Algebra II CP Final Exam Review Non-Calculator Questions A. Determine the equation of each of the lines shown in the following graphs. 1. 2. 3. P=(-2,2) 2 2 2

-2 -2 -2

B. Determine the equation of each of the functions shown in the following graphs 4. 4 5. 4 6. 2 B=(3,3) P=(3,1) A=(-1,3) A=(-1,3) B=(1,3)

2 2 5

-2

V=(1,-1) -2

C. Determine the domain and range of each of the functions shown in the following graphs. 2 7. 8. 4 9. 2

1 3 1

-2 2 2 2

-1 1 -1

-2 -2 -2 D. For each of the given graphs: a. Determine whether or not each graph is the graph of a function. b. Determine whether or not the inverse of the graph is a function

1 2 8. 9. 4 10.

1 2

2

-2 2

-1

-2 -2

2 E. Write a correct equation or a correct system of equations to represent each of the given problem situations. 13. The intensity I of light varies inversely as the square of the observer’s distance D from the light.

14. The volume V of a spherical balloon is directly proportional to the cube of its radius r.

15. The cost C of a square oak butcher block varies jointly as the thickness t and the square of the length of a side s.

16. The gravitational pull p of a star on a planet with mass m varies directly as the mass and inversely with the square of the distance d of the planet from the star.

17. Let P represent the cost of a slice of pizza and L represent the cost of a lemonade. Jay bought 3 slices of pizza and one lemonade $5.60. Tara bought 2 slices of pizza and 2 lemonades for $5.20.

18. Let F represent the cost of a yard of a particular fabric and T represent the cost of a spool of thread. Five yards of fabric and three spools of thread cost $40.12. Two yards of fabric and ten spools of thread cost $23.88.

F. Answer each of the given questions 19. Determine the vertex and the equation of the axis of symmetry of the parabola whose equation is y=3( x + 2)2 - 1

20. Jamie opened a college savings account with $200.00. Each month she adds $25.00 to the account. Write a recursive formula for the amount of money in the account after n months.

21. Write an explicit formula for the nth term of the sequence -3,1,5,9,...

22. Determine the equation of the inverse, f-1( x ) , for the function f( x )= 4 x + 3

23. Determine the equation of the inverse, g-1( x ) , for the function g( x )= 2 x , and find g( g-1( x ))

24. In the equation y= 6 x2 , what is the effect on y if x is tripled

25. 24 In the equation y = , what is the effect on y if x is doubled. x3 3 26. The formula for the distance d an object falls during time t when it is dropped near the earth’s surface is 1 d= gt 2 . Solve the equation for g. 2

27. The sum S of the measures of the angles of a polygon with n sides is S=180( n - 2) . Solve this equation for n.

G. Determine the value of x in each of the given equations. 28. logx = - 1 29. ln e= x

30. log2 x = 3 31. 骣1 logx 琪 = - 2 桫9

32. 33. log 8 = x log6 6 = x 4

H. Write each of the following expressions as the sum and/or difference of logarithms. 34. log a b 35. 骣p3 ln琪 桫q2

I. Determine the value of each of the given expressions. Write your answer as an integer or a fraction (no decimals). 1 3 36. - 37. 49 2 骣9 2 琪 桫4

2 2 38. 39. - 83 骣8 3 琪 桫27

J. Rewrite each of the given logarithmic equations in equivalent exponential form.

40. logb 12= - 3 41. ln 20 2.9957

K. Rewrite each of the given exponential equations in equivalent logarithmic form. 42. 5x = 20 43. e 1.6487

4 Calculator Questions L. Answer each of the given questions. 44. 5n - 1 45. Given t = 2(3)n-1 , find t and t Given a = , find a n 1 9 n 4 95

46. Determine the slope and the intercepts of the graph of the equation 3x- 4 y = 12 .

47. Given y = 50(3)x , find the rate of change between x = 2 and x = 4 .

48. Find the mean, median, and mode of {3,5,8,13,21,8,15,8,24}

49. Simplify 5(5- 2i ) - 2(7 + i ) 50. (5- 3i )(5 + 3 i )

M. Determine the equation of each of the lines with the given conditions. Write the equation of the line in standard form. 51. 2 Through P =(6, - 1) with slope m = - 3

52. Through Q =( - 3,2) and R = (5,6)

53. Through T =( - 3,4) and parallel to the line determined by the equation 3x- 4 y = 13

54. Through A =(4, - 1) and perpendicular to the line determined by the equation x+2 y = 5

N. Solve each of the given equations. 55. 31-x = 27 56. x 骣1 x+2 琪 = 25 桫5

2x- 1 x + 1 57. 4= 8 58. log3 (4x + 5) = 4

O. Solve each of the given inequalities and graph the solution set on a number line. 59. 16- 3x > 1 60. -x +12� 4 x 3

5 P. Graph the solution set of each of the given systems of inequalities on = -2the coordinate planes below. = -2 61. y +2 < 0  62. x- y 4  = -x   = -x 2 x+ y > 0 2 2x+ y 1

-2 -2

-4 Q. Determine the domain and range of each of the given functions. 63. f( x )= 5 x - 3 64. 12 g( x ) = x

65. h( x )= 5(2)x 66. j( x ) = - x2

R. Answer each of the following 67. 骣b The Henderson-Hasselbach formula pH =6.1 + log琪 gives the pH of a patient’s blood as a function of 桫c the bicarbonate concentration B and the carbonic acid concentration C. A sick patient has a bicarbonation concentration of 24 and carbonic acid concentration of 2. Find the pH (correct to the nearest tenth) of the patient’s blood. The normal pH is about 7.4.

68. The maximum velocity v of a rocket is v= cln R , where c is the velocity of the exhaust and R is the ratio m of the mass of the rocket with fuel to its mass without fuel. Find R of a rocket if c = 2000 and s m v = 2,200 s

S. Solve each of the given equations (give exact answers) 69. 5(2x - 3) + 4 = 34 70. 23x+ 15 = 19 x - 5

71. b2 -36 = 0 72. 3x2 + 11 x = 4

73. x2 +1 = 3 x

6 T. Solve each of the given systems of equations. 74. y= -5 x + 7 75. 5x- 6 y = 3 x- y = 83 2x+ 12 y = 12

U. Factor each of the given expressions completely. If any expression is not factorable, write prime. 76. 15a4- 20 a 3 77. b2 - 9

78. 2n2 - 8 79. c2 +5 c + 6

80. d2 - d - 20 81. 2r2 + r - 3

82. x2+ y 2 83. 12pr5+ 18 p 4 r 3

84. 6x2 - x - 12 85. z2 +2 z + 10

V. Use the given matrices to evaluate each of the following expressions. 轾2- 3 6 轾-1 7 8 A = [5 2] B = 犏 C = 犏 臌0 8 1 臌2 3- 4 86. B- C 87. 3C 88. AB

W. Use the functions below to evaluate each of the following. f( x )= 4 x - 7 g( x )= 3 x - 10 h( x )= 2 x2 - 5 x + 12 89. f( g (2)) = 90. f( h (- 2)) =

91. g( g (0)) = 92. f( h ( x )) =

X. Solve each of the following. 93. Nicole invested $1,200 in an account which is paying 6.35% interest compounded monthly. How much money will be in the account if the money is left untouched for six years?

94. In 1995, the population of Austin, Texas was approximately 834,000. Since 1995 the population has been growing at a rate of approximately 2.15% annually. If the annual growth rate remains the same, what is the expected population of Austin in the year 2010?

7 95. Valerie bought a new car at a cost of $23,975.00. The estimated depreciation rate is 10.2% per year. Find the estimated value of the car after five years.

96. If $5,000.00 is invested at an interest rate of 5.65% to be compounded continuously, what is the amount in the account after eight years?

Y. Solve each of the given equations. Round answers correct to the nearest thousandth. 97. 12x = 2,116 98. 6e2x = 900

99. log6 512= 3x - 6 100. log2 (3x+ 1) - log 2 ( x - 3) = 2log 2 3

Z. Determine the exact values of each of the given trigonometric ratios for the triangle below: 101. a. sin A = B b. cos A = 2 c. tan A = 7 C d. cos B =

e. tan B = A AA. Find the measure of x or y (correct to the nearest tenth) in each of the given diagrams. 102. P 103.

36.4 32.4 x 122.0 18.5 22.5 x

R Q

104. 105.

30.2 76.4 18.7 x

y 40.4 72.3  x 21.4 8 BB. Solve each of the given triangles. ° ° 106. VABC , with mR C = 90 , mR A = 57.2 , and b = 22.4 cm.

107. VDEF with d = 27.2 cm, e = 25.9 cm, and f = 22.8 cm.

CC. Solve 108. A plane flying at an altitude of 37,500 feet is 134.5 miles (along the ground) from the airport when it begins it decent in order to land. If the angle of descent is constant, find the angle of depression the pilot should use to successfully land the plane. (5,280ft= 1 mile )

109. If a tower 18 meters high casts a shadow 9.5 meters long, what is the angle of elevation of the sun?

110. Fire stations X and Y are 53.4 miles apart. The ranger at station X sees a fire at a point Z such that ° mR XYZ = 70.7 . How far is the fire from station X?

P

In the given drawing, find PS, which is the height 111. of the mountain (mountain is shaded gray)

31.2 57.5 Q 130 meters R S

9