Grades 9-10 Video Solutions 2011-Grades 9-10 Video Solutions 2011 part3

Video Transcription

Video Summary

The video tackles mathematical problems primarily from geometry, algebra, and combinatorics, offering a detailed walk-through of solving each question. Problem 21 involves calculating the volume of a cube with given side length conditions, featuring factoring of cubic equations, and determining the side measure through a quadratic solution, ultimately finding the larger cube's volume to be 729. Question 22 explores overlapping circle areas and requires computing sector and triangle areas. It demonstrates solving for the shaded region using relationships between circle radii and sectors. In problem 23, it discusses forming a "good" 5-digit number under certain rules and enumerates possibilities by examining digit selections that satisfy conditions, concluding with 168 valid numbers. Question 24 involves optimizing expressions involving variables and factoring strategies to determine the largest quotient value, while Question 25 explores geometric properties in a cube, calculating possible non-vertex-sharing edge combinations, yielding nine combinations. Continuing, Question 26 finds integer solutions for an equation involving reciprocals leading to three possibilities, and Question 27 deals with analyzing prime numbers' characteristics within given expressions, finding a single valid integer. Question 28 maximizes angle variety within nested triangles, and Question 29 involves rotating cube boxes to reach a specific configuration. Finally, Question 30 explores painting squares, confirming all units can meet the described coverage conditions, resulting in all choices being viable. These mathematical explorations illustrate deep reasoning and methodical problem-solving approaches.

Keywords

geometry

algebra

combinatorics

cubic equations

circle areas

5-digit numbers

prime numbers

nested triangles