Spring 011 Final Exam Review Show all work and answers on SEPARATE PAPER The review for the final must be completed b the date of the original final exam in order to be eligible for a reassessment in the event of a failing final exam grade. Calculator permitted: 1. Determine which binomial is not a factor of. pg.37, ex a. x + c. x 5 b. x + 3 d. x + 3. Write x (x + 5x 3 ) in standard form. Then classif it b degree and number of terms. pg.313, ex1 3. Write a polnomial function in standard form with zeros at 1,, and 3. pg. 313, ex 1. Classif 3x 5 + 8x + x 3 b degree and b number of terms. pg. 313, ex 1 5. Write 5x 3 + 15x 90x in factored form. pg. 30, ex 6. Find the zeros of and state the multiplicit. pg. 3, ex 6 7. Find a third-degree polnomial equation with rational coefficients that has roots and + i. pg. 3 ex 5 DIVIDE: 8. b x +. pg. 38, ex3 9. For the equation, find the number of complex roots, the possible number of real roots, and the possible rational roots. 10. pg. 38, ex 1 11. Use snthetic division to find P( 1) for. pg. 39, ex 5 Find the roots of the polnomial equation. pg. 38, ex 1. 13. Factor the expression. pg. 33, ex 3 1. Use Pascal s Triangle to expand the binomial. 15. pg. 360, ex 1 16. Simplif. Assume that all variables are positive. Divide and simplif. Assume that all variables are positive. Rationalize the denominator of the expression if necessar. pg. 38, ex 5 17. 18. 19. The formula for the volume of a sphere is. Find the radius, to the nearest hundredth, of a sphere with a volume of 1 in. 3. Simplif. 0. pg.387, ex 3 Solve the equation. 1. pg.397, ex 1. pg. 397, ex 1 Multipl. 3. pg. 387, ex. Let and. Find 3f(x) g(x). pg.0, ex 1
5. Let and. Find and its domain. 6. Let and. Find. pg.05, ex 3 7. Find the inverse of. pg. 13, ex 8. An initial population of 50 quail increases at an annual rate of 17%. Write an exponential function to model the quail population. pg. 39, ex 9. Write an exponential function for a graph that includes (0, 5) and (, 5). pg.0, ex 3 30. The half-life of a certain radioactive material is 83 hours. An initial amount of the material has a mass of 179 kg. Write an exponential function that models the deca of this material. Find how much radioactive material remains after hours. Round our answer to the nearest thousandth. pg. 8, ex 3 31. Suppose ou invest $1700 at an annual interest rate of 7.3% compounded continuousl. How much will ou have in the account after ears? pg. 50, ex 5 3. Write the equation in logarithmic form pg. 55, ex 33. Write the equation in exponential form. Write the expression as a single logarithm. 38-: pg. 63, ex, 3 3. 35. Expand the logarithmic expression. 36. Solve for x. Round to the nearest thousandth. 37. 38.. 39. Suppose that varies jointl with w and x and inversel with z and = 70 when w =, x = 10 and z =. Write the equation that models the relationship. Then find when w = 8, x = 5 and z = 7.pg. 98, ex, 5 0. Identif the points of discontinuit: are the holes or vertical asmptotes AND horizontal asmptote. pg. 510, ex1--3 1. Describe the vertical asmptote(s) and hole(s) for the graph of.. 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. pg. 97, ex 1 x 7 1 105 60 15 60 Multipl or divide. State an restrictions on the variables. pg. 518, ex1-3..
Add or subtract. Simplif if possible. pg. 53, ex - 5. 6. Simplif the complex fraction. pg. 5, ex5-6 7. 8. Solve the equation. Check the solution. pg. 530, ex1-9. 50. 51. Write an equation of an ellipse with center (3, ), horizontal major axis of length 16, and minor axis of length 10. pg. 593 ex 1 5. Write an equation for the translation of, 8 units right and 6 units up. 10.3 53. Write an equation of a parabola with a vertex at the origin and a directrix at = 6 10. 5. Identif the vertex, focus, and directrix of the graph of. Identif the conic section. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hperbola, give the center and foci. 10.6 55. 56. 57. The table shows the number of llamas born on llama ranches worldwide since 1988. Find a cubic function to model the data and use it to estimate the number of births in 1999. Years since 1988 1 3 5 7 9 Llamas born (in thousands) 1.6 0 79. 03. 16 58. The volume in cubic feet of Long John Silver s treasure chest can be expressed as, or as the product of three linear factors with integer coefficients. The width of the box is a. Find linear expressions with integer coefficients for the other dimensions. b. If the width of the chest is 3 feet, what are the other dimensions? 59. The optimal height h of the letters of a message printed on pavement is given b the formula. Here d is the distance of the driver from the letters and e is the height of the driver s ee above the pavement. All of the distances are in meters. Find h for d = 90 m and e = 1. m. Show our work. 60. Suppose ou are shopping at Best Bu over Memorial Da Weekend. The are having a store sale of 0% off an single item. You also have a coupon worht $5 off an item. a. Write a function f(x) to model the cost of an item with the 0% discount. b. Write a function g(x) to model the cost of an item with the $5 coupon.
c. Use a compostiton of our two functions to model how much ou would pa for an item if the clerk applies the coupon first and then the discount. 61. The velocit of sound in air is given b the equation, where v is the velocit in meters per second and t is the temperature in degrees Celsius. a. Find the temperature when the velocit of sound in air is 318 meters per second. Round the answer to the nearest degree. b. Find the velocit of sound in meters per second when the temperature is 0 C. Round the answer to the nearest meter per second. 6. Ms. Dot bought herself a new blue Lexus convertible. The cost of this brand new auto is $9,950.00. Well, it is estimated to depreciate in value at an annual rate of 1%. What will the value of her car be when it is ears old? 63. A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is located inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward. 6. The maximum load a clindrical column can support varies directl as the fourth power of the diameter and inversel as the square of the height. A column that is ft. in diameter and 10 ft. high can support up to 6 tons. If a column is 1 ft. in diameter and 1 ft. high, what is the maximum load it can support? 65. A group of college students are volunteering for Help the Homeless during their spring break. The are putting the finishing touches on a house the built. Working alone, Irina can paint a certain room in 7 hours. Paulo can paint the same room in 6 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How man hours will it take them to paint the room? If necessar, round our answer to the nearest hundredth. 66. The landscape plans of a public park include a circular fountain. The plans have been gridded where the units are meters. The center of the fountain is located on the plans at the coordinates of. The diameter of the fountain is 1 meters. a. Write an equation that models the outline of the fountain as located on the landscape plans. b. Find the circumference of the fountain (round to the nearest meter). 67. The adult population of a cit is 1,150,000. A consultant to a law firm uses the function to estimate the number of people P(t) who have heard about a major crime t das after the crime was first reported. About how man das does it take for 60% of the population to have been exposed to news of the crime? ***** Non-Calculator Section ***** Graph: 68. pg. 1, ex1-3 69. Graph the conic section. 70. pg. 568 ex 1 71. pg. 580, ex 7.. pg. 573 ex 73.. pg. 568 ex5 Graph the exponential function. Use a table of values. 7. pg. 7 ex1
Graph the logarithmic equation. 75. pg. 56 ex 5-6 Sketch the asmptotes and graph the function. Use a table of values. pg. 505, ex 76. pg.505 ex. 77. Find the horizontal asmptote of the graph of. 78. Simplif pg. 79 sec. 8.6
Spring 011 Final Exam Review Answer Section 1. A. 0x 5 + 8x ; quintic binomial 3.. quintic trinomial 5. 5x(x + 6)(x 3) 6. 5, multiplicit 3;, multiplicit 5 7. 8., R 90 9. 10. 7 complex roots; 1, 3, 5, or 7 real roots; possible rational roots: ±1, ±5 11. 1. 13. 1. 15. 16. 17. 18. 19. 1. in. 0. 1. 10. 1 3.. 5. 3; all real numbers except x 6. 18 7. 8. 9. 30. ; 18.957 kg 31. $1,967.3 3. 33. 3. 35. 36. 37. 0.06 38. 0.07 39. 0 0. Vert. asmptote x=3, x=6; Horizontal asmptote =0 1. asmptote: x = 5 and hole: x =. direct variation; 3.. 5. 6. 7. 8. 16 17 9. 53 75 13 50. 3 51. 5. 53. 5. vertex ( 5, 3), focus ( 5, 6), directrix at = 0 55. ellipse with center (, 3), foci at 56. hperbola with center ( 3, 5), foci at 57. ; 71,600 llamas 58. a. b. feet and feet
59. [] Write the formula. = Substitute for d and e. 69. 9.1 The distance is about 9.1 meters. 60. a. b. c. 61. a. 0 C b. 3 meters per second 6. $,957 63. 6. 0.6 tons 65. ; 3.3 hours 66. a. b. about meters 67. about 31 das 68. x 70. 71. x 8 6 8 6 6 8 x 6 8 6 6 6 x 6
7. 7. 0 8 16 1 8 8 x 8 8 6 6 x 73. vertex ( 5, ), focus ( 5, 6), directrix at = 75. 5 3 1 x 10 8 6 1 6 8 10 x 3 5 76. 10 5 10 5 5 10 x 5 10 77. 78. 3