2005_Solutions_Grades 9-10-2005_Solutions_Levels

2005_Solutions_Levels_9&10
Pdf Summary
This summary contains solutions and explanations for each question in the 2005 Math Kangaroo competition for Levels 9-10. Here is a brief overview of some of the solutions:<br /><br />1. <strong>Eva's Score Position</strong>: Since each student has a different score, and Eva is the 50th best and 50th poorest, there are 99 students total.<br />   <br />2. <strong>Fraction Product</strong>: Multiplying given fractions simplifies to 1/2005. The reciprocal gives the answer, which is 2005.<br /><br />3. <strong>Angle Calculation</strong>: Using properties of angles and triangles, the missing angle is calculated to be 50 degrees.<br /><br />4. <strong>Dimension Increase Impact on Volume</strong>: A 60% increase in one dimension results in a 60% increase in volume.<br /><br />5. <strong>Counting Students in Pairs</strong>: By pairing numbers and adding results, there are 14 boys.<br /><br />6. <strong>Counting Squares and Triangles</strong>: Counting smaller and larger figures results in 3 larger triangles identified.<br /><br />7. <strong>Arranging Strips</strong>: The picture strategy in the exam explains the arrangement solution, resulting in the answer 20.<br /><br />8. <strong>Production Calculation</strong>: The number of components produced, factoring in defect rates, equals 288 non-defective parts.<br /><br />9. <strong>Range of Integer Solutions</strong>: With calculations, numbers like n that fit within given parameters included 2000 to 2004, resulting in 5 integers.<br /><br />10. <strong>Chasing Problem</strong>: For a calculated distance on the track, it took Jumpy’s mother 51 seconds to catch up.<br /><br />11. <strong>Pattern Recognition in Sequence</strong>: A systematic examination of operations result in a final value of 1.<br /><br />12. <strong>Square Area via Integer Sides</strong>: Using integer side lengths, the area calculation result is 121.<br /><br />13. <strong>Rectangle and Circle Area Comparison</strong>: Percentage comparison results in a 48% area for a rectangle compared to a square.<br /><br />14. <strong>Triangle Side Comparison</strong>: Through logical deductions regarding triangles, segment CD is the shortest.<br /><br />15. <strong>Number Ball Pairing</strong>: enough pairs are deduced to get a 10-ball outcome.<br /><br />16. <strong>Juice and Water Mixture Ratio</strong>: Calculating ratios end up with an 11:4 ratio of water to juice.<br /><br />17. <strong>Sum of Triangular Angles</strong>: Using geometric properties, a result of 720 degrees is reached.<br /><br />18. <strong>Prime Factors and Large Divisor</strong>: Detailed factor combination results in 5 four-digit divisors.<br /><br />19. <strong>Solution Omitted</strong>: The problem solutions further continue in original material.<br /><br />These solutions offer structured reasoning and steps to determine correct answers for the questions posed.
Keywords
Math Kangaroo
2005 competition
Level 9-10
Eva's score
fraction product
angle calculation
volume increase
counting students
pattern recognition
prime factors