Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 8 Algebra
Problem
Hint
1) Study the sequence of shapes below built out of squares. How many squares would be in the nth term of the sequence?
 Let n = the term number (1, 2, 3, ...) These shapes are made up of 3 parts:
  1. The top horizontal row which is (in terms of n) ______
  2. The bottom vertical shapes which are (in terms of n) ____
  3. the ones in between which are (in terms of n) _____
  • Add these 3 parts together to get an expression for the total number of squares for each n:

    Squares in shape n = ______________
    • 2) What is the next term in this sequence:
        1, 2, 2, 4, 8, 32, 256, __

    Each term is the product of the previous 2 terms,
    so the next term is ______
    3) What is the 8th term in the following sequence?
        0th     SOHCAHTOA
        1st     AOTHACHOS
        2nd     AOHACHOS
        3rd     SOHCAHOA
        4th     SOCAHOA
    1. The input sequence with some spaces to clarify:
          0th     SOHCAHTOA
          1st     AOTHACHOS
          2nd     AO   HACHOS
          3rd     SOHCAHOA
          4th     SO   CAHOA
    2. With the spaces, above, you should be able to figure out the sequence of actions. Write out each term until you get to the 8th:

      5th term:

      6th term:

      7th term:

      8th term: ______________

    Problem
    Hint
    4)A shape is formed by the lines x = 3, y = 2x + 6 and y = 0. Use the coordinate grid to draw the shape. What is the area of the shape?
    1. Plot a couple of points for the equation
      y = 2x + 6:
      This is enough to plot the line.

    2. Plot the other 2 lines, forming the right triangle.

    3. Plug x=3 into y = 2x+6 to get the height:

    4. The area is __________ sq. units.
    5) Mary realizes that she can buy 5 tops and 2 pairs of jeans for $96 because of store deals. She also figures out that she can buy 3 tops and 4 pairs of jeans for $115. If the tops all cost the same and the jeans all cost the same how much is just one pair of jeans? This is 2 equations and 2 unknowns.
    Let t = the cost of a top and j = the cost of a single pair of jeans.
    1. Equation 1:

    2. Equation 2:

    3. Turn the first equation around into an expressin for t and then plug this value for t into the second equation and solve for j:




      j = _______