1998_Questions_Grades 11-12-1998_Questions_Levels

1998_Questions_Levels_11&12
Pdf Summary
The Math Kangaroo 1998 for levels 11-12 presents participants with 30 challenging math problems, scored either 3, 4, or 5 points each. The problems cover a diverse range of mathematical concepts including algebra, geometry, trigonometry, combinatorics, and logic.<br /><br />**3-point problems**: These introductory problems test basic mathematical understanding. For instance, participants need to determine the equal value of a mathematical expression, calculate areas of geometric shapes, identify patterns in numbers, and solve equations involving basic trigonometric identities.<br /><br />**4-point problems**: Problems in this category escalate in complexity. They're designed to evaluate participants' abilities to solve real-world scenarios mathematically, such as determining the age of a grandfather based on a unique family-related word problem, extracting jars of different types of jams under specific constraints, and working with inverse functions. Participants are also challenged with divisibility rules, number games involving square natural numbers, and logical statements regarding participation in Math Kangaroo.<br /><br />**5-point problems**: These problems require the most advanced mathematical skills, knowledge of calculus concepts like local extrema, understanding unique geometric properties, and solving complex algebraic equations. For example, participants may need to calculate the number of local extrema of a function, determine specific conditions on a wrapped cube, analyze sequential numbers, and work with the volumes and geometry of 3D shapes like cones and tetrahedrons. Participants must also apply logical reasoning to deduce the greatest possible number of planes tangent to three spheres.<br /><br />Overall, Math Kangaroo 1998 challenges students to apply their mathematical knowledge creatively and logically across a variety of contexts, fostering deeper understanding and problem-solving skills in mathematics.
Keywords
Math Kangaroo 1998
levels 11-12
algebra
geometry
trigonometry
combinatorics
logic
mathematical problems
calculus
problem-solving