Name ________________________________ Date ________________ Period _________

1ST Semester Final Exam Review 1st SIX WEEKS Solve the following linear equations. 1. 4x – 5(x – 2) = 9x – 14

2. 6x + 2(3 – x) = 7x + 1

3. 6x – 3(6 – 5x) + 3x = 10 – 4(2 – x)

4. 2(x – 3) = 4x

Solve the following linear inequalities. 5. 3y + 6 < 15 or 1 – 3y < -11

6. –6 < 4 – 2x < 12

7. –4y + 8 > 16 or 3y – 5 > 5

Solve the following absolute value inequalities. 8. 53x2 ≥−

9. 84x2 ≤+

10. 31x =+

Write the equation of the line with the following conditions. 11. Passing through ( -3, 8) and (5, 4) 12. passing through ( 2, -4) and (2, 0) 13. Passing through ( -5, 2) with a slope of 3 14. The table 15. passing through ( 5, -2) and (9, -2)

x y -4 13 -2 9 1 3 4 -3

1ST SEM EXAM REVIEW

Graph each of the following. 16. 2x – 3y= 12 17. 2x + y > 1 18. x – y >2 Solve the following system of equations using any method. 19. x – 4y = 1

-2x + 5y = 4

20. x + y = 10 3x – 2y = 5

1ST SEM EXAM REVIEW

21. 4x + 3y = -2 3x + 2y = 1

22. x + 3y = 9 3x + 2y = -1

Solve the following word problems. 23. A group of 42 people go to the zoo. The admission price is $6 for adults and $3 for kids. If the group spends $162, how many adults and kids were in the group? 24. To call London, a long distance phone company charges a fixed rate for the first minute and a different rate for each additional minute. If a 12 minute phone call costs $2.35 and a 25 minute call costs $3.65, how much are their rates?

1ST SEM EXAM REVIEW

2nd SIX WEEKS Find each answer if possible.

⎥⎦

⎤⎢⎣

⎡−

−=

3412

A ⎥⎦

⎤⎢⎣

⎡−

−=

6335

B ⎥⎦

⎤⎢⎣

⎡=

3142

C

25. A + C = 26. 3A – 2C = 27. B² = 28. C x A =

29. =−

−3412

30. =−

−6335

31. =−1A

32. =−1B

1ST SEM EXAM REVIEW

Use matrix equations to solve the following systems. 33. 4x - 2y + z = 2

-x - 3y + 2z = -5 2x + y + 3z = -4

34. 4x - y + z = 3 x + 2y + z = 0 3x + 7y - 3z = 6 Use Cramer’s Rule to solve the following systems. 35. 2x - 3y + 3z = -12 3x - 2y - 2z = 4 -3x + 2y - z = 5

1ST SEM EXAM REVIEW

36. x + 4y - 5z = -7 3x + 2y + 3z = 7 2x + y + 5z = 8

Factor the following. 37. x² + x – 6 _________________ 38. 4x² - 49 _________________ 39. 3x² - 12x _________________ 40. 6x² - 5x + 1 _________________ 41. x² + 6x + 8 _________________ 42. 3x² - 4x – 4 _________________ 43. x² - 100 _________________ 44. 4x² - 16 _________________

1ST SEM EXAM REVIEW

Simplify the following radicals. 45. 250 __________ 46. 160 __________ State the domain and range of the following relations. 47. {(-1, 3) (5, 2) (2, 3) (-1, 2) (4, 3)} Domain ____________________ Range _____________________

48. {(-2, 1) (5, 1) (-3, 1) (4, 1)} Domain ____________________ Range _____________________

Analyze the following quadratic functions. 49. y = 2(x – 3)(x – 1) Vertex _______________________

Axis of Symmetry _________________

Max or Min Value_________________

Domain: _______________________

Range: _______________________

Roots: _______________________

50. y = -(x – 4)² + 4 Vertex _______________________

Axis of Symmetry _________________

Max or Min Value_________________

Domain: _______________________

Range: _______________________

Roots: _______________________

1ST SEM EXAM REVIEW

51. y = x² - 2x - 3 Vertex _______________________

Axis of Symmetry _________________

Max or Min Value_________________

Domain: _______________________

Range: _______________________

Roots: _______________________

Write the equation of the following quadratic functions. 52. Vertex (3, -5) f(1) = 3 53. Roots: 4, 2 f(-2) = 8 3rd SIX WEEKS Solve the following word problems. 54. A rectangular pen is made up of 200 feet of fencing. What is the maximum area that can be enclosed?

1ST SEM EXAM REVIEW

55. A gardener is building a walk around his 10 ft. x 12 ft. garden of width x. If he has only 600 square feet of area to use for the garden and the walk, how wide should he make the walk? Solve the following quadratic equations. Use a graphing calculator if the roots are real and the quadratic formula if the roots are imaginary. 56. x² - 4x + 5 = 0 57. x² - 6x + 10 = 0 Solve the following quadratic inequalities. 58. x² - 3x – 4 < 0 59. 4x² - 1 > 0

1ST SEM EXAM REVIEW

Use the laws of exponents to simplify the following.

60. 4

53

5

34

y6yx3

x8yx5 ⋅

61. ( )624cab2

62. 21

22

yxyx3−−

−

63. ( )0132 cba5 −−

64. 32

y2x3

⎟⎟⎠

⎞⎜⎜⎝

⎛−

65. ( )2

122

4

3

x15xy

yx12

−

−−−⋅

Use nt

nr1PA ⎟⎠⎞⎜

⎝⎛ += to solve the following word problems.

66. $800 is deposited in an account that pays 9% semiannually. Find the balance after 4 years.

1ST SEM EXAM REVIEW

67. How much had you deposited in an account that pays 8% annual interest, compounded monthly, to have a balance of $1000 after 1 year? Simplify the following radicals. 68. 3 6x64 69. 3 33 42 xy4yx2 ⋅ 70. 203454 − 71. 3 43 4 x163x542 − Evaluate the following rational exponents.

72. 23

25 73. 32

125−

74. 21

91 −

⎟⎠⎞⎜

⎝⎛

Simplify the expression. 75. ( ) ( ) 434

133 •

76. ( )31126nm8

1ST SEM EXAM REVIEW

77. 32

123

69

banm27

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−

78. 43

32

45

31

yx

yx

79. 42

41

45

43

ba5ba3−−

• Solve the following equations.

80. 04)1x7(2 31

=−− 81. 8)4x(2 32

=+ 82. 1x1x3 =−+ 83. 5x7x −=+

1ST SEM EXAM REVIEW

ANSWERS

1. x = 512

2. x = 35

3. x = 1 4. x = -3 5. y < 3 or y > 4 6. –4 < x < 5

7. y < -2 or y > 310

8. x ≤ -1 or x ≥4 9. –6 ≤ x ≤ 2 10. x = 2 or x = -4

11.213

x21y +−=

12. x = 2 13. y = 3x + 17 14. y = -2x + 5 15. y = -2 16. 17. 18. 19. (-7, -2) 20. (5, 5) 21. (7, -10)

22. (-3, 4) 23. 12 adults and 30 children 24. $1.25 for the 1st minute and $.10 each additional minute

25. ⎥⎦

⎤⎢⎣

⎡0550

26. ⎥⎦

⎤⎢⎣

⎡−−−1510510

27. ⎥⎦

⎤⎢⎣

⎡−

−45333334

28. ⎥⎦

⎤⎢⎣

⎡−−8101012

29. 2 30. 21

31. ⎥⎦

⎤⎢⎣

⎡−−−−125.5.1

32.

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

215

71

71

72

33. (1, 0, -2) 34. (1, 0, -1) 35. (0, 1, -3) 36. (2, -1, 1) 37. (x + 3)(x – 2) 38. (2x + 7)(2x – 7) 39. 3x(x – 4) 40. (2x – 1)(3x – 1) 41. (x + 4)(x + 2) 42. (3x + 2)(x – 2) 43. (x + 10)(x – 10) 44. (x + 2)(x – 2) 45. 105

46. 104 47. Domain: -1, 5, 2, 4

Range: 3, 2 48. Domain: -2, 5, -3, 4

Range: 1 49. Vertex: (2, -2)

Axis of Symmetry: x = 2 Min at -2 Domain: All Real Numbers Range: y ≥ -2 Roots: 3 and 1

50. Vertex: (4, 4) Axis of Symmetry: x = 4 Max at 4 Domain: All Real Numbers Range: y ≤ 4

Roots: 2 and 6 51. Vertex: (1, -4)

Axis of Symmetry: x = 1 Min at -4

Domain: All Real Numbers Range: y ≥ -4

Roots: 3 and –1 52. y = (x – 3)2 – 5

53. y = 31 (x – 4)(x – 2)

54. 2500 ft 2 55. 6.76 ft 56. i2 ± 57. i3 ± 58. –1 < x < 4 59. x < -.5 or x > .5

60. 16yx5 42

61. 12246 cba64 62. 3x3 63. 1

64. 3

6

y8x27

−

65. 23yx5

4

66. $1,137.68 67. $923. 36 68. 2x4 69. 32 yxy2

70. 56 71. 0 72. 125

73. 251

74. 3 75. 3 76. 42nm2

77. 42

86

nanm9

78. 31

21

x

y

79.21

43

a

b15−

80. x = 79

81. x = 4 82. x = 8 or x = -1 83. x = 9

1ST SEM EXAM REVIEW