Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 8 Number Sense
Problem
Hint
1) Insert an additional set of parenthesis to make the following number sentence true.
8 - 6 - 3 x (4 - 10) ÷ 2 + 1 = 18
  1. The problem is that "+1" at the end of the expression. That means the rest of the expression must resolve to 17, an odd number.
  2. There is no way with a single set of parentheses to separate the 4 and the 10, so combine those:
    8 - 6 - 3 x -6 ÷ 2 + 1 = 18
  3. At this point, try several groupings of parentheses to get the left side to evaluate to
    17 + 1:



  4. The answer is

    ____________________________
2) What is the smallest whole number exponent, n, for which
    1 - (1⁄3) n is greater than 1 - (0.2)3 ?
  1. (0.2)3 = the fraction ___________

  2. So, (1⁄3) n must be less than _________________, so
    3n must be greater than the denominator ________.
  3. Take powers of 3 until you find one greater than the denominator:



  4. n = _____

Problem
Hint
3) A builder orders 2 by 4 lumber for a project and always tags on an extra 5% rounded up just in case. If the total number of 2 by 4s is 625 how many of those are extra 2 by 4s that the builder may not need? Let A = the number of 2x4s necessary for the project, without the extras. Then the equation is:

_______________

A = _________

625 is _____ more than this value of A.
4) A sequence is created as follows:

What is the distance between the 9th and 10th term of the sequence when plotted on a number line?
Express your answer as a fraction.
  1. Evaluating the 4 terms:

    1, .5, .75, .625
  2. The difference between these terms is:

  3. Each difference is _____ the previous difference, so the expression for the differences is:

    D = _________
  4. Evaluating this expression for
    n = 9:

    D = _______________

5) A government program has a cost overrun of 0.3% on a total budget of 2 billion dollars. What will the overrun cost the tax payers? Express your answer in scientific notation. 		Express the 2 billion and the .3% overrun in scientific notation and multiply them together:



= _____________ dollars.