2014_Solutions_Grades 7-8-2014_Solutions_Levels

2014_Solutions_Levels_7&8
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The Math Kangaroo 2014 solution suggestions for levels 7-8 consist of a series of problems alongside their solutions, focusing on various types of mathematical reasoning. Here is a summary of the key points covered in the solutions:<br /><br />1. Problem 1 identified March 21st as the latest possible competition date, given calendar constraints.<br />2. Problem 2 quantified 4 quadrilaterals in a diagram.<br />3. Problem 3 arrived at a result of 0 through algebraic manipulation.<br />4. Problem 4 calculated half of the rectangle’s area as 5 using geometric reasoning.<br />5. Problem 5 identified the difference of numbers 36 and 1 as 35.<br />6. Problem 6 found the area of a shape (a bird) to be 6 square units by rearranging pieces into a square.<br />7. Problem 7 concluded that the capacity of a bucket is 8 liters due to a quartic expansion.<br />8. Problem 8 calculated 20 more cubes are needed to form a complete cube with a side length of 3.<br />9. Problem 9 found the largest product of numbers as 55 x 666.<br />10. Problem 10 found the maximum number of removable white beads to be 7.<br />11. Problem 11 calculated a lesson difference over 10 weeks to be 15.<br />12. Problem 12 evaluated overlapping circles to find an area of \(\frac{9}{2}\) square cm.<br />13. Problem 13 solved that a sum involving powers of 2 gives a granddaughter's age as 4.<br />14. Problem 14 determined rectangle area to be 32 cm² through length and width calculations.<br />15. Problem 15 concluded certain moves in a heptagon will never align specific elements.<br />16. Problem 16 solved angle-related equations for angles of 60 degrees.<br />17. Problem 17 optimized bathroom use, finishing tasks in 46 minutes.<br />18. Problem 18 reasoned triangle division to identify 5cm, 1cm, and 5cm lengths.<br />19. Problem 19 deduced total coins among pirates as 150.<br />20. Problem 20 discovered a comparative percentage of 75%.<br />21. Problem 21 solved for a “neighbor” sum configuration resulting in 27.<br />22. Problem 22 determined weight D as the heaviest based on given conditions.<br />23. Problem 23 found area relations in geometric figures summing to 45.<br />24. Problem 24 derived a system of equations to determine common questions solved by both participants.<br />25. Problem 25 compared travel speeds arriving at a ratio of 3:2.<br />26. Problem 26 identified the opposite side of a cube from its markings.<br />27. Problem 27 deduced the number of knights as 5.<br />28. Problem 28 calculated the smallest possible \(M\) as 273.<br />29. Problem 29 theorized maximum frog reaches as 16.<br />30. Problem 30 described the smallest segment count as 5.<br /><br />The solutions utilize a variety of mathematical tactics, such as arithmetic operations, logical reasoning, algebra, and geometric insights, to solve the diverse and complex problems presented in the Math Kangaroo competition.
Keywords
Math Kangaroo 2014
mathematical reasoning
problem solutions
geometric reasoning
algebraic manipulation
arithmetic operations
logical reasoning
competition problems
geometry
algebra