Standard Five – Top Level Problems
Prompt: Grandma had to cook her biscuits for exactly 10 minutes. However, the only
times she had were a 4 minute egg timer and a 7 minute egg time. How did she use the
two egg timers to measure exactly 10 minutes?
Math’s Mate Gold, J.B. Wright, 1995
Prompt: The Gibb’s Hill Lighthouse, Southampton, Bermuda, in operation since 1846,
stands 117 feet high on a hill 245 feet high, so its beam of light is 362 feet above sea
level. A brochure states that the light itself can be seen on the horizon about 26 miles
distant. Verify the correctness of this information.
Precalculus, Sullivan and Sullivan, 2006
Prompt: To measure the height of Lincoln’s caricature on Mt. Rushmore, two sightings
800 feet from the base of the mountain are taken. If the angle of elevation to the bottom
of Lincoln’s face is 32 degrees and the angle of elevation to the top is 35 degrees, what
is the height of Lincoln’s face?
Precalculus, Sullivan and Sullivan, 2006
Prompt: A cone-shaped tent is made from a circular piece of canvas 24 feet in
diameter by removing a sector with central angle of 100 degrees and connecting the
ends. What is the surface area of the tent?
Precalculus, Sullivan and Sullivan, 2006
Prompt: The maximum safe load for a horizontal rectangular beam varies jointly with
the width of the beam and the square of the thickness of the beam and inversely with its
length. If an 8-foot beam will support up to 750 pounds when the beam is 4 inches wide
and 2 inches thick, what is the maximum safe load in a similar beam 10 feet long, 6
inches wide, and 2 inches thick?
Precalculus, Sullivan and Sullivan, 2006