2001_Solutions_Grades 9-10-2001_Solutions_Levels

2001_Solutions_Levels_9&10
Pdf Summary
The Math Kangaroo 2001 Solution Suggestions for Levels 9-10 offers answers and methods for solving a range of mathematical problems typical of the competition for high school students. Here is a summary of the problem solutions provided in the document:<br /><br />1. **Dice Sum**: The sum of dots on three dice can range from 3 to 18, yielding 16 possible values.<br />   <br />2. **Student Arrangement**: Student 'A' is positioned third from an end in both possible seating arrangements.<br /><br />3. **Polygon Diagonal**: Using given conditions, the length of the diagonal in the polygon is calculated to be 10 cm.<br /><br />4. **Cube Completion**: To complete the figure into a 5x5x5 cube, 110 more cubes are needed.<br /><br />5. **Trapezoid Area**: After removing the triangles, the calculated remaining area is 10 cm².<br /><br />6. **Expression Evaluation**: With x = 0, possible outcomes for the given expression are -2, 0, or 2.<br /><br />7. **Prime Numbers**: Only 2, 11, and 101 are prime with digit sums of 2 within the range less than 2001.<br /><br />8. **Fence Length**: Using the Pythagorean Theorem, the missing fence side is determined to be 13 m, totaling a length of 46 m.<br /><br />9. **Divisibility**: If the GCF of m and 35 is 35, then m must be a multiple of 35.<br /><br />10. **Ring Cutting**: Ring C, which holds all the other rings, must be cut to separate them.<br /><br />11. **Natural Number Sets**: For different conditions of d, five possible natural numbers are determined.<br /><br />12. **Angle Calculation**: From given angle conditions in geometry, an angle is calculated to be 40°.<br /><br />13. **Time Calculation**: Calculates watch delay over one week using seconds per hour.<br /><br />14. **Remaining Money**: After purchasing candies, Adam remains with $56.<br /><br />15. **Digit Product**: Based on divisibility by 9 and 25 constraints, a viable 11-digit number is created.<br /><br />16. **Camel's Mass**: Determines the thirsty camel’s mass to be 750 kg.<br /><br />17. **Family Age**: By analyzing factorization of a number, three children’s ages are concluded.<br /><br />18. **Price Reduction**: The reduction of the calculator's price is calculated to be 40%.<br /><br />19. **Candy Distribution**: Peter and Mary’s candies are determined from provided daily consumption.<br /><br />20. **Division Remainder**: Concludes the remainder when 2001 is divided is 9.<br /><br />21. **Divisibility by 4**: The expression results in numbers divisible by 4; identifies an exception.<br /><br />22. **Similar Triangles**: Uses triangle similarity to equate areas as S4 = 9S1.<br /><br />23. **Polynomial Zeros**: Proves impossibility for one zero in given conditions.<br /><br />24. **Equation Solve**: Solves for \(q\) using Pythagorean equation.<br /><br />25. **Power Digit**: Identifies the units digit of a large power expression as 5.<br /><br />26. **Area Calculation**: Determines the area of triangle PQR using side length claims.<br /><br />27. **Line Segments**: Counts 36 line segments in a grid, including horizontals, verticals, and diagonals.<br /><br />28. **Digit Expression**: Finds two possible numbers satisfying the digit equation 14a = 10a + b.<br /><br />29. **Shaded Area**: Computes shaded area in a configuration involving tangent circles.<br /><br />30. **Box Problem**: Utilizes constraint equations to find the total number of boxes as 115.<br /><br />These solutions demonstrate various mathematical skills, including algebra, geometry, number theory, and logical reasoning, geared toward helping participants successfully solve competition-style math problems.
Keywords
Math Kangaroo
mathematical problems
high school students
competition solutions
algebra
geometry
number theory
logical reasoning
problem solving
math competition