2005_Solutions_Grades 11-12-2005_Solutions_Levels

2005_Solutions_Levels_11&12

Pdf Summary

Math Kangaroo 2005 for grades 11-12 features a series of mathematical problems, each with multiple-choice answers. The paper tests a variety of mathematical skills including algebra, geometry, number theory, and logic. Here's a concise summary of some notable problems and solutions:<br /><br />1. Decreasing Function: Problem 1 finds the smallest value of a certain expression involving fractions.<br />2. Cubes: Problem 2 identifies the only cubes between 2 and 100.<br />3. Digits: For Problem 5, it identifies patterns in digits to solve for a specific term.<br />4. Irrational Numbers: Problem 7 involves proving whether a number is irrational.<br />5. Volume and Surface Area: Problems center on understanding shapes and their geometric properties, such as cubes and tetrahedrons (Problem 23).<br />6. Suitability of Divisors: Problems also cover understanding number properties like divisors and solving equations based on such properties.<br />7. Angles and Triangles: Geometric problems explore angle calculations and properties of shapes, such as inscribed angles in circles (Problem 30).<br /><br />Each question is followed by detailed solutions showcasing logical steps and mathematical reasoning needed to arrive at the correct choice. This paper emphasizes problem-solving abilities and understanding complex mathematical concepts that are ideal for high-achieving students in senior grades.

Keywords

Math Kangaroo 2005

grades 11-12

mathematical problems

algebra

geometry

number theory

logic

problem-solving

cubes

irrational numbers