2009_Solutions_Grades 9-10-2009_Solutions_Levels

2009_Solutions_Levels_9&10
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The Math Kangaroo 2009 Solutions document for levels 9-10 outlines solutions to 30 challenging math problems presented during the competition. Below is a summary of the problems and their corresponding solutions:<br /><br />1. <strong>Divisibility</strong>: Identify numbers divisible by 3 by summing their digits. Solution: 29 is not divisible.<br />2. <strong>Removing Dots</strong>: Calculation of dots removed to maintain symmetry. Solution: 3.<br />3. <strong>Finishing Position</strong>: Solve for Peter's race position using a formula. Solution: 503.<br />4. <strong>Numerical Calculation</strong>: Step-by-step calculation using given equations. Solution: 60.<br />5. <strong>Counting Appearances</strong>: Adjust a count based on divisibility error. Solution: 18072.<br />6. <strong>Face Value</strong>: Determine values using geometric shapes. Solution: 18.<br />7. <strong>Integer Check</strong>: Compare square and cube numbers. Solution: 3.<br />8. <strong>Angles</strong>: Calculate necessary angle measures. Solution: 80 - 2π.<br />9. <strong>Sequence Prediction</strong>: Determine next number in a sequence. Solution: 24.<br />10. <strong>Angle Sum</strong>: Derive angle from triangle properties. Solution: 124°.<br />11. <strong>Score Analysis</strong>: Find possible scores given constraints. Solution: Betty scored 3 points on exactly 3 tests.<br />12. <strong>Connectivity of Rings</strong>: Remove to retain connectivity. Solution: Specific connectivity based on ring color.<br />13. <strong>Truth-Telling</strong>: Solve deduction-based sequence. Solution: 13 liars.<br />14. <strong>Equation Solving</strong>: Solve for x in a linear equation. Solution: 7.<br />15. <strong>Circle and Square Relationship</strong>: Calculate k from geometric relationships. Solution: \(1/\sqrt{2}\).<br />16. <strong>Number Range</strong>: Find integer range between squares. Solution: 39.<br />17. <strong>Sequence Construction</strong>: Work with number combinations. Solution: 9.<br />18. <strong>Bee Movement</strong>: Return to starting point after steps. Solution: 6 turns.<br />19. <strong>Decimal Calculation</strong>: Number of zeros required. Solution: 3.<br />20. <strong>Numerical Comparison</strong>: Determine greatest number. Solution: c < b < a.<br />21. <strong>Number Possibilities</strong>: Count number possibilities based on conditions. Solution: 64.<br />22. <strong>Sticker Usage</strong>: Calculate unused stickers. Solution: 763 stickers.<br />23. <strong>Piece Arrangement</strong>: Find minimum configuration. Solution: 14 pieces.<br />24. <strong>Word Construction</strong>: Example given. Solution: OABOP BAOBP APO.<br />25. <strong>Prime Factorization</strong>: Make squares from factorization. Solution: 8.<br />26. <strong>Divisibility Check</strong>: Analyze even and odd divisors. Solution: 2.<br />27. <strong>Kangaroo Jumps</strong>: Count possible jump positions. Solution: 121.<br />28. <strong>Geometric Angles</strong>: Calculate angles using properties. Solution: 30°.<br />29. <strong>Sequence of Scores</strong>: Determine possible score sequence. Solution: 8.<br />30. <strong>Special Prime Numbers</strong>: Identify special prime numbers. Solution: 9 special primes.<br /><br />The solutions explore mathematical reasoning, number theory, geometry, logic puzzles, and sequential analysis used for solving complex problems often seen in competitive math environments.
Keywords
Math Kangaroo
2009 Solutions
levels 9-10
divisibility
geometry
number theory
logic puzzles
sequential analysis
competitive math
problem-solving