2021_Solutions_Grades 11-12-2021_Solutions_Levels

2021_Solutions_Levels_11&12
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The Math Kangaroo 2021 solution suggestions provide detailed answers to problems from Levels 11 and 12, focusing on various mathematical concepts and problem-solving techniques. <br /><br />1. It starts with a problem about interpreting temperature changes, concluding that the graph (E) is correct as it accurately reflects temperature variations over days.<br />2. Next, a problem is tackled using inequalities to find an integer count that fits within a specified range, leading to the solution of 9.<br />3. Following this, surface area calculations of cuboids obtained from an original cube are explored, yielding a solution of 4.<br />4. A problem involving proportional geometric areas leads to identifying the constant π/4.<br />5. Considerations of perspectives and orientations help deduce a flagpole’s direction, solving it with choice (A).<br />6. The volume ratio between cylinders formed from a rectangle is computed as y:x.<br />7. Exponent comparison leads to the largest value selection with choice (E).<br />8. Combinatorics determine that there are 9 numbers formed under specific divisibility conditions.<br />9. Basic geometry helps calculate triangle areas based on points' coordinates, resulting in 2pq.<br />10. Analyzing parabolas and lines finds the solution lies with expression (D).<br />11. A fraction of odd divisors from a factorial is calculated resulting in 1/5.<br />12. Interval overlap analysis yields a range determination, concluding with set (1,3) ∪ (3,5) ∪ (5,7).<br />13. Combination examination shows there are 80 numbers matching a given difference pattern.<br />14. A sequence pattern adds up products of digits to sum up to 2025.<br />15. Calculating perimeters and missing values results in an overall perimeter of 34.<br />16. Multiplying and adding products of digits from numbers lead to a sum of 2025.<br />17. Solving a number puzzle grants the solution as 10.<br />18. Probability theory in mirror reflections finds a solution as 1/4.<br />19. Interpreting a graph trend leads to the correct choice (E).<br />20. Coordinate geometry determines specific triangle areas.<br />21. Analyzing composite functions leads to identifying eight solutions.<br />22. Logical deduction shows the remaining number to be 9.<br />23. A function's iteration results in a consistent sum of 4040.<br />24. Identifying relationships between images leads to deducing child-photo pairing as D.<br />25. Calculation of faces and noted values leads to a total score of 50.<br />26. Analyzing triangles in a geometric configuration leads to counting 19 distinct forms.<br />27. Logic puzzle analysis concludes that the mouse resides in house A.<br />28. Geometric reflection calculations result in an answer of 5.<br />29. Optimizing algebraic expressions finds the maximum at 9/2.<br />30. Probabilistic scenarios yield a winning probability of 2/3 for player A. <br /><br />Each problem involves a blend of mathematical reasoning, geometric insights, and combinatorial logic to reach precise outcomes, reflecting diverse mathematical challenges.
Keywords
Math Kangaroo 2021
solution suggestions
Levels 11 and 12
mathematical concepts
problem-solving techniques
geometry
combinatorics
probability theory
algebraic expressions
graph interpretation