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. **Problem 1:** The smallest number using multiplication is 0 (from multiplying 2, 0, 0, and 8).<br /><br />2. **Problem 2:** To find the product 36, use (2x3) x (2x3).<br /><br />3. **Problem 3:** For the equation \(3 \times 2 \times 3 - 1 = 14\), the correct sequence is PJN.<br /><br />4. **Problem 4:** Substituting zero gives \(1 \times 101 - 2 \times 100\).<br /><br />5. **Problem 5:** Two equilateral triangles can’t form a square because the angles sum to 120 degrees.<br /><br />6. **Problem 6:** Calculate fractions of black to total squares, reducing to find those resulting in 3/5.<br /><br />7. **Problem 7:** 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. **Problem 8:** Solve for initial money using the equation \(x - 17 - 21 = 15\), leading to \(x = 19\).<br /><br />9. **Problem 9:** Use 5 as a factor in the second row to sum to 30 using sequences like 6x9.<br /><br />10. **Problem 10:** Count blocks visible in the view from above, considering those under black blocks too.<br /><br />11. **Problem 11:** Box elimination process to find correct letter placements and remaining letter is O.<br /><br />12. **Problem 12:** Calculate the perimeter incorporating various dimensions.<br /><br />13. **Problem 13:** Utilize the triangle inequality to determine valid triangle configurations.<br /><br />14. **Problem 14:** Side of a square with area 121 is 11, then increasing and squaring gives 256 area.<br /><br />15. **Problem 15:** 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