Algebra 2 College 2013 Midterm Review. Solve each equation: 2. -4(24 + 8y) = n 24 = 14 30n 4. 5x x = x 8.

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1 Algebra 2 College 2013 Midterm Review Name: 1. Dan paid a total of $25.80 last month for his international calls. He makes international calls only to England. Dan pays $0.06 per minute in addition to $10.98 fixed monthly payment. How many minutes of international calls did Dan make last month? Minutes = Solve each equation: 2. -4(24 + 8y) = n 24 = 14 30n 4. 5x x = x 8 y = n = x = 5. There was $1,400 in Naomi s school art and music fund when school began. Then the parents group held a 12 day fundraiser to reach the school s goal of $6,000. Find the average amount of money per day the parents raised. 6. Determine whether the data set could represent a linear function. If so, write the equation. Average = x f(x) Linear? Equation 7. Write an equation of a line with slope -1/3 that passes through (-6, 4). Your equation needs to be written in slopeintercept form. Equation 8. What is the slope of the line whose equation is 3x + 2y = 16? Slope

2 9. Find the intercepts of 5x + 10y = -20. X-int Y-int 10. Determine whether the data in the table are linear. Explain. Session Length (min) Cost($) Find the slope of the line that passes through the points (1, 3) and (9, 7). Slope 12. In slope-intercept form, write the equation of the line that contains the points in the table. x y Equation 13. In slope-intercept form, write the equation of the line that is parallel to y = -2x 9 and passes through (-2, -4). Equation 14. Two snow resorts offer private lessons to their customers. Big Time Ski Mountain charges $5 per hour plus $50 insurance. Powder Hills charges $30 per hour plus $10 insurance. For what number of hours is the cost of lessons the same for each resort? Hours

3 15. Consider the function f(x) = -4x² - 8x + 6. Determine whether the graph opens up or down. Find the a.) axis of symmetry b.) vertex c.) y-intercept d.) maximum or minimum Then graph the function. 16. Find the minimum or maximum value of f(x) = x² - 2x The distance d in meters traveled by a skate-board on a ramp is related to the time traveled t in seconds. This is modeled by the function: d(t) = -4.9t² + 23t + 5. What is the maximum distance the skateboard can travel, and at what time would it achieve this distance? Round your answers to the nearest hundredth. Distance = 18. Find the zeros of f(x) = x² + 4x 5 by using a graphing calculator. Zeros 19. Find the zeros of the function h(x) = x² + 23x + 60 by factoring. Zeros 20. Write a quadratic function in standard form with zeros 6 and -8. Function

4 21. Complete the square for the expression x² - 16x +. The resulting binomial squared is 22. Solve by completing the square: x²+ 2x = Identify the vertex of f(x) = (x 3) Identify the vertex of f(x) = -2(x + 3) Solve the equation x² - 10x + 30 = Solve x 2 7x 8 > Solve x Determine whether the data set could represent a quadratic function. Explain. x y Write a quadratic function that fits the points (0, 6), (2, 4), and (3, 6)

5 30. The table shows approximate fuel consumption in miles per gallon, given the tread height of the tire in mm. Find a quadratic model for the fuel consumption given the tread height. Use the model to estimate the fuel consumption for a car with a tread height of 15 mm. Fuel Consumption (miles per gallon) Tread Height (mm) Solve the equation 2x² + 18 = 0. x = 32. Use the quadratic formula to find the zeros of the function f(x) = x² + 6x Zeros 33. Find the zeros of f(x) = x² + 7x + 9 by using the quadratic formula. Zeros 34. Write the complex conjugate of 3i Simplify i 42.

6 36. Subtract (5 2i) (6 + 8i). 37. Multiply 6i(4 6i). 38. Simplify 2 2i. 39. Simplify (3 2i)². 5 3i 40. Identify the degree of the monomial -5r³s Rewrite the polynomial 12x² + 6 7x 5 + 3x³ + 7x 4 5x in standard form. Standard form Identify the following: Leading coefficient: Degree: Number of Terms: Name: Simplify the following: 42. (4d 5 - d³) + (d 5 + 6d³ - 4) 43. (3a 4 2a 3 + a 2 1) (2a 4-4a 2 + 3)

7 44. 2cd³(-4c³d² - cd³) 45. (5x 3)(x³ - 5x + 2) 46. (x 2y)³ 47. (4x + 3) Divide by using synthetic division: 49. Divide by using synthetic division: (5x + 6x³ - 8) (x 2) (x² - 9x + 2) (x 2) 50. Factor x³+ 5x² - 9x Factor the expression 27x Solve the polynomial equation 3x 5 + 6x 4 72x³ = 0 by factoring.

8 53. Identify the roots of -3x³ - 21x² + 72x = 0. State the multiplicity of each root. 54. Write the simplest polynomial 55. Write the factors and state the function with zeros -2 (multiplicity 2) and 7. degree of the simplest function with zeros 2 i and Identify the leading coefficient, 57. Identify whether the function graphed degree, and end behavior of the function has an odd or even degree and a positive or P(x) = -5x 4 6x² + 6. negative leading coefficient. 58. Use finite differences to determine the degree of the polynomial that best describes the following data. Use your graphing calculator to find the polynomial function that models this data. 59. Tell whether the function y = 3(2) x shows growth or decay. 60. A bacteria population starts at 2,032 and decreases at about 15% per day. Write a function representing the number of bacteria present each day. Graph the function on your graphing calculator. After how many days will there be fewer than 350 bacteria? 61. An initial investment of $10,000 grows at 11% per year. Write the function that represents the value of the investment after t years.

9 62. Write the inverse of f(x) = Write the exponential equation 2³ = 8 in logarithmic form. 64. Write the logarithmic equation log 4 16 = 2 in exponential form. 65. Evaluate log 4 by using mental math. 66. Express log log as a single logarithm. Simplify, if possible. 67. Express log 2 64 log 2 4 as a single logarithm. Simplify, if possible. 68. Express log as a product. Simplify, if possible. 69. Simplify the expression log Evaluate log If necessary, round your answer to the nearest tenth. 71. Solve 3 x = Solve 8 x+8 = 32 x. 73. Solve log 5 x 10 log 5 x 6 = 20.