1999_Questions_Grades 11-12-1999_Questions_Levels

1999_Questions_Levels_11&12

Pdf Summary

The 1999 Math Kangaroo competition for levels 11-12 consisted of multiple-choice questions divided into different point categories: 3, 4, and 5 points each.<br /><br />**3 Points Each:**<br /><br />1. The problem features geometry with a square and a hexagon asking for the number of sides in a certain regular polygon (options: 8 to 18 sides).<br />2. Participants calculate the angle between diagonals in a cube.<br />3. A problem about finding positive integers less than 1000 as a product of two even numbers.<br />4. Determining the ones digit of a large number, 199919981997...21.<br />5. A problem involving a unique real-valued function's properties.<br />6. A currency exchange rate problem comparing three offices after rate alterations.<br />7. An equation-solving problem to find an equal numerical expression.<br />8. A geometry problem involving the perimeter and sum of the squares of a right triangle, leading to finding the area.<br />9. Medians BD and CE are perpendicular in triangle ABC; determine the area.<br />10. A problem involving rearranging digits of a number to express ages and match conditions.<br /><br />**4 Points Each:**<br /><br />11-20: A mix of problems covering number theory, geometry, inequalities, and sequences, requiring deeper mathematical reasoning and calculation skills, including determining the number of solutions to specific equations and the properties of geometric and arithmetic objects.<br /><br />**5 Points Each:**<br /><br />21-30: These problems are more advanced, covering complex geometry, sequences, optimal strategies in series or conceptually deeper operations, real-life applications adapted for mathematical analysis, and theoretical queries that test comprehensive problem-solving abilities.<br /><br />Each question is designed to test different mathematical concepts and application skills, encouraging students to showcase their proficiency in geometry, algebra, number theory, and deductive reasoning. The competitive structure underscores problem-solving under time constraints, typical in such mathematics contests.

Keywords

Math Kangaroo 1999

geometry problems

number theory

multiple-choice questions

mathematical reasoning

algebra

deductive reasoning

competitive math

problem-solving skills

time constraints