Directions:

1.
A wooden bead is to be placed on a 6 foot piece of rope to divide the rope in such a manner that one section is three times the other. Find the length of the longer section of rope created by the bead.
(Assume the center of the bead to be the partition point.)

Choose:
 1½ feet 3 feet 4 feet 4½ feet

2.
For centuries, cliff swallows have returned, in the thousands, to a mission in San Juan Capistrano (California) from their yearly 6,000 mile winter migration to Goya, Argentina.
 In 2009, the birds stopped returning to the mission due to urbanization of the area and restoration of the mission (which destroyed many of the nesting spots). The birds now fly further north into California.
The birds, traveling in flocks of thousands, have been reported at two major feeding stops in Peru and Mexico. Using the grid overlay showing Capistrano (0,8) and Goya (6,0):
a) determine the coordinates of the Mexico feeding stop if it is one third of the 6000 mile straight line distance from Capistrano to Goya.
Choose:

b)
determine the coordinates of the Peru feeding stop if the Peru stop partitions the line segment from Goya to Capistrano in a ratio of 1:2.
Choose:

3.
Pirate Pete has buried his treasure in a shallow lagoon. He drew the map at the right to help remember the exact location. Follow these 3 steps to find the coordinates of the treasure:
P1 partitions the directed segment from the Rock to the Coral in a ratio of 1:2. Find P1.
P2 partitions the directed segment from Water Plant to Log in a ratio of 4:1. Find P2.
The treasure will be located at the midpoint of the segment connecting P1 to P2.
At what point is the treasure buried?
Choose:
 (4, 5) (5.5, 4.1) (5.2, 6) (7, 3.2)

4.
A straight line ski lift goes up a hill starting at point B(-1,-1) and ending at drop off point C. A support pole at point P partitions the lift ride between B and C in a ratio of 1:3 with B as the initial point. What are the coordinates of the drop off point C ?

Choose:
 (5, 8) (7, 11) (6, 9) (8, 12)

5.
A regular pentagram was viewed as a symbol of mathematical perfection by Pythagoras due to its proportions. A number, approximately 1.618, known as the Golden Ratio resides inside the pentagram.
We will be using a rounded version of the Golden Ratio (1.618).

This pentagram is placed on a coordinate axes such that point A is located at (1,6) and point D is located at (9,6).
Express answers to the nearest hundredth.
a) Point B partitions in a ratio of 1:1.618. Find AB.
Choose:
 3.69 3.44 3.06 3

b)
Find BC.
Choose:
 3.06 2.12 2.06 1.89