2017_Solutions_Grades 7-8-2017_Solutions_Levels

2017_Solutions_Levels_7&8
Pdf Summary
The document is a solution guide for the Math Kangaroo 2017 Level 7-8 competition held on March 16, 2017. It provides detailed solutions and explanations for each of the problems in the competition. Here's a summary of some of the problems covered:<br /><br />1. <strong>Time Calculation</strong>: Solutions involve calculating time differences, converting PM to AM (Problem 1).<br /><br />2. <strong>Counting People</strong>: Figuring out the total number of girls in a group given partial counts (Problem 2).<br /><br />3. <strong>Geometry and Symmetry</strong>: Problems related to shapes, symmetry, and understanding geometric areas (Problems 4, 6, 7).<br /><br />4. <strong>Algebra and Arithmetic</strong>: Problems involve finding quantities using basic arithmetic, such as the distribution of money, calculating products, and optimizing sequences (Problems 5, 10, 16, 26).<br /><br />5. <strong>Logical Reasoning</strong>: This includes pattern recognition and exclusion of certain possibilities based on given criteria (Problems 8, 17, 19, 23).<br /><br />6. <strong>Optimization</strong>: Finding minimum or maximum solutions in given situations, like minimizing or maximizing days for certain tasks or identifying the minimum number of different results (Problems 15, 21, 29).<br /><br />7. <strong>Combinatorial and Probability Concepts</strong>: Solutions often include combinatorial logic and basic probability, seen in arranging objects or determining possible outcomes (Problems 12, 20, 24).<br /><br />8. <strong>Geometry and Measurement</strong>: Calculating areas and perimeters of various geometrical figures, and understanding volumes such as considering cubes and their arrangements (Problems 11, 25, 27, 28).<br /><br />9. <strong>Advanced Mathematical Concepts</strong>: Some problems require applying more complex mathematical formulas, such as handling proportions or finding unit ratios (Problem 30).<br /><br />The solutions demonstrate the application of various mathematical principles like arithmetic, algebra, geometry, and logical reasoning typical of middle school mathematics competitions. Each solution is presented with its method, reasoning, and the final answer.
Keywords
Math Kangaroo 2017
Level 7-8
time calculation
geometry
algebra
logical reasoning
optimization
combinatorial concepts
probability
mathematical principles