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FST Name: _______________________ Final Exam Review Guide Period: ____ Date: _____________ Trigonometry Unit: I. Triangles a. Right Triangle Trig (SOH-CAH-TOA) b. Law of Sines and Law of Cosines II. Angles a. Drawing positive and negative b. Finding coterminal angles c. Converting from degrees to radians/radians to degrees d. Finding reference angles III. Evaluating trig functions a. No calculator b. ASTC IV. Graphing trig functions a. Amplitude b. Period c. Vertical and horizontal (phase) shifts You will be given the following information on the test: 6 2 3 2 1 4 60 o 1 Law of Sines: 1 sinA a sinB b 45 o sinC c 3 Round to the tenth. 45 o 60o S A T C Law of Cosines: c 2 a 2 b 2 2ab cosC In addition, I will give you a unit circle. 1. Solve for x. 30o a) b) 21 x o 16 c) x 64 45 14.5 19o 2. Two boats leave the same port at the same time. 91o x 46o The angle between their paths is 46o . One boat is traveling at a speed of 49 km/hr and the other boat is traveling at a speed of 34 km/hr. How far apart are the boats after 2.5 hours? 3. Nick and Patty are walking down a straight path in the woods. Nick is 100 yards ahead of Patty. In the distance, they each see a bald eagle in a tree. Patty’s line of sight to the bird makes an angle of 28o with the ground and Nick’s line of sight makes an angle of 52o with the ground. What is the altitude of the bald eagle in the tree? Convert measures in degrees to radians and measures in radians to degrees. 4. 120o 5. 42o 6. 5 3 7. 2 9 Find a coterminal angle x such that 0 x 360o or 0 x 2 . 8. 273o 9. 825o 10. 17 3 11. 43 8 Find the reference angle for the given angles. 12. 300o 13. 540o 14. 135o 15. 16. 17. 13 6 7 12 4 5 18. 42o 19. 11 12 20. 14 3 Draw the following angles on a coordinate plane. 21. 750o 22. 145o 23. 370o 24. 4 5 25. 8 3 All answers must be between 0 and 360 degrees. 26. the sin 0.8192. (No Calc) If sin125o 0.8192, find another angle, , such that 27. the tan 0.6249. If tan148o 0.6249, find another angle, , such that 28. the sec 1.0223. If sec12o 1.0223, find another angle, , such that 29. Find all values of such that sin 1 2 . Evaluate the function. (No Calc) 30. sin240o 31. csc135o 32. sec225o 33. tan(150o ) 34. cos(420o ) 35. 3 sin 4 36. tan 7 4 Answer the questions below. (No Calc) 37. If cos 38. If tan 39. If csc 4 3 5 13 and 180 360, then find sin and cot . and 0 180, then find csc and sec . 25 7 and 90 270, then find tan and cos . (Remember: 72 242 252 ) Find the sine, cosine, and tangent values based upon the following points. (No Calc) 40. 41. 24, 7 Remember: 7 24 25 6, 8 Remember: 6 8 10 2 2 2 2 2 2 Graph the following functions on the interval [0 2 ] . scaled appropriately and labeled. 42. 43. 44. 45. 46. y y y y y All axes must be 2sinx cos3x 4cos2x 5sin2x 2 cos2x 47. y 3 sin x 4 48. y 1 4 cos 1 4 x 49. y 2 3sin2 x 2 Graph the following functions until two full cycles are complete. axes must be scaled appropriately and labeled. 1 50. y cos x 3 51. y 5sin3x Write the equation of the function from the graph or the given information. 52. 53. y = asinbx amplitude = 5 period = 6 54. y = acosbx amplitude = 4 period = 2 vertical shift: up 2 units Statistics Unit 1. Determine if any of the data sets contain outliers. All Cars99 CityMPG HwyMpg FuelCapacity Acc030 Acc060 QtrMile 17 19 20.5 23 30 S1 = min S2 = Q1 CityMPG S3 = median S4 = Q3 S5 = max 23 26 28.5 31 38 10.3 14.5 16.2 18.45 23.7 2.4 3.3 3.5 3.9 4.5 5.6 8.8 9.5 10.9 12.5 14.1 16.8 17.4 18.2 19.1 HwyMPG FuelCapacity Acc030 Acc060 QtrMile 2. Below is a graph of the number of losses for National League teams during the 1999 season. Describe the distribution seen below. Also state the relationship between the mean and median. 3. The graph below shows Skull measurements of 150 male Egyptian skulls from 5 different time periods. Describe the distribution seen below. Also state the relationship between the mean and median. 4. The five number summary of a data set is (17, 27, 35, 49, 90) a) Are there any outliers in this data set? work) Explain. (Show all b) Is the mean less than, equal to, or greater than the median? Why? 5. Since Pascack Valley High School eliminated the use of bells, teachers have noticed an increase in tardiness. One statistics teacher decided to collect data on the accuracy of students’ and teachers’ watches. The ordered data from 9 randomly selected teachers and 9 randomly selected students are shown below. Negative values mean that the watch showed a time earlier than the true time (in minutes), positive values indicate later than the true time. Students Teachers –3.5 -6 –2 –2 –2 0 –1 0 –0.5 0.5 –0.5 1 1 1 2 1 3.5 1.5 a. Construct parallel boxplots using the given data. Show your plots on the grid below. Be sure to properly indicate outliers if any exist. –6 -5 -4 -3 -2 -1 0 1 2 3 4 b. Compare the two data sets. c. Based on the boxplots, which of these two groups, students or teachers, tends to have watches set closer to the true time? Explain your choice using appropriate statistical analysis. 1. The heights of all 10-year old children are normally distributed, with a mean of 138 cm and a standard deviation of 5 cm. a. Find the percent of heights greater than 133 cm. b. Find the percent of heights less than 130 cm. c. Find the percent of heights between 131 cm and 142 cm d. Find the percent of heights between 125 cm and 135 cm e. Find the approximate height of a 10-year old that is taller than at than 80% of all 10-year olds. f. Find the approximate height of a 10-year old that has 30% of the other 10-year olds taller than him/her. g. Find the heights of the middle 70%. 2. A school district administered IQ tests to all students in the district and found the distribution to be normal with a mean of 102 and the standard deviation of 12. a. Find the percent of scores between 96 and 110. b. Find the percent of scores between 105 and 120. c. Find the percent of scores less than 120. d. Find the percent of scores greater than 114. e. Find the approximate IQ score of a student that has a score less than 65% of other students IQ scores. f. What are the approximate IQ scores for the top 5% of the students? g. What is the smallest range containing 20% of the scores 4. Adult female Dalmatians weigh an average of 50 pounds with a standard deviation of 3.3 pounds. Adult female Boxers weigh an average of 57.5 pounds with a standard deviation of 1.7 pounds. One statistics teacher owns an underweight Dalmatian and an underweight Boxer. The Dalmatian weighs 45 pounds, and the Boxer weighs 52 pounds. Which dog is more underweight? Explain using percents and z-scores. 5. Marks on a Chemistry test follow a normal distribution with a mean of 65 and a standard deviation of 12. a. Approximately what percentages of the students have scores below 50? b. What is the approximate 90th percentile of the mark distribution? c. If the standard deviation calculated was wrong and actually 20% of the scores were below 50, what would be the correct standard deviation. 6. PROBABILITY REVIEW: 1. A calculator is chosen at random from a display case that contains four graphing calculators and eight scientific calculators. What is the probability that the calculator is graphing? 2. The employees of a company are in six departments. 31 are in sales, 54 are in research, 42 are in marketing, 20 are in engineering, 47 are in finance and 58 are in production. If one employees paycheck is lost, what is the probability that the employee is not in the research department? 3. In how many ways can you order the letters A, B, C, and D? 4. A computer generates random integers from 1 through 20. probability that the first two numbers are 5 or less? What is the 5. There are 34 students in your homeroom. Numbers from 1 through 34 are randomly assigned to the students to determine the order in which your school pictures will be taken. What is the probability that you and your best friend will be there first and second to get your pictures taken (in either order)? 6. Find the indicated probability: P(A) P(B) 1 4 1 5 P(A B) P(A B) 2 15 ? ? 7. You have time to listen to 3 songs on your iPod that contains 40 songs. If the iPod is on the random shuffle setting, what is the probability that your three favorite songs will be the three that play? 8. In how many ways can three letters be chosen from the alphabet? order of the three letters is not important. The 9. Five cards are dealt at random from a standard deck of 52 playing cards. What is the probability that all five cards are face cards or aces? 10. Suppose that you decide to buy a car. Among the options you may choose 6 paint colors (red, yellow, blue, brown, black, and white), 3 interior colors (brown, black, white), and 2 transmissions (manual, automatic). a. If a car dealer has, in the parking lot, one of every type of car made using these options, how many cars are there in the lot? b. How many cars of each color are in the parking lot? c. What is the probability that if you choose a car at random that it will be red? 11. Suppose you go out to a movie with 6 of your friends. many ways can you form a line at the ticket booth? In how 12. The probability that it will rain today is 0.4, and the probability that it will rain tomorrow is 0.2. The probability that it will rain both days is 0.1. What is the probability that it will rain today or tomorrow? 13. Consider all families that have exactly 3 children. What is the probability that a family of 3 children chosen at random has all 3 daughters?