)?
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Answer: 3
(8 + 5 + 7) = 20. (30 − 4 − 9) = 17. The difference is 20 − 17 = 3. Work out each bracket completely before you compare them — that is where most points get lost.
- 2
The symbol ★ means: double the first number, then add the second. For example, 4 ★ 3 = (4 × 2) + 3 = 11. What is 7 ★ 5?
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Answer: 19
Follow the rule exactly as written: (7 × 2) + 5 = 14 + 5 = 19. A made-up symbol looks alarming, but it is only ever a set of instructions. Read them twice, then do exactly what they say.
- 3
Ben has 6 coins that are all nickels and dimes. Together they are worth 45¢. How many dimes does he have?
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Answer: 3
If all 6 coins were nickels, that would be 30¢ — 15¢ short. Swapping a nickel for a dime adds 5¢ each time, so you need 15 ÷ 5 = 3 swaps. That gives 3 dimes and 3 nickels: 30 + 15 = 45¢. ✓
- 4
Mrs. Diaz lines up 12 chairs in a row. She puts a red cushion on every 2nd chair and a blue cushion on every 3rd chair. How many chairs get both cushions?
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Answer: 2
A chair needs to be both a 2nd chair and a 3rd chair, so it has to be a 6th chair. In a row of 12, that is chair 6 and chair 12 — 2 chairs.
- 5
There are 9 birds on a fence. Some fly away, then 4 more land. Now there are 8 birds. How many flew away?
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Answer: 5
Start with 9 and end with 8, having gained 4 along the way. Without the 4 landing, there would be 8 − 4 = 4 birds left. So 9 − 4 = 5 flew away.
- 6
In the addition below, A and B stand for two different digits. What is A + B? A5 + 2B —— 71
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Answer: 10
The ones column gives 5 + B ending in 1, so B = 6 and 1 carries. The tens column is then A + 2 + 1 = 7, so A = 4. Check: 45 + 26 = 71. ✓ A + B = 4 + 6 = 10.
Practice Meet — Grades 4–6
From grade 4 up CML splits into Euclidean and Pythagorean divisions. This meet sits around the Euclidean level.
6 problems · 30 minutes · write your answer for each
- 1
What is the smallest whole number greater than 1 that leaves a remainder of 1 when divided by 2, by 3, and by 4?
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Answer: 13
A number leaving remainder 1 each time is 1 more than a common multiple of 2, 3 and 4. The smallest number divisible by all three is 12, so the answer is 12 + 1 = 13. Check: 13 ÷ 2, ÷ 3 and ÷ 4 all leave 1. ✓
- 2
For any two numbers, a ⊗ b means (a × b) − (a + b). What is 6 ⊗ 4?
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Answer: 14
(6 × 4) − (6 + 4) = 24 − 10 = 14. Do each bracket first, then subtract. Rushing straight to a single line is how this one goes wrong.
- 3
Nina has 9 coins worth $1.20 altogether. She has only nickels, dimes, and quarters, and at least one of each. How many nickels does she have?
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Answer: 3
Let n, d, q be the counts. Then n + d + q = 9 and 5n + 10d + 25q = 120. Divide the second by 5: n + 2d + 5q = 24. Subtract the first: d + 4q = 15. Now test quarters. q = 1 gives d = 11 — too many coins. q = 2 gives d = 7, leaving 0 nickels, which breaks "at least one of each". q = 3 gives d = 3 and n = 3. ✓ Check: 15 + 30 + 75 = 120¢ in 9 coins.
- 4
A rectangle is 3 times as long as it is wide. Its perimeter is 64 cm. What is its area, in square centimeters?
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Answer: 192
Half the perimeter is one length plus one width: 32 cm. If the width is w, the length is 3w, so 4w = 32 and w = 8. The length is 24. Area = 8 × 24 = 192 cm². Check the perimeter: 2 × (8 + 24) = 64. ✓
- 5
Tom thinks of a number. He doubles it, subtracts 7, then multiplies the result by 3. He ends up with 39. What number did he think of?
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Answer: 10
Undo each step backwards. Before multiplying by 3: 39 ÷ 3 = 13. Before subtracting 7: 13 + 7 = 20. Before doubling: 20 ÷ 2 = 10. Check forwards: 10 → 20 → 13 → 39. ✓
- 6
In a class of 30 students, 18 play soccer and 15 play basketball. Every student plays at least one of the two sports. How many play both?
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Answer: 3
Adding 18 and 15 gives 33, which is 3 more than the 30 students in the class. Those 3 extra are the students counted twice — the ones who play both. Check: 15 play soccer only, 12 basketball only, 3 both, and 15 + 12 + 3 = 30. ✓
Want a printable set?
We'll email you a free printable sample from our CML guide — more original problems, with the full worked solutions.
Ready for a full season of practice?
Our Continental Math League prep guide for Grades 2–6 covers the strategies behind every topic area, with 80+ original practice problems, full practice meets, and step-by-step solutions throughout.
See the CML guide — $5CML practice: common questions
Are there free Continental Math League practice problems? +
Yes. The two practice meets on this page are completely free to read, with full step-by-step solutions and no sign-up. Every problem is original, written in the style and difficulty of a real CML meet. You can also download a free printable sample of our CML guide by email.
How many questions are on a CML math meet, and what is the time limit? +
Every elementary CML math meet has 6 questions with a 30-minute time limit — five minutes per problem. CML is not multiple choice: students write each answer in an answer column on the paper.
How many CML meets are there in a season? +
It depends on the grade. Grades 2 and 3 have 3 meets, running January to March. Grades 4 through 9 have 5 meets, starting in November. Scores are cumulative across the season, so an early meet never decides anything on its own.
What grade levels does Continental Math League cover? +
CML runs math contests from grade 2 up through grade 9, plus a Calculus league. Grades 2 and 3 sit the same paper. From grade 4 upward, schools choose between the Euclidean and Pythagorean divisions.
Can my child do CML if their school does not take part? +
Yes. CML has a Home School option, which covers any student whose school does not participate — not only children educated at home. The fee is reduced to $25 per child per league, and you register an account first, buy nothing, then email support@cmleague.com to have the pricing applied.
Keep exploring
All problems on this page are original, written in the style and difficulty of CML meets. This guide is not affiliated with or endorsed by Continental Mathematics League. “Continental Mathematics League” is a trademark of its respective owners.