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CML Grade 2-3 mock test

CML Mock Contests for Grades 2-3 | Continental Math League Practice Tests

Continental Math League (CML) Mock Contests for Grades 2-3

Practice with real-format CML tests designed to simulate the actual competition experience. Each mock contest contains 6 challenging word problems and is timed for 30 minutes - just like in the real Continental Math League meets.

CML Mock Contest Instructions

How to Take These Practice Tests

  1. Set up a quiet environment with minimal distractions, just like during a real contest.
  2. Use the 30-minute timer provided with each test to simulate actual contest conditions.
  3. Try to solve all 6 problems within the time limit.
  4. Show your work for each problem on a separate sheet of paper.
  5. Check your answers using the solutions provided after completing the test.
  6. Review your mistakes to understand where you went wrong and learn from them.

Available Mock Contests

Each contest below mimics the format of an actual CML meet, containing 6 word problems that test different mathematical concepts and problem-solving skills.

Mock Contest 1

Difficulty: Beginning Time: 30 minutes

Focus areas: Basic arithmetic, patterns, simple word problems

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Mock Contest 2

Difficulty: Beginning Time: 30 minutes

Focus areas: Money problems, time, basic logic

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Mock Contest 3

Difficulty: Intermediate Time: 30 minutes

Focus areas: Multi-step problems, measurement, patterns

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Mock Contest 4

Difficulty: Intermediate Time: 30 minutes

Focus areas: Geometry, logical reasoning, number sense

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Mock Contest 5

Difficulty: Advanced Time: 30 minutes

Focus areas: Complex word problems, patterns, critical thinking

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Mock Contest 6

Difficulty: Advanced Time: 30 minutes

Focus areas: Mixed topics, challenging problems

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Sample Mock Contest

30:00

Instructions: Solve all 6 problems within 30 minutes. Show your work on a separate sheet of paper.

Problem 1

Sam has 8 stickers. Mia has 5 stickers. How many more stickers does Sam need to give Mia so they both have the same number?

Problem 2

A rectangle has 4 sides. Each side is 6 inches long. What is the distance all the way around the rectangle?

Problem 3

What number is missing? 5, 8, 11, 14, _____, 20

Problem 4

Tom is taller than Sam. Sam is taller than Ben. Who is the shortest?

Problem 5

Grandma gives Sam 8 pennies, 3 nickels, and 2 dimes. How much money does Sam have in total?

Problem 6

A clock shows 3:00. What time will it show in 2 hours?

Click to View Answers and Solutions

Problem 1

Answer: 1.5 or 2 stickers

Solution: Sam has 8 stickers and Mia has 5. For them to have equal numbers, Sam needs to give Mia enough stickers so they both have the same amount.

Let x be the number of stickers Sam gives to Mia. Then:

  • Sam will have: 8 - x stickers
  • Mia will have: 5 + x stickers

For them to be equal: 8 - x = 5 + x

Solving for x: 8 - 5 = 2x, so x = 1.5

Since we can't give half a sticker, Sam would need to give 2 stickers to Mia. Then Sam would have 6 stickers and Mia would have 7 stickers.

Problem 2

Answer: 24 inches

Solution: A rectangle has 4 sides. If each side is 6 inches, then the perimeter (distance all the way around) is:

6 + 6 + 6 + 6 = 24 inches

Problem 3

Answer: 17

Solution: Looking at the pattern:

  • 5 to 8: +3
  • 8 to 11: +3
  • 11 to 14: +3
  • 14 to ?: +3 = 17
  • 17 to 20: +3

The pattern adds 3 each time, so the missing number is 17.

Problem 4

Answer: Ben

Solution: We know that Tom is taller than Sam, and Sam is taller than Ben. This means:

Tom > Sam > Ben

So Ben is the shortest.

Problem 5

Answer: 43¢

Solution: We need to find the total value of the coins:

  • 8 pennies = 8 × 1¢ = 8¢
  • 3 nickels = 3 × 5¢ = 15¢
  • 2 dimes = 2 × 10¢ = 20¢

Total: 8¢ + 15¢ + 20¢ = 43¢

Problem 6

Answer: 5:00

Solution: If the clock shows 3:00, then after 2 hours, it will show 5:00.

Tips for CML Success

Beyond practicing with these mock contests, here are some strategies that can help students succeed in Continental Math League competitions:

  • Read carefully: Pay close attention to what each problem is asking.
  • Draw pictures: Visual representations can help solve many types of problems.
  • Look for patterns: Many CML problems involve recognizing and extending patterns.
  • Eliminate wrong answers: If you're stuck, try ruling out answers that can't be correct.
  • Check your work: If you have time, review your answers for calculation errors.
  • Don't get stuck: If a problem seems too difficult, move on and come back to it if time permits.
  • Practice regularly: The more you practice, the more comfortable you'll become with CML-style problems.
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