Algebra 2B Review for the Final Exam, 2015

Transcription

1 Name:: Period: Grp #: Date: Algebra 2B Review for the Final Exam, 2015 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Tell whether the function y = 2( 5) x shows growth or decay. Then graph the function. a. This is an exponential growth function. c. This is an exponential decay function. d. This is an exponential growth function. b. This is an exponential growth function. 2. Use inverse operations to write the inverse of f( x) = x 1. 7 a. f 1 ( x) = x 1 b. f 1 ( x) = x c. f 1 ( x) = x 6 d. f 1 ( x) = x

2 3. Write the exponential equation 2 3 = 8 in logarithmic form. a. log 3 8 = 2 b. log 2 8 = 3 c. log 2 3 = 8 d. log 8 2 = 3 4. Express log 2 64 log 2 4 as a single logarithm. Simplify, if possible. a. log 2 4 b. 8 c. 4 d. log Express log as a product. Simplify, if possible. a. 9 b. 3 c d Simplify log 7 x 3 log 7 x. a. log 7 (x 3 x) b. 2log 7 x c. log 7 2x d. 2(x 3 x) 9. f( x) = 0.1 x is transformed 9 units right, compressed vertically by a factor of 1, and reflected across the 2 x-axis. Write the transformed function g( x). a. g( x) = 0.1 2( x 9) b. g( x) = 1 2 Ë Á Ê c. g( x) = 1 2 Ë Á ˆ 0.1 x + 9 Ê d. g x Ë Á Ê ( ) = 1 2 ˆ 0.1 x + 9 ˆ 0.1 x Simplify 10 x 2 3x. Identify any x-values for x 2 + 2x 8 which the expression is undefined. x 5 a. x + 4 The expression is undefined at x = 4. x 5 b. x + 4 The expression is undefined at x = 2 and x = 4. x + 5 c. x + 4 The expression is undefined at x = 2 and x = 4. x + 5 d. x + 4 The expression is undefined at x = Solve 25 x 2 = 125 x. a. x = 4 b. x = 4 c. x = 5 d. x = 5 8. Nadav invests $6,000 in an account that earns 5% interest compounded continuously. What is the total amount of her investment after 8 years? Round your answer to the nearest cent. a. $ b. $327, c. $ d. $14, Divide 5x 3 3x 2 y 25. Assume that all expressions 9 3y are defined. a. xy 8 5 b. 125x 9y 10 c. x 5y 8 d. 5 xy 8 2

3 12. Subtract 6x 2 + x 3 a. 6x 2 x 7 c. 6x 2 + 3x + 1 2x 4. Identify any x-values for which the expression is undefined. ; The expression is always defined. b. 6x 2 x 7 ; The expression is undefined at x = ±3. ; The expression is undefined at x = ±3. d. 6x 2 + 3x + 1 ; The expression is always defined. 13. Identify the asymptotes, domain, and range of the 1 function g(x) = x a. Vertical asymptote: x = 7 Domain: {x x 7} Horizontal asymptote: y = 3 Range: {y y 3 } b. Vertical asymptote: x = 7 Domain: {x x 7} Horizontal asymptote: y = 3 Range: {y y 3 } c. Vertical asymptote: x = 7 Domain: {x x 7} Horizontal asymptote: y = 3 Range: {y y 3 } d. Vertical asymptote: x = 7 Domain: {x x 7} Horizontal asymptote: y = 3 Range: {y y 3 } 14. Identify the zeros and asymptotes of f(x) = 2x 2 18 x a. Zeros: 4 and 4 Vertical asymptotes: x = 3, x = 3 Horizontal asymptote: y = 2 b. Zeros: 3 and 3 Vertical asymptotes: x = 4, x = 4 Horizontal asymptote: y = 1 c. Zeros: 3 and 3 Vertical asymptotes: x = 4, x = 4 Horizontal asymptote: y = 2 d. Zeros: 4 and 4 Vertical asymptotes: x = 3, x = 3 Horizontal asymptote: y = Identify holes in the graph of f( x) = x x + 6 a. There is a hole in the graph at x = 6. b. There is a hole in the graph at x = 6. c. There are no holes in the graph. d. There is a hole in the graph at x = 3. 3

4 16. Solve the equation x 9 = 18 x. a. x = 6 b. x = 3 or x = 6 c. x = 3 or x = 6 d. x = Find the probability of rolling a 1 or an odd number on a number cube. Express your answer as a fraction in simplest form. a. 1 b. 2 3 c. 1 6 d. 1 2 x 17. Solve 1 algebraically. x 6 a. x 3 or x 6 b. x 3 or x > 6 c. 3 x 6 d. 3 x < Joel owns 12 shirts and is selecting the ones he will wear to school next week. How many different ways can Joel choose a group of 5 shirts? (Note that he will not wear the same shirt more than once during the week.) a. 792 ways b. 95,040 ways c. 60 ways d. 17 ways 19. A person is selected at random. What is the probability that the person was not born on a Monday? Express your answer as a percent. If necessary, round your answer to the nearest tenth of a percent. a. 20.0% b. 80.0% c. 14.3% d. 85.7% 20. A bag contains hair ribbons for a spirit rally. The bag contains 8 black ribbons and 7 green ribbons. Lila selects a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. What is the probability that Lila selects a black ribbon and Jessica selects a green ribbon? Express your answer as a fraction in simplest form. a. 8 b c. d In a survey about a change in public policy, 100 people were asked if they favor the change, oppose the change, or have no opinion about the change. Of the 100 people surveyed, 40 are male and 35 oppose the change in policy. Of the 35 who oppose the change, 15 are female. What is the probability that a randomly selected respondent to the survey is a female or opposes the change in policy? Express your answer as a percent. a. 80% b. 75% c. 50% d. 100% 23. A group of 4 students went to drink pearl tea and study at a local tea shop. The shop offers 12 different flavors of pearl tea. What is the probability that at least 2 students ordered the same flavor? Express your answer as a decimal, and round to the nearest ten thousandths. a b c d The data {0, 2, 3, 7, 7} represent a random sample of the number of days absent from school for five students at Monta Vista High. Find the mean and the standard deviation of the data. a. The mean is 3.8, and the standard deviation is about b. The mean is 19, and the standard deviation is about c. The mean is 4.2, and the standard deviation is about d. The mean is 3.8, and the standard deviation is about

5 25. Use the Binomial Theorem to expand the binomial (4x 4y) 4. a. 256x x 3 y x 2 y xy y 4 b. 256x y 4 c. 256x x 3 y x 2 y xy y 4 d. 256x 4 256y Students randomly receive 1 of 4 versions (A, B, C, D) of a math test. What is the probability that at least 3 of the 5 students tested will get version A of the test? Express your answer as a percent, and round to the nearest tenth. a. 10.4% b. 8.8% c. 1.6% d. 74.7% 30. Write the arithmetic series in summation notation. 7 a. ( 5 4k) b. Ê Ë Á9 4(k 1) ˆ k = k = 1 c. Ê Ë Á5 4(k + 1) ˆ d. ( 9 4k) k = 1 7 k = Find the first 5 terms of the sequence with a 1 = 6 and a n = 2a n 1 1 for n 2. a. 1, 2, 3, 4, 5 b. 6, 11, 21, 41, 81 c. 6, 12, 24, 48, 96 d. 6, 7, 8, 9, Find the 7th term of the geometric sequence with a 3 = 16 and a 5 = 64. a. 384 b. 112 c. 512 d Expand the series ( 1) k (7 k)k and evaluate. k = 2 a. 0 b. 56 c. 50 d Determine if the geometric series converges or diverges. a. diverges b. converges 29. Find the 5th term of the arithmetic sequence with a 7 = 25 and a 13 = 55. a. 5 b. 20 c. 15 d. 5 5

6 33. Use a trigonometric function to find the value of x. 38. Find all possible values of sin a. π 3 + (2π)n, 2π 3 + (2π)n b c. π 6 + (2π)n, 5π 6 + (2π)n d. π 4 + (2π)n, 3π 4 + (2π)n a. x = 50 3 b. x = 25 2 c. x = 50 2 d. x = A surveyor whose eye level is 5 feet above the ground determines the angle of elevation to the top of an office building to be If the surveyor is standing 40 feet from the base of the building, what is the height of the building to the nearest foot? a. 41 ft b. 50 ft c. 32 ft d. 36 ft 35. Find the measures of a positive angle and a negative angle that are coterminal with 296. a. 116 and 476 b. 206 and 386 c. 656 and 296 d. 64 and Find the measure of the reference angle for θ = 137. a. 133 b. 223 c. 43 d Convert 5π from radians to degrees. 6 a. 300º b. 150º c. 126º d. 225º 39. A triangle has a side with length 4 feet and another side with length 10 feet. The angle between the sides measures 61º. Find the area of the triangle. Round your answer to the nearest tenth. a ft 2 b ft 2 c ft 2 d. 9.7 ft Adolfo surveyed a triangular region of land and sent the measurements: a = 130 meters, b = 150 meters, m A = 49º to the engineer at the office. The engineer called back asking for more information. Determine how many, if any, triangles can be formed using Adolfo s measurements. If possible, find the unknown measurements. a. Two triangles are possible. c 1 = m; c 2 = 34.6 m; m B 1 = 60.6 ; m B 2 = m C 1 = 70.4 ; m C 2 = 11.6 b. One triangle is possible. c = m; m B = 80.7 ; m C = 50.3 c. Two triangles are possible. c 1 = m; c 2 = 86.9 m; m B 1 = 80.7 ; m B 2 = 99.3 m C 1 = 50.3 ; m C 2 = 31.7 d. No triangles are possible. 41. Using f(x) = sin x as a guide, graph g(x) = 2sin 3x. Identify the amplitude and period. 6

7 a. amplitude = 2; period = 2 3 π d. amplitude = 4; period = 3π b. amplitude = 4; period = 3π 42. Using f(x) = cos x as a guide, graph g(x) = cos(x π ). Identify the x-intercepts and 4 phase shift. a. c. amplitude = 2; period = 2 3 π x-intercepts: x = π 4 + nx where n is an integer; phase shift: π units to the left 4 7

8 b. d. x-intercepts: x = π 4 + nx where n is an integer; x-intercepts: x = π 4 + nx where n is an integer; phase shift: π 4 units down phase shift: π 4 units up c. 43. Find the period for f(x) = 3sin5x. a. 10π b. 2π 3 c. 2π 5 d. 6π x-intercepts: x = π 4 + nπ where n is an integer; 44. A initial investment of $10,000 grows at 11% per year. What function represents the value of the investment after t years? a. f(t) = 10000(0.11) t b. f(t) = 10000(12) t c. f(t) = 10000(1.11)t d. f(t) = 10000(1.11) t phase shift: π 4 units to the right 8

9 45. Find the inverse of f(x) = 5x 1. a. (x 1) f 1 (x) = 5 b. (x + 1) f 1 (x) = 5 c. f 1 (x) = 5x + 1 d. f 1 (x) = x Simplify lne 7x. a. e 7x b. 7x c. 7 d. e Find the period of f(x) = tan 1 6 x. a. 6π b. 1 3 π c. 12π d. 1 6 π 9

10 ID: A Algebra 2B Review for the Final Exam, 2015 Answer Section MULTIPLE CHOICE 1. B 2. D 3. B 4. C 5. A 6. B 7. A 8. A 9. D 10. B 11. A 12. D 13. D 14. C 15. A 16. B 17. B 18. A 19. D 20. D 21. D 22. A 23. A 24. A 25. C 26. A 27. B 28. D 29. C 30. D 31. D 32. A 33. B 34. A 35. D 36. C 37. B 38. A 39. B 1

11 ID: A 40. A 41. A 42. C 43. C 44. D 45. B 46. B 47. A 2