2018_Solutions_Grades 7-8-2018_Solutions_Levels

2018_Solutions_Levels_7&8

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The document provides solutions for the 2018 Math Kangaroo competition, focusing on levels 7 and 8. Here is a summary of some selected problem solutions and their logic:<br /><br />1. Calculating the operation within parentheses, problem 1 simplifies to 19.<br />2. Problem 2 requires identifying a word with vertical symmetry, which is "TOOT".<br />3. Problem 3 involves calculating the perimeter of a triangle, solved to be 27, then finding the side length of an equivalent equilateral triangle as 9.<br />4. Problem 4 uses the balancing of ratios, where the solution is found to be 12.<br />5. Problem 5 outlines understanding reflection symmetry for finding correct panels of a fallen fence.<br />6. Problem 6 determines the number of 15 cm steps needed to equal 300 cm as 20.<br />7. In problem 7, counting distinct paths for a ball to reach a bin results in 4 paths.<br />   <br />Problems 8 through 30 include analysis involving geometric calculations, logic puzzles, and algebraic manipulations. Some highlights include:<br /><br />- Problem 8 involves calculating the perimeter of a large rectangle made from small rectangles, resulting in 76 cm.<br />- Problem 15 relates the calculation to a geometric problem involving triangles, concluding with an angle measure of 11 degrees.<br />- Problem 21 discusses a voting issue to determine how many additional votes one needs to certainly remain the winner, finding 17.<br />- Problem 25 analyzes the area of a given "dove," determining the flag area using given blocks as 24 cm by 16 cm.<br /><br />The key throughout these problems is understanding and correctly applying mathematical principles like symmetry, geometry, arithmetic operations, and algebra to arrive at the correct answers.

Keywords

Math Kangaroo

2018 competition

problem solutions

levels 7 and 8

symmetry

geometry

algebra

perimeter

logic puzzles

triangle calculations