Tennessee State University

Transcription

1 Tennessee State University College of Engineering and Mathematical Sciences College Algebra Final Exam Review Package In order to watch the videos with the solutions of the problems, make sure to complete the following steps (If you are already using Moodle in your course then you can start in Step 5) : 1. Write down your student address that looks like username@my.tnstate.edu. 2. Write down your username. For example if your student address is johndaw5@my.tnstate.edu then your username is johndaw5. 3. Create an Account in by using the SAME username of step 2 and the SAME address of step Verify your identity by confirming an send to your MyTSU address 5. Once you verify your identity in Step 4 (or if you already have an account in Moodle), you can click in any video icon of this sample package. However, after login into Moodle for the first time, you must answer Yes to the question: You are about to enroll yourself as a member of this course. Are you sure you wish to do this? 6. Finally, you have to allow pop-ups for in your browser (Explorer, Firefox, or Safari). If you have problems login into the system, please drop by 315B-Boswell Science Hall during Office Hours Final Exam Review Package 1. Let f(x) = x and g(x) = x + 1. Find the composition function (f g)(x). m = 2 15 m = 2 15 (f g)(x) = x+1 (f g)(x) = 4 x (f g)(x) = x+1 (d) (f g)(x) = x+2 2. Find the domain of the rational function y = x2 x 7. (,1) (1, ) (,8) (8, ) (,6) (6, ) (d) (,7) (7, ) m = 2 29 (d) m = Solve the inequality x+3 > 10. Express the solution set in interval notation ( 13, 7) (, 13) (7, ) (7,13) (d) (,7) (13, ) 6. Write the equation of the line that passes through the point P(3,4) and is perpendicular to the line y = 4x Complete the square to make the bionomial x 2 8x a perfect trinomial. x = 13 4 y y = 1 4 x+14 y = 1 4 x (d) y = 1 4 x x 2 4x 16 x 2 8x+16 x 2 8x+64 (d) x 2 16x Tell whether the graphs of the lines y = 5x+5 and y = 5x 1 are parallel, perpendicular, or neither. 4. Find the slope of the line 2x+15y = 29. Perpendicular Page 1 of 14

2 Parallel Neither parallel nor perpendicular 16. Let f(x) = 2x 1 and g(x) = 3x 2. Find the domain of the function (f g)(x) 8. Solve the inequality 8 x > 2 [0,4) (0,4] (0,4) (d) [0,4] [0, ) (,0) (,0] (d) (0, ) (e) (, ) 9. Simplify (4 + 16)(4 9) and express it in the a+bi form. 17. Select each graph that represents a function 4+4i 28+4i 28 4i (d) 28+4i 10. A printer charges a fixed setup cost, plus $0.40 for every 40 copies. If 320 copies cost $43.20, how much will it cost to print 1200 copies? $160 $48.8 $128 (d) $ Let f(x) = 3x 2 2 and g(x) = 4x+4. Find the value of the function (g g)( 2). (g g)( 2) = 11 (g g)( 2) = 10 (g g)( 2) = 13 (d) (g g)( 2) = Find the real solutions of x = x+6 x = 144 x = 0 x = 9 (d) x = Simplify 5 and express it in the form a+bi i27 5i 5 5 (d) 5i 14. Solve the inequality 2x 15 3 (6, ) (,6] (,6) (d) [6, ) 15. Find the slope of the line passing through the points P(15, 7) and Q( 7,15) m = 2 m = 1 m = 1 (d) m = Solve the inequality 6(x 2) 5 (7, ) [ 7, ) 3(x+1) 4 ( 7, ) (d) [7, ) Page 2 of 14

3 19. Find the graph of the equation 2x+y = 4 x = 76 and y = 76 x = 76 and y = 76 x = 76 and y = 76 (d) x = 76 and y = Simplify the expression i 37 i 1 i (d) Find the slope of the line 13(y+x) = 13(x 4) m = 1 m = 0 m = 17 (d) m = Find the vertex of the parabolay = 7(x 9) 2 +8 (81,8) (9,8) (9,7) (d) (8,9) 26. Find the slope of the line passing through the pair of points P( 14,6) and Q(11,11) m = 1 5 m = 5 m = 1 5 (d) m = The ratio of women to men in a mathematics class is 13 to 4. How many women are in the class if there are 20 men? (d) Solve the equation 2log 2 (x) = 1+log 2 (x+112) x = 14 x = 18 x = 14 (d) x = Use the quadratic formula to solve the equation 2x(x+7) = 5 x = 7± 11 2 x = 7± 11 4 x = 7± 39 2 (d) x = 7± Find the values of x and y from the complex number x+76i = y yi 28. Solve the proportion x 21 = 2 x+1 x 1 = 7 and x 2 = 6 x 1 = 7 and x 2 = 6 x 1 = 7 and x 2 = 6 (d) No solutions 29. Solve the proportion x 12 = 2 x+2 x 1 = 6 and x 2 = 4 x 1 = 6 and x 2 = 4 x 1 = 6 and x 2 = 4 (d) No solutions Page 3 of 14

4 30. Simplify (6 49) (7i 4) and express it in the form a+bi 10 14i 10+14i 10 14i (d) 10+14i 31. Let f(x) = 31 x 2. Find f(5). +28 f(5) = f(5) = f(5) = Solve the equation x 3 8x 2 +15x = 0 for the real values of the variable x by factoring. x = 0 x = 5 x = 8 (d) x = Solve the equation z 3 2 7z 1 2 = 0 for the real variable z by factoring. 38. Solve the inequality 14 x 2 > 4 3 (,14) [44, ) (14,44] (,14] [44, ) (d) (,14] (44, ) 39. Find the equation in general form of the circle with center at (2,2) and r = 9 x 2 +y 2 4x 4y 73 = 0 x 2 +y 2 +4x+4y 73 = 0 x 2 +y 2 +4x+4y 89 = 0 (d) x 2 +y 2 4x 4y 89 = Determine whether the lines with the slopes m 1 = 10 and m 2 = 1 are parallel, perpendicular, 10 or neither. Perpendicular Neither Parallel z = 49 z = 0 z = 49 (d) z = 7 (e) z = If a and h are real numbers and f(x) = 7x 8. Find the difference quotient f(a+h) f for h h Find all the real solutions of the equation 5x+6 = 3x+14 7x 7x 8 (d) 7 x = 4 x = 0 x = 4 (d) x = Find the distance between the point P(4,6) and Q(6, 5) (d) Find the value of x if log x (27) = 3 x = 27 x = 3 x = 3 (d) No solution 37. Find the inverse of f(x) = 2x+7 f 1 (x) = x 7 2 f 1 (x) = x 2 7 f 1 (x) = x If f(x) = 11 10x 2. Find f(8) Solve the equation 8x 2 16x 120 = 0 x = 3 and x = 8 x = 8 and x = 120 x = 4 and x = 5 (d) x = 3 and x = Given that P varies jointly with r and s. If P = 7 when r = 3 and s = 6, find P when r = 9 and s = 24. P = 9 P = 24 P = 3 (d) P = 84 Page 4 of 14

5 45. Find the graph of f(x) = x The function f(x) = 5 is one-to-one on the x2 domain (0, ). Find f 1 (x). f 1 (x) = x 5 f 1 (x) = x2 5 x f 1 (x) = 5 5 (d) f 1 (x) = x 49. An account now contains $9300 and has been accumulating interest at a 10% annual rate, compounded continuously, for 12 years. Find the initial deposit. $2, $2, $2, (d) $2, (e) $2, Let f(x) = x 2 + x and g(x) = x 2 1. Find (f +g)(x) 46. Solve the equation 8x 2 x = 7. x = 30 and x = 2 x = 2 15 and x = 2 x = 2 and x = 2 15 (d) x = 2 and x = Solve the inequality (,5) [8, ) (,5] [8, ) (5,8] 6 x 5 2 (d) (,5] (8, ) (e) (,5) (8, ) (f +g)(x) = x 4 +x 3 x 2 x (f +g)(x) = 2x 2 +x 1 (f +g)(x) = x+1 (d) (f +g)(x) = x x Tell whether the graphs of y = 5x + 4 and y = 5x 6 are parallel, perpendicular, or neither Perpendicular Neither parallel nor perpendicular Parallel 52. Let f(x) = x and g(x) = x + 1. Find the domain of the composition function (f g)(x) (0, ) [0, ] (,0) (d) [0, ) (e) (,0] 53. Solve the equation log(x 17) log(5) = log(x 8) log(x) x = 2 x = 22 x = 20 (d) x = 24 Page 5 of 14

6 54. What is the degree of the polynomial f(x) = x (d) 8 barn walls form two sides of the stall, and the farmer has 58 feet of partition for the remaining two sides. If a = 58 in the picture below 55. Find the graph of the function g(x) = (x+4) 2 What dimensions will maximize the area of the partition? 14.5ft by 43.5ft 23.2ft by 34.8ft 11.6ft by 46.4ft (d) 29ft by 29ft 58. Find the value of x if log 4 (x) = 2. x = 16 x = 2 x = 1 16 (d) x = 4 (e) No solution 59. Find the range of f(x) = 2 x 2 f(x) (2, ) f(x) (,2) f(x) (,2] 60. Let f(x) = 3x and g(x) = x + 1. Find the composition function (f g)(x) (f g)(x) = x+3 (f g)(x) = 3x+3 (f g)(x) = 3x+1 (d) (f g)(x) = 9x 61. Find the range of f(x) = 4x. Hint: Find the x 3 domain of f 1 (x) 56. Given that m varies jointly with the square of n and the square root of q. If m = 30 when n = 3 and q = 8, find m when n = 15 and q = 32. m = 3 m = 30 m = 1,500 (d) m = A farmer wants to partition a rectangular feed storage area in a corner of his barn. The (,3) (3, ) (0, ) (,0) (0, ) (d) (,4) (4, ) (e) (, ) ( ) 7x Solve the equation log = 0 2x+29 x = 4 x = 5 x = 7 (d) x = 1 Page 6 of 14

7 63. Solve the inequality 7+x 3x 9 > 5x+15 ( 12,8] [8, ) [ 12,8) (d) (, 12) 64. Find the inverse function of f(x) = 3x 3 5 f 1 (x) = 3 3+x 5 f 1 (x) = 3 5+x 11 f 1 (x) = 3 5+x 3 (d) f 1 (x) = 3 11+x Find all the real solutions for the equation x 9 = 3 x = 0 x = Simplify i x = 18 (d) No solution i (d) i 67. R is inversely proportional to the square of I. If I = 12 when R = 60. Find the constant of proportionality. k = 12 k = 720 k = 8640 (d) k = Find the graph of the function g(x) = (x 1) Find the vertical and horizontal assymptotes of f(x) = x+9 x+5 Horizontal y = 9 and Vertical x = 5. Horizontal y = 1 and Vertical x = 14. Horizontal y = 1 and Vertical x = 5. (d) Horizontal y = 5 and Vertical x = Solve the inequality 2x 15 > 5 (, 5) (,5] [5, ) (d) (,5) 71. If a and h are real numbers and f(x) = x 2 x+2, find f+f(h). f+f(h) = a 2 +h 2 +a+h f+f(h) = a 2 +h 2 a h+4 f+f(h) = a 2 +h 2 a h (d) f+f(h) = a 2 +h 2 +a+h Find the inverse function of f(x) = 9x+8 f 1 (x) = x 8 9 f 1 (x) = x 9 8 f 1 (x) = 9 x 8 (d) f 1 (x) = x+8 9 Page 7 of 14

8 73. Simplify (8+6i) 2 in the form a+bi i 28 8i 28 6i (d) 8+96i 74. Let f(x) = x 2 1 and g(x) = 3x 2. Find (f +g)(7) (f +g)(7) = 66 (f +g)(7) = 65 (f +g)(7) = 67 (d) (f +g)(7) = Find the line that passes through the points P(5,5) and Q( 3, 3). y = 5x y = x y = 5 (d) x = Find the graph of f(x) = x Findthegraphofthefunctiong(x) = (x+3) Tell whether the graphs of y = 6x + 1 and 2y = 4x 8 are parallel, perpendicular, or neither. 76. Solve the inequality 2x 13 1 (6, ) (,6) (,6] (d) [6, ) Perpendicular Parallel Neither parallel nor perpendicular Page 8 of 14

9 80. Find the graph of the function g(x) = x 2 +1 x = 1 x = 2 and x = 1 (d) x = 2 and x = Solve the equation x = 2 x = 3 8 x = 1 x+30 x = 0 (d) x = Solvetheequationx 2 2x 8 = 0bycompleting the square. x = 2 and x = 1 x = 2 and x = 4 x = 3 and x = 4 (d) x = 1 and x = Find the equatio of the circle with center at (1, 2) and passing through the origin x 2 +y 2 +2x+4y 5 = 0 x 2 +y 2 2x 4y = 0 x 2 +y 2 2x 4y 5 = 0 (d) x 2 +y 2 +2x+4y = Find the graph of f(x) = x Find the midpoint of the line segment obtained by joining the points P(8,5) and Q(6,5) M(7,5) M(7,4) M(9,5) (d) M(12,8) 82. Simplifytheexpression(5 49)+(4 25) in the form a+bi. 9 2i 9+2i 9+2i (d) 9 2i 83. Solve the equation 2x+1 = 3 x = 1 and x = 2 Page 9 of 14

10 88. Iff(x) = x 2 andg(x) = 2x. Findthecomposite function (f f)(x) (f f)(x) = 4x 2 (f f)(x) = x 4 (f f)(x) = 4x (d) (f f)(x) = 2x Let y be directly proportional to x. If x = 8 when y = 72; Find the constant of proportionality. k = 9 k = 8 k = 72 (d) k = Solve the equation log(9x 6) = log(4x+24) x = 6 x = 4 x = 9 (d) x = Find the graph of g(x) = (x+2) Find the vertex of the parabola y = x 2 8x+16 (0,4) (4,0) ( 8,0) (d) (16,0) 93. Find the y-intercept of the function 2x+4y = 4 (0, 4) (0, 1) (0,1) (d) (0,4) 94. Find the line that passes through the point P(0,0)andisperpendiculartotheliney = 10x+ 5 y = 10x y = 1 5 x y = 1 10 x (d) y = 1 10 x+5 Page 10 of 14

11 95. Find the slope of the line y = 2x+6 m = 2 m = 1 m = 3 (d) m = 6 (e) m = Let f(x) = x 3 4. After simplifying the quotient f(x) f (for x a) one obtains x a f(x) f x a f(x) f x a f(x) f x a (d) f(x) f x a = x 2 +2ax+a 2 = x 2 +ax+a 2 = x 2 2ax+a 2 = x 2 a Let x, y, and d be positive numbers. Use the properties of logarithms to write the expression log d ( xy ) in terms of logarithms of x and y. log b (x)+log b (y) 1 2 log b(x)+ 1 2 log b(y) 2log b (x)+2log b (y) (d) 1 2 log b(x)+log b (y) 101. Find where the function f(x) = 16 x 2 is increasing. (0, ) It is always constant It is always decreasing (d) (,0) 102. Find the domain of f(x) = 6x+18 (,6) [ 3, ) (3, ) (d) [3, ) 98. Let f(x) = 11x 89. Find f(10) f(10) = 21 f(10) = 92 f(10) = Let f(x) = 10x 3. Find the difference quotient f(x+h) f(x) for h 0. h 10x Find the solution of the inequality 9x 2 < 11 (9,13) (, 13 9 ) ( 1, ) ( 1, 13 9 ) (d) (1, 13 9 ) 103. Assume that x, y and c are positive numbers. Use the properties of logarithms to write the expression log c (x 5 y 9 ) in terms of the logarithms of x and y. 45log c (x)+9log c (y) 5log c (x)+45log c (y) 5log c (x)+9log c (y) (d) 5log c (x)+5log c (y) Page 11 of 14

12 104. Find the graph of the equation x 2 +y = Find the inverse function of f(x) = 3x+7 f 1 (x) = x+7 3 f 1 (x) = 3 x 7 f 1 (x) = x 7 3 (d) f 1 (x) = x The ratio of women to men in a mathematics class is 5 to 8. How many women are in the class if there are 48 men? (d) Let x, y, and z be positive numbers. Use the properties of the logarithms to write the expression 2log b (x) 6log b (y)+ 1 7 log b(z) as the logarithm of one expression. ( ) z 1 7 log b x 2 y 6 ( ) z 1 6 log b x 2 y 7 ( ) z 1 7 log b x 6 y 2 ( ) z 1 2 (d) log b x 7 y Find the graph of the equation x = Solve for x the equation f = k x. q x = f kq x = k fq x = fq k (d) x = kq f 106. Solve the equation x(x 5) 23 = (x 1) 2 x = 3 x = Solve the equation x = 3 x = 1 x = 8 (d) x = 1 9 x = 1 x+70 x = 6 (d) x = 2 Page 12 of 14

13 112. Solve the equation log(10x 10) = log(5x+20) x = 9 x = 6 x = 5 (d) x = Find the graph of the function f(x) = x Find the domain of the function f(x) = x2 x 5 (,4) (4, ) (,1) (1, ) (,5) (5, ) (d) (,6) (6, ) 115. Let f(x) = 2x + 1 and g(x) = 3x 2. Find (f g)(x) (f g)(x) = 2x+1 3x 2 (f g)(x) = 5x 1 (f g)(x) = 6x 2 x 2 (d) (f g)(x) = 3 x 116. The ratio of lime to sand in a mortar is 7 to 4. How much lime must be mixed with 32 bags of sand to make mortar? 7 bags 4 bags 56 bags (d) 32 bags Page 13 of 14

14 Answer Key Problem Answer Problem Answer Problem Answer Problem Answer Problem Answer 1 C 25 B 49 D 73 A 97 B 2 D 26 C 50 B 74 C 98 A 3 B 27 A 51 C 75 A 99 C 4 C 28 C 52 D 76 D 100 C 5 B 29 A 53 C 77 B 101 D 6 C 30 C 54 D 78 C 102 B 7 B 31 A 55 D 79 C 103 C 8 C 32 A,B, and C 56 C 80 B 104 A 9 D 33 B and E 57 D 81 A 105 B 10 D 34 A 58 C 82 D 106 C 11 D 35 D 59 B 83 C 107 D 12 C 36 B 60 B 84 D 108 C 13 D 37 B 61 D 85 B 109 B 14 C 38 B 62 A 86 B 110 A 15 C 39 A 63 D 87 B 111 A 16 E 40 B 64 C 88 B 112 B 17 A and B 41 D 65 C 89 D 113 B 18 D 42 C 66 B 90 A 114 C 19 B 43 D 67 C 91 C 115 D 20 D 44 D 68 C 92 B 116 C 21 C 45 A 69 C 93 C 22 D 46 B 70 A 94 C 23 B 47 A 71 B 95 E 24 B 48 D 72 A 96 B Last Update: Nov 15, 2013 Page 14 of 14