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Review

Review. EOC Algebra II http :// www.ncpublicschools.org/accountability/testing/eoc/sampleitems/3. Goal 1.

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Review

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  1. Review EOC Algebra II http://www.ncpublicschools.org/accountability/testing/eoc/sampleitems/3

  2. Goal 1

  3. 1. The resting heat rate (h), in beats per minute, for a mammal is related to its mass (m) in kilograms by the equation h = 241m-1/4. What is the approximate resting heart rate, in beats per minute, of a polar bear weighing 326 kilograms?

  4. 2. Atmospheric pressure can be determined by using the equation P = 14.7(10)-0.02h, where P is the atmospheric pressure in pounds per square inch (psi) and h is the elevation above sea level in miles. What is the approximate elevation if the atmospheric pressure is 12.3 psi? • 3.7 miles below sea level • 3.9 miles above sea level • 8.3 miles above sea level • 13.2 miles above sea level

  5. 3. Simplify:

  6. 4. Simplify (x + y)4 • x4 + y4 • x4 + 4xy +y4 • x4 + 4x3y + 4x2y2 + 4xy3 + y4 • x4 + 4x3y + 6x2y2 + 4xy3 + y4

  7. 5. Simplify:

  8. 6. Simplify:

  9. 7. The distance required for a car to stop is directly proportional to the square of its velocity. If a car can stop in 112.5 meters at 15 kilometers per hour, how many meters are needed to stop at 25 kilometers per hour? • 250.75 • 298.00 • 312.50 • 337.50

  10. Goal 2

  11. 1. Which of the following equations is an equation for the circle shown below? • x2 + y2 + 6x – 2y + 1 = 0 • x2+ y2 –6x – 2y + 1 = 0 • x2 + y2 + 6x + 2y + 7 = 0 • x2 + y2 –6x – 2y + 7 = 0

  12. 2. Which is the equation for the parabola that has vertex (-2, 3) and passes through the point (-1, 5) • y = x2 + 4x + 7 • y = x2– 4x + 7 • y = 2x2 – 8x + 11 • y = 2x2+ 8x + 11

  13. 3. Which curve opens to the left? • y2 = 8x + 24 • y = • y2 = –8x – 24 • y = –

  14. 4. Which is the graph of a circle with the equation x2 + 4x + y2 – 6y = 3

  15. 5. Which of the following points is in the interior of the graph of the relation ? • (3, 5) • (2, 4) • (0, -5) • (-2, -3)

  16. 6. Which of the following are the x-intercepts for ? • {-3, 3} • {-4, 4} • {-5, 5} • {-8, 8}

  17. 7. Which is the correct graph of x2 – y2 + 6x + 10y – 17 = 0

  18. 8. Which of the following is a point on the graph of • (-4, -1) • (-4, 1) • (4, 1) • (4, -1)

  19. Goal 3

  20. 1. Gas prices at a local gas station for the year 1999 – 2000 are as follows: Which type of function best models the data? • Exponential • Logarithmic • Polynomial • Rational

  21. 2. Thomas rented a van for $75 a day plus $0.25 for each mile that he would go over 3,000 miles. How can Thomas represent the cost, C, of renting the van for d days and driving for m miles (m ≥ 3,000) • C = 75d + 0.25(m – 3,000) • C = 75d + 0.25(m + 3,000) • C = 75d + 25(m – 3,000) • C = 75d + 25(m + 3,000)

  22. 3. Which set contains the zeros of ? • {-6, -4} • {-12, 2} • {6, 4} • {12, -2}

  23. 4. The graph shows the relationship between hours spent studying and the test score obtained. Which statement best describes this relationship? • The time spent studying is inversely proportional to the square root of the test scores. • The time spent studying is the dependent variable, and the test score is the independent variable. • The time spent studying is inversely proportional to test scores. • The time spent studying is the independent variable, and the test score is the dependent variable.

  24. 5. The Ace Insurance Company has a special plan for safe drivers. For each year that a driver has no tickets or violations, the premium is reduced by 10% and a credit of $15.00 is awarded. Which equation shows the amount a driver with no tickets or violations owes in the (n + 1)th year as a function of the amount owed in the nth year? • f(n+1) = f(n) – 0.10 f(n) – 15 • f(n+1) = f(n) + 0.10 f(n) + 15 • f(n+1) = f(n) + 0.10 f(n) – 15 • f(n+1) = f(n) – 0.10 f(n) + 15

  25. 6. A building contractor is hired to build a rectangular deck. The length needs to be 5 feet less than twice the width (w). His budget is not to exceed $4,000. The cost to build the deck is $25 per square foot. Which relation models the situation? • 50w2 – 125w – 4,000 ≤ 0 • 50w2 – 125w – 4,000 ≥ 0 • 2w2– 5w – 4,000 ≤ 0 • 2w2– 5w – 4,000 ≥ 0

  26. 7. An oxygen mask is placed on a patient. Oxygen is administered to the patient for 5 minutes. Then the oxygen mask is removed and the amount of oxygen in the body decreases exponentially. Which Graph best describe the amount of oxygen in the patient’s bloodstream beginning with the moment when oxygen is first administered?

  27. 7.

  28. 8. Three consecutive integers are such that the sum of the first integer and the product of the other two is 62. Which equation could be used to find the integers? • x2 – x – 1 = 62 • 2x2 – 1 = 62 • x2 + 4x + 2 = 62 • 2x2 + x + 1 = 62

  29. 9. The Graph of f(x) is given. Which is the graph of y = f(x + 1) – 2?

  30. 10. What are the zeros of f(x) = x4 – 7x3 + 15x2 – 9x ? • x = 1, x = 3 • x = 0, x = 1 • x = 0, x = 1, x = 3 • x = 0, x = 1, x = 2, x = 3

  31. 11. A model rocket is fired upward at an initial velocity v0 of 240 ft/s. The height h(t) of the rocket is a function of time t in seconds and is given by the formula h(t) = v0t – 16t2. How long will it take the rocket to hit the ground after takeoff? • 16 seconds B. 15 seconds C. 7.5 seconds D. 4 seconds

  32. 12. If f(x) = x2 – x and g(x) = x – 1, what is f(g(x)) ?

  33. 13. A box of laundry detergent sells for $3.25. The price the store pays is determined by the function f(x) = x – 1, where x is the selling price of the detergent. The wholesale price is determined by g(x) = x – , where x is the price the store pays. What is the wholesale price? • $1.25 B. $1.50 C. $2.25 D. $2.50

  34. 14. What is the inverse of ?

  35. 15. If f(x) = 2x + 3, at what point do the graphs of y = f(x) and y = f -1(x) intersect? • (-1.5, 0) • (0, -1.5) • (-3, -3) • (3, 0)

  36. 16. What are the approximate solutions to the following equation?6x2 – 8x + 1 = 0 • {-0.19, -2.14} • {-0.14, -1.19} • {0.14, 1.19} • {0.19, 2.14}

  37. 17. The Gardners wish to double the area of their 6-by-4-foot garden by adding an equal amount to each dimension. How much should be added to each dimension? • ½ foot B. 1 foot C. 2 feet D. 4 feet

  38. 18. Solve: x2+ 4x + 9 = 0

  39. 19. Solve: 3x2 + 7x = 2 • { , } • { , } • {–2, } • { , 2}

  40. 20. A ball is thrown upward. Its height (h, in feet) is given by the function h= –16t2 + 64t + 3, where t is the length of time (in seconds) that the ball has been in the air. What is the maximum height that the ball reaches? • 3 ft. B. 51 ft C. 63 ft D. 67 ft

  41. 21. The director of a local preschool plans to enclose a rectangular area for a playground. One side will be the side of the building itself. If 60 feet of fence are to be used, what is the maximum area that can be enclosed? • 575 ft2 B. 450 ft2 C. 400 ft2 D. 225 ft2

  42. 22. What is the largest value that can be obtained by multiplying two real numbers whose sum is 3? Round your answer to two decimal places. • 1.51 B. 1.58 C. 2.17 D. 2.25

  43. 23. What are the dimensions of a rectangle having the greatest area with a perimeter of 20 feet? • 15 feet by 5 feet • 10 feet by 10 feet • 6 feet by 4 feet • 5 feet by 5 feet

  44. 24. What are the approximate zeros of the function f(x) = x3 – 2x2 – 3x + 1? • {3, -1} • {4, 0} • {-1.2, 0.3, 2.9} • {-1.1, 0.2, 3.0}

  45. 25. What is the approximate positive zero of P(x) = 2x4 – 5x – 16 • 2.01 • 1.97 • 1.89 • 1.75

  46. 26. A company’s total revenue R (in millions of dollars) is related to its expenses by the equation R = 4x3 – 16x2 + 12x, where x is the amount of expenses (in tens of thousands of dollars). What values of x will produce zero revenue? • x = 0, x = 1, x = 3 • x = 1, x = 3, x = 4 • x = 1, x = 3 • x = 0, x = -1, x = -3

  47. 27.

  48. 28. The height, h(t), in feet, of an object shot from a cannon with initial velocity of 20 feet per second can be modeled by the equation h(t) = -16t2 + 20t + 6, where t is the time, in seconds, after the cannon is fired. What is the maximum altitude that the object reaches? • 13.5 feet B. 12.25 feet C. 10.25 feet D. 1.5 feet

  49. 29. With respect to which line is the graph of f(x) = x4 – 3x2 + 6 symmetric? • x = 0 • y = 0 • y = x • x = 6

  50. 30. A company found that its monthly profit, P, is given by P = -10x2 + 120x – 150 where x is the selling price for each unit of product. Which of the following is the best estimate of the maximum price that the company can charge without losing money? • $300.24 B. $210.00 C. $10.58 D. $6.00

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