2008_Solutions_Grades 5-6-2008_Solutions_Levels

2008_Solutions_Levels_5&6
Pdf Summary
The document provides solutions and explanations for the 2008 Math Kangaroo competition questions for levels 5-6. Key concepts include arithmetic operations, number properties, geometry, algebra, and logical reasoning. Below is a summary of selected problems and their solutions:<br /><br />1. <strong>Problem 1:</strong> The smallest number using multiplication is 0 (from multiplying 2, 0, 0, and 8).<br /><br />2. <strong>Problem 2:</strong> To find the product 36, use (2x3) x (2x3).<br /><br />3. <strong>Problem 3:</strong> For the equation \(3 \times 2 \times 3 - 1 = 14\), the correct sequence is PJN.<br /><br />4. <strong>Problem 4:</strong> Substituting zero gives \(1 \times 101 - 2 \times 100\).<br /><br />5. <strong>Problem 5:</strong> Two equilateral triangles can’t form a square because the angles sum to 120 degrees.<br /><br />6. <strong>Problem 6:</strong> Calculate fractions of black to total squares, reducing to find those resulting in 3/5.<br /><br />7. <strong>Problem 7:</strong> Achieve a total of 9 by placing 6 with 3 in the first row and 4 and 2 in the second, totaling 6.<br /><br />8. <strong>Problem 8:</strong> Solve for initial money using the equation \(x - 17 - 21 = 15\), leading to \(x = 19\).<br /><br />9. <strong>Problem 9:</strong> Use 5 as a factor in the second row to sum to 30 using sequences like 6x9.<br /><br />10. <strong>Problem 10:</strong> Count blocks visible in the view from above, considering those under black blocks too.<br /><br />11. <strong>Problem 11:</strong> Box elimination process to find correct letter placements and remaining letter is O.<br /><br />12. <strong>Problem 12:</strong> Calculate the perimeter incorporating various dimensions.<br /><br />13. <strong>Problem 13:</strong> Utilize the triangle inequality to determine valid triangle configurations.<br /><br />14. <strong>Problem 14:</strong> Side of a square with area 121 is 11, then increasing and squaring gives 256 area.<br /><br />15. <strong>Problem 15:</strong> Calculation through proportions results in juice left being 1/6.<br /><br />Overall, the document is structured around step-by-step logical and mathematical operations, teaching problem-solving and applications of basic geometric, algebraic, and arithmetic principles vital for approaching Math Kangaroo questions.
Keywords
Math Kangaroo 2008
arithmetic operations
number properties
geometry
algebra
logical reasoning
problem-solving
equilateral triangles
triangle inequality
perimeter calculation