Algebra 2-2nd Semester Exam Review 11

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1 Algebra 2-2nd Semester Eam Review 11 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Determine which binomial is a factor of. a. 14 b. + 4 c. 4 d. + 8 Short Answer Factor the epression. 2. Factor: 3. Factor: 4. Factor: 5. Solve by factoring. = 0 6. Solve. Solve the equation by finding square roots. 7. Solve by using the square root method: Use the Quadratic Formula to solve the equation. 8. Solve by using the quadratic formula: 9. Solve by using the quadratic formula the equation. If necessary, round to the nearest hundredth. 10. Zach wrote the formula w(w 1)(6w + 4) for the volume of a rectangular prism he is designing, with width w, which is always has a positive value greater than 1. Find the product and then classify this polynomial by degree and by number of terms. 11. Write 5 2 ( ) in standard form. Then classify it by degree and number of terms. 12. Write the epression ( 5)( + 2) as a polynomial in standard form. 13. Write in factored form.

2 14. Find the zeros of. 15. Find the zeros of and state the multiplicity. 16. Write a polynomial function in standard form with zeros at 2, 4, and Use the Rational Root Theorem to list all possible rational roots of the polynomial equation. Do not find the actual roots. 18. Divide by Use synthetic division to find P(2) for. Divide using synthetic division. 20. Divide using synthetic division: 21. Divide using synthetic division: Find the roots of the polynomial equation. 22. Find the roots of 23. Find the roots of 24. Simplify. Assume that all variables are positive. 25. Subtract if possible. Multiply Simplify.

3 28. Simplify: 29. Simplify using smaller bases and fractional eponents: 30. Simplify using smaller bases and fractional eponents: 31. Simplify using smaller bases and fractional eponents: 32. Find the real-number root. 33. Multiply and simplify if possible. 34. Simplify: 35. Multiply and simplify. Assume that all variables are positive. Divide and simplify. Assume that all variables are positive. 36. Simplify: Rationalize the denominator of the epression. Assume that all variables are positive. 37. Simplify by rationalizing the denominator: Add if possible. 38. Simplify if possible 39. Write in simplest form by using smaller bases and fractional eponents. Solve. Check for etraneous solutions.

4 40. Solve and check your answers: 41. A garden has width and length. What is the perimeter of the garden in simplest radical form? 42. Consider the function. Does the function represent eponential growth or decay? What is the initial value? What is the rate of growth/decay? 43. Graph. Is this eponential growth or decay? 44. You invest $200 in a savings account that earns 5% interest compounded quarterly. How much will you have in the account after 7 years? 45. The half-life of a radioactive material is 3 days. If you have 100 g of the material now, approimately how much will you have left after 11 days? Round to the nearest hundredth. Write the equation in logarithmic form. 46. Write the equation in logarithmic form: Evaluate the logarithm. 47. Evaluate 48. Evaluate 49. Write the equation in eponential form. 50. A single-celled bacterium divides every hour. The number N of bacteria after t hours is given by the formula. After how many hours will there be 32 bacteria? 51. Solve. Round to the nearest ten-thousandth. 52. Solve. 53. Solve. Solve the equation. Check the solution.

5 54. Solve the equation and check your solution: 55. Solve the equation and check your solution: 56. Solve the equation and check your solution: 57. Solve the equation and check your solution: Solve the equation. 58. Solve and check your answers: 59. Solve and check your answers: 60. Solve and check your answers: Simplify the rational epression. State any restrictions on the variable. 61. Simplify and state restrictions: 62. Describe the vertical asymptote(s) and hole(s) for the graph of. 63. Find the least common multiple of and. Add or subtract. Simplify if possible. 64. Simplify and state restrictions: 65. Simplify and state restrictions:

6 66. Simplify and state restrictions: Multiply or divide. State any restrictions on the variables. 67. Simplify and state restrictions: 68. Simplify and state restrictions: 69. Simplify and state restrictions: 70. The line of sight from a small boat to the light at the top of a 35-foot lighthouse built on a cliff 15 feet above the water makes a 16 angle with the water. To the nearest foot, how far is the boat from the cliff? 35 ft ft Drawing is not to scale. Find the length. Round to the nearest tenth

7 Find the measure of in the right triangle In, is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. 75. a = 3, c = Use the Law of Sines. Find b to the nearest tenth. C 57 b B A

8 Find the remaining sides and angles in the triangle. Round your answers to the nearest tenth. 77. = 55, = 44, and b = Use the Law of Cosines. Find b to the nearest tenth. C 22 b B A 79. Use the Law of Cosines. AB = 73, BC = 40, and AC = 67. Find to the nearest tenth of a degree. Draw a picture!

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