2007_Solutions_Grades 7-8-2007_Solutions_Levels

2007_Solutions_Levels_7&8

Pdf Summary

The document provided offers suggested solutions for the Math Kangaroo 2007 competition, specifically for Levels 7-8. Each problem has an accompanying solution and explanation, though some explanations are more detailed than others. <br /><br />1. Problem 1 involves performing long division to find the quotient, resulting in the answer 223. <br />2. Problem 2 asks for counting bushes in an alley, ultimately leading to a total count of 22.<br />3. Problem 3 involves converting time into minutes to achieve a sum of 161 minutes.<br />4. Problem 4 calculates the sum of hidden faces of a die, resulting in 27.<br />5. Problem 5 involves circle's geometry where perimeter calculation leads to a result of 100 cm.<br />6. Problem 6 focuses on coordinate geometry, determining parallelism to an axis.<br />7. Problem 7 applies the Pythagorean theorem in geometry, finding an area of 34.<br />8. Problem 8 is an arithmetic problem about adding odd numbers, resulting in a sum divisible by 2.<br />9. Problem 9 calculates the difference between palindromic numbers, resulting in a difference of 989,998.<br />10. Problem 10 hints at a setup involving exponents.<br />11. Problem 11 involves algebraic manipulation, concluding that \(-2x\) is the evaluated expression.<br />12. Problem 12 is about segment perimeters leading to 72 cm.<br />13. Problem 13 is a combinatorial geometry, counting triangles to get 16.<br />14. Problem 14 suggests the Kangaroo moves in an endless loop.<br />15. Problem 15 and 16 involve angle calculations and algebra.<br />17. Problem 17 determines a percentage of perfect squares within a range.<br />18. Problem 18 explores geometric areas.<br />19. Problem 19 finds sums along a diagonal.<br />20. Problem 20 employs symmetry to shade parts of a grid.<br />21. Problem 21 yields the number of ways digit one can be inserted.<br />22. Problem 22 involves kinematic equations.<br />23. Problems proceed to offer different mathematical challenges up to the involved operations problem in 30.<br /><br />These solutions are designed to help participants understand the logic and steps required to solve each problem, enhancing their problem-solving skills in mathematics.

Keywords

Math Kangaroo 2007

Levels 7-8

long division

coordinate geometry

Pythagorean theorem

palindromic numbers

algebraic manipulation

combinatorial geometry

kinematic equations

problem-solving skills