MCR 3U Grade 11 University Preparation
Cumulative Review 4 - 6
4. The population of a town is growing at an average rate of 5% per
year. In 2000, its population was 15 000. What is the best estimate of the
population in 2020 if the town continues to grow at this rate?
a) 40 000
b) 30 000
c) 35 000
d) 45 000
5. Point P (27, 24) is on the terminal arm of an angle in standard
position. What is the measure of the related acute angle and the principal
angle to the nearest degree?
a) 74° and 106°
c) 16° and 164°
b) 16° and 344°
d) 74° and 286°
12. A weather balloon is spotted from two angles of elevation, 57° and
83°, from two different tracking stations. The tracking stations are 15
km apart. Determine the altitude of the balloon if the tracking stations
and the point directly below the balloon lie along the same straight line.
a) 28.5 km
b) 32 km
c) 984 km
d) 23.7 km
13. At a concert, a spotlight is placed at a height of 12.0 m. The spotlight
beam shines down at an angle of depression of 35°. How far is the
spotlight from the stage?
a) 20.9 m
b) 12.1 m
c) 25 m
d) 9.6 m
29. The Paper Folding Problem
The Paper Folding Problem was a well-known challenge to fold paper in
half more than seven or eight times, using paper of any size or shape.
The task was commonly known to be impossible until April 2005, when
Britney Gallivan solved it.
A sheet of letter paper is about 0.1 mm thick. On the third fold it is about
as thick as your fingernail. On the 7th fold it is about as thick as a
notebook. If it was possible to keep folding indefinitely, how many folds
would be required to end up with a thickness that surpasses the height of
the CN Tower, which is 553 m?
30. Lawn Chairs
The manufacturer of a reclining lawn chair would like to have the chair
positioned at the following angles: 105°, 125°, 145°, 165°, and 175°. In
the figure, AC is 75 cm and AB is 55 cm. Determine the positions for the
notches on BC that will produce the required angles. Give a complete
solution.
31. Dock Dilemma
The Arps recently bought a cottage on a small, sheltered inlet on Prince
Edward Island. They wish to build a dock on an outcropping of level
rocks. To determine the tide’s effect at this position, they measured the
depth of the water every hour over a 24 h period.
a) Graph the data, and determine an equation that models this situation
over a 24 h period.
b) What is the maximum depth of the water at this location?
c) The hull of their boat must have a clearance of at least 1 m at all
times. Is this location suitable for their dock? Explain.