Review Chapters 10-12

Transcription

1 Name: lass: ate: I: Review hapters Multiple hoice Identify the choice that best completes the statement or answers the question. Find the midpoint of the line segment with endpoints at the given coordinates. 1. Ê Á 11, 13 ˆ and Ê Á 4, 11 ˆ a. (0, 13) c. ( 7 2, 12) b. ( 15, 1) 2 d. (7, 24) Without writing the equation in standard form, state whether the graph of the equation is a parabola, circle, ellipse, or hyperbola x 2 280x + 40y 2 80y = 20 a. parabola c. hyperbola b. circle d. ellipse Find the geometric means in the following sequence. 3. 9,?,?,?,?, 9,216 a. 144, 576, 2,304, 9,231 c. 720, 1,080, 1,440, 1,800 b. 36, 144, 576, 2,304 d. 36, 144, 576, 2,304 Find the first three iterates of the function for the given initial value. 4. f(x) = x 2 + 2x + 3, x 0 = 1 a. x 1 = 0; x 2 = 3; x 3 = 18 c. x 1 = 6; x 2 = 51; x 3 = 2706 b. x 1 = 3; x 2 = 18; x 3 = 363 d. x 1 = 6; x 2 = 11; x 3 = ) Which of the following statements is (are) true for all positive integers? n(n + 1) = Ê ˆ n n + 1 2) n = Á 5 n a. oth statements are true. c. Only the first statement is true. b. None of the statements are true. d. Only the second statement is true. 1

2 Name: I: Which of the following is a counterexample for the given statement n + 6n is divisible by 12. a. n = 1 c. n = 3 b. n = 2 d. n = n + 4n 2 is divisible by 8. a. n = 1 c. n = 3 b. n = 2 d. n = 4 8. n 2 + n + 7 is prime. a. n = 1 c. n = 3 b. n = 2 d. n = n + 1 is divisible by 3. a. n = 1 c. n = 2 b. n = 3 d. n = n 3 + n + 1 is a prime. a. n = 1 c. n = 3 b. n = 2 d. n = n + 4 n is not a prime. a. n = 1 c. n = 3 b. n = 2 d. n = n + 2n is a divisible by 4. a. n = 1 c. n = 3 b. n = 2 d. n = n + 1 is divisible by 6. a. n = 1 c. n = 3 b. n = 2 d. n = n 3 + n 2 + n is divisible by 3. a. n = 1 c. n = 3 b. n = 2 d. n = n 2 + n + 5 is a prime. a. n = 1 c. n = 3 b. n = 2 d. n = lan s online test has 10 true-false questions and 5 multiple-choice questions. Each multiple-choice question has 4 different answer choices. How many different choices for answering the 15 questions are possible? a. 15 c. 300 b. 100 d. 1,048,576 2

3 Name: I: 17. garment company has been contracted to make uniforms for players of a football tournament. There are 12 different colors and 12 designs selected for the uniforms. How many combinations of colors and designs can be made for the uniforms of different teams? a. 12 c. 64 b. 24 d There are 9 children playing in a playground. In a game, they all have to stand in a line such that the youngest child is at the beginning of the line. How many ways can the children be arranged in the line? a. 40,320 c. 16,777,216 b. 362,880 d. 387,420,489 Evaluate the given expression. 19. (9, 6) a. 84 c. 60,480 b. 54 d. 36 Laura has moved to a new apartment. Her schoolbooks comprising of different subjects are mixed in a bag during the move. Four books are of mathematics, three are English, and six are science. If Laura opens the bag and selects books at random, find the given probability. 20. P(3 English books) a b c. d etermine whether the given event is independent or dependent. Then find the probability. 21. fruit basket has a capacity of 12 pieces of fruit. When harles randomly chooses a fruit from the basket containing apples and oranges, the odds are 5 to 3 that he will select an orange. What is the probability that he chooses 2 oranges, if fruits are not replaced? a. dependent, 5 14 b. dependent, c. independent, 5 16 d. independent, 5 14 Each letter of the alphabet is written on a different piece of paper. These pieces of paper are folded and kept in a bag. One folded paper is drawn at random from this bag. 22. What is the probability of selecting a vowel or a letter from the word palindrome? a c b d

4 Name: I: 23. The table shows the number of children (in hundreds) visiting the Mconalds counter outside Jackson High School on thirteen different days Find the mean, median, and mode (in hundreds) of the number of children. a. 2.3, 2.5, and 2.2 c. 2.4, 2.5, and 2.5 b. 2.4, 2.1, and 2.5 d. 2.4, 2.5, and The table shows the population (in millions) of five continents. ontinents Population (millions) frica sia ustralia Europe North merica Find the mean and median of the population in millions. a and c and b and d and The table shows the gross national product (in thousands) of the following countries. ountry GNP ($) ustralia 400 hina 1000 France 1400 Germany 2100 Japan 4100 United Kingdom 1400 United States 8900 Find the mean, median, and mode of the gross national product. a. 2757, 1400, and 1400 c. 2757, 2100, and 1400 b. 3587, 1400, and 400 d. 3587, 1400, and 1400 Find the variance and standard deviation of the given set of data to the nearest tenth. 26. {9.1, 13.6, 24.4, 35.7, 30, 45, 12.7, 47.8, 29, 66} a. variance = 289, standard deviation = 17 b. variance = 289, standard deviation = c. variance = 321.1, standard deviation = 17.9 d. variance = 17, standard deviation = 289 4

5 Name: I: The measurement of the height of 600 students of a college is normally distributed with a mean of 175 centimeters and a standard deviation of 5 centimeters. 27. What percent of students are taller than 175 centimeters? a. 34 c. 68 b. 50 d. 84 etermine whether the following situation would produce a random sample. Write Yes or No and explain your answer. 28. surveying two hundred students at a school basketball game to find the students favorite sport a. Yes, students preferring different sports may be in the group. b. Yes, this may be the only sporting event occurring that day. c. No, students attending this event are more likely to enjoy basketball. d. No, student attendance may have been required at this event. 29. surveying students of an engineering college to determine how often people in that city visit a restaurant near to that college a. No, the average person of the city might have a different frequency of visiting that restaurant than an average college student. b. Yes, the remaining people of the city might be visiting that restaurant more often than the college students. c. No, the remaining people of the city might be visiting that restaurant less often than the college students. d. Yes, the students of that college might be visiting that restaurant more frequently. 30. The names of all the students of a class are written on slips of paper. These slips are folded and kept in a bowl. student whose eyes are closed draws a handful of slips to find a sample of students in the class. a. Yes, all the students have equal chances of being selected. b. Yes, the slips on the top have higher chances of being selected. c. No, all the students have equal chances of being selected. d. No, the slips can have some sort of identification marks. Short nswer 31. The figure below shows the trajectory followed by a tennis ball on the first volley. ssuming that the ball was served at the origin, write an equation of the parabola that models the trajectory of the ball. 5

6 Name: I: 32. Suppose the maximum height jumped by the high jumper is 2.36 meters. ssuming that the jumper started jumping at the origin, write an equation of the parabola that models the path followed by the high jumper. 33. The base of a building is an ellipse that has a major axis of 615 feet and a minor axis of 510 feet. Write an equation in standard form for the base of the building if the origin is at the central point of the base of the building. 34. ssume that Halley s comet follows an elliptical path. Find the equation of the path of Halley s comet by assuming the sun at the origin. The length of the major axis of the orbit of Halley s comet is approximately 36 astronomical units (36 U), and the length of the minor axis is 10 U. 35. t its closest distance, Saturn is million miles from the center of the sun. t its farthest point, Saturn is million miles from the center of the sun. Write an equation for the orbit of Saturn, assuming that the center of the orbit is the origin. 36. Helen and Greg live 4 miles apart and are talking on the phone. Helen hears a crack of thunder, and 6 seconds later Greg hears the crack. Find an equation that gives the possible places where the lightning could have occurred if sound travels about 1 mile every 5 seconds. 37. curved mirror is placed in a store for a wide-angle view of the room. The equation x 2 25 y 2 = 1 models the 144 curvature of the mirror. small security camera is placed 21 meters from the vertex of the mirror so that a diameter of 20 meters of the mirror is visible. If the back of the room lies on x = 19, what width of the back of the room is visible to the camera? 38. Isaac is practicing for an upcoming cycling competition. The first day he practiced for 45 minutes. He increases his practicing time by 15 minutes each day. How much time will he spend practicing on the 25th day? Find S n for each arithmetic series described. 39. a 1 = 56, n = 16, a n = radley dropped a ball from a roof 16 feet high. Each time the ball hits the ground, it bounces 3 the previous 5 height. Find the height the ball will bounce after hitting the ground the fourth time. 6

7 Name: I: 41. rew dropped a tennis ball from a 42-foot-high terrace. fter striking the ground, the ball rebounds 30% of the height from which it fell. For every rebound of the ball, there is another rebound, 30% as high. etermine the vertical distance the ball travels before coming to a rest. 42. lex won a $1,000,000 lottery prize. He was given $50,000 right away. The lottery commission then put just enough money into an account to pay him $50,000 per year for the next 19 years, leaving a zero balance in the account after the 19th payment from the account. The account has a fixed annual interest rate of 5.2%. The recursive formula a n = 1.052a n 1 50,000 determines the amount of money left in the account after the nth payment. Here, a 0 is the amount of money that the lottery commission put into the account. alculate the amount left in the account after four payments. 43. dancer has to choose 2 songs out of 10 songs in order to perform in a show. How many ways can he choose the songs? etermine whether the events are independent or dependent. Then find the probability. 44. What is the probability of getting 3 each time if a six-sided die numbered 1 6 is rolled 4 times? The table below shows the ages of the senior members in a retirement community Which measure of central tendency best represents the data? Explain your answer. The heart rates of a number of people are normally distributed with a mean of 85 beats per minute and a standard deviation of 5 beats per minute. 46. bout what percent of the heart rates is more than 90 beats per minute? 47. bout what percent of the heart rates is less than 75 beats per minute? 48. The average amount of time that a student in Mr. eck s math class spends on homework each day is 2.5 hours. In this class, 75% of the students spend less than how many hours per day on homework? 49. In a survey, 49% of the people said that they like winter better than summer. The margin of error was 2%. How many people were surveyed? 50. survey found that 61% of the people polled prefer juice after exercise. Suppose the survey had a margin of error of 5%. How many people were surveyed? 7

8 Name: I: Essay 51. Mr. ameron purchased a motion detector light and installed it in the center of his backyard. It can detect motion within a range of 10.5 units in any direction. person walks northwest through the backyard along a line defined by the equation y = 2x 2. Explain how system of equations apply to the technology of detector light. Include a linear-quadratic system of equations that applies to this situation and the coordinates of the point at which the motion detector light will turn on. ssume the center of the backyard is the origin of the coordinate system. 52. Mr. asim teaches dance and music classes. He began with 10 students. He enrolls 5 new students each month. Write a formula that can be used to find the number of students that Mr. asim has in n months. Explain the relationship between n and a n + 1 in the formula where n represents the number of months and a n + 1 represents the number of students that Mr. asim has in n + 1 months. Graph the equation assuming that n is the independent variable and a n + 1 is the dependent variable. Tell the meaning of the number of learners in the first month and the meaning of the increase in the number of students each month in the context of the graph. 53. radioactive isotope with an initial amount of 75 pounds decays to 50% each year for four years. Explain how decay of a radioactive substance is related to a geometric series. Include an explanation of how the situation could be changed to make it better to use a formula than to add terms. 54. efore coming to rest, a rotating flywheel makes 450 revolutions in the first minute and in each minute afterward makes 3 as many revolutions as in the preceding minute. Explain how an infinite geometric series 8 can be used to determine the number of revolutions the flywheel makes before it comes to rest. 55. Imagine the positive integers as a never-ending multi-story building. Explain how this concept can help us prove statements about numbers. 56. Two cards are drawn in succession from a standard deck of cards without replacement. Find each of the following probabilities. a. P(both cards are multiples of 5) b. P(both cards are spades) c. P(both are black aces) 57. The weather report predicted that the possibility of snow in the town on Friday is 2 in 5 and the chance of snowfall to be significant enough to require closing of schools is 1 in 5. The weather forecasting also reported that the possibility of rainstorm on Wednesday in the town is 4 in 5 and the chance of rainstorm to be significant enough to require closing of schools is 2 in 9. Explain how probability helps in weather forecasting. Include a description of the meaning of success and failure in the case of snowfall. 58. mani s family is planning a three-day trip to the mountains. weather forecast gives the probability of rain each day as 15%. Explain how probability applies to this situation. ssume that the daily probabilities of rain are independent. Explain how the predicted value of daily rain can be used to find the possibilities of rainfall occurring on 0, 1, 2, or 3 days of their vacation. Include an explanation of why the daily probabilities of rain might not be independent. 8

9 Name: I: 59. asim is in charge of collecting contributions for a food bank. So far he has received the following contributions: $45 $55 $20 $95 $100 $65 $75 $50 $80 $45 $20 $80 $100 $25 $70 $40 Find the mean, median, and mode of the contributions. The next potential contributor wants to give an amount in line with the other contributions so he asks about an acceptable amount to give. Which measure of central tendency should be used to answer his question? How will the measures of central tendency be affected if $10 is added to each contribution? 60. The table below lists the ages of the employees of a certain company. ge in Years Number of Employees less than more than a. Explain how the ages of the company s employees are distributed. b. Include a histogram of the given data, and an explanation of whether you think the data is normally distributed. 9

10 I: Review hapters nswer Section MULTIPLE HOIE 1. NS: The coordinates of the midpoint are the means of the coordinates of the endpoints. Take the mean of the x-coordinates and the y-coordinates of the endpoints. Take the mean of the coordinates according to their integral values. id you consider the mean of the coordinates of the endpoints? PTS: 1 IF: verage REF: Lesson 10-1 OJ: Find a midpoint of a segment on the coordinate plane. TOP: Find the midpoint of a segment on the coordinate plane. KEY: Midpoint Formula istance Formula Midpoint of a Segment 2. NS: You can determine the type of conic section represented by the equation x 2 + xy + y 2 + x + Ey + F = 0, where = 0, by checking the relationship between and. The coefficients of x 2 and y 2 are both non zero. The coefficients of x 2 and y 2 are not equal. The coefficients of x 2 and y 2 have the same signs. PTS: 1 IF: asic REF: Lesson 10-6 OJ: Identify conic sections from their equations. ST: 17.0 TOP: Identify conic sections from their equations. KEY: onic Sections Equations of onic Sections Identify onic Sections MS: Key 3. NS: Use the formula a n = a 1 r n 1 to find the nth term of a geometric sequence. id you substitute the correct values? id you check the order of the answer? id you use the correct formula? PTS: 1 IF: verage REF: Lesson 11-3 OJ: Find geometric means. ST: 22.0 TOP: Find geometric means. KEY: Sequences Geometric Sequences Geometric Means 1

11 I: 4. NS: Find the value of the function for the given initial value to get the first iterate x 1. Substitute this value in the function to obtain the second iterate x 2, and so on. id you use the correct equation? heck the initial value. id you calculate correctly? PTS: 1 IF: verage REF: Lesson 11-6 OJ: Iterate functions. TOP: Iterate functions. KEY: Iterate Functions 5. NS: Verify the statements for some integer and introduce an inductive hypothesis. id you use mathematical induction? id you perform the required steps correctly? o you have a counterexample? PTS: 1 IF: dvanced REF: Lesson 11-8 OJ: Prove statements by using mathematical induction. ST: 21.0 TOP: Prove statements by using mathematical induction. KEY: Mathematical Induction Proofs 6. NS: Substitute positive integers in place of n and verify. heck the given statement. id you substitute correctly in the statement? id you calculate correctly? PTS: 1 IF: verage REF: Lesson 11-8 OJ: isprove statements by finding a counterexample. ST: 21.0 TOP: isprove statements by finding a counterexample. KEY: Proofs ounterexamples 2

12 I: 7. NS: Substitute positive integers in place of n and verify. heck the given statement. id you substitute correctly? id you calculate correctly? PTS: 1 IF: verage REF: Lesson 11-8 OJ: isprove statements by finding a counterexample. ST: 21.0 TOP: isprove statements by finding a counterexample. KEY: Proofs ounterexamples 8. NS: Substitute positive integers in place of n and verify. id you substitute correctly in the given statement? heck the given statement. id you calculate correctly? PTS: 1 IF: verage REF: Lesson 11-8 OJ: isprove statements by finding a counterexample. ST: 21.0 TOP: isprove statements by finding a counterexample. KEY: Proofs ounterexamples 9. NS: Substitute positive integers in place of n and verify. id you substitute correctly in both sides of the statement? id you calculate correctly? heck the given statement. PTS: 1 IF: verage REF: Lesson 11-8 OJ: isprove statements by finding a counterexample. ST: 21.0 TOP: isprove statements by finding a counterexample. KEY: Proofs ounterexamples 3

13 I: 10. NS: Substitute positive integers in place of n and verify. heck the given statement. id you substitute correctly? id you calculate correctly? PTS: 1 IF: verage REF: Lesson 11-8 OJ: isprove statements by finding a counterexample. ST: 21.0 TOP: isprove statements by finding a counterexample. KEY: Proofs ounterexamples 11. NS: Substitute positive integers in place of n and verify. id you substitute correctly in both sides of the statement? id you calculate correctly? heck the statement. PTS: 1 IF: verage REF: Lesson 11-8 OJ: isprove statements by finding a counterexample. ST: 21.0 TOP: isprove statements by finding a counterexample. KEY: Proofs ounterexamples 12. NS: Substitute positive integers in place of n and verify. id you substitute correctly in the statement? id you calculate correctly? heck the given statement. PTS: 1 IF: verage REF: Lesson 11-8 OJ: isprove statements by finding a counterexample. ST: 21.0 TOP: isprove statements by finding a counterexample. KEY: Proofs ounterexamples 4

14 I: 13. NS: Substitute positive integers in place of n and verify. id you substitute correctly in the statement? heck the statement. id you calculate correctly? PTS: 1 IF: verage REF: Lesson 11-8 OJ: isprove statements by finding a counterexample. ST: 21.0 TOP: isprove statements by finding a counterexample. KEY: Proofs ounterexamples 14. NS: Substitute positive integers in place of n and verify. id you substitute correctly in both sides of the statement? heck the statement. id you calculate correctly? PTS: 1 IF: verage REF: Lesson 11-8 OJ: isprove statements by finding a counterexample. ST: 21.0 TOP: isprove statements by finding a counterexample. KEY: Proofs ounterexamples 15. NS: Substitute positive integers in place of n and verify. id you substitute correctly in the statement? id you calculate correctly? heck the statement. PTS: 1 IF: verage REF: Lesson 11-8 OJ: isprove statements by finding a counterexample. ST: 21.0 TOP: isprove statements by finding a counterexample. KEY: Proofs ounterexamples 5

15 I: 16. NS: y the Fundamental ounting Principle, the total number of ways in which lan can answer the 15 questions is Recalculate the ways of attempting a question. How many possible answer choices are there in multiple-choice questions? Have you used the Fundamental ounting Principle correctly? PTS: 1 IF: dvanced REF: Lesson 12-1 OJ: Solve problems involving independent events. ST: {Key}18.0 TOP: Solve problems involving independent events. KEY: Solve Problems Probability Independent Events MS: Key 17. NS: Use the Fundamental ounting Principle to find the number of combinations of colors and designs for the uniforms. There are more combinations possible with 12 colors and 12 designs. The Fundamental ounting Principle must be used. id you apply the Fundamental ounting Principle correctly? PTS: 1 IF: verage REF: Lesson 12-1 OJ: Solve problems involving independent events. ST: {Key}18.0 TOP: Solve problems involving independent events. KEY: Solve Problems Probability Independent Events MS: Key 18. NS: The selection of children for various positions in the line is a dependent event. Recalculate the number of ways of arrangement. What type of event do the selections for the second to the eighth positions in the line involve? What type of event does the arrangement of nine children in a line involve? PTS: 1 IF: dvanced REF: Lesson 12-1 OJ: Solve problems involving dependent events. TOP: Solve problems involving dependent events. KEY: Solve Problems Probability ependent Events ST: {Key}18.0 MS: Key 6

16 I: 19. NS: The number of combinations of n distinct objects taken r at a time is given by n! (n, r) = (n r)! r!. What is the combinations formula? id you use the permutaiton formula? id you substitute the correct numbers into the formula? PTS: 1 IF: verage REF: Lesson 12-2 OJ: Solve problems involving combinations. ST: {Key}18.0 TOP: Solve problems involving combinations. KEY: Solve Problems Probability ombinations MS: Key 20. NS: Use the Fundamental ounting Principle to find the number of successes (3, 3) (4, 0) (6, 0). etermine the probability P(3 English books) by using the probability formula s (3, 3) (4, 0) (6, 0) =. s + f (13,3) id you substitute the correct values in the formula? id you use the correct formula? You have added the combinations. PTS: 1 IF: verage REF: Lesson 12-3 OJ: Use combinations and permutations to find probability. ST: {Key}19.0 TOP: Use combinations and permutations to find probability. KEY: Probability MS: Key 21. NS: etermine the type of event and then apply the appropriate formula to find the solution. The formula used to calculate the probability of dependent events is incorrect. The selection of fruit is done without replacement. id you identify the type of event correctly? PTS: 1 IF: dvanced REF: Lesson 12-4 OJ: Find the probability of two dependent events. TOP: Find the probability of two dependent events. MS: Key ST: {Key}1.0 {Key}2.0 KEY: Probability ependent Events 7

17 I: 22. NS: Identify the type of event and calculate the probability by using the correct formula. What is the number of vowels in the given word? This is not a mutually exclusive event. How is the probability of such events calculated? PTS: 1 IF: dvanced REF: Lesson 12-5 OJ: Find the probability of inclusive events. ST: {Key}1.0 TOP: Find the probability of inclusive events. KEY: Probability Inclusive Events MS: Key 23. NS: dding the given values and dividing the sum by the number of values gives the mean of the given set of values. The median of a group of values is the value which divides the group into two equal parts. The mode of a group of values is the value which occurs most frequently in the given group. id you apply the correct formula for calculating the mean and the mode? id you apply the correct formula for calculating the median? id you find the correct mode? PTS: 1 IF: verage REF: Lesson 12-6 OJ: Use measures of central tendency to represent a set of data. ST: {Key}7.0 TOP: Use measures of central tendency to represent a set of data. KEY: Measures of entral Tendency ata Represent ata MS: Key 24. NS: dding the given values and dividing the sum by the number of values gives the mean of the given set of values. The median of a group of values is the value which divides the group into two equal parts. id you calculate the mean of the populations precisely? id you apply the correct formula for calculating the median? You have interchanged the values of the mean and the median. PTS: 1 IF: verage REF: Lesson 12-6 OJ: Use measures of central tendency to represent a set of data. ST: {Key}7.0 TOP: Use measures of central tendency to represent a set of data. KEY: Measures of entral Tendency ata Represent ata MS: Key 8

18 I: 25. NS: dding the given values and dividing the sum by the number of values gives the mean of the given set of values. The median of a group of values is the value which divides the group into two equal parts. The mode of a group of given value is the value which occurs most frequently in the given group. id you apply the correct formula for calculating the mean and the mode? id you apply the correct formula for calculating the median? id you apply the correct formula for calculating the mean? PTS: 1 IF: verage REF: Lesson 12-6 OJ: Use measures of central tendency to represent a set of data. ST: {Key}7.0 TOP: Use measures of central tendency to represent a set of data. KEY: Measures of entral Tendency ata Represent ata MS: Key 26. NS: pply the appropriate formula to find the mean first, and then find the variance and the standard deviation. id you apply the correct formula for calculating the standard deviation? id you apply the correct formula for calculating the variance? You have interchanged the values. PTS: 1 IF: verage REF: Lesson 12-6 OJ: Find measures of variation for a set of data. TOP: Find measures of variation for a set of data. MS: Key 27. NS: The mean of the given distribution is 175. ST: {Key}7.0 KEY: Measures of Variation ata This is the number of students having height between 175 centimeters and 180 centimeters. The mean of this distribution is 175 centimeters. The data in a normal distribution is equally distributed on both sides of its mean value. PTS: 1 IF: verage REF: Lesson 12-7 OJ: Solve problems involving normally distributed data. ST: {Key}4.0 {Key}5.0 TOP: Solve problems involving normally distributed data. KEY: Solve Problems ata Normal istribution MS: Key 9

19 I: 28. NS: sample of size n is unbiased when every possible sample of size n of a population has an equal chance of being selected. The identification of the type of sample is incorrect. This is not a random sample. That it is the only sporting event of the day does not guarantee a sample of all students. The explanation is not a valid assumption. PTS: 1 IF: verage REF: Lesson 12-9 OJ: etermine whether a sample is biased. ST: {Key}20.0 TOP: etermine whether a sample is biased. KEY: Samples ias MS: Key 29. NS: sample of size n is unbiased when every possible sample of size n of a population has an equal chance of being selected. The identification of the type of sample is incorrect. The remaining people of the city might be visiting that restaurant more often than the college students. Some other method should be selected to produce an unbiased sample. PTS: 1 IF: verage REF: Lesson 12-9 OJ: etermine whether a sample is biased. ST: {Key}20.0 TOP: etermine whether a sample is biased. KEY: Samples ias MS: Key 30. NS: sample of size n is unbiased when every possible sample of size n of a population has an equal chance of being selected. In the case of an unbiased sample, such factors are controlled. The identification of the type of sample is incorrect. The eyes of the student selecting the slips are closed. PTS: 1 IF: verage REF: Lesson 12-9 OJ: etermine whether a sample is biased. TOP: etermine whether a sample is biased. MS: Key ST: {Key}20.0 KEY: Samples ias 10

20 I: SHORT NSWER 31. NS: y = ( x 90) Ê Find an equation of the parabola of the form x = aê Á y k ˆ 2 + h, with vertex Ê Áh, k ˆ and focus h, k + 1 ˆ Á 4a. PTS: 1 IF: verage REF: Lesson 10-2 OJ: Solve multi-step problems. ST: 16.0 TOP: Solve multi-step problems. KEY: Multi-step Problem Solving MS: Key 32. NS: y = 1.05( x 1.5) Ê Find an equation of the parabola of the form x = aê Á y k ˆ 2 + h, with vertex Ê Áh, k ˆ and focus h, k + 1 ˆ Á 4a. PTS: 1 IF: dvanced REF: Lesson 10-2 OJ: Solve multi-step problems. ST: 16.0 TOP: Solve multi-step problems. KEY: Multi-step Problem Solving MS: Key 33. NS: x y = 1 ( x h) 2 2 (y k) The equation of the ellipse is + = 1, where Êh, k a 2 b 2 Á ˆ is the center of the ellipse, 2a is the length of the major axis, and 2b is the length of the minor axis. PTS: 1 IF: asic REF: Lesson 10-4 OJ: Solve multi-step problems. ST: 16.0 TOP: Solve multi-step problems. KEY: Multi-step Problem Solving MS: Key 34. NS: x y 2 25 = 1 ( x h) 2 2 (y k) The equation of the ellipse is + = 1, where Êh, k a 2 b 2 Á ˆ is the center of the ellipse, 2a is the length of the major axis, and 2b is the length of the minor axis. PTS: 1 IF: verage REF: Lesson 10-4 OJ: Solve multi-step problems. ST: 16.0 TOP: Solve multi-step problems. KEY: Multi-step Problem Solving MS: Key 11

21 I: 35. NS: x y = 1 ( x h) 2 2 (y k) The equation of the ellipse is + = 1, where Êh, k a 2 b 2 Á ˆ is the center of the ellipse, 2a is the length of the major axis, and 2b is the length of the minor axis. PTS: 1 IF: dvanced REF: Lesson 10-4 OJ: Solve multi-step problems. ST: 16.0 TOP: Solve multi-step problems. KEY: Multi-step Problem Solving MS: Key 36. NS: x y = 1 The equation for the hyperbola with a transverse axis of length 2a units (distance between Helen and Greg) and coordinates of the foci as Ê Á±c, 0ˆ, where c = a 2 + b 2 is x 2 a y 2 2 b = 1. 2 PTS: 1 IF: verage REF: Lesson 10-5 OJ: Solve multi-step problems. ST: 16.0 TOP: Solve multi-step problems. KEY: Multi-step Problem Solving MS: Key 37. NS: m For the hyperbola with the equation x 2 a y 2 2 b 2 = 1, the coordinates of the vertices are Ê Á0, ± aˆ and the coordinates of the foci are Ê Á0, ± cˆ, where c = a 2 + b 2. The equation of the asymptotes is y =± b a x. PTS: 1 IF: dvanced REF: Lesson 10-5 OJ: Solve multi-step problems. ST: 16.0 TOP: Solve multi-step problems. KEY: Multi-step Problem Solving MS: Key 38. NS: 6.75 h pply the formula for the nth term of an arithmetic sequence: a n = a 1 + ( n 1)d, where a 1 is the first term, a n is the nth term, and d is the common difference. PTS: 1 IF: dvanced REF: Lesson 11-1 OJ: Solve multi-step problems. ST: 22.0 TOP: Solve multi-step problems. KEY: Multi-step Problem Solving 12

22 I: 39. NS: 1632 Use the formula S n = n 2 Ê Á a + a 1 n ˆ to find the sum of the arithmetic series. PTS: 1 IF: asic REF: Lesson 11-2 OJ: Solve multi-step problems. ST: 22.0 {Key}23.0 TOP: Solve multi-step problems. KEY: Multi-step Problem Solving MS: Key 40. NS: about 2.1 ft pply the formula for the nth term of a geometric sequence: a n = a 1 r n 1, where a 1 is the first term, a n is the nth term, and r is the common ratio. PTS: 1 IF: verage REF: Lesson 11-3 OJ: Solve multi-step problems. ST: 22.0 TOP: Solve multi-step problems. KEY: Multi-step Problem Solving 41. NS: 78 ft The distance is given by the following series ë This series can be rewritten as the sum of two infinite geometric series as follows. ( ë) + ( ë) Use the formula S = a 1 1 r to find the sum of the infinite geometric series. PTS: 1 IF: dvanced REF: Lesson 11-5 OJ: Solve multi-step problems. ST: 22.0 {Key}23.0 TOP: Solve multi-step problems. KEY: Multi-step Problem Solving MS: Key 42. NS: about $947, Use the recursive formula a n = 1.052a n 1 50,000 for n = 1 to 4. The amount left in the account after four payments is given by a 4. PTS: 1 IF: dvanced REF: Lesson 11-6 OJ: Solve multi-step problems. TOP: Solve multi-step problems. KEY: Multi-step Problem Solving 43. NS: 45 The number of combinations of n distinct objects taken r at a time is given by n! (n, r) = (n r)! r!. PTS: 1 IF: verage REF: Lesson 12-2 OJ: Solve multi-step problems. ST: {Key}18.0 TOP: Solve multi-step problems. KEY: Multi-step Problem solving MS: Key 13

23 I: 44. NS: independent; Find the type of event and then determine the probability by applying the appropriate formula. PTS: 1 IF: asic REF: Lesson 12-4 OJ: Solve multi-step problems. ST: {Key}1.0 {Key}2.0 TOP: Solve multi-step problems. KEY: Multi-step Problem solving MS: Key 45. NS: The mean, median, and mode are nearly equal and seem to represent the center of the data. dding the given values and dividing the sum by the number of values gives the mean of the given set of values. The median of a group of values is the value which divides the group into two equal parts. The mode of a group of values is the value which occurs most frequently in the given group. PTS: 1 IF: verage REF: Lesson 12-6 OJ: Solve multi-step problems. ST: {Key}7.0 TOP: Solve multi-step problems. KEY: Multi-step Problem solving MS: Key 46. NS: 16% alculate the percent of data of this normal distribution lying between the values 90 beats per minute and 110 beats per minute. PTS: 1 IF: dvanced REF: Lesson 12-7 OJ: Solve multi-step problems. ST: {Key}4.0 {Key}5.0 TOP: Solve multi-step problems. KEY: Multi-step Problem solving MS: Key 47. NS: 2.5% alculate the percent of data of this normal distribution lying between the values 65 beats per minute and 75 beats per minute. PTS: 1 IF: dvanced REF: Lesson 12-7 OJ: Solve multi-step problems. ST: {Key}4.0 {Key}5.0 TOP: Solve multi-step problems. KEY: Multi-step Problem solving MS: Key 48. NS: 3.47 hours Use the exponential distribution function for the probability that a nnumber is less than some other number. Substitute appropriate values into the function equation and solve to find what the number must be to result in the given probability. PTS: 1 IF: dvanced REF: Lesson 12-8 OJ: Solve multi-step problems. ST: {Key}4.0 TOP: Solve multi-step problems. KEY: Multi-step Problem solving MS: Key 14

24 I: 49. NS: 2499 pê Á1 pˆ Use the formula ME = 2, where ME is the margin of error, p is the percent of people in a sample n responding in a certain way, n is the size of the sample, for the margin of sampling error to find the number of people surveyed. PTS: 1 IF: dvanced REF: Lesson 12-9 OJ: Solve multi-step problems. ST: {Key}20.0 TOP: Solve multi-step problems. KEY: Multi-step Problem solving MS: Key 50. NS: about 381 pê Á1 pˆ Use the formula ME = 2, where ME is the margin of error, p is the percent of people in a sample n responding in a certain way, n is the size of the sample, for the margin of sampling error to find the number of people surveyed. PTS: 1 IF: dvanced REF: Lesson 12-9 OJ: Solve multi-step problems. ST: {Key}20.0 TOP: Solve multi-step problems. KEY: Multi-step Problem solving MS: Key 15

25 I: ESSY 51. NS: system of equations can be used to represent the location of the point at which the motion detector light will turn on. linear-quadratic system of equations would be x 2 + y 2 = and y = 2x 2. The motion detector light will turn on at the point Ê Á3.88, 9.76ˆ approximately. Systems of equations can be used to detect the points of movement. system of linear-quadratic equations that applies to the situation is x 2 + y 2 = and y = 2x 2. Solve the system to find the point at which the motion detector light will turn on. ssessment Rubric Level 3 Superior *Shows thorough understanding of concepts. *omputation is correct. *Written explanation is exemplary. *iagram/table/chart is accurate (as applicable). *Goes beyond requirements of problem. Level 2 Satisfactory *Shows understanding of concepts. *omputation is mostly correct. *Written explanation is effective. *iagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements of problem. Level 1 Nearly Satisfactory *Shows understanding of most concepts. *omputation is mostly correct. *Written explanation is satisfactory. *iagram/table/chart is mostly accurate (as applicable). *Satisfies most of the requirements of problem. Level 0 Unsatisfactory *Shows little or no understanding of the concept. *omputation is incorrect. *Written explanation is not satisfactory. *iagram/table/chart is not accurate (as applicable). *oes not satisfy requirements of problem. PTS: 1 IF: dvanced REF: Lesson 10-7 OJ: Solve problems and show solutions. KEY: Problem Solving Show Solutions TOP: Solve problems and show solutions. 16

26 I: 52. NS: The formula a n + 1 = n, n = 0,1,2, can be used to find the number of students that Mr. asim has in n + 1 months. The relationship between n and a n + 1 is linear. In the first month, Mr. asim has 10 students, represented by the y-intercept of the graph. lso, an increase of five in the number of learners each month is represented by the slope of the graph. The formula for the nth term of an arithmetic sequence: a n = a 1 + ( n 1)d can be used to find the number of learners in n months. relationship of the form y = mx + c where y is the dependent variable, x is the independent variable, and m and c are constants, is called a linear relationship between x and y. Here, m represents the slope and c represents the y-intercept of the graph of the equation ssessment Rubric Level 3 Superior *Shows thorough understanding of concepts. *omputation is correct. *Written explanation is exemplary. *iagram/table/chart is accurate (as applicable). *Goes beyond requirements of problem. Level 2 Satisfactory *Shows understanding of concepts. *omputation is mostly correct. *Written explanation is effective. *iagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements of problem. Level 1 Nearly Satisfactory 17

27 I: *Shows understanding of most concepts. *omputation is mostly correct. *Written explanation is satisfactory. *iagram/table/chart is mostly accurate (as applicable). *Satisfies most of the requirements of problem. Level 0 Unsatisfactory *Shows little or no understanding of the concept. *omputation is incorrect. *Written explanation is not satisfactory. *iagram/table/chart is not accurate (as applicable). *oes not satisfy requirements of problem. PTS: 1 IF: dvanced REF: Lesson 11-1 OJ: Solve problems and show solutions. ST: 22.0 TOP: Solve problems and show solutions. KEY: Problem Solving Show Solutions 18

28 I: 53. NS: If the radioactive substance decays by the same amount each year, then the total amount of decay is the sum of a geometric series. If the number of years for which the radioactive isotope decay increases, it will be difficult to find and add all the terms and in this case it will be better to use the formula. If a radioactive substance decays at a constant rate, then the total amount of left each year can be modeled as a geometric series. When the number of terms in a series increases, it is convenient to apply the formula for the sum of the series rather than adding up all the terms. ssessment Rubric Level 3 Superior *Shows thorough understanding of concepts. *omputation is correct. *Written explanation is exemplary. *iagram/table/chart is accurate (as applicable). *Goes beyond requirements of problem. Level 2 Satisfactory *Shows understanding of concepts. *omputation is mostly correct. *Written explanation is effective. *iagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements of problem. Level 1 Nearly Satisfactory *Shows understanding of most concepts. *omputation is mostly correct. *Written explanation is satisfactory. *iagram/table/chart is mostly accurate (as applicable). *Satisfies most of the requirements of problem. Level 0 Unsatisfactory *Shows little or no understanding of the concept. *omputation is incorrect. *Written explanation is not satisfactory. *iagram/table/chart is not accurate (as applicable). *oes not satisfy requirements of problem. PTS: 1 IF: dvanced REF: Lesson 11-4 OJ: Solve problems and show solutions. TOP: Solve problems and show solutions. MS: Key ST: 22.0 {Key}23.0 KEY: Problem Solving Show Solutions 19

29 I: 54. NS: The total number of revolutions that the flywheel makes before coming to rest is the sum of the infinite Ê geometric series ˆ Á Ê ˆ + ë. The sum of the series is 450 Á or 720. Thus, the flywheel 8 makes 720 revolutions before it comes to rest. pply the formula S = a 1 1 r ssessment Rubric Level 3 Superior *Shows thorough understanding of concepts. *omputation is correct. *Written explanation is exemplary. *iagram/table/chart is accurate (as applicable). *Goes beyond requirements of problem. Level 2 Satisfactory *Shows understanding of concepts. *omputation is mostly correct. *Written explanation is effective. *iagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements of problem. Level 1 Nearly Satisfactory *Shows understanding of most concepts. *omputation is mostly correct. *Written explanation is satisfactory. *iagram/table/chart is mostly accurate (as applicable). *Satisfies most of the requirements of problem. Level 0 Unsatisfactory *Shows little or no understanding of the concept. *omputation is incorrect. *Written explanation is not satisfactory. *iagram/table/chart is not accurate (as applicable). *oes not satisfy requirements of problem. to find the number of revolutions the flywheel makes before coming to rest. PTS: 1 IF: dvanced REF: Lesson 11-5 OJ: Solve problems and show solutions. TOP: Solve problems and show solutions. MS: Key ST: 22.0 {Key}23.0 KEY: Problem Solving Show Solutions 20

30 I: 55. NS: Mathematical induction depends on a recursive process that is much like going up floor by floor of a multi-story building. We can certainly reach the first floor. Then, we must be able to move from one floor to the next. Thus, if we can reach the first floor, we can definitely reach the second. fter reaching the second floor, we can reach the third, and so on indefinitely for all floors. Therefore, a correspondence can be made between mathematical induction and a multi-story building with the positive integers on the floors. Showing that the statement is true for n = 1 (Step 1) corresponds to reaching the first floor. ssuming that the statement is true for some positive integer k and showing that it is true for k + 1 (Steps 2 and 3) corresponds to knowing that you can reach from one floor to the next floor. Verify the concept for the first floor of the building. ssuming that the concept holds for the kth floor, prove that it holds for ( k + 1)th floor. ssessment Rubric Level 3 Superior *Shows thorough understanding of concepts. *omputation is correct. *Written explanation is exemplary. *iagram/table/chart is accurate (as applicable). *Goes beyond requirements of problem. Level 2 Satisfactory *Shows understanding of concepts. *omputation is mostly correct. *Written explanation is effective. *iagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements of problem. Level 1 Nearly Satisfactory *Shows understanding of most concepts. *omputation is mostly correct. *Written explanation is satisfactory. *iagram/table/chart is mostly accurate (as applicable). *Satisfies most of the requirements of problem. Level 0 Unsatisfactory *Shows little or no understanding of the concept. *omputation is incorrect. *Written explanation is not satisfactory. *iagram/table/chart is not accurate (as applicable). *oes not satisfy requirements of problem. PTS: 1 IF: dvanced REF: Lesson 11-8 OJ: Solve problems and show solutions. ST: 21.0 TOP: Solve problems and show solutions. KEY: Problem Solving Show Solutions 21

31 I: 56. NS: ecause the first card is not replaced, the events are dependent. a. P(first card is a multiple of 5) = 8 52 P(second card is also a multiple of 5) = 7 51 P(both cards are multiples of 5) = P(first card is a multiple of 5) P(second card is also a multiple of 5) = or b. P(both cards are spades) = P(first card is a spade) P(second card is also a spade) = or 1 17 c. P(both cards are black aces) = P(first card is a black ace) P(second card is also a black ace) = or ssessment Rubric Level 3 Superior *Shows thorough understanding of concepts. *omputation is correct. *Written explanation is exemplary. *iagram/table/chart is accurate (as applicable). *Goes beyond requirements of problem. Level 2 Satisfactory *Shows understanding of concepts. *omputation is mostly correct. *Written explanation is effective. *iagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements of problem. Level 1 Nearly Satisfactory *Shows understanding of most concepts. *omputation is mostly correct. *Written explanation is satisfactory. *iagram/table/chart is mostly accurate (as applicable). *Satisfies most of the requirements of problem. Level 0 Unsatisfactory *Shows little or no understanding of the concept. *omputation is incorrect. *Written explanation is not satisfactory. *iagram/table/chart is not accurate (as applicable). PTS: 1 IF: dvanced REF: Lesson

32 I: OJ: Solve problems and show solutions. TOP: Solve problems and show solutions. MS: Key ST: {Key}18.0 KEY: Problem Solving Show Solutions 23

33 I: 57. NS: Probability is a good tool for expressing the possibilities and chances of rain, snow, and other features in preparing weather forecasts. In the case of snowfall, success is the occurrence of snow in the town on Friday or the snowfall being heavy enough that would require the closing of the schools. Here, failure means no snow on Friday in the town or insignificant snowfall. If an event can succeed in s ways and fail in f ways, then the possibilities of success, P(s), and of failure, P(f), are as follows: s f P(s) = P(f) = s + f s + f ssessment Rubric Level 3 Superior *Shows thorough understanding of concepts. *omputation is correct. *Written explanation is exemplary. *iagram/table/chart is accurate (as applicable). *Goes beyond requirements of problem. Level 2 Satisfactory *Shows understanding of concepts. *omputation is mostly correct. *Written explanation is effective. *iagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements of problem. Level 1 Nearly Satisfactory *Shows understanding of most concepts. *omputation is mostly correct. *Written explanation is satisfactory. *iagram/table/chart is mostly accurate (as applicable). *Satisfies most of the requirements of problem. Level 0 Unsatisfactory *Shows little or no understanding of the concept. *omputation is incorrect. *Written explanation is not satisfactory. *iagram/table/chart is not accurate (as applicable). *oes not satisfy requirements of problem. PTS: 1 IF: dvanced REF: Lesson 12-3 OJ: Solve problems and show solutions. TOP: Solve problems and show solutions. MS: Key ST: {Key}19.0 KEY: Problem Solving Show Solutions 24

34 I: 58. NS: Probability can be used to analyze the possibilities of rainfall occurring on 0, 1, 2, or 3 days of their vacation. The probability for no rain will be given by ( ) 3 or 0.61 approximately. The probability that it rains on any one day is given by ( ) 2 or approximately. The probability that it rains any two days is given by 3 ( 0.15) 2 ( ) or about The probability that it rains all the three days is given by ( 0.15) 3 or about The daily probabilities of rain might not be independent because the forecasting method usually assumes that tomorrow's weather will be the same as today's, that is, the conditions at the time of the forecast will not change. Two events, and, are said to be independent if the probability of both events occuring is Pand ( ) = P ( ) P ( ). ssessment Rubric Level 3 Superior *Shows thorough understanding of concepts. *omputation is correct. *Written explanation is exemplary. *iagram/table/chart is accurate (as applicable). *Goes beyond requirements of problem. Level 2 Satisfactory *Shows understanding of concepts. *omputation is mostly correct. *Written explanation is effective. *iagram/table/chart is mostly accurate (as applicable). *Satisfies all requirements of problem. Level 1 Nearly Satisfactory *Shows understanding of most concepts. *omputation is mostly correct. *Written explanation is satisfactory. *iagram/table/chart is mostly accurate (as applicable). *Satisfies most of the requirements of problem. Level 0 Unsatisfactory *Shows little or no understanding of the concept. *omputation is incorrect. *Written explanation is not satisfactory. *iagram/table/chart is not accurate (as applicable). *oes not satisfy requirements of problem. PTS: 1 IF: dvanced REF: Lesson 12-4 OJ: Solve problems and show solutions. TOP: Solve problems and show solutions. MS: Key ST: {Key}1.0 {Key}2.0 KEY: Problem Solving Show Solutions 25