Class: Date: Algebra 2 Trig Midterm Exam Review 2014 loose-leaf paper Do all work in a neat and organzied manner on Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which is the graph of y = 2(x 2) 2 4? a. c. b. d. 2. The volume of a shipping box in cubic feet can be expressed as the polynomial 2x 3 + 11x 2 + 17x + 6. Each dimension of the box can be expressed as a linear expression with integer coefficients. Which expression could represent one of the three dimensions of the box? a. x + 6 c. 2x + 3 b. x + 1 d. 2x + 1 1
3. Use a graphing calculator to determine which type of model best fits the values in the table. x 6 2 0 2 6 y 6 2 0 2 6 a. quadratic model c. linear model b. cubic model d. none of these 4. A biologist took a count of the number of migrating waterfowl at a particular lake, and recounted the lake s population of waterfowl on each of the next six weeks. Week 0 1 2 3 4 5 6 Population 585 582 629 726 873 1,070 1,317 a. Find a quadratic function that models the data as a function of x, the number of weeks. b. Use the model to estimate the number of waterfowl at the lake on week 8. a. P(x) = 25x 2 28x + 585; 1,614 waterfowl b. P(x) = 30x 2 + 28x + 535; 2,679 waterfowl c. P(x) = 25x 2 28x + 585; 1,961 waterfowl d. P(x) = 30x 2 + 28x + 535; 2,201 waterfowl Short Answer Describe the pattern in the sequence. Find the next three terms. 5. 1, 2, 6, 16, 44,... 6. Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth. 7. Write a recursive formula for the sequence 8, 10, 12, 14, 16,... Then find the next term. 8. Write an explicit formula for the sequence 7, 2, 3, 8, 13,... Then find a 14. 9. The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit formula for the sequence of the number of bacteria. Hours (n) 1 2 3 4 5 Number of Bacteria 19 38 57 76 95 10. Is the formula a n = 4n(n 1) is explicit or recursive? Find the first five terms of the sequence. 2
Is the sequence arithmetic? If so, identify the common difference. 11. 13, 20, 27, 34,... 12. 14, 21, 42, 77,... 13. Find the missing term of the arithmetic sequence 22,, 34,... 14. Find the arithmetic mean a n of a n 1 = 3.9, a n + 1 = 7.1. 15. A grocery clerk sets up a display of 12-pack cartons of cola. There are 15 cartons at the base of the triangle and one at the top. How many cartons of cola are needed for the complete display? Is the sequence geometric? If so, identify the common ratio. 16. 6, 12, 24, 48,... 17. 2, 4, 16, 36,... Write the explicit formula for the sequence. Then find the fifth term in the sequence. 18. a 1 = 3, r = 3 Find the missing term of the geometric sequence. 19. 45,, 1620,... Use the finite sequence. Write the related series. Then evaluate the series. 20. 26, 29, 32, 35, 38, 41, 44 21. The sequence 15, 21, 27, 33, 39,..., 75 has 11 terms. Evaluate the related series. 22. 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. 23. Evaluate the series 1 + 2 + 4 + 8 to S 10. 3
24. In June, Cory begins to save money for a video game and a TV he wants to buy in December. He starts with $20. Each month he plans to save 10% more than the previous month. How much money will he have at the end of December? Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms. 25. y = (x + 1)(6x 6) 6x 2 26. f(x) = (3x + 2)( 6x 3) Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q. 27. 28. A manufacturer determines that the number of drills it can sell is given by the formula D = 3p 2 + 180p 285, where p is the price of the drills in dollars. a. At what price will the manufacturer sell the maximum number of drills? b. What is the maximum number of drills that can be sold? 4
29. Use the vertex form to write the equation of the parabola. 30. Identify the vertex and the y-intercept of the graph of the function y = 3(x + 2) 2 + 5. 31. Write y = 2x 2 + 12x + 14 in vertex form. Write the equation of the parabola in vertex form. 32. vertex ( 4, 3), point (4, 131) Factor the expression. 33. 15x 2 21x 34. 8x 2 + 12x 16 35. x 2 2x 63 36. 3x 2 + 26x + 35 37. 16x 2 + 40x + 25 38. 9x 2 16 39. x 3 + 216 40. x 4 20x 2 + 64 41. Solve by factoring. 4x 2 + 28x 32 = 0 5
Solve the equation by finding square roots. 42. 3x 2 = 21 43. The function y = 16t 2 + 486 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second. 44. Use a graphing calculator to solve the equation 5x 2 + 6x 9 = 0. If necessary, round to the nearest hundredth. 45. Simplify 175 using the imaginary number i. Write the number in the form a + bi. 46. 4 + 10 47. 6 48 Simplify the expression. 48. (2 5i) (3 + 4i) 49. (2 + 5i)( 1 + 5i) Solve the equation. 50. 9x 2 + 16 = 0 51. Find the missing value to complete the square. x 2 + 2x + Solve the quadratic equation by completing the square. 52. x 2 + 10x + 14 = 0 Rewrite the equation in vertex form. 53. y = x 2 + 10x + 16 Use the Quadratic Formula to solve the equation. 54. 5x 2 + 9x 2 = 0 6
55. 4x 2 x + 3 = 0 56. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 155 square yards. The situation is modeled by the equation h 2 + 5h = 155. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard. 57. Classify 7x 5 6x 4 + 4x 3 by degree and by number of terms. 58. The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1995. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 2006. Years since 1995 1 3 5 7 9 Trees planted (in thousands) 1.3 18.3 70.5 177.1 357.3 59. Write 4x 3 + 8x 2 96x in factored form. 60. Use a graphing calculator to find the relative minimum, relative maximum, and zeros of y = 3x 3 + 15x 2 12x 60. If necessary, round to the nearest hundredth. 61. Find the zeros of y = x(x 3)(x 2). Then graph the equation. 62. Write a polynomial function in standard form with zeros at 5, 4, and 1. 63. Find the zeros of f(x) = (x + 3) 2 (x 5) 6 and state the multiplicity. 64. Divide 3x 3 3x 2 4x + 3 by x + 3. 65. Use synthetic division to find P(2) for P(x) = x 4 + 3x 3 6x 2 10x + 8. Find the roots of the polynomial equation. 66. x 3 2x 2 + 10x + 136 = 0 67. A polynomial equation with rational coefficients has the roots 3 + 6, 2 5. Find two additional roots. For the equation, find the number of complex roots, the possible number of real roots, and the possible rational roots. 68. x 7 2x 6 + 3x 2 2x + 5 = 0 69. Find all zeros of 2x 4 5x 3 + 53x 2 125x + 75 = 0. 7
Sketch the asymptotes and graph the function. 70. y = x 2 7x + 12 x 2 1 Find any points of discontinuity for the rational function. 71. y = x 8 x 2 + 6x 7 72. Describe the vertical asymptote(s) and hole(s) for the graph of y = (x 5)(x 2) (x 2)(x + 4). 73. Find the horizontal asymptote of the graph of y = 6x 2 + 5x + 9 7x 2 x + 9. Simplify the rational expression. State any restrictions on the variable. 74. n 4 11n 2 + 30 n 4 7n 2 + 10 Multiply or divide. State any restrictions on the variables. 75. 76. z 2 z + 1 z 2 + 3z + 2 z 2 + 3z x + 2 x 1 x + 4 x 2 + 4x 5 Add or subtract. Simplify if possible. 77. 78. w 2 + 2w 24 w 2 + w 30 + 8 w 5 a 2 2a 3 a 2 9a + 18 a 2 5a 6 a 2 + 9a + 8 Solve the equation. Check the solution. 79. g + 4 g 2 = g 5 g 8 8
80. 5 6w + 1 w = 4 81. A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they 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 many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth. 9
Algebra 2 Trig Midterm Exam Review 2014 loose-leaf paper Answer Section Do all work in a neat and organzied manner on MULTIPLE CHOICE 1. A 2. D 3. C 4. C SHORT ANSWER 5. Add the two previous terms and then multiply by 2; 120, 328, 896 6. 9.2 feet 7. a n = a n 1 + 2, where a 1 = 8; 18 8. a n = 5n + 12; 58 9. a n = 19n 10. explicit; 0, 8, 24, 48, 80 11. yes, 7 12. no 13. 28 14. 5.5 15. 120 cartons 16. yes, 2 17. no 18. a n = 3 ( 3) n 1 ; 243 19. 270 20. 26 + 29 + 32 + 35 + 38 + 41 + 44 = 245 21. 495 22. $92,077.48 23. 1023 24. $189.74 25. linear function linear term: 0x constant term: 6 26. quadratic function quadratic term: 18x 2 linear term: 21x constant term: 6 27. ( 1, 2), x = 1 P'(0, 1), Q'( 3, 2) 28. $30; 2,415 drills 1
29. y = 3(x + 2) 2 + 2 30. vertex: ( 2, 5); y-intercept: 7 31. y = 2(x + 3) 2 4 32. y = 2(x + 4) 2 + 3 33. 3x(5x + 7) Ê 34. 4 2x 2 ˆ + 3x 4 Ë Á 35. (x 9)(x + 7) 36. (3x + 5)(x + 7) 37. (4x + 5) 2 38. (3x + 4)(3x 4) 39. (x + 6)(x 2 6x + 36) 40. (x 2)(x + 2)(x 4)(x + 4) 41. 8, 1 42. 7, 7 43. 5.51 seconds 44. 0.87, 2.07 45. 5i 7 46. 10 + 2i 47. 6 4i 3 48. 1 9i 49. 27 + 5i 50. 4 3 i, 4 3 i 51. 1 52. 5 ± 11 53. y = (x + 5) 2 9 1 54. 5, 2 1 55. 8 ± i 47 8 56. 10.20 yards 57. quintic trinomial 58. T(x) = 0.4x 3 + 0.8x 2 + 0.1x; 630.3 thousand trees 59. 4x(x 4)(x + 6) 60. relative minimum: (0.36, 62.24), relative maximum: ( 3.69, 37.79), zeros: x = 5, 2, 2 2
61. 0, 3, 2 62. f(x) = x 3 2x 2 19x + 20 63. 3, multiplicity 2; 5, multiplicity 6 64. 3x 2 12x + 32, R 93 65. 4 66. 3 ± 5i, 4 67. 3 6, 2 + 5 68. 7 complex roots; 1, 3, 5, or 7 real roots; possible rational roots: ±1, ±5 69. 1, 3 2, ± 5i 70. 71. x = 1, x = 7 72. asymptote: x = 4 and hole: x = 2 73. y = 6 7 74. n 2 6 n 2 2 ; n ± 5, n ± 2 3
75. 76. 77. 78. z 2 + 2z, z 1, 0, 3 z + 3 (x + 2)(x + 5), x 1, 4 x + 4 w + 4 w 5 21a 28 (a 6)(a + 8) 79. 14 80. 11 24 x 81. 7 + x 6 = 1; 3.23 hours 4