11 ( 9) 6(10 4) 1. Simplif: 4 8 3 + 8 ( 7). Simplif: 34 3. Simplif ( 5 7) 3( ) 8 6 4. Simplif: (4 3 ) 9 5. Simplif: 4 7 3 6. Evaluate 3 4 5 when and 3 Write each of the values below in decimal or standard notation. 7. 3.113 5 10 8. 1.01 10 9 Write each of the values below in scientific notation. 9. 87,000,000 10. 0.000017 Solve for. 11. ( 3) 5 8( 1) 1. 1 3 1 1 3 5 5 3 13. 3 6
For each problem define a variable in words, write an equation, solve algebraicall, and write our answer in a complete sentence. 14. Seven subtracted from five times a number is 08. Find the number 15. An 87-inch board is cut into three pieces. The longest piece is 10 inches longer than twice the shortest piece and the middle-sized piece is 17 inches longer than the shortest piece. How long are the pieces? 16. A landscape architect charged a customer $971, listing $350 for plants and the remainder for labor. If the architect charged $3 per hour, how man hours did the architect work? 17. A universit with 176 people on the facult wants to maintain a student-to-facult ratio of 3:. How man students should the enroll to maintain that ratio? 18. To earn a B in a course, a student must have a final average of at least 80%. On the first three eaminations, a student has scores of 76%, 74%, and 78%. What must the student earn on the fourth eamination to earn a B in the course? 19. A motorccle traveling at 50 mph overtakes a car traveling at 30 mph that had a three-hour head start. How far from the starting point are the two vehicles?
0. Solve the inequalit, show the solution in set notation, interval notation and graphed on the number line. 30 5 1. Solve the inequalit, show our solution in set notation, interval notation and graphed on the number line. 33 33 3(4 3). Sketch the line 54 0 using - and -intercepts and a checkpoint on the ais provided. Write our intercepts as ordered pairs. 3. Sketch the line 3 6 using - and -intercepts and a checkpoint on the ais provided. Write our intercepts as ordered pairs.
1 4. Use the slope and -intercept to sketch 3 on the aes provided. State the slope and the -intercept. 5. Sketch the line with slope points on the graph. m that contains the point (-1, -3). Label the given point and at least other 3 6. Find an equation for the line which passes through (-, 5) and is parallel to the line 3. Leave the final answer in slope-intercept form. 7. Find the equation of the line that passes through the points (3, -4) and (5, 0). 8. Find an equation for the line with undefined slope which passes through the point (-7, ). 9. Find an equation for the line parallel to the line = - which passes through the point (3, -1)
Perform the indicated operations. Leave our answer in simplified form. 30. ( 9 1) ( 4 3 11) 31. (7 8 11) (7 9 1) 3. 3 3 3 a b(7a b ab 4 a) 33. ( 4)( 3 1) 34. 3 3 ( 3 11) 35. ( 9)( 9) Completel factor each of the following epressions. If the epression cannot be factored write PRIME. 36. m 1m 36 37. p 100 38. r r 39. t t 15 40. v v 3 41. 3 8 6 4. Simplif each epression. Leave our answer in the form of a simplified radical, if necessar. a. 49 54 6 b. 5 16 c. 5 16 d. 16 43. Use rules for square roots to simplif completel. DO NOT use a calculator to approimate an answer. a. 7 b. 40 c. 34 d. 700
44. The length of a rectangular garden is 4 feet longer than the width. If the area of the garden is 140 sq. feet, find the dimensions of the garden. Solve the quadratics using the method of our choice. 45. 16t 4 0 46. 3 10 47. 8 1 48. Solve P l w for w 49. Find the height of a tree that casts an 80 foot shadow at the same time that a telephone pole 18 feet tall casts a 1 foot shadow. 50. Use the Pthagorean Theorem to find the length of side BC on the right triangle below. Leave our answers in simplified radical form. Assume all units are in centimeters. A 10 cm 1 cm C B 51. Solve the following problem b A) defining a variable, B) writing an equation, C) solving the equation and D) answering the question in contet. A 13 foot ladder is set 5 feet from the base of the wall. How far up the wall will the ladder reach?
5. Find the area and perimeter of the figure. 10 in. 5 in. 4 in. 13 in. 53. Find the circumference and area of the following circle. Leave our answer in terms of π. 6 ft. 54. Given the lengths of the shadows of each tree as well as the height of the smaller tree, find the height of the taller tree. 55. 6 3 56. b b 10 3 57. (3 ) 3 Given the following equation, determine the slope and the -intercept. 58. 43 6 59. 3 5 60. 58 30
61. Sunn had $10,400 in her bank account that she used just for her monthl rent. After five months, she had $7150 in her account. a. Find the rate of change in her bank account. (Use appropriate labels.) (0, 10,400) b. Write an equation for the line that models the amount in Sunn s account. (5, 7150) c. Assuming she never adds an more mone into the account, when will she run out of mone? 6. Solve each sstem of equations b graphing. a. 3 3 b. 3 3 6 c. 3 3 3 3 d. 3 4
63. Solve each compound inequalit. Graph the solution set on the number line, and write it in interval notation. a. 4 1 OR 3 8 11 b. 6 1 5 3 AND 9 6 c. 4 3 6 15 64. Graph the linear inequalit in variables. a. 4 0 b. 34 1 65. Graph the solution of the sstem of linear inequalities.
a. 1 b. 6 66. Use the quadratic formula to solve the equation. a. 6 1 0 b. t t 4 67. Write the first 5 terms of each sequence. a. a n 6n b. a n n 3 c. a n 1 n n 5 68. Find each sum. 7 a. k 3 b. 4k 1 k 6 k 4
69. Beck borrowed $7000 (interest free) from her mother. She is paing back the loan in monthl installments of $30. Write the first 4 terms of the sequence that gives the balance at the beginning of each month, and find the general term, a n. What is the balance due at the beginning of the 18 month? 70. A rubber ball is dropped from a height of 19 feet and it continues to bounce ½ the height from which it last fell. Write out the first 4 terms of the sequence, and find the general term, a n. How man bounces does it take for the ball to rebound less than 1 foot? 71. Simplif a. 5 3 b. 4 7 7. We have information for the number of students at ARCC taking a college level math class, and the number of students at ARCC taking a science course. Use a Venn diagram to illustrate the number that are in each region. We know 850 students are taking a college level math class, 1100 students are taking a science course, and 65 students are taking both a college level math class and a science course. a. The number of people taking a college level math class, but not a science course is. b. Suppose we want to mail scholarship information to all of the individuals who are taking a college level math course or taking a science course or both but we don t want anone to receive two mailings. How man mailings do we need to send so that each person receives onl one mailing? 73. Given the sets A m, a, t, h, B m,, t, h, C f, u, n a. AB, find the following:
b. AB c. AC