Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 8 Number Sense

Problem
1) Grandpa tells Nelli he has an investment in a fund that has a history of increasing in values by 6.2% every year. He has $32,000 invested in that fund. He asks her to compute how much the fund will earn him over five years if he makes no changes to his investment.

2) A dime is 1.25x10-3 meter thick and is worth 1x 10-1 dollars. How many meters high is a stack of dimes worth 1x106 dollars? Express your answer in meters without using scientific notation.

3) The numbers 1 - 32 can be represented with a set of five lights using the binary system. An "on" light is recorded with a 1, an "off" light is recorded with a 0. With the pattern given in the table, how would the number 23 be represented in 1's and 0's?

Problem
4) The Golden Ratio is the ratio of a Golden rectangle's length to width that is most pleasing to the eye. This ratio is (1 + √ 5) / 2. If a Golden Rectangle has width 2√ 5 , then what is its length? Give an exact answer leaving radicals in your answer if needed.

5) In the equation (2x)3 (4x2)-2 = 25 4-3 , what is x?