6. The angle can be written equivalently as which of the following in the radian system?

Transcription

1 Common Core Algebra 2 Review Session 3 NAME Date 1. Which of the following angles is coterminal with an angle of 130!, assuming both angles are drawn in the standard position? (1) (2) 230! (3) (4) 2. If drawn in the standard position, which of the following angles terminates in the third quadrant? (1) 120! (2) 60! (3) 210! (4) 240! 3. A rotation angle, drawn in standard position, measures 1200!. In which quadrant does its terminal ray lie? (1) I (2) II (3) III (4) IV 4. Which of the following has the same reference angle as 150!? (1) 210! (2) 300! (3) 120! (4) 70! 5. The radian angle 3π 4 is equivalent to (1) (2) (3) (4) 6. The angle can be written equivalently as which of the following in the radian system? (1) 7π 6 (2) 5π 4 (3) 3π 2 (4) 4π 3 7. A point lies on the unit circle whose x-coordinate is 1. If the point lies in the fourth quadrant, then 4 which of the following is its y-coordinate? (1) 3 4 (2) 15 4 (3) 7 4 (4) 11 2

2 8. For an angle A that terminates in the second quadrant, sin A = 2. Which of the following 3 represents the value of cos A? (1) (2) (3) (4) Which of the following could not be the value of the cosine of an angle? (1) 4 5 (2) 7 3 (3) 11 4 (4) If f ( x) = 10sin( 2x) + 8 then what is the value of f (1) 4 2 (2) 8 (3) 18 (4) 28 3 π 4? 11. If an angle has a positive cosine but a negative sine then it must terminate in which of the following quadrants? (1) I (2) II (3) III (4) IV 12. Which of the following represents the range of the function y = 6sin( x) +10? (1) 60 y 60 (2) 0 y 20 (3) 16 y 4 (4) 4 y Given the sinusoidal graph with coordinates shown below, which of the following is the value of its amplitude? (1) 14 (3) 12 (2) 6 (4) 28

3 14. A periodic function has an equation y = 10cos( 8x) 2. What is the horizontal distance between any two consecutive relative maximum values on this graph? (1) 10 (2) π 2 (3) 8 (4) π The graph shown below can be described using the equation y = Acos( Bx) + k. Which of the following is the value of B + k? (1) 5π (2) 13 (3) 11 (4) π Which of the following lines does the graph of y = 5sin( x) +14 not intersect? (1) x = 0 (2) x = π (3) y = 20 (4) y = A person riding a Ferris wheel at a local fair made one complete trip around in 10 minutes. Their height is modeled using a sine function of the form y = Asin(Bt) + C, where t is the amount of time the person has been traveling, in minutes. Which of the following must be the value of B? (1) 10 (2) 1 (3) 10π (4) π The volume of water in a tank varies periodically. At t = 0 it is at its maximum of 650 gallons and at t = 5 it is at its minimum of 120 gallons. Which of the following functions would best model the volume of water in this tank as a function of time in hours? (1) V = 265cos 2π 10 t (2) V = 770sin 10t (3) V = 385cos( 5t ) ( ) (4) V = 265sin π 10 t + 770

4 19. The terminal ray of an angle drawn in standard position passes through the point (.508,.862) on the unit circle. Which of the following is closest to the tangent of this angle? (1).685 (2) (3) (4) If α is an angle drawn in the standard position with its terminal ray landing in the fourth quadrant and csc( α ) = 5, then which of the following is the exact value of cos( α )? (1) 1 5 (2) (3) 24 5 (4) For the angle it's known that cot θ ray of θ lie? (1) I (2) II (3) III (4) IV ( ) < 0 and sin( θ ) > 0. In which quadrant does the terminal 22. An angle drawn in standard position measures 10 radians. In what quadrant does its terminal ray lie? Show the reasoning that leads to your answer.

5 23. Given the following circle (note that it is not the unit circle) with the angle marked, state the values of each of the following: a) The radius of the circle b) sinθ = e) secθ = c) cosθ = f) cscθ = d) tanθ = g) cotθ = 24. For an angle A it is known that sin A = 3 4 and cos A < 0. Determine the value of tan A. Show how you arrived at your answer. 25. Given the function f x solutions. ( ) = 6sin( 10x) + 8, explain why the equation f ( x) = 0 does not have any 26. For the function f x equal 7. ( ) = Asin π 5 x + k, it is known that f ( 3) = 7. Explain why f ( 13) must also

6 27. A person's height, in feet above the ground, on a Ferris wheel can be modeled using the equation h( t) = 45cos πt , where t is the time the rider has been on the wheel in minutes. a) What is the maximum height the rider will reach? b) How much time will it take to first reach this height if they get on at? Explain how you arrived at your answer. 28. On the axes below, graph one cycle of a cosine function with amplitude 3, period π 2, midline y = 1, and passing through the point ( 0,2).

7 29. a) On the axes below, sketch at least one cycle of a sine curve with an amplitude of 2, a midline at y = 3, and a period of 2π. 2 b) Explain any differences between a sketch of y = 2sin x π and the sketch from part a. 30. The quadratic function f x of g x ( )? ( ) has vertex at 5, 8 (1) ( 2, 11) (2) ( 12, 11) (3) ( 7, 3) ( ). If g x ( ) = f ( x + 7) 3, then what is the vertex (4) ( 12, 5) 31. What is the vertex of y = 1 2 x 8 + 3? (1) ( 4, 3) (2) ( 4, 3) (3) ( 8, 3) (4) ( 8, 3)

8 32. The function f x ( ) is shown below graphed in solid while the function g( x) is shown dashed. Which of the following equations describes the relationship between the two functions? (1) g( x) = f ( x) 6 (2) g( x) = 1 2 f ( x ) (3) g( x) = 2 f ( x) (4) g( x) = f 1 2 x 33. The range of the function f x the range of g x ( )? ( ) is 4 y 10. If g( x) = f ( x) + 3 then which of the following is (1) 7 y 7 (2) 5 y 15 (3) 13 y 1 (4) 3 y Which graph below shows an even function? (1) (3) (2) (4)

9 35) a) Algebraically determine whether f ( x) = x4 8 4x is an even function or an odd function. b) How can you tell by looking at the graph that the function is even or odd? 36. Which of the following could not be the probability that event A occurs? (1) (2) 0.49 (3) 1.25 (4) 37. The following table shows the results of a survey of people in terms of what type of breakfast they prefer. Based on the table, what is the probability that a person picked at random is over 40 and eats eggs for breakfast? Eats Eats (1) 0.32 (3) 0.63 Cereal Eggs (2) 0.47 (4) and under Over If a standard six sided die is rolled once, what is the probability that the number rolled is either an even or a multiple of 3? (1) 1 6 (2) 1 2 (3) 5 6 (4) Prime numbers are positive integers that are only divisible by 1 and themselves. If a random number is generated from 1 to 20, what is the probability that it is not prime? (1) 0.2 (2) 0.5 (3) 0.6 (4) 0.8

10 40. Of all the tourists who visit Florida, 38% of them will visit an amusement park and 54% will visit a beach. If 22% will visit both an amusement park and a beach, then what percent will visit either a park or a beach? (1) 16% (2) 70% (3) 30% (4) 92% 41. There is an 84% chance that a restaurant is open on Sunday and a 42% chance that it is open on Monday. If there is a 96% chance it is open on either Sunday or Monday, what is the probability that it is open both days? (1) 30% (2) 38% (3) 44% (4) 50% 42. A single standard six-sided die is rolled. What is the probability the roll is a multiple of three given that it is an even number? (1) 1 6 (2) 1 3 (3) 1 2 (4) The probability on any given work day that Kirk gets less than five hours of sleep the night before and doesn't shave is If there is a 0.80 probability on any given day that he doesn't shave and a 0.70 probability he gets less than five hours of sleep, then what is the probability he doesn't shave given that he got less than five hours of sleep? (1) 0.73 (2) 0.78 (3) 0.81 (4) If two events, A and B, are independent then which of the following statements is always true about their probabilities? ( ) = P( A) + P( B) (1) P A or B (2) P( A) + P( B) = 1 (4) P( B) = (3) P( A and B) = P( A) P( B) 1 P A ( )

11 45. In a local neighborhood, there are nine total children who range in age from three years old to eleven. Their names, genders, and ages are shown below arranged in alphabetical order. Answer the following questions. a) If a child is chosen at random, what is the probability it is a girl? Name Gender Age Evie Girl 7 Elliette Girl 8 b) What is the probability that a child chosen at random will have a name beginning with an E given they are a girl? Luca Boy 6 Max Boy 11 Niko Boy 5 Phoebe Girl 3 Rosie Girl 7 c) If a child is chosen at random, what the probability they are either a girl or older than 6? Zeke Boy 7 Zoe Girl A school system did not use up all of its snow days and will get four of them back as vacation days, either in April or in May. The student body was asked during which month they would prefer to have off from school. The results are presented below arranged by class. a) What percent of the students preferred having the days off in April? Round to the nearest percent. b) If a student from this survey were chosen at random, what is the probability they are an upperclassman (11 th or 12 th ) and preferred having days off in May? April May 9 th Grade th Grade th Grade th Grade c) If a student is chosen at random, what is the probability that they are a 10 th grader given that they preferred to have the days off in April? d) Is the preference for the month independent of the grade of the student? Explain how you made your determination.

12 47. In a survey of 500 high school students, 85% said they liked pizza while 68% said they liked hot dogs and 61% reported liking both. How many students in the survey reported liking neither pizza nor hot dogs? Show how you arrived at your answer. 48. Solve the following system of equations algebraically. 3x 5y + 2z = 5 5x + y + 6z = 33 2x +10y 3z = 40

13 49. Given a parabola that passes through the points : a) Substitute each point into the general form y = ax 2 + bx + c, to produce three equations with the three unknowns a, b, and c. b) Solve this system for a, b, and c and state the equation of the parabola.

14 50. In which of the following situations is a survey least likely to contain bias? (1) surveying a sample of people leaving a concert about their favorite musicians (2) surveying the members of a basketball team to determine the average height of high school boys (3) surveying people leaving a grocery store about their political party affiliation (4) surveying teenagers who use social networking websites about their favorite communication methods 51. In a survey of 236 freshmen, it was found that 151 of them owned cell phones. Which of the following is closest to the proportion of freshmen who do not own cell phones? (1) 0.21 (2) 0.36 (3) 0.43 (4) Students did poorly on a recent test, so their teacher decided to add 6 points to each student's grade. Which of the following statistical measures will not be affected by the addition of these points? (1) the mean score (3) the median score (2) the first quartile (4) the standard deviation of the scores 53. In 2013, the mean gas mileage for cars was 27.6 miles per gallon. If the distribution of gas mileage in cars is normal with a standard deviation of 3.8 miles per gallon, then what percent of cars had gas mileages between 20 and 30 miles per gallon? (1) 28% (2) 56% (3) 71% (4) 98% 54. The gestation time for cows is normally distributed with a mean of 284 days and a standard deviation of 12 days. At a local ranch, over the course of a year there are 820 calf births. Of these, how many would be expected to have a gestation time less than 270 days? (1) 12 (2) 78 (3) 100 (4) A value's percentile rank is the percent of a data set that lies at or below it. On a standardized test where the scores were normally distributed, Jeremy's score was 1.75 standard deviations above the mean. Which of the following is closest to his percentile rank? (1) 54 th (2) 67 th (3) 83 rd (4) 96 th

15 56. Mr. Richmond s traffic engineering class is trying to determine people s attitudes towards their evening commute. Students in his class decide to stop drivers on their way home to conduct this survey. Why would this survey method introduce bias into their results? 57. At a local PTA meeting, a sample of parents were surveyed to determine how many children they currently had attending school. Their results are shown in the frequency table below: Determine the mean, median, and standard deviation for this sample. Round any non-integer answers to the nearest tenth. Number of Children Number of Families Determine how many of the 55 families surveyed have a number of children that was within one standard deviation of the mean. Show your analysis The scores on a standardized test that Jeremy took were normally distributed with a mean of 82 and a standard deviation of 5. On the test, Jeremy scored a 90. a) What percent of students scored better than Jeremy on this test? Round to the nearest tenth of a percent. b) If Lisa took the same test, at a different time, and the scores were again normally distributed with a mean of 83 and a standard deviation of 6.4, what score, to the nearest integer, would make her percentile rank the same as Jeremy's? Show how you arrived at your answer.

16 59. Environmental engineers are trying to determine the characteristic fuel economy of cars on the road today. They surveyed 250 drivers about their cars and found the following distribution of fuel efficiencies as rated by the miles per gallon that a given car used while driving on the highway. Find the mean and standard deviation for this sample of cars. Round both answers to the nearest hundredth of a mile per gallon. Determine the percent of these cars that fall within one standard deviation of the mean. Would this sample be well modeled by a normal distribution? Explain your response. Fuel Efficiency (mpg) Number of Cars Water is flowing out of a reservoir such that the depth of the water is a decreasing function of the number of hours since water was released. Engineers measure the depth of the water and their results are shown in the table below. Time, x (hours) Depth of Water, y (ft) Find an exponential equation, of the form , that best fits this data set. Round your coefficients to the nearest hundredth. Then, use your equation to predict the depth of water after 2 days have elapsed. Round your depth to the nearest tenth of a foot.