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. **Day of the Month Problem**: By identifying compatible days of the week with given conditions, Monday is determined to be the correct day.<br />   <br />2. and 3. **Numerical and Path Problems**: These problems involve organizing sequences or identifying numbers and paths, with solutions derived through pattern recognition.<br /><br />4. **Stone Problem**: Uses arithmetic progressions and identifying patterns of increase to find the number of stones after repeated steps.<br /><br />5. **Cube Problem**: Determines the number of visible faces of cubes using logic about glued positions.<br /><br />6. **Aliens on Planets**: Examines logical statements about alien types and their locations, concluding that no green aliens are on Venus.<br /><br />7. **Geometric Angles**: Uses properties of regular polygons and rhombuses to calculate angles.<br /><br />8. **Probability of Ball Selection**: Determines the minimum moves required to ensure a certain selection occurs by evaluating sequential operations.<br /><br />9. **Brick Volume**: Involves understanding geometric dimensions and relationships between surface areas.<br /><br />10. **Prime Numbers and Sums**: Demonstrates finding numbers based on properties of primes.<br /><br />11. **Volume Ratios**: Uses percentage comparisons to derive proportional relationships.<br /><br />12. **Graph Shape Analysis**: 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. **Numerical Summations and Geometry**: Use algebraic manipulations and geometric formulas to solve classifying problems and calculating volumes.<br /><br />15. & 16. **Predictions in Games**: Analyzes scenarios using given predictions to determine outcomes in sports or lotteries.<br /><br />17. & 18. **Geometry and Factorizations**: Rotate objects or numbers to determine positions and factorizations.<br /><br />19. **Game Strategy and Prime Sums**: Involves selecting game strategies that result in prime outcomes or numbers.<br /><br />20. – 25. **Advanced Geometry and Analysis**: These problems involve higher-level geometry, mathematical proofs, logical assessments, and algebraic manipulations to derive solutions.<br /><br />26. – 30. **Complex Calculations and Probabilities**: 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