2007_Questions_Grades 11-12-2007_Questions_Levels

2007_Questions_Levels_11&12

Pdf Summary

The Math Kangaroo 2007 competition for grades 11 and 12 consists of a series of multiple-choice math problems divided into three sections, each increasing in difficulty and point value: 3-point, 4-point, and 5-point questions. Here is an overview of the types of questions asked in each section:<br /><br />**3-Point Questions:**<br />- Questions on geometric properties, such as the trajectory of a billiard ball and the configuration of shapes like triangles. For example, one question asks in which pocket a billiard ball, bouncing at a 45-degree angle, will land.<br />- Arithmetic questions, including finding the number of zeros at the end of a number or determining initial quantities after exchanges.<br />- Trigonometric identities and percentages are addressed, such as calculating angles and interpreting test scores.<br />- Ratio problems involving geometric figures.<br /><br />**4-Point Questions:**<br />- More complex geometrical problems, such as squares overlapping and the calculation of angle measurements as a percentage of other angles.<br />- Questions requiring knowledge of integer solutions and the properties of integers.<br />- Simple harmonic motion calculations and a historical math application involving the construction of right triangles.<br />- Logical reasoning problems on truth-tellers and liars.<br /><br />**5-Point Questions:**<br />- Advanced problems include calculating angles in a rhombus, determining graphs of functions, and solving sequences and series.<br />- Combinatorial problems, such as organizing gift exchanges and arranging specific patterns in an infinite sequence.<br />- Probability problems, focusing on dice outcomes and counting acceptable real number solutions to certain polynomial equations.<br /><br />Math Kangaroo aims to challenge students' mathematical reasoning and problem-solving skills across various mathematical concepts, including geometry, algebra, probability, logic, and trigonometry. Each question encourages creative and analytical thinking, often requiring knowledge of multiple math disciplines to solve.

Keywords

Math Kangaroo 2007

grades 11 and 12

multiple-choice math problems

geometric properties

trigonometric identities

integer solutions

combinatorial problems

probability problems

mathematical reasoning

problem-solving skills