2004_Solutions_Grades 7-8-2004_Solutions_Levels

2004_Solutions_Levels_7&8
Pdf Summary
The Math Kangaroo 2004 competition for Levels 7-8 features a series of mathematical problems followed by their solutions. Here's a brief summary of some of the solutions provided:<br /><br />1. **Problem 1** involves the simple arithmetic operation using the order of operations (PEMDAS), resulting in the answer 1204.<br />2. **Problem 2** involves setting up and solving an equation based on the exchange of money between two individuals, yielding x = 11.<br />3. **Problem 3** focuses on modular arithmetic and summation of specific integers, resulting in the remainder of 1999 when divided by 2004.<br />4. **Problem 4** presents a combinatorial grid issue where Karolina can substitute two different values for x in a missing grid position.<br />5. **Problem 5** uses negative numbers in an arithmetic sequence to find a solution of 4.<br />6. **Problem 6** describes how folding a perforated line in a cube’s net results in an equilateral triangle.<br />7. **Problem 7** calculates the increased area of a rectangle upon incremental enlargement, and provides an increase of 21%.<br />8. **Problem 8** requires geometric reasoning to confirm that the circle’s diameter is 10 units.<br />9. **Problem 9** deals with combinations of ice cream flavors, resulting in 10 combinations.<br />10. **Problem 10** involves algebraic equations to find a solution of 42.<br />11. **Problem 11** uses time conversion to determine that Friday at 11:11 AM is the answer.<br />12. **Problem 12** utilizes a diagonal in a square to divide the area and subsequently calculates the shaded area as 2.<br />13. **Problem 13** considers divisibility properties of powers of ten, resulting in 641.<br />14. **Problem 14** investigates an iterative sequence of weekdays, finding Friday as occurring more frequently.<br />15. **Problem 15** requires counting potential configurations of triangle bases and results in 4 isosceles triangles.<br />16. **Problem 16** evaluates prime factor combinations to find 32 divisors.<br />17. **Problem 17** considers geometric volume resulting in a requirement for 36 building blocks.<br /><br />This collection of problems covers various mathematical concepts such as arithmetic operations, modular arithmetic, geometry, combinatorics, and logical reasoning, designed to challenge students' mathematical understanding and problem-solving skills.
Keywords
Math Kangaroo 2004
Levels 7-8
arithmetic operations
modular arithmetic
combinatorics
geometry
problem-solving
algebraic equations
prime factors
mathematical concepts