Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write a description of the set. 1) {January, February, March, April, May, June, July, August, September, October, November, December} A) days of the week B) days of the year C) seasons of the year D) months of the year 1) List the elements in the set. 2) The set of the days of the week 2) A) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} B) {Friday, Monday, Saturday, Sunday, Thursday, Tuesday, Wednesday} C) {Tuesday, Thursday} D) {Saturday, Sunday} The bar graph shows the percentage of adults that use the Internet for specific tasks. Use the graph to represent the given set using the roster method. 3) 3) 27 32 11 16 23 the set of tasks in which usage exceeds 21% A) {e-mail, information searches, news} B) {e-mail, information searches} C) {job, school} D) {e-mail, information searches, news, job} 1
4) 4) 30 25 21 14 9 {x x is a task in which usage lies between 11% and 29%} A) {news} B) {email, information searches, news, job, school} C) {news, job} D) {information searches, news, job} 5) 5) 29 24 20 13 8 {x x is a task in which usage lies between 10% and 28%} A) {email, information searches, news, job, school} B) {information searches, news, job} C) {news} D) {news, job} Determine whether the statement is true or false. 6) 7 {1, 2, 3,..., 40} 6) A) True B) False Express the set using the roster method. 7) {x x N and x is greater than 7} 7) A) {7,8,9,...} B) {8,10,12,...} C) {8,9,10,...} D) {8,9,10} 8) {x x N and x lies between 0 and 4} 8) A) {1, 2, 3} B) {0, 1, 2, 3} C) {0, 1, 2, 3, 4} D) {1, 2, 3, 4} 2
Express the set using set-builder notation. Use inequality notation to express the consition x must meet in order to be a member of the set. 9) A = {600, 601, 602,..., 6000} 9) A) {x x N and x 600 } B) {x x N and x 6000} C) {x x N and 600 x 6000} D) {x 600 < x < 6000} Find the cardinal number for the set. 10) {27, 29, 31, 33, 35} 10) A) 6 B) 27 C) 4 D) 5 11) Determine the cardinal number of the set {x x is a letter of the alphabet} 11) A) 26 B) 30 C) 23 D) 25 Are the sets equivalent? 12) A = {Larry, Moe, Curly. Shemp} B = {Posh, Sporty, Baby, Scary} A) Yes B) No 12) Determine whether the set is finite or infinite. 13) The set of natural numbers less than 100 13) A) Finite B) Infinite 14) {x x N and x 1000} 14) A) Finite B) Infinite Are the sets equal? 15) A = {13, 14, 15, 16, 17} B = {12, 13, 14, 15, 16} A) Yes B) No 15) Determine whether the statement is true or false. 16) {France, Germany, Switzerland} 16) A) True B) False List all the subsets of the given set. 17) {Siamese, domestic shorthair} 17) A) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, { } B) {Siamese, domestic shorthair}, {domestic shorthair}, { } C) {Siamese}, {domestic shorthair}, { } D) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, Use the formula for the number of subsets of a set with n elements to solve the problem. 18) Pasta comes with tomato sauce and can be ordered with some, all, or none of these ingredients in the sauce: {onions, garlic, carrots, broccoli, shrimp, mushrooms, zucchini, green pepper}. How many different variations are available for ordering pasta with tomato sauce? A) 127 B) 256 C) 255 D) 128 18) 3
Place the various elements in the proper regions of the following Venn diagram. 19) Let U = {8, 9, 10, 11, 12, 13, 14} and A = {8, 9, 12}. Find A' and place the elements in the proper region. A) A' = {10, 11, 13, 14} B) A' = {11, 12, 13, 14} 19) C) A' = {8, 9, 12} D) A' = {8, 9, 10, 11, 12, 13, 14} 4
Use the Venn diagram to list the elements of the set in roster form. 20) The set of students who studied Saturday 20) A) {Sam, Sophia} B) {Karen, Charly, Vijay} C) {Karen, Charly, Sam, Sophia} D) {Karen, Charly} 5
Use the following definition to place the indicated natural number in the correct region of the Venn diagram. A palindromic number is a natural number whose values does not change if its digits are reversed. U = the set of natural numbers A = the set of palindromic numbers B = the set of odd numbers 21) 8190 21) A) B) 8190 8190 C) D) 8190 8190 Let U = {1, 2, 4, 5, a, b, c, d, e}. Use the roster method to write the complement of the set. 22) T = {2, 4, b, d} 22) A) {1, 3, 5, a, c, e} B) {1, 5, a, c, e} C) {1, 5, a, e} D) {1, 2, 4, 5, a, b, c, d, e} L 23) A B' 23) A) {t, v, x} B) {u, w} C) {r, s, t, u, v, w, x, z} D) {q, s, t, u, v, w, x, y} 24) C' A' 24) A) {w, y} B) {q, r, s, t, u, v, x, z} C) {q, s, u, v, w, x, y, z} D) {r, t} 6
25) (A B)' 25) A) {t, v, x} B) {s, u, w} C) {r, s, t, u, v, w, x, z} D) {r, t, v, x} 26) A' B 26) A) {q, s, t, u, v, w, x, y} B) {r, s, t, u, v, w, x, z} C) {q, r, s, t, v, x, y, z} D) {s, u, w} 27) A B' 27) A) {t, v, x} B) {r, s, t, u, v, w, x, z} C) {u, w} D) {q, s, t, u, v, w, x, y} 28) (A B)' 28) A) {r, t, v, x} B) {t, v, x} C) {r, s, t, u, v, w, x, z} D) {s, u, w} Use the formula for the cardinal number of the union of two sets to solve the problem. 29) Set A contains 5 elements, set B contains 11 elements, and 3 elements are common to sets A and B. How many elements are in A B? A) 14 B) 13 C) 16 D) 12 29) 30) Set A contains 12 letters and 8 numbers. Set B contains 7 letters and 8 numbers. Four letters and 5 numbers are common to both sets A and B. Find the number of elements in set A or set B. A) 44 B) 29 C) 35 D) 26 30) Use the Venn diagram shown to answer the question. 31) Which regions represent set E? 31) A) II, III, V, VI B) III C) VIII D) I, IV, VII 32) Which regions represent set D F? 32) A) I, II, IV, V, VI, VII B) I, II, IV, V, VI, VII, VIII C) VIII D) III 7
33) Which regions represent set D E? 33) A) VIII B) II, V C) I, III, IV, VI D) IV, V 34) Which regions represent set E'? 34) A) II, III, V, VI B) I, IV, VII, VIII C) VIII D) II, V, VI Use set notation to identify the shaded region. 35) 35) A) A B B) A - B C) A B D) A B 36) 36) A) (A B) C' B) (A B) C' C) (A B) C' D) (A B C)' Solve the problem by applying the Fundamental Counting Principle with two groups of items. 37) A restaurant offers 10 entrees and 6 desserts. In how many ways can a person order a two-course meal? A) 120 B) 16 C) 18 D) 60 37) 38) In how many ways can a girl choose a two-piece outfit from 5 blouses and 6 skirts? 38) A) 60 B) 30 C) 11 D) 13 Use the Fundamental Counting Principle to solve the problem. 39) There are 6 performers who are to present their acts at a variety show. How many different ways are there to schedule their appearances? A) 720 B) 30 C) 36 D) 6 39) 40) There are 9 performers who are to present their acts at a variety show. One of them insists on being the first act of the evening. If this request is granted, how many different ways are there to schedule the appearances? A) 72 B) 81 C) 362,880 D) 40,320 40) Evaluate the factorial expression. 6! 41) (6-4)! A) 360 B) 180 C) 4 D) 30 41) 8
Solve the problem. 42) In how many distinct ways can the letters in ENGINEERING be arranged? 42) A) 25,200 B) 554,400 C) 39,916,800 D) 277,200 Use the formula for n C r to evaluate the expression. 43) From 8 names on a ballot, a committee of 3 will be elected to attend a political national convention. How many different committees are possible? A) 336 B) 6720 C) 56 D) 168 43) 44) A physics exam consists of 9 multiple-choice questions and 6 open-ended problems in which all work must be shown. If an examinee must answer 7 of the multiple-choice questions and 3 of the open-ended problems, in how many ways can the questions and problems be chosen? A) 1134 B) 21,772,800 C) 261,273,600 D) 720 44) Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 45) Use the spinner below to answer the question. Assume that it is equally probable 45) that the pointer will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that the arrow will land on 2 or 4. A) 4 3 B) 2 5 C) 3 2 D) 2 46) You are dealt one card from a standard 52-card deck. Find the probability of being dealt an ace or a 9. 2 A) B) 10 C) 13 5 D) 13 2 13 46) 47) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 7. 47) A) 7 B) 1 C) 7 6 D) 0 48) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is less than 13. 48) A) 1 4 B) 0 C) 1 D) 1 2 9
Use the empirical probability formula to solve the exercise. Express the answer as a fraction. Then express the probability as a decimal, rounded to the nearest thousandth, if necessary. 49) The table below represents a random sample of the number of deaths per 100 cases for a certain 49) illness over time. If a person infected with this illness is randomly selected from all infected people, find the probability that the person lives 3-4 years after diagnosis. Years after Diagnosis Number deaths 1-2 15 3-4 35 5-6 16 7-8 9 9-10 6 11-12 4 13-14 2 15+ 13 A) 35 65 ; 0.538 B) 1 35 ; 0.029 C) 35 100 ; 0.35 D) 7 120 ; 0.058 The chart below shows the percentage of people in a questionnaire who bought or leased the listed car models and were very satisfied with the experience. Model A 81% Model B 79% Model C 73% Model D 61% Model E 59% Model F 57% 50) The empirical probability that a person with a model shown is very satisfied with the experience is 61. What is the model? 100 A) D B) E C) A D) F 50) 10