2025_Team_Competition_Questions_Grades_11-12-2025 Team Competition Questions Grades 11-12

2025 Team Competition Questions Grades 11-12

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The document is the Math Kangaroo USA Team Competition 2025 for Grades 11 and 12. It states that the test must remain confidential until December 8, 2025, and that it contains 20 multiple-choice questions and 10 short-answer questions to be completed in 60 minutes.<br /><br />The multiple-choice section covers a wide range of math topics, including:<br />- angles in triangles and ratios,<br />- intervals and counting integers,<br />- rational numbers and divisibility,<br />- domino tiling and geometric optimization,<br />- shortest paths on the surface of a solid,<br />- prime factorization and repeated die rolls,<br />- polynomial roots and symmetry,<br />- logic and truth-tellers,<br />- polygon unions and maximum number of sides,<br />- cube-vertex number constraints,<br />- regular octagons and area,<br />- iterative digit-like transformations,<br />- combinatorics and constrained pairings,<br />- integer roots of quadratics with prime products,<br />- cube coloring and visible surface area,<br />- probabilistic/combination game outcomes,<br />- evaluating a polynomial from a special value,<br />- and a number-placement puzzle on circles.<br /><br />The short-answer section includes more advanced counting, geometry, combinatorics, and number theory problems, such as:<br />- counting numbers of the form \(m^2 n^4\),<br />- counting rotationally distinct cube colorings with 9 colors,<br />- determining the number of cards from ordering conditions on triples,<br />- counting ant paths on a cube without collisions,<br />- finding the minimum number of kangaroos from a weight ratio puzzle,<br />- solving a divisibility/counting problem involving 6,<br />- finding the volume of water in a triangular prism container from two orientations,<br />- counting integers whose largest proper divisor is 17,<br />- determining the largest non-buyable number of toffees from box sizes 6, 10, and 15,<br />- and a self-referential apples-and-plates counting puzzle.<br /><br />Overall, the document is a contest problem set testing algebra, geometry, number theory, combinatorics, and logic.

Keywords

Math Kangaroo USA

team competition 2025

grades 11 and 12

multiple-choice questions

short-answer questions

algebra and geometry

number theory

combinatorics

logic puzzles

contest problem set