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Algebra 1Chapter 12 Assessment Book246

Answers

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

Cumulative TestFor use after Chapters 7212

Solve the linear system.

1. 2x 1 5y 5 216 2. 7x 1 4y 5 26

6x 1 y 5 220 3x 2 8y 5 218

3. 5x 1 3y 5 19 4. 3x 2 9y 5 3

2y 5 5x 1 21 5x 2 8y 5 12

Tell whether the linear system has one solution, no solution, or infi nitely many solutions.

5. 4x 2 3y 5 6 6. 3x 1 7y 5 8

8x 5 6y 1 10 21y 5 29x 1 24

7. Graph the system of linear inequalities.

x

y

26

226226 22

6

2 y >

4 } 7 x 2 2

y < 3x 1 4

Simplify the expression. Write your answer using exponents.

8. (22)2(22)(22)5 9. (63)5 10. 411

} 47

Simplify the expression.

11. 1 }

528 12. (4m2n)2 13. 1 2 3 } r 2

3

Simplify the expression. Write your answer using only positive exponents.

14. 1 2x22 }

yz23 2 2 15. 1 1 }

2a 2

2 p 3ab

} c2 16. (6m)22 p (2m3)4

Evaluate the expression.

17. 365/2 18. 6421/3

19. Write 0.00384 in scientifi c notation.

20. Write 5.26 3 1025 in standard form.

CHAPTERS

7–12

See left.

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Algebra 1Chapter 12 Assessment Book 247

Answers

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

Cumulative Test continuedFor use after Chapters 7212

In Exercises 21 and 22, use the following information.

A company is offering its employees a retirement benefi t of $24,000 per year and guarantees an annual cost of living increase of 2% of the benefi t.

21. Write a function that models the retirement benefi t over time. Assume that the retirement benefi t only increases by the cost of living increase.

22. Use the function to fi nd the amount of the retirement benefi t after 6 years.

23. Tell whether the sequence is arithmetic or geometric. Then graph the sequence.

2, 6, 18, 54, 162, ...

Find the sum or difference.

24. (3x3 1 7x2 2 5x 1 3) 1 (x3 2 3x)

25. (17y2 2 6y 1 5) 2 (11y2 2 2y 1 8)

Find the product.

26. (7t 1 2)(t2 2 5t 2 3) 27. (3a 2 5b)2

Factor the polynomial.

28. x2 1 10x 1 21 29. 4y2 1 23y 2 6

30. x2 2 121 31. t3 1 2t2 2 9t 2 18

Solve the equation.

32. x2 1 x 2 56 5 0 33. z2 1 169 5 26z

34. 11n2 1 21n 5 2 35. r3 5 36r

In Exercises 36 and 37, use the following information.

A kangaroo jumps off the ground with an initial velocity of 18 feet per second.

36. Write an equation that gives the height (in feet) of the kangaroo as a function of time (in seconds) since it jumps.

37. After how many seconds does the kangaroo land on the ground?

CHAPTERS

7–12

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Algebra 1Chapter 12 Assessment Book248

Answers

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

Cumulative Test continuedFor use after Chapters 7212

CHAPTERS

7–12

In Exercises 38 and 39, use the following information.

A pizza box has a length of (x 1 11) inches, a width of (x 1 12) inches, and a height of (x 2 2) inches.

38. Write a polynomial that represents the volume of the pizza box.

39. The volume of the pizza box is 480 cubic inches. What are the length, width, and height of the pizza box?

Graph the function. Label the vertex and axis of symmetry.

40. y 5 x2 2 5 41. y 5 2x2 2 8x 1 3

x

y1

12121

23

25

23 3

x

y1

12121

23

25

3 5

42. Graph y 5 2(x 2 4)(x 1 2)

Solve the equation. Round the solutions to the nearest hundredth, if necessary.

43. x2 2 225 5 0 44. 81x2 2 18 5 7

Use the quadratic formula to solve the equation. Round the solutions to the nearest hundredth, if necessary.

45. 9x2 2 11x 1 3 5 0 46. 7x2 5 2x 2 5

Tell whether the equation has two solutions, one solution, or no solution.

47. 24x2 1 12x 2 9 5 0 48. 2w2 1 9w 5 2w 2 4

49. The distance d (in feet) that it takes a roller coaster train to come to a complete stop can be modeled by the equation d 5 0.7s2 1 0.5s where s is the speed of the train (in feet per second). If the train has 30 feet to come to a complete stop, fi nd the speed at which the train should be traveling. Round your answer to the nearest tenth of a foot per second.

See left.

See left.

See left.

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Algebra 1Chapter 12 Assessment Book 249

See left.

See left.

Answers

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

Cumulative Test continuedFor use after Chapters 7212

Graph the function. Identify its domain and range.

50. y 5 Ï}

x 2 5 51. y 5 1 }

3 Ï}

x 1 2

x

y

2

6

22222

26

6 10

x

y

1

3

1212321

23

3

Simplify the expression.

52. Î}

108

} 4x2 53. Ï

}

18x p 2 Ï}

x3 54. 3 Ï}

375 2 3 Ï}

3000

55. A 12-foot long sliding board is attached to an 8-foot high platform. How far is the bottom of the sliding board from the base of the platform? Round your answer to the nearest tenth of a foot.

56. A treasure hunt is mapped out on a coordinate grid. The fi rst clue is located at (2, 5). The second clue is located at (23, 7). What is the distance between clues if the distance between grid lines represents 25 feet? Round your answer to the nearest tenth of a foot.

Given that y varies inversely with x, use the specifi ed values to write an inverse variation equation that relates x and y. Then fi nd y when x 5 6.

57. x 5 4, y 5 3 58. x 5 23, y 5 8

Divide.

59. (x2 1 2x 2 12) 4 (x 2 3) 60. (6x3 2 5x2 2 3x 1 4) 4 (3x 1 2)

Find the sum, difference, product, or quotient.

61. x2 1 8x 1 15

} x2 2 5x 2 14

p x 2 7 }

x2 2 25 62.

x2 2 4x 1 4 }}

x2 1 11x 1 30 4

x2

} x2 1 7x 1 10

63. 5 }

x 2 1 2

2x } x 1 7 64.

3x }

x2 1 3x 2 18 1

7 }

x2 1 8x 1 12

Simplify the complex fraction.

65. 5x3

} 12

}

8x2 66. x2 1 3x 1 2

} 6x 2 24

}

x2 1 5x 1 6

}} 3x2 2 3x 2 36

CHAPTERS

7–12

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Algebra 1Assessment BookA32

e. x > 0; C > 4.75 f. The average cost per person decreases toward 4.75 as the number of people increases. The decreases are rapid at fi rst, but become more gradual. g. No, the average cost per person cannot go below $4.75. This value is a horizontal asymptote for the function. Because the extra items cost $4.75 per person and a portion of the pavilion cost will be added to this amount, the average cost per person will never drop below this amount.

Chapters 7–12

Cumulative Test

1. (23, 22) 2. (2, 3) 3. (21, 8) 4. (4, 1)

5. no solution 6. infi nitely many solutions

7.

x

y

26

626

6

8. (22)8 9. 615 10. 44 11. 58 12. 16m4n2

13. 227

} r3 14.

4z6 }

x4y2 15. 3b

} 4ac2 16.

4m10 }

9

17. 7776 18. 1 }

4 19. 3.84 3 1023

20. 0.0000526 21. p 5 24,000(1.02)t

22. $27,027.90

23. geometric;

24. 4x3 1 7x2 2 8x 1 3 25. 6y2 2 4y 2 3

26. 7t3 2 33t2 2 31t 2 6 27. 9a2 2 30ab 1 25b2

28. (x 1 3)(x 1 7) 29. (4y 2 1)( y 1 6)

30. (x 1 11)(x 2 11) 31. (t 1 3)(t 2 3)(t 1 2)

32. 28, 7 33. 13 34. 1 }

11 , 22 35. 26, 0, 6

36. h 5 216t2 1 18t 37. t 5 1.125

38. x3 1 21x2 1 86x 2 264

39. l 5 15 in., w 5 16 in., h 5 2 in.

40.

x

y1

12121

23

23 3

(0, 25)

x 5 0 41.

x

y1

12121

23

25

3 5

(2, 25)

x 5 2

42.

43. 615 44. 6 5 } 9 45. 0.81, 0.41

46. no solution 47. one solution

48. two solutions 49. 6.2 ft/sec

50.

x

y

2

6

22222

26

6 10

51.

x

y

1

3

1212321

23

3

domain: x ≥ 5; domain: x ≥ 22;range: y ≥ 0 range: y ≥ 0

52. 3 Ï

}

3 }

x 53. 6x2 Ï

}

2 54. 25 3 Ï}

3 55. 8.9 ft

56. 134.6 ft 57. y 5 12

} x ; 2 58. y 5 224

} x ; 24

59. x 1 5 1 3 }

x 2 3 60. 2x2 2 3x 1 1 1

2 }

3x 1 2

61. x 1 3 }}

(x 1 2)(x 2 5) 62.

(x 2 2)(x2 2 4) }}

(x 1 6)x2

63. 22x2 1 7x 1 35

}} (x 2 1)(x 1 7)

64. 3x2 1 13x 2 21

}} (x 1 6)(x 2 2)(x 2 3)

65. 5x

} 96

66. x 1 1

} 2

Chapters 1–12

End-of-Course Test

1. 21 2. 2 3. 51 4. 211 5. $2.50, $2.75, 18-holes 6. y 5 2x 1 26; independent variable: x, dependent variable: y, domain: x ≥ 0, range: y ≥ 26 7. 225 8. 42 9. 235 10. 0.16

11. 225 12. 5 }

3 13. 3 14. 294 15. 2

3 } 11

Lesson 12, continuedA

NS

WE

RS

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