Algebra 2 Final Exam Review Ch 6-9, 11, 13, 14

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1 Algebra 2 Final Exam Review Ch 6-9, 11, 13, 14 Short Answer 1. Write 4x 2 ( 2x 2 + 5x 3 ) in standard form. Then classify it by degree and number of terms. 2. The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in Years since Trees planted (in thousands) Write the expression (x + 6)(x 4) as a polynomial in standard form. 4. Write 4x 3 + 8x 2 96x in factored form. 5. Find the zeros of and state the multiplicity. 6. Divide by x Divide using synthetic division. 8. Solve the equation by graphing. 9. Factor the expression. 10. Use Pascal s Triangle to expand the binomial. Simplify the radical expression. Use absolute value symbols if needed Simplify. Assume that all variables are positive.

2 13. Multiply and simplify. Assume that all variables are positive. Divide and simplify. 14. Rationalize the denominator of the expression. Assume that all variables are positive Add if possible. Simplify Multiply Write the exponential expression in radical form. 22. Write the radical expression in exponential form. Solve the equation.

3 Let and. Find f(x) g(x). 26. Let and. Find. 27. Find the inverse of. 28. Graph and its inverse. y x An initial population of 895 quail increases at an annual rate of 7%. Write an exponential function to model the quail population. 30. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years? 31. Write the equation in logarithmic form. Evaluate the logarithm. 32.

4 33. The ph of a liquid is a measure of how acidic or basic it is. The concentration of hydrogen ions in a liquid is labeled. Use the formula to answer questions about ph. 34. Find the ph level, to the nearest tenth, of a liquid with [H + ] about. 35. Write the equation in exponential form. 36. Write the expression as a single logarithm. 37. Expand the logarithmic expression Use the properties of logarithms to evaluate. 41. Solve. Round to the nearest ten-thousandth. 42. Solve. 43. Solve. Round to the nearest ten-thousandth. 44. Solve. Round to the nearest hundredth if necessary. 45. Write the expression as a single natural logarithm. 46. Without graphing, determine whether the function represents exponential growth or exponential decay.

5 Graph the exponential function. 47. y x 4 Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If it is a direct or inverse variation, write a function to model it. 48. x y Suppose that y varies jointly with w and x and inversely with z and y = 360 when w = 8, x = 25 and z = 5. Write the equation that models the relationship. Then find y when w = 4, x = 4 and z = 3. Find any points of discontinuity for the rational function Describe the vertical asymptote(s) and hole(s) for the graph of. 52. Find the horizontal asymptote of the graph of. Simplify the rational expression. State any restrictions on the variable.

6 53. Multiply or divide. State any restrictions on the variables Add or subtract. Simplify if possible. 56. Simplify the complex fraction. 57. Solve the equation. Check the solution Write a recursive formula for the sequence 8, 10, 12, 14, 16,... Then find the next term. 61. Write an explicit formula for the sequence 7, 2, 3, 8, 13,... Then find. 62. Is the formula is explicit or recursive? Find the first five terms of the sequence. Is the sequence arithmetic? If so, identify the common difference.

7 63. 13, 20, 27, 34, Find the 50th term of the sequence 5, 2, 9, 16,... Is the sequence geometric? If so, identify the common ratio , 12, 24, 48, Write the explicit formula for the sequence. Then find the fifth term in the sequence. 67. The sequence 15, 21, 27, 33, 39,..., 75 has 11 terms. Evaluate the related series. 68. Use summation notation to write the series for 14 terms. 69. For the series, find the first and the last term. 70. Justine earned $17,000 during the first year of her job at city hall. After each year she received a 4% raise. Find her total earnings during the first five years on the job. 71. Does the infinite geometric series diverge or converge? Explain. 72. Evaluate the infinite geometric series. Round to the nearest hundredth if necessary. 73. Find the measure of an angle between 0º and 360º coterminal with an angle of 110º in standard position. 74. Find the exact value of cos 300º and sin 300º. 75. For an angle in standard position measuring 163º, find the values of cos and sin. Round your answers to the nearest hundredth º Write the measure in radians. Express the answer in terms of.

8 Write the measure in degrees. 77. radians 78. Find the exact values of and. 79. A particular sound wave can be graphed using the function. Find the amplitude and period of the function. 80. Use the circle below. Find the length s to the nearest tenth. s 7_ 5 5 ft Use the graph to find the value of y = sin for the value of º y Find the period of the graph shown below.

9 1 y O Write an equation of the cosine function with amplitude 2 and period Find the amplitude of the sine curve shown below. 4 y 2 O Solve the equation for 0 < 2. Write your answer as a multiple of, if possible cos 1 2cos In XYZ, Y is a right angle and. Find cos X in fraction and in decimal form. Round to the nearest hundredth, if necessary.

10 Z X Y 88. Find the length x. Round to the nearest tenth. x In, is a right angle. Find to the nearest tenth of a degree. B x A 24 C In, is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. 90. a = 3.4, c = Use the Law of Sines. Find b to the nearest tenth.

11 C 31 b B A Find the remaining sides and angles in the triangle. Round your answers to the nearest tenth. 92. a = 11, b = 12, and c = Use the Law of Cosines. Find b to the nearest tenth. C 60 b B A 94. Use the Law of Cosines. Find to the nearest tenth of a degree. C B 30 A

12 95. In, b = 7, c = 10, and = 146. Find a. Round your answer to the nearest tenth.

13 Algebra 2 Final Exam Review Ch 6-9, 11, 13, 14 Answer Section SHORT ANSWER 1. 20x 5 8x 4 ; quintic binomial 2. ; thousand trees 3. x 2 + 2x x(x 4)(x + 6) 5. 3, multiplicity 2; 5, multiplicity 6 6., R no solution ; x

14 28. 4 y x $1, exponential growth y x 4

15 48. direct variation; x = 9, x = asymptote: x = 4 and hole: x = y = ; ; explicit; 0, 8, 24, 48, yes, yes, ; , $92, It diverges; it does not have a sum º , º 78.

16 79. amplitude = 3, period = ft = 54.1, = 35.9, b = = 40.1, = 44.7, =