Algebra 2 – Final Exam Review #___-____ Name _________________________________

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(Fall 2005 – Genord)

Date __________________________________

Complete the work on notebook paper and not on this worksheet and circle you answers.

* * * * * * * * * * * * * NO CALCULATOR SECTION * * * * * * * * * * * * * * *

1. Write the equation of the in slope-intercept form for the line that has a y-intercept (0, –2) and is perpendicular to the line 2x + 5y = 5.

2. Write the equation of the in slope-intercept form for the line that is parallel to the line 4x – 8y = 0 and goes through the point (–6, 7).

3-4. Determine whether y-varies directly as x. If so write the equation. If not explain why.

3. 4.

x | –8 | –2 | 4 | 12 |

y | –4 | –1 | 2 | 6 |

x | 2 | 3 | 4 | 5 |

y | 5 | 7 | 8 | 11 |

5-6. Simplify the expression, assume that no variables equal zero. Write answer with positive exponents.

5. (3a–5b8)4(–2a2b–3c)3 6. m–1n2 5

m–3n

7. Write the inverse function equation of f(x)= ½x – 5.

8. Find the inverse for the following relation and determine whether the inverse is a function.

{(–2,3), (1, 9), (15, 3), (–6,–3)}

9-10. Find the solution to the system:

### The Report on Equations of Lines

Clearest Point- Writing Assignment Chapter 1 There is one subject area in Chapter 1 that I am very confident in and that is Lines. I understand the different equations for lines like the point-slope form; ( y- y1 = m (x-x1) with m=slope and (x1, y1) being a point on the line), the slope-intercept form; ( y= mx + b, with m=slope and b=the y-intercept) and the standard form; (ax + by = c , a and b≠0 ...

9. y = –3x + 8 10. 3x – 4y = 16

2x + 4x = 42 2x + 5y = 3

11-12. Factor completely.

11. 3×2 – 6x + 12 12. x2 + 21x + 80

13-14. Find the zeros of the quadratic function.

13. f(x) = x2 – 5x – 36 14. g(x) = 2×2 – 7x + 3

15. Determine whether the quadratic opens up or down, then determine if it has a maximum or minimum value. f(x) = –(x + 2)(x + 3).

16. What is the exact value of x if 3x = 57 A) log 57 B) 57 C) log 3 D) 3

log 3 log 3 log 57 log 57

17-19. Evaluate the logarithm.

17. log5 625 18. Evaluate log9 3 19. log2 (¼)

20. Write the expression as a single logarithm. (4log3 x + log3 y) – 2log3 z.

21. If log2w = x, then log2 8w equals which of these? A) 4x B) 4 + x C) 3 + x D) 3x

Algebra 2 Final Exam Review, (Fall 2005-Genord) page 2

22. Find the domain, holes, and asymptotes for the function: f(x) = x2 – 25

x2 – x + 20

23. Graph the function g(x) = 2x .

x – 3

0

5

13

12

24-25. Simplify the radical expression.

24. 3 m7n9p5 25. 6xy3 15xy

26. Find the exact values for the six trigonometric functions (sin, cos, tan, sec, csc, cot) of 0.

27-31. Find the exact value for the following:

27. sin 3150 28. tan 2250 29. cos –2100 30. cos 5 31. tan 17

6 3

32-33. Convert degrees to radians.

32. 700 33. 3400

34-35. Convert radians to degrees.

34. 3 35. –5

8 6

36-38. State the domain and range for the given trigonometric functions.

36. f(x) = sin x 37. g(x) = cos x 38. h(x) = tan x

39-42. Find all the possible values of the expressions.

39. sin–1 2 40. Cos–1 (–1) 41. tan–1 1 42. Sin–1 ½

2

43-44. Evaluate the trigonometric expression.

43. sin (Cos–1 ½) 44. Tan–1 (sin 2700)

45-50. Multiple Choice: Which is the correct function family for the given equations (choices may be used more than once).

### The Term Paper on History Of Trigonometric Functions

Trigonometric functions seem to have had their origins with the Greek’s investigation of the indirect measurement of distances and angles in the “celestial sphere”. (The ancient Egyptians had used some elementary geometry to build the pyramids and remeasure lands flooded by the Nile, but neither they nor the ancient Babylonians had developed the concept of angle measure). The word trigonometry, ...

45. y = x2 – 5 A) Linear Function

46. y = ½ (3)x B) Quadratic Function

47. y = 4x + 7 C) Exponential Function

48. y = (x + 2)(x – 7) D) None of the Above

49. 3x – 7y = 8x + 9y – 11

50. y = (x + 2)1/2

* * * * * * * * * * * * * WITH CALCULATOR SECTION * * * * * * * * * * * * * * *

51. Given the line of best fit for a set of data as d = 3.2t + 1.07 predict the d-value if the t-value is 0.5.

52-53. Solve the literal equation for the indicated variable.

52. A=P(1+RT) solve for T 53. I=prt solve for r

54-58. Solve and graph the inequalities.

54. 5(2–4c) < 13 55. 8w–2 < 4 or 3w+6 > 12 56. 4m+6 > –10 and –3m–5 > –17

57. |n + 6| > 1 58. |3x – 5| < 10

Algebra 2 Final Exam Review, (Fall 2005-Genord) page 3

61. Determine which of the following is a function. A) B) C) D)

x | –2 | –1 | 0 | 1 | 2 |

y | 5 | 2 | 1 | 2 | 5 |

59. Determine whether the given table represents a function.

Explain why or why not.

60. Determine whether the given sets of ordered pairs represent a function. Explain why or why not.

{(–1, 0), (4, 2), (5, 9), (–1,–7)}

62-64. Describe the transformation of the graph from its parent function.

62. g(x) = 3(x – 4)2 63. h(x) = – |x + 2| – 4 64. k(x) = (½)x + 5

65-67. Given the function f(x), find the indicated values.

65. f(x) = x3 + 2x – 8; f(–1)=? 66. f(x) = –x2 – 5x; f(4)=? 67. f(x) = 9 – 4×2 ; f(–3)=?

x

68-70. Determine how may solutions each system has.

68. y = 5 – 2x 69. –x – y = 10 70. 2y = x + 6

–4x – 2y = –2 4x – 3y = 9 3x – 6y = –18

71. The math department is having a party. One teacher bought 20 bags of chips and 15 soft drink bottles for $44.65. A second teacher bought 15 bags of chips and 30 bottles of soft drinks bottles and spent $52.05. If both teachers got the same priced items at the same store, how much does one bag of chips cost?

72. Write the system of inequalities for the given graph (both axes are scaled by one).

### The Research paper on Critical Thinking and Problem solving

Numerous decisions are taken every day. People choose when to get up on a certain morning, what clothing to wear, and whether to read a particular book. Most of the decisions made throughout the day are relatively trivial or inconsequential. It probably does not matter too much if it is decided to sleep an extra 15 minutes on a certain morning or if a blue shirt is selected rather than a green ...

73-75. Solve the equations (find the exact answers in simplest radical form).

73. 23 + 3×2 = 59 74. 2×2 + 14x + 20 = 0

75. 4×2 + 7x – 10 = 0

76. How much will $500 invested at 4.5% compounded quarterly be worth after 7 years?

77. How long will it take to double an investment of $2,000 compounded continuously with a 5% rate? (Round to hundredths)

78-79. Write the polynomial in standard form.

78. (x + 5)(x – 7)(x – 1) 79. (x + 3)2(x – 7)

80. Write the zeros of the given graph below. 81. Write the factors of the graph below.

(both axes are scaled by one) (both axes are scaled by one)

Algebra 2 Final Exam Review, (Fall 2005-Genord) page 4

82. Find the remainder when –5×3 + 3×2 + 4x – 2 is divided by (x – 5).

83. Find all the solutions to the equations x3 + 3×2 – 7x – 18 = 0.

84. If a varies jointly as b and c and inversely as d, and a=3 when b= –2, c=6, d=12. Find a when b=5,

c= –4, and d = ½.

85-88. Simplify the rational expressions by performing the indicated operation.

85. x+1 x–3 86. 3x 5 87. x2+x–6 2x–8 88. x2–25 x2–9x+20

x–4 x–5 x2–1 x+1 x2–6x+8 x x2+2x–15 x2 – 9

89-90. Solve the equation.

89. x + 4 x + 1 90. 2 3 2x – 2

x – 6 x + 7 x + 3 x – 4 x2 – x – 12

91. Write the next 5 terms in the sequence. t1 = 0, tn = 4 – 3tn–1

92-93. Determine whether the sequences are arithmetic or geometric. Then find the 7th term of each sequence.

92. 4, –1, –6, –11,… 93. 30, 12, 4.8, 1.92,…

94-95. Determine if the series is arithmetic or geometric, then find the S10 of each series. (Round to hundredths)

94. 10 + 5 + 2.5 + 1.25 +… 95. 50 + 47 + 44 + 41 + …

96. Find the coordinates of point P, to the nearest tenths, if 0 = 2000 and r = 3.

97-98. Find the length of the side x. (Round to tenths)

x

20 in

### The Essay on Arthur We Find Round Table

We find in his life and court a representation of our own dreams and struggles. Why does Arthurian legend fascinate so many people? From the simple fact that each age has retold the story to embody its own values. Arthurs of every age provide motives and meanings significant to there time. The Arthur of legend is much greater than Arthur the real man. To fully understand the real man Arthur we ...

75o

x

7 cm

15o

97. 98.

C

B

A

16

11

400

99-101. Find the measure of the angle A. (Round to nearest whole degree)

A

14

50

A

8

15

99. 100. 101.

B

A

C

8.6

1250

160

A

B

C

9

10

1100

102-103. Find the length of the side BC on each of the triangles. (Round to tenths)

102. 103.