2000_Solutions_Grades 9-10-2000_Solutions_Levels

2000_Solutions_Levels_9&10
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The document is a set of solution suggestions for the Math Kangaroo 2000 competition, targeting levels 9 and 10. Each solution provides step-by-step reasoning to solve mathematical problems presented in the competition. Here is a summary of the solutions for selected problems:<br /><br />1. **Problem 1:** The expression simplifies to zero.<br /><br />2. **Problem 2:** There are 48 different triangles with a given base in a figure.<br /><br />3. **Problem 3:** Enlarging an area three times maintains the proportion, so 25% stays white.<br /><br />4. **Problem 4:** There are four pairs \( (a, b) \) where conditions given in the problem are met.<br /><br />5. **Problem 5:** The area of the shaded figure, composed of squares, totals 32 cm².<br /><br />6. **Problem 6:** After certain rotations, the kangaroo's nose points to the letter E.<br /><br />7. **Problem 7:** There are 12 different ways to create specific squares.<br /><br />8. **Problem 8:** The total length of arcs in a circle is 12.<br /><br />9. **Problem 9:** Solving an equation gives 28 as the correct number of answers.<br /><br />10. **Problem 10:** The ratio of trapezoid areas is 5:24.<br /><br />11. **Problem 11:** Calculations based on equations provided lead to an answer of 1.<br /><br />12. **Problem 12:** An angle in an isosceles triangle is 66 degrees.<br /><br />13. **Problem 13:** The number of people in a room, satisfying conditions, is 14.<br /><br />14. **Problem 14:** The number that doesn't fit divisibility conditions is 10.<br /><br />15. **Problem 15:** The big cube retains 44 cubes after some are removed.<br /><br />16. **Problem 16:** A convex octagon can have a maximum of three right angles.<br /><br />17. **Problem 17:** After a game, John wins, Charles loses, while Peter's tokens remain unchanged.<br /><br />18. **Problem 18:** Calculations yield the remaining number of blocks as 300.<br /><br />19. **Problem 19:** The area ratios for certain figures are calculated as 3:2.<br /><br />20. **Problem 20:** Solving a line equation solution for a specific point provides the result.<br /><br />21. **Problem 21:** Mark talks to Mary on a Monday, matching conditions given.<br /><br />22. **Problem 22:** A solution shows X equals 40 through similar triangle calculations.<br /><br />23. **Problem 23:** Analyzing divisibility conditions reveals 4 as meeting set criteria.<br /><br />24. **Problem 24:** Solving for dimensions in similar triangles shows CE as 3.75.<br /><br />25. **Problem 25:** Determining constants leads to A being 1.<br /><br />26. **Problem 26:** Summing sequences results in 0.<br /><br />27. **Problem 27:** Addressing configurations of a geometric figure shows x equals 8.<br /><br />28. **Problem 28:** Rule regarding remainders shows an answer of 4.<br /><br />29. **Problem 29:** The symmetrical solution to an equation sums to 0.<br /><br />30. **Problem 30:** Observations of a structure determine 12 wooden cubes present.<br /><br />The document is comprehensive in tackling mathematical problem-solving by applying algebraic, geometric, and logical reasoning to derive each solution.
Keywords
Math Kangaroo
competition
solutions
levels 9 and 10
mathematical problems
step-by-step reasoning
algebraic reasoning
geometric reasoning
logical reasoning
problem-solving