Learning to Ride the Waves is a pre-test for a periodic functions class. The test contains 4 multiple choice questions and 1 free response question about periodic functions, including determining the period and amplitude of sinusoidal functions, using sinusoidal functions to model real world data like tides and sunrise times, and finding the regression equation for sinusoidal pattern data. The last question asks students to sketch and use a sinusoidal function to predict the earliest sunrise time in Saskatoon.

1. Learning to Ride the Waves
Periodic Functions Pre-Test
Surfing at the Hook by flickr user richardmasoner

2. (1) What is the period of this function?
(A) 0.51 (B) 0.80 (C) 6.16 (D) 12.32

3. (2) A sailboat is tied to the dock and requires a depth of at least 4 m.
During the first 12 h, what is the longest time the sailboat can remain
at the dock without contacting the bottom?
(A) 3.84 h (B) 7.50 h (C) 8.16 h (D) 11.34 h

4. (3) The height of a bicycle pedal above
the ground can be modelled by the
sinusoidal function graphed at right.
Determine the amplitude and average
value of this function.

5. (4) The table below shows the average monthly temperature, in
degrees Celsius, for a northern BC town. Determine the sine
regression equation for this data. (Round constants to one decimal
place. Let January be month 1, February be month 2,….)

8. (c) Sketch a graph for the function ƒ(n) that approximates the time of
sunrise in Saskatoon. Predict the approximate time of the earliest
sunrise to the nearest tenth of an hour.