Standardized Test Prep

SAT/ACT

36. A periodic function goes through 5 complete cycles in 4 min. What is the period of the function?
    1. 1 5 min 1 fifth , min
    2. 1 4 min 1 fourth , min
    3. 48 s
    4. 75 s
37. The period of a periodic function is 8 s. How many cycles does it go through in 30 s?
    6. 4 15 4 fifteenths  cycle
    7. 3.75 cycles
    8. 22 cycles
    9. 240 cycles
38. Which graph is NOT the graph of a periodic function?
    1. 
    2. 
    3. 
    1. I only
    2. II only
    3. III only
    4. II and III only
39. The amplitude of a periodic function is 2.5 and its minimum value is 0. What is the function's maximum value?
    6. − 2 . 5 negative 2 . 5
    7. 0
    8. 2.5
    9. 5.0

Extended Response

40. Two periodic functions have periods of 6 s and 7 s. A machine records the two functions reaching their maximum values at the same time. Twenty seconds later, the machine records a new periodic function reaching its maximum value. The new function has a period of 8 s. How many seconds after that will all the functions reach their maximum values at the same time? Explain.

Mixed Review

See Lesson 12-6.

41. An airplane has a speed of 300 mi/h in still air. Suppose the airplane flies due north and encounters a wind blowing 35 mi/h due west. What is the resultant speed of the airplane?
42. Sketch a normal curve for a distribution that has mean 57 and standard deviation 12. Label the x-axis values at one, two, and three standard deviations from the mean. See Lesson 11-9.

Get Ready! To prepare for Lesson 13-2, do Exercises 43–48.

Write an equation of the circle that passes through the given point and has its center at the origin. (Hint: Use the distance formula to find the radius.) See Lesson 10-3.

43. (0, 1)
44. (2, 3)
45. (3, 4)
46. ( − 1 , − 1 ) open negative 1 comma negative 1 close
47. ( 3 2 , 1 2 ) open . fraction square root of 3 , over 2 end fraction , comma , 1 half . close
48. ( 2 2 , 2 2 ) open . fraction square root of 2 , over 2 end fraction , comma , fraction square root of 2 , over 2 end fraction . close

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