2015_Solutions_Grades 7-8-2015_Solutions_Levels

2015_Solutions_Levels_7&8

Pdf Summary

The document titled "MATH KANGAROO 2015 Solution Suggestions for Levels 7 and 8" provides solutions and explanations for a series of math problems posed in the 2015 Math Kangaroo competition for students in levels 7 and 8. <br /><br />1. **Problem 1 (Simplifying Fractions):** The solution involves finding which expression simplifies to \(\frac{4}{3}\). The correct expression is identified as \( \frac{2015}{158} \).<br /><br />2. **Problem 2 (Time Calculation):** It involves calculating the duration of a journey by subtracting the time in minutes and converting it back to hours and minutes.<br /><br />3. **Problem 3 (Geometrical Length):** This problem calculates the length of a geometric shape by summing specific segments, using the relationship \( AD = AB + BC + \ldots + 2DE \).<br /><br />4. **Problem 4 (Approximation):** An approximation method is used, involving estimation of the product being slightly more than 1000.<br /><br />5. **Problem 5 (Cube Opposite Sides):** It's about visualizing a folded cube and identifying opposite faces in terms of numbered sides.<br /><br />6. **Problem 6 (Divisibility):** Discusses the rules of divisibility and demonstrates why \( 2014/4 \) is not an integer.<br /><br />7. **Problem 7 (Geometry - Triangle):** Calculates the side length of an equilateral triangle using given relations.<br /><br />8. **Problem 8 (Prism Folding):** Involves visualizing the folding of a geometric shape into a prism and identifying the resulting shape's edges.<br /><br />9. **Problem 9 (Circle Geometry):** Calculates possible coverage areas relative to two circles with equal radii.<br /><br />10. **Problem 10 (Cyclist and Rotation):** Determines the repetitiveness of wheel rotations using given distances and circumference.<br /><br />The document then continues with progressively more complex problems, typically entailing logical reasoning, geometry, arithmetic patterns, and algebraic expressions. It guides through each problem, step-by-step, ensuring understanding and using mathematical principles pertinent to levels 7 and 8 in the competition.<br /><br />Overall, the document serves as a mathematical guide meant to assist students in solving typical Math Kangaroo competition problems and to get accustomed to the logical handling of mathematical challenges at their educational level.

Keywords

Math Kangaroo 2015

solution suggestions

levels 7 and 8

simplifying fractions

time calculation

geometrical length

approximation method

cube opposite sides

divisibility rules

circle geometry