FOM 12 Practice Test Chapter 8 Sinusoidal Functions Name: Multiple Choice Identify the choice that best completes the statement or answers the question. Block: _ 1. Convert 120 into radians. A. 2 3 B. 4.7 C. 2.8 D. 3 2 2. Imagine that it is now 2 p.m. What time will it be when the minute hand has rotated through 1260? A. 5:30 B. 4:50 C. 6:00 D. 4:10 3. How many turning points does the graph of y = sin x have from 0 to 360? A. 0 B. 1 C. 2 D. 3 4. Determine the midline of the following graph. A. y = 2 B. y = 3 C. y = 4 D. y = 5
5. Determine the amplitude of the following graph. A. 2 B. 3 C. 4 D. 5 6. Determine the period of the following graph. A. 5 B. 6 C. 7 D. 8 7. A sinusoidal graph has an amplitude of 10 and a maximum at the point (18, 5). Determine the midline of the graph. A. y = 0 B. y = 5 C. y = 13 D. y = 8 8. Select the function with the greatest amplitude. A. y = 2 sin 3(x + 90 ) + 5 B. y = 3 sin 2(x 90 ) 3 C. y = sin (x + 90 ) 1 D. y = sin 0.5(x 90 ) 9. Determine the period of the following function. y = 3 sin 2(x + 90 ) 1 A. 180 B. 360 C. 720 D. 1080
10. Determine the midline of the following function. y = cos x + 12 A. y = 12 B. y = 3 C. y = 4 D. y = 0 11. Determine the range of the following function. y = 0.5 sin (x 2) A. 3 y 1 B. 0.5 y 0.5 C. 2 y 2 D. y R 12. The amount of daylight in a town can be modelled by the sinusoidal function d = 4.37 cos 0.017t + 12.52 where d represents the hours of daylight and t represents the number of days since June 20, 2012. How many hours of daylight should be expected on August 20, 2012? (There are 30 days in June, and 31 days in July) A. 16.89 h B. 15.04 h C. 14.84 h D. 14.74 h 13. Determine the equation of the sinusoidal regression function for the data. x 0 1 2 3 4 5 6 7 y 15.4 14.2 13.1 12.4 12.0 12.1 12.6 13.5 A. y = 4.35 sin (0.63x + 3.13) + 15.43 B. y = 4.35 sin (0.36x 3.13) + 15.43 C. y = 3.44 sin (0.63x + 3.13) + 15.43 D. y = 3.44 sin (0.36x 3.13) + 15.43 Short Answer 14. Convert 1.2 radians into degrees. Round your answer to the nearest degree.
15. For the following pair of angle measures, determine which measure is greater. 450, 7.5 radians 16. Determine the midline of the following graph. 17. Determine the amplitude of the following graph. 18. A sinusoidal graph has a maximum at the point ( 40, 3) and a midline of y = 12. Determine the amplitude of the graph. 19. A sinusoidal graph has an amplitude of 9 and a midline of y = 2. Determine the range of the graph. 20. Determine the range of the following function. y = 10 cos 4(x 180 ) + 2
21. A seat s position on a Ferris wheel can be modelled by the function y = 18 cos 2.8(x + 1.2) + 21, where y represents the height in feet and x represents the time in minutes. Determine the diameter of the Ferris wheel. 22. Determine the equation of the sinusoidal regression function for the data. Round values to the nearest tenth. x 5 4 3 2 1 0 1 2 y 1.5 22.5 41.0 53.0 56.5 51.0 38.5 19.5 23. Brianna s position on a Ferris wheel can be modelled by the function h(t) = 15.4 sin (2.3t 1.4) + 17.2 where h(t) represents her height in metres and t represents the time in minutes. How much higher is she after 30 s than at the start of the ride? Round your answer to the nearest tenth of a metre. Problem 24. The graph of a sinusoidal function is shown. Describe this graph by determining its range, the equation of its midline, and its amplitude. Explain your answers.
25. Kira is sitting in an inner tube in the wave pool. The depth of the water below her, in terms of time, during a series of waves can be represented by the graph shown. a) What is the depth of the water below Kira when no waves are being generated? Explain how you know. b) How high is each wave? Show your work. 26. Match each graph with the corresponding equation below. Explain your answers. i) y = 2 cos 2.5(x 0.8) 1 iv) y = 3 cos 2.5(x + 0.6) 1 ii) y = 3 cos 2(x + 0.8) + 1 v) y = 3 cos 2.5(x 0.6) + 1 iii) y = 3 cos 2(x 0.8) 1 vi) y = 2 cos 2(x 0.6) 1
27. The average depth of the water at an ocean port can be modelled by the function h(t) = 0.76 cos (0.25t) + 3.82 where h(t) represents the depth in metres and t represents the time in hours after 5:00 p.m. on April 19, 2012. a) What is the minimum depth of water, to the hundredth of a metre? b) Estimate the depth of the water at 10:30 a.m. on April 20, 2012. c) When was the depth of the water 3.75 metres? Give two times between 5:00p.m. on April 19 th, and 5:00 p.m. on April 20 th. 28. The following table gives the average temperature in an Alberta town for the first nine months of the year. Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Average Temperature ( C) 10.8 3.1 1.6 8.8 15.2 20.3 23.0 22.7 17.8 a) Determine the equation of the sinusoidal regression function for the data (January = month 1) Round all values to the nearest hundredth. b) Use your regression function above to estimate the average temperatures for October, November, and December, to the nearest tenth of a degree. Show your work
29. Use what you know of equations of Sinusoidal Functions to graph the equation 4 sin 2 135 3 Draw the graph from 0⁰ x 540⁰
FOM 12 Chapter 8 Practice Test Sinusoidal Functions Answer Section MULTIPLE CHOICE 1. A 2. A 3. C 4. A 5. C 6. D SHORT ANSWER 14. 69 15. 450 is greater. is 16. y = 1 17. 8 18. 15 7. B 8. B 9. A 10. A 11. B 12. D 13. D 19. 11 y 7 20. 8 y 12 21. 36 feet 22. y = 52.6 sin (0.4x 1.1) 4.0 OR y = 52.6 sin 0.4(x 2.8) 4.0 23. 11.4 m higher PROBLEM 24. Range: 8 y 4 equation of the midline is y = 2 Amplitude is 6 25. a) depth of the water would be 2.0 m. b) height of each wave is 0.8 m. 26. GRAPH A: Equation v) GRAPH B: Equation iii) 27. a) 3.06 m b) about 3.57 m. c) 11:39 p.m. on April 19 th and 11:29 a.m on April 20 th. 28. a) y = 18.03 sin (0.41x 1.39) + 5.02 OR y = 18.03 sin 0.41(x 3.39) + 5.02 b) October is 12.6 C. November is 5.4 C. December is 1.8 C. 29. See solutions on website for graph.