MAT103: Fundamentals of Mathematics I Final Exam Review Packet
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1 MAT103: Fundamentals of Mathematics I Final Exam Review Packet A. Using the information below, write the appropriate numerical value in each region of the Venn diagram provided and answer the questions that follow. Be sure to place the proper value in each region based on the labels provided in the diagram. Place appropriate values in ALL regions. 1. A company conducts a survey of employees to determine which of the following items they feel are important contract issues: health benefits; vacation time; or retirement plans. The results are as follows: said health benefits said vacation time said retirement plans said health benefits and vacation time said health benefits and retirement plans said vacation time and retirement plans said all three are important contract issues Health Benefits Vacation Time 2. How many employees feel that only health benefits are an important contract issue? B. Use the following set definitions to write the indicated set for each exercise below ( ) C. Express each Hindu-Arabic number below using Roman numerals Retirement Plans
2 D. Convert each number below, expressed in Roman numerals, to its decimal (i.e., base-10) equivalent. 9. LIX 10. CDV 11. MMDCXCVIII E. Use the given sequence to complete each exercise below. 12. Determine how many terms are in the following sequence: 13. Give the explicit formula for the following arithmetic sequence: F. Identify each of the following sequences as arithmetic, geometric, or neither: G. Use the given Venn diagram to write the set of numbered regions representing each statement below ( ) 20. H. Determine the next term in each sequence below
3 I. Completely simplify each expression below ( ) ( ) ( ) 30. ( ) 31. ( ) ( ) J. Perform the indicated operation and write the final answer in proper form for each exercise below. If an exercise specifies a particular method to be used, you MUST use that method. You must perform all calculations in the indicated base (base-10 if no other base is specified). 34. Use lattice multiplication: 35. Use the left-to-right algorithm:
4 36. Use the scratch algorithm: K. Convert each number below to base-10 from the indicated base L. Convert each number below from base-10 to the indicated base. 42. to quinary 43. to base-8 M. Complete each exercise below. 44. Determine the greatest common factor (GCF) of and. 45. How many divisors does have? 46. Determine the least common multiple (LCM) of,, and. 47. Which fraction is smaller: or? 48. Is prime? 49. Determine all positive single-digit integers to replace such that the following number is divisible by the number given in each exercise below: a. b.
5 50. Give the prime factorization of. 51. Determine the fraction with a denominator of that is equivalent to the fraction. 52. Give the explicit form for the following arithmetic sequence: 53. Solve the following equation: ( ) ( ) ( ) N. Solve each word problem below. You must write a proper equation for each exercise. 54. Roberta earns per hour at her part time job. She wants to earn enough money to buy a prom dress that costs. If she works hours each day she goes to work, how many days must Roberta work in order to afford the dress? 55. At soccer practice, the coach makes George and Victor run around the field as punishment for acting up during a team meeting. George runs one lap in seconds, and Victor runs one lap in seconds. If the two start running together, after how long (in seconds) will they next cross the starting line at the same time? 56. Jack and Jill have a total of. If Jill has times as much money as Jack, how much do they each have? 57. One number is more than times another. Determine both numbers if their sum is. 58. The sum of three consecutive odd integers is. Determine all three integers. 59. The sum of four consecutive integers is. State the value of the largest integer. 60. A farmer sells his land to a developer when he retires. The land is divided evenly into regions zoned for commercial, residential, and recreational use. The entirety of the residential area is to be developed such that the entire zone will be filled with a combination of single family homes and duplexes. If three times as many single family homes are to be built as duplexes, and the single family homes will cover an area of 12 acres, how many acres of land did the farmer sell when he retired?
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