2018_Solutions_Grades 11-12-2018_Solutions_Levels

2018_Solutions_Levels_11&12
Pdf Summary
The Math Kangaroo 2018 Solutions for Level 11-12 involve a variety of problems requiring logical reasoning and calculations. Here’s a concise summary of the solutions:<br /><br />1. <strong>Day of the Month Problem</strong>: By identifying compatible days of the week with given conditions, Monday is determined to be the correct day.<br />   <br />2. and 3. <strong>Numerical and Path Problems</strong>: These problems involve organizing sequences or identifying numbers and paths, with solutions derived through pattern recognition.<br /><br />4. <strong>Stone Problem</strong>: Uses arithmetic progressions and identifying patterns of increase to find the number of stones after repeated steps.<br /><br />5. <strong>Cube Problem</strong>: Determines the number of visible faces of cubes using logic about glued positions.<br /><br />6. <strong>Aliens on Planets</strong>: Examines logical statements about alien types and their locations, concluding that no green aliens are on Venus.<br /><br />7. <strong>Geometric Angles</strong>: Uses properties of regular polygons and rhombuses to calculate angles.<br /><br />8. <strong>Probability of Ball Selection</strong>: Determines the minimum moves required to ensure a certain selection occurs by evaluating sequential operations.<br /><br />9. <strong>Brick Volume</strong>: Involves understanding geometric dimensions and relationships between surface areas.<br /><br />10. <strong>Prime Numbers and Sums</strong>: Demonstrates finding numbers based on properties of primes.<br /><br />11. <strong>Volume Ratios</strong>: Uses percentage comparisons to derive proportional relationships.<br /><br />12. <strong>Graph Shape Analysis</strong>: Assesses the relationship between graphical representations and physical attributes, such as describing a vase’s shape based on water filling rates.<br /><br />13. & 14. <strong>Numerical Summations and Geometry</strong>: Use algebraic manipulations and geometric formulas to solve classifying problems and calculating volumes.<br /><br />15. & 16. <strong>Predictions in Games</strong>: Analyzes scenarios using given predictions to determine outcomes in sports or lotteries.<br /><br />17. & 18. <strong>Geometry and Factorizations</strong>: Rotate objects or numbers to determine positions and factorizations.<br /><br />19. <strong>Game Strategy and Prime Sums</strong>: Involves selecting game strategies that result in prime outcomes or numbers.<br /><br />20. – 25. <strong>Advanced Geometry and Analysis</strong>: These problems involve higher-level geometry, mathematical proofs, logical assessments, and algebraic manipulations to derive solutions.<br /><br />26. – 30. <strong>Complex Calculations and Probabilities</strong>: Use principles of physics, probability in unique setups, and high-level arithmetic to solve permutations and calculate factorials.<br /><br />Overall, the solutions rely heavily on logical reasoning, algebraic manipulation, and geometric properties, tailored to challenge and build the problem-solving skills of high school students in mathematics.
Keywords
Math Kangaroo 2018
logical reasoning
arithmetic progressions
geometric properties
probability
prime numbers
algebraic manipulation
pattern recognition
game strategy
complex calculations