Final Review Algebra 2 Semester 2
Final Review Algebra 2 Semester 2 Graph the function. 1. 2.
3.
4. 5. The value of a new car purchased for $24,900 decreases by 10% per year. Write an exponential decay model for the value of the car. After about how many years will the car be worth half its purchase price? Graph the function. State the domain and range. 6. 7. Simplify the expression. 8. Evaluate the expression without using a calculator. 9. 10. Expand the expression ln 2yx. 11. Condense the expression 2(log 2 + log 5)
log 20.
Solve the equation. Check for extraneous solutions. 12.
13. 8 = The table gives the mean weight w (in kilograms) and age x (in years) of Atlantic cod from the Gulf of Maine.
14. x w
1 0.751
2 1.079
3 1.702
4 2.198
5 3.438
6 4.347
7 7.701
8 11.518
a. Draw a scatter plot of versus x. Is an exponential model a good fit for the original data? b. Find an exponential model for the original data. Estimate the weight of a cod that is 9 years old. 15. Find a power function of the form
whose graph passes through the points (3, 5) and (6, 30).
16. A lever pivots on a support called a fulcrum. For a balanced lever, the distance d (in feet) an object is from the fulcrum varies inversely with the object's weight w (in pounds). An object weighing 140 pounds is placed 6 feet from a fulcrum. How far from the fulcrum must a 112 pound object be placed to balance the lever? The variable z varies jointly with x and y. Use the given values to write an equation relating x, y, and z. Then find z when x = 2 and y = 4. 17. Perform the indicated operation. Simplify the result. 18.
19.
20.
21. Simplify the complex fraction.
22.
Solve the equation using any method. Check each solution. 23.
Find the distance between the two points. Then find the midpoint of the line segment connecting the two points. 24. ( 11, 5), (–3, 7) Graph the equation. 25. 26.
27. 28. Write an equation for the conic section. 29. Parabola with vertex at (3, 6) and focus at (3, 4) 30. Ellipse with center at (0, 0), vertex at (4, 0), and co-vertex at (0, 2) 31. Hyperbola with vertex at (4, 2), focus at (4, 4), and center at (4, 1) Classify the conic section and write its equation in standard form. 32. 33. Find the points of intersection, if any, of the graphs in the system. 34.
35. A search team of three members splits to search an area in the woods. Each member carries a family service radio with a circular range of 3 miles. They agree to communicate from their bases every hour. One member sets up base 2 miles north of the first member. Where should the other member set up base to be as far east as possible but within range of communication? 36. A school shirt is available either long-sleeved or short-sleeved, in sizes small, medium, large, or extra large, and in one of two colors. How many different choices for a school shirt are there? Find the number of permutations or combinations.
37.
14P2
38.
5C4
39. Find the number of distinguishable permutations of the letters in MONTANA. Expand the power of the binomial. 40. A card is drawn randomly from a standard 52-card deck. Find the probability of drawing the given card. 41. a black card Find the indicated probability.
42.
43.
44. A and B are independent events.
A standard deck of playing cards consists of 52 cards, with 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Suppose two cards are drawn at random, one after the other, without replacing the first card before drawing the second. Find the probability of each event. 45. The second card is an ace, given that the first card is an ace. A 10 question true-false quiz is given. Find the probability of randomly guessing each number of questions correctly. 46. exactly 8 questions
47. For a certain light bulb manufacturer, there is a 5% chance that any given light bulb is defective. An inspector examines 30 light bulbs. What is the probability that exactly one is defective? Find the mean, median, and mode of the data. 48. 11, 13, 25, 16, 12, 14, 12, 23, 10, 19, 22, 12 49. Find the standard deviation of the data set 22, 25, 29, 31, 34, 35, 41. A manufacturer produces bags of navy beans marked "Net Weight 8 oz." A machine is set to fill each bag with 8.2 oz, but the actual weights are normally distributed with mean 8.2 oz and standard deviation 0.09 oz. What is the probability that a given bag will contain each amount of beans? 50. more than 8.47 oz 51. A principal wants to know if the students at her school like the food served in the cafeteria, so she asks the first 25 students in the line at lunch. Identify the type of sample and describe the population. Then tell if the sample is biased. Explain. 52. The drama club at Pioneer High School randomly surveyed 100 students and found that 62 students would attend the next drama production. Find the sample percent of students that would attend the production. Find the margin of error for the sample proportion. Then find an interval that is likely to contain the exact percent of all students at Pioneer High who would attend the next production. Name the type of model suggested by the graph.
53. Write the first six terms of the sequence. 54.
55.
Write the next term of the sequence, and then write a rule for the nth term. 56. 1.1, 2.2, 3.3, 4.4, ...
57. 4, 9, 14, 19, ... 58. 59. Write the series
with summation notation.
Find the sum of the series. 60.
61. 62.
Tell whether the sequence is arithmetic, geometric, or neither. Explain your answer. 63. 64. In early growth of an embryo, a human cell divides into two cells, each of which divides into two cells, and so on. The number of new cells formed after the nth division is . Find the sum of the first 9 terms of the series to find the total number of new cells after the 8th division. 65. Write the repeating decimal 0.7575 ... as a fraction. Write a recursive rule for the sequence. 66. 40, 20, 10, 5, ...
Final Review Algebra 2 Semester 2 Answer Section 1. ANS: Answer:
PTS: 1 REF: A2.CR.7_9.Eng.01 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 2. ANS: Answer:
PTS: 1 REF: A2.CR.7_9.Eng.15 NAT: NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 3. ANS: Answer:
PTS: NAT: KEY: NOT: 4. ANS:
1 REF: A2.CR.7_9.Eng.16 NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Chapters 7-9 Pre-made Test MSC: Comprehension 978-0-547-31541-6
Answer:
PTS: NAT: KEY: NOT: 5. ANS:
1 REF: A2.CR.7_9.Eng.17 NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Chapters 7-9 Pre-made Test MSC: Comprehension 978-0-547-31541-6 ; half purchase price in about 6.58 years
PTS: 1 REF: A2.CR.7_9.Eng.02 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 6. ANS: Domain: all real numbers Range: y > 0
PTS: 1 REF: A2.CR.7_9.Eng.03 NAT: NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 7. ANS: Domain: x > 0 Range: all real numbers
PTS: 1 REF: A2.CR.7_9.Eng.06 NAT: NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension
NOT: 978-0-547-31541-6 8. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.04 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 9. ANS: PTS: 1 REF: A2.CR.7_9.Eng.05 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 10. ANS:
PTS: NAT: KEY: NOT: 11. ANS: log 5
1 REF: A2.CR.7_9.Eng.07 NCTM.PSSM.00.MTH.9-12.NOP.1.a TOP: Chapters 7-9 Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: 1 REF: A2.CR.7_9.Eng.08 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 12. ANS: PTS: 1 REF: A2.CR.7_9.Eng.09 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 13. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.10 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 14. ANS: a. See scatter plot below. b.
;
PTS: 1 REF: A2.CR.7_9.Eng.11 NAT: NCTM.PSSM.00.MTH.9-12.ALG.3.a | NCTM.PSSM.00.MTH.9-12.MEA.2.c | NCTM.PSSM.00.MTH.9-12.DAP.1.d | NCTM.PSSM.00.MTH.9-12.DAP.2.b | NCTM.PSSM.00.MTH.9-12.DAP.2.e TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 15. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.12 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 16. ANS: 7.5 ft PTS: 1 REF: A2.CR.7_9.Eng.13 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 17. ANS: ; PTS: 1 REF: A2.CR.7_9.Eng.14 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 18. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.18 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 19. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.19 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6
20. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.20 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 21. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.21 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 22. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.22 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 23. ANS:
PTS: NAT: TOP: NOT: 24. ANS:
1 REF: A2.CR.7_9.Eng.23 NCTM.PSSM.00.MTH.9-12.NOP.3.b | NCTM.PSSM.00.MTH.9-12.PRS.4 Chapters 7-9 KEY: Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: 1 REF: A2.CR.7_9.Eng.24 NAT: NCTM.PSSM.00.MTH.9-12.GEO.2.a TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 25. ANS: Answer:
PTS: 1 REF: A2.CR.7_9.Eng.25 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension
NOT: 978-0-547-31541-6 26. ANS: Answer:
PTS: 1 REF: A2.CR.7_9.Eng.27 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 27. ANS: Answer
PTS: 1 REF: A2.CR.7_9.Eng.28 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 28. ANS: Answer:
PTS: 1 REF: A2.CR.7_9.Eng.30 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 29. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.26 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 30. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.29 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 31. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.31 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 32. ANS: parabola; PTS: 1 REF: A2.CR.7_9.Eng.32 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 33. ANS: hyperbola;
PTS: 1 REF: A2.CR.7_9.Eng.33 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 34. ANS: none PTS: 1 REF: A2.CR.7_9.Eng.34 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 35. ANS: , or about 2.83 miles east of the midpoint between the other two members PTS: 1 REF: A2.CR.7_9.Eng.35 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 36. ANS: 16
PTS: NAT: KEY: NOT: 37. ANS: 182
1 REF: A2.CR.10_12.Eng.01 NCTM.PSSM.00.MTH.9-12.NOP.2.c TOP: Chapters 10-12 Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: NAT: TOP: MSC: 38. ANS: 5
1 REF: A2.CR.10_12.Eng.02 NCTM.PSSM.00.MTH.9-12.NOP.2.c | NCTM.PSSM.00.MTH.9-12.DAP.4.e Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: NAT: TOP: MSC: 39. ANS: 1260
1 REF: A2.CR.10_12.Eng.04 NCTM.PSSM.00.MTH.9-12.NOP.2.c | NCTM.PSSM.00.MTH.9-12.DAP.4.e Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: NAT: KEY: NOT: 40. ANS:
1 REF: A2.CR.10_12.Eng.03 NCTM.PSSM.00.MTH.9-12.NOP.2.c TOP: Chapters 10-12 Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: NAT: TOP: MSC: 41. ANS: 0.5
1 REF: A2.CR.10_12.Eng.05 NCTM.PSSM.00.MTH.9-12.NOP.2.c | NCTM.PSSM.00.MTH.9-12.DAP.4.e Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.06 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 42. ANS: 0.17 PTS: NAT: TOP: MSC: 43. ANS:
1 REF: A2.CR.10_12.Eng.07 NCTM.PSSM.00.MTH.9-12.DAP.4.d | NCTM.PSSM.00.MTH.9-12.DAP.4.e Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.08 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 44. ANS: 0.1875 PTS: NAT: TOP: MSC: 45. ANS:
1 REF: A2.CR.10_12.Eng.10 NCTM.PSSM.00.MTH.9-12.DAP.4.d | NCTM.PSSM.00.MTH.9-12.DAP.4.e Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.09 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 46. ANS:
PTS: 1 REF: A2.CR.10_12.Eng.11 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 47. ANS: 1.1% PTS: 1 REF: A2.CR.10_12.Eng.12 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 48. ANS: mean: 15.75, median: 13.5, mode: 12 PTS: NAT: TOP: MSC: 49. ANS: 6
1 REF: A2.CR.10_12.Eng.13 NCTM.PSSM.00.MTH.9-12.DAP.1.e | NCTM.PSSM.00.MTH.9-12.DAP.2.a Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.14 NAT: NCTM.PSSM.00.MTH.9-12.DAP.1.e | NCTM.PSSM.00.MTH.9-12.DAP.2.a TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 50. ANS: 0.15% PTS: 1 REF: A2.CR.10_12.Eng.16 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6
51. ANS: convenience sample; students in the school; biased; The sample is biased because students standing in line for lunch at school are more likely to like the food served than students who are not in line. PTS: NAT: TOP: MSC: 52. ANS:
1 REF: A2.CR.10_12.Eng.17 NCTM.PSSM.00.MTH.9-12.DAP.1.b | NCTM.PSSM.00.MTH.9-12.DAP.3.b Chapters 10-12 KEY: Pre-made Test Analysis NOT: 978-0-547-31541-6 ; between 61.9% and 62.1%
PTS: 1 REF: A2.CR.10_12.Eng.18 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 53. ANS: exponential PTS: 1 REF: A2.CR.10_12.Eng.19 KEY: Pre-made Test MSC: Knowledge 54. ANS: 2, 5, 10, 17, 26, 37
TOP: Chapters 10-12 NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.20 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 55. ANS: 4, 6, 9, 13, 18, 24 PTS: 1 REF: A2.CR.10_12.Eng.31 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 56. ANS: 5.5; PTS: NAT: KEY: NOT: 57. ANS: 24;
1 REF: A2.CR.10_12.Eng.21 NCTM.PSSM.00.MTH.9-12.ALG.1.a TOP: Chapters 10-12 Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: NAT: KEY: NOT: 58. ANS:
1 REF: A2.CR.10_12.Eng.24 NCTM.PSSM.00.MTH.9-12.ALG.1.a TOP: Chapters 10-12 Pre-made Test MSC: Comprehension 978-0-547-31541-6
;
PTS: NAT: KEY: NOT: 59. ANS:
1 REF: A2.CR.10_12.Eng.26 NCTM.PSSM.00.MTH.9-12.ALG.1.a TOP: Chapters 10-12 Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.22 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 60. ANS: PTS: 1 REF: A2.CR.10_12.Eng.23 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 61. ANS: 77 PTS: 1 REF: A2.CR.10_12.Eng.27 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 62. ANS:
PTS: 1 REF: A2.CR.10_12.Eng.29 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 63. ANS: geometric; PTS: 1 REF: A2.CR.10_12.Eng.25 KEY: Pre-made Test MSC: Knowledge 64. ANS: 511
TOP: Chapters 10-12 NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.28 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 65. ANS:
PTS: 1 REF: A2.CR.10_12.Eng.30 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 66. ANS:
PTS: 1 REF: A2.CR.10_12.Eng.32 NAT: NCTM.PSSM.00.MTH.9-12.ALG.1.a | NCTM.PSSM.00.MTH.9-12.ALG.2.d | NCTM.PSSM.00.MTH.9-12.ALG.3.b TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6
3.
4. 5. The value of a new car purchased for $24,900 decreases by 10% per year. Write an exponential decay model for the value of the car. After about how many years will the car be worth half its purchase price? Graph the function. State the domain and range. 6. 7. Simplify the expression. 8. Evaluate the expression without using a calculator. 9. 10. Expand the expression ln 2yx. 11. Condense the expression 2(log 2 + log 5)
log 20.
Solve the equation. Check for extraneous solutions. 12.
13. 8 = The table gives the mean weight w (in kilograms) and age x (in years) of Atlantic cod from the Gulf of Maine.
14. x w
1 0.751
2 1.079
3 1.702
4 2.198
5 3.438
6 4.347
7 7.701
8 11.518
a. Draw a scatter plot of versus x. Is an exponential model a good fit for the original data? b. Find an exponential model for the original data. Estimate the weight of a cod that is 9 years old. 15. Find a power function of the form
whose graph passes through the points (3, 5) and (6, 30).
16. A lever pivots on a support called a fulcrum. For a balanced lever, the distance d (in feet) an object is from the fulcrum varies inversely with the object's weight w (in pounds). An object weighing 140 pounds is placed 6 feet from a fulcrum. How far from the fulcrum must a 112 pound object be placed to balance the lever? The variable z varies jointly with x and y. Use the given values to write an equation relating x, y, and z. Then find z when x = 2 and y = 4. 17. Perform the indicated operation. Simplify the result. 18.
19.
20.
21. Simplify the complex fraction.
22.
Solve the equation using any method. Check each solution. 23.
Find the distance between the two points. Then find the midpoint of the line segment connecting the two points. 24. ( 11, 5), (–3, 7) Graph the equation. 25. 26.
27. 28. Write an equation for the conic section. 29. Parabola with vertex at (3, 6) and focus at (3, 4) 30. Ellipse with center at (0, 0), vertex at (4, 0), and co-vertex at (0, 2) 31. Hyperbola with vertex at (4, 2), focus at (4, 4), and center at (4, 1) Classify the conic section and write its equation in standard form. 32. 33. Find the points of intersection, if any, of the graphs in the system. 34.
35. A search team of three members splits to search an area in the woods. Each member carries a family service radio with a circular range of 3 miles. They agree to communicate from their bases every hour. One member sets up base 2 miles north of the first member. Where should the other member set up base to be as far east as possible but within range of communication? 36. A school shirt is available either long-sleeved or short-sleeved, in sizes small, medium, large, or extra large, and in one of two colors. How many different choices for a school shirt are there? Find the number of permutations or combinations.
37.
14P2
38.
5C4
39. Find the number of distinguishable permutations of the letters in MONTANA. Expand the power of the binomial. 40. A card is drawn randomly from a standard 52-card deck. Find the probability of drawing the given card. 41. a black card Find the indicated probability.
42.
43.
44. A and B are independent events.
A standard deck of playing cards consists of 52 cards, with 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Suppose two cards are drawn at random, one after the other, without replacing the first card before drawing the second. Find the probability of each event. 45. The second card is an ace, given that the first card is an ace. A 10 question true-false quiz is given. Find the probability of randomly guessing each number of questions correctly. 46. exactly 8 questions
47. For a certain light bulb manufacturer, there is a 5% chance that any given light bulb is defective. An inspector examines 30 light bulbs. What is the probability that exactly one is defective? Find the mean, median, and mode of the data. 48. 11, 13, 25, 16, 12, 14, 12, 23, 10, 19, 22, 12 49. Find the standard deviation of the data set 22, 25, 29, 31, 34, 35, 41. A manufacturer produces bags of navy beans marked "Net Weight 8 oz." A machine is set to fill each bag with 8.2 oz, but the actual weights are normally distributed with mean 8.2 oz and standard deviation 0.09 oz. What is the probability that a given bag will contain each amount of beans? 50. more than 8.47 oz 51. A principal wants to know if the students at her school like the food served in the cafeteria, so she asks the first 25 students in the line at lunch. Identify the type of sample and describe the population. Then tell if the sample is biased. Explain. 52. The drama club at Pioneer High School randomly surveyed 100 students and found that 62 students would attend the next drama production. Find the sample percent of students that would attend the production. Find the margin of error for the sample proportion. Then find an interval that is likely to contain the exact percent of all students at Pioneer High who would attend the next production. Name the type of model suggested by the graph.
53. Write the first six terms of the sequence. 54.
55.
Write the next term of the sequence, and then write a rule for the nth term. 56. 1.1, 2.2, 3.3, 4.4, ...
57. 4, 9, 14, 19, ... 58. 59. Write the series
with summation notation.
Find the sum of the series. 60.
61. 62.
Tell whether the sequence is arithmetic, geometric, or neither. Explain your answer. 63. 64. In early growth of an embryo, a human cell divides into two cells, each of which divides into two cells, and so on. The number of new cells formed after the nth division is . Find the sum of the first 9 terms of the series to find the total number of new cells after the 8th division. 65. Write the repeating decimal 0.7575 ... as a fraction. Write a recursive rule for the sequence. 66. 40, 20, 10, 5, ...
Final Review Algebra 2 Semester 2 Answer Section 1. ANS: Answer:
PTS: 1 REF: A2.CR.7_9.Eng.01 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 2. ANS: Answer:
PTS: 1 REF: A2.CR.7_9.Eng.15 NAT: NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 3. ANS: Answer:
PTS: NAT: KEY: NOT: 4. ANS:
1 REF: A2.CR.7_9.Eng.16 NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Chapters 7-9 Pre-made Test MSC: Comprehension 978-0-547-31541-6
Answer:
PTS: NAT: KEY: NOT: 5. ANS:
1 REF: A2.CR.7_9.Eng.17 NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Chapters 7-9 Pre-made Test MSC: Comprehension 978-0-547-31541-6 ; half purchase price in about 6.58 years
PTS: 1 REF: A2.CR.7_9.Eng.02 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 6. ANS: Domain: all real numbers Range: y > 0
PTS: 1 REF: A2.CR.7_9.Eng.03 NAT: NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 7. ANS: Domain: x > 0 Range: all real numbers
PTS: 1 REF: A2.CR.7_9.Eng.06 NAT: NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension
NOT: 978-0-547-31541-6 8. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.04 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 9. ANS: PTS: 1 REF: A2.CR.7_9.Eng.05 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 10. ANS:
PTS: NAT: KEY: NOT: 11. ANS: log 5
1 REF: A2.CR.7_9.Eng.07 NCTM.PSSM.00.MTH.9-12.NOP.1.a TOP: Chapters 7-9 Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: 1 REF: A2.CR.7_9.Eng.08 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 12. ANS: PTS: 1 REF: A2.CR.7_9.Eng.09 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 13. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.10 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 14. ANS: a. See scatter plot below. b.
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PTS: 1 REF: A2.CR.7_9.Eng.11 NAT: NCTM.PSSM.00.MTH.9-12.ALG.3.a | NCTM.PSSM.00.MTH.9-12.MEA.2.c | NCTM.PSSM.00.MTH.9-12.DAP.1.d | NCTM.PSSM.00.MTH.9-12.DAP.2.b | NCTM.PSSM.00.MTH.9-12.DAP.2.e TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 15. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.12 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 16. ANS: 7.5 ft PTS: 1 REF: A2.CR.7_9.Eng.13 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 17. ANS: ; PTS: 1 REF: A2.CR.7_9.Eng.14 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 18. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.18 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 19. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.19 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6
20. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.20 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 21. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.21 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 22. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.22 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 23. ANS:
PTS: NAT: TOP: NOT: 24. ANS:
1 REF: A2.CR.7_9.Eng.23 NCTM.PSSM.00.MTH.9-12.NOP.3.b | NCTM.PSSM.00.MTH.9-12.PRS.4 Chapters 7-9 KEY: Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: 1 REF: A2.CR.7_9.Eng.24 NAT: NCTM.PSSM.00.MTH.9-12.GEO.2.a TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 25. ANS: Answer:
PTS: 1 REF: A2.CR.7_9.Eng.25 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension
NOT: 978-0-547-31541-6 26. ANS: Answer:
PTS: 1 REF: A2.CR.7_9.Eng.27 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 27. ANS: Answer
PTS: 1 REF: A2.CR.7_9.Eng.28 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 28. ANS: Answer:
PTS: 1 REF: A2.CR.7_9.Eng.30 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 29. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.26 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 30. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.29 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 31. ANS:
PTS: 1 REF: A2.CR.7_9.Eng.31 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 32. ANS: parabola; PTS: 1 REF: A2.CR.7_9.Eng.32 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 33. ANS: hyperbola;
PTS: 1 REF: A2.CR.7_9.Eng.33 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 34. ANS: none PTS: 1 REF: A2.CR.7_9.Eng.34 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 35. ANS: , or about 2.83 miles east of the midpoint between the other two members PTS: 1 REF: A2.CR.7_9.Eng.35 TOP: Chapters 7-9 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 36. ANS: 16
PTS: NAT: KEY: NOT: 37. ANS: 182
1 REF: A2.CR.10_12.Eng.01 NCTM.PSSM.00.MTH.9-12.NOP.2.c TOP: Chapters 10-12 Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: NAT: TOP: MSC: 38. ANS: 5
1 REF: A2.CR.10_12.Eng.02 NCTM.PSSM.00.MTH.9-12.NOP.2.c | NCTM.PSSM.00.MTH.9-12.DAP.4.e Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: NAT: TOP: MSC: 39. ANS: 1260
1 REF: A2.CR.10_12.Eng.04 NCTM.PSSM.00.MTH.9-12.NOP.2.c | NCTM.PSSM.00.MTH.9-12.DAP.4.e Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: NAT: KEY: NOT: 40. ANS:
1 REF: A2.CR.10_12.Eng.03 NCTM.PSSM.00.MTH.9-12.NOP.2.c TOP: Chapters 10-12 Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: NAT: TOP: MSC: 41. ANS: 0.5
1 REF: A2.CR.10_12.Eng.05 NCTM.PSSM.00.MTH.9-12.NOP.2.c | NCTM.PSSM.00.MTH.9-12.DAP.4.e Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.06 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 42. ANS: 0.17 PTS: NAT: TOP: MSC: 43. ANS:
1 REF: A2.CR.10_12.Eng.07 NCTM.PSSM.00.MTH.9-12.DAP.4.d | NCTM.PSSM.00.MTH.9-12.DAP.4.e Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.08 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 44. ANS: 0.1875 PTS: NAT: TOP: MSC: 45. ANS:
1 REF: A2.CR.10_12.Eng.10 NCTM.PSSM.00.MTH.9-12.DAP.4.d | NCTM.PSSM.00.MTH.9-12.DAP.4.e Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.09 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 46. ANS:
PTS: 1 REF: A2.CR.10_12.Eng.11 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 47. ANS: 1.1% PTS: 1 REF: A2.CR.10_12.Eng.12 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 48. ANS: mean: 15.75, median: 13.5, mode: 12 PTS: NAT: TOP: MSC: 49. ANS: 6
1 REF: A2.CR.10_12.Eng.13 NCTM.PSSM.00.MTH.9-12.DAP.1.e | NCTM.PSSM.00.MTH.9-12.DAP.2.a Chapters 10-12 KEY: Pre-made Test Comprehension NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.14 NAT: NCTM.PSSM.00.MTH.9-12.DAP.1.e | NCTM.PSSM.00.MTH.9-12.DAP.2.a TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 50. ANS: 0.15% PTS: 1 REF: A2.CR.10_12.Eng.16 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6
51. ANS: convenience sample; students in the school; biased; The sample is biased because students standing in line for lunch at school are more likely to like the food served than students who are not in line. PTS: NAT: TOP: MSC: 52. ANS:
1 REF: A2.CR.10_12.Eng.17 NCTM.PSSM.00.MTH.9-12.DAP.1.b | NCTM.PSSM.00.MTH.9-12.DAP.3.b Chapters 10-12 KEY: Pre-made Test Analysis NOT: 978-0-547-31541-6 ; between 61.9% and 62.1%
PTS: 1 REF: A2.CR.10_12.Eng.18 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 53. ANS: exponential PTS: 1 REF: A2.CR.10_12.Eng.19 KEY: Pre-made Test MSC: Knowledge 54. ANS: 2, 5, 10, 17, 26, 37
TOP: Chapters 10-12 NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.20 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 55. ANS: 4, 6, 9, 13, 18, 24 PTS: 1 REF: A2.CR.10_12.Eng.31 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 56. ANS: 5.5; PTS: NAT: KEY: NOT: 57. ANS: 24;
1 REF: A2.CR.10_12.Eng.21 NCTM.PSSM.00.MTH.9-12.ALG.1.a TOP: Chapters 10-12 Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: NAT: KEY: NOT: 58. ANS:
1 REF: A2.CR.10_12.Eng.24 NCTM.PSSM.00.MTH.9-12.ALG.1.a TOP: Chapters 10-12 Pre-made Test MSC: Comprehension 978-0-547-31541-6
;
PTS: NAT: KEY: NOT: 59. ANS:
1 REF: A2.CR.10_12.Eng.26 NCTM.PSSM.00.MTH.9-12.ALG.1.a TOP: Chapters 10-12 Pre-made Test MSC: Comprehension 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.22 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 60. ANS: PTS: 1 REF: A2.CR.10_12.Eng.23 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 61. ANS: 77 PTS: 1 REF: A2.CR.10_12.Eng.27 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 62. ANS:
PTS: 1 REF: A2.CR.10_12.Eng.29 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 63. ANS: geometric; PTS: 1 REF: A2.CR.10_12.Eng.25 KEY: Pre-made Test MSC: Knowledge 64. ANS: 511
TOP: Chapters 10-12 NOT: 978-0-547-31541-6
PTS: 1 REF: A2.CR.10_12.Eng.28 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 65. ANS:
PTS: 1 REF: A2.CR.10_12.Eng.30 TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6 66. ANS:
PTS: 1 REF: A2.CR.10_12.Eng.32 NAT: NCTM.PSSM.00.MTH.9-12.ALG.1.a | NCTM.PSSM.00.MTH.9-12.ALG.2.d | NCTM.PSSM.00.MTH.9-12.ALG.3.b TOP: Chapters 10-12 KEY: Pre-made Test MSC: Comprehension NOT: 978-0-547-31541-6
