2016_Solutions_Grades 11-12-2016_Solutions_Levels

2016_Solutions_Levels_11&12

Pdf Summary

This document provides solutions and explanations to the Math Kangaroo 2016 competition problems for levels 11 and 12, presented by Math Kangaroo in USA. It details step-by-step the mathematical reasoning behind each provided answer, spanning a variety of mathematical topics including algebra, geometry, trigonometry, number theory, and combinatorial problems. <br /><br />The solutions are structured problem by problem, beginning with giving the correct option choice (marked as A, B, C, D, or E) and then offering a detailed solution to explain why that choice is correct. For instance, problem 1 involves determining ages from a set of equations, ultimately identifying Alex's age as 13. Another example is problem 6, which discusses the minimum number of planes needed to form a 3-dimensional polyhedron, concluding with 4 as the correct answer, which allows for constructing a tetrahedron.<br /><br />The document also provides mathematical proofs and computations, such as determining the conditions under which certain figures intersect or finding the minimum number of moves to achieve a particular diagram state. The solutions use a combination of algebraic manipulation, logical deductions, and sometimes geometric interpretations to arrive at the correct answers.<br /><br />Throughout the document, advanced mathematical concepts suitable for high-school-level students involved in math competitions are employed, with a focus on clear and concise explanations aimed at enhancing the problem-solving skills of participants. The variety of problems covered in the document helps in tackling issues like identifying prime numbers, areas and perimeters of geometrical shapes, and solving polynomial equations, reflecting the comprehensive nature of competitive mathematics exams like the Math Kangaroo.

Keywords

Math Kangaroo 2016

competition problems

levels 11 and 12

mathematical reasoning

algebra

geometry

trigonometry

number theory

combinatorial problems

problem-solving skills