2009_Questions_Grades 9-10-2009_Questions_Levels

2009_Questions_Levels_9&10
Pdf Summary
The Math Kangaroo 2009 competition for levels 9-10 presents a series of multiple-choice mathematics problems, each with a set number of points. Here is a concise summary of some of the questions from the test:<br /><br />1. <strong>Multiple of 3</strong>: Determine which number is a multiple of 3 from a given set.<br />2. <strong>Dots and Collinearity</strong>: Find the minimum number of dots to remove from a set so that no three remaining dots are collinear.<br />3. <strong>Marathon Problem</strong>: Calculate Peter’s finishing position given specific conditions about other runners.<br />4. <strong>Percentage Calculation</strong>: Compute 75% of half of two-thirds of 240.<br />5. <strong>Sequence and Sum</strong>: Deal with a sequence where the number 2009 is repeated and find the sum of specific digits.<br />6. <strong>Solid Vertices and Sum</strong>: With given numbers on solid's vertices and conditions on face sums, find the total sum of all vertex labels.<br />7. <strong>Squares and Cubes</strong>: Determine how many positive integers have squares and cubes with the same number of digits.<br />8. <strong>Shaded Area Computation</strong>: Calculate an area involving triangles and circles.<br />9. <strong>Sequence Continuation</strong>: Given a sequence pattern, find the seventh number.<br />10. <strong>Triangle and Angles</strong>: Determine a specific angle in a triangle given angle bisectors.<br /><br />For more complex problems, the test also includes puzzles and logical reasoning challenges, focusing on imaginative mathematical scenarios like:<br />- Properties of Borromean rings.<br />- Combinatorial arrangements of game pieces on a grid.<br />- Constraints of constructing numbers with specific digital properties.<br /><br />The test concludes with high-level problems requiring deeper mathematical insight, such as:<br />- Finding peculiar numbers like special primes.<br />- Exploring divisor properties in natural numbers.<br />- Paths and distances in the coordinate plane.<br /><br />Through these questions, the Math Kangaroo aims to test diverse mathematical concepts ranging from basic arithmetic to more deductive logic and spatial reasoning, challenging students' problem-solving skills comprehensively.
Keywords
Math Kangaroo 2009
multiple-choice
mathematics problems
collinearity
percentage calculation
sequence sum
solid vertices
squares and cubes
shaded area
angle bisectors