Math For Liberal Arts Spring 2011 Final Exam. Practice Version Name A spinner has a pointer which can land on one of three regions labelled 1, 2, and 3 respectively. 1) Compute the expected value for the number on which the pointer lands if the probabilities for the three regions are 1 2, 1 3, and 1 6 respectively. 1) A) 11 6 B) 7 6 C) 5 3 D) 17 6 Calculate the number of subsets and the number of proper subsets for the set. 2) {x x is a day of the week} A) 128; 129 B) 127; 126 C) 128; 127 D) 64; 65 2) Construct a truth table for the statement. 3) (q p) ~ q A) p q q p ~ q (q p) ~ q T T T F F T F T T T F T F F F F F T T T C) p q q p ~ q (q p) ~ q T T T F F T F F T F F T T F F F T T F F B) D) p q q p ~ q (q p) ~ q T T T F T T F T T T F T F F T F T T F F p q q p ~ q (q p) ~ q T T T F F T F T T T F T F F T F T T F F 3) 1
4) ~r ~p A) r p (~r ~p) T T F T F T F T T F F T C) r p (~r ~p) T T T F F T F F F F F F B) r p (~r ~p) T T T T F F F T F F F T D) r p (~r ~p) T T F T F F F T F F F T 4) Convert the numeral to a numeral in base ten. 5) 231four A) 45 B) 6 C) 24 D) 21 5) Draw a valid conclusion from the given premises. 6) All birds have wings. None of my pets are birds. All animals with wings can flap them. Therefore... A) All birds can flap their wings. B) All my pets can flap their wings. C) No birds can flap their wings. D) None of my pets can flap their wings. 6) 7) It is either day or night. If it is daytime, then the squirrels are scurrying. It is not nighttime. Therefore... A) Squirrels do not scurry at night. B) The squirrels are not scurrying. C) Squirrels do not scurry during the day. D) The squirrels are scurrying. 7) Evaluate the factorial expression. 8) 7! 5! 8) A) 7 5 B) 7 C) 2! D) 42 2
Express the expanded form as a Hindu-Arabic numeral. 9) (7 105) + (7 104) + (9 103) + (4 102) + (8 101) + (5 1) A) 779,485 B) 400 C) 40 D) 70,560 9) Express the quantified statement in an equivalent way, that is, in a way that has exactly the same meaning. 10) Some mammals are cats. 10) A) At least one mammal is a cat. B) There exists at least one cat that is a mammal. C) All cats are mammals. D) No mammals are cats. Find the cardinal number for the set. 11) {2, 4, 6,..., 60} A) 20 B) 15 C) 30 D) 60 11) Find the mean for the group of data items. Round to the nearest hundredth, if necessary. 12) 5, 10, 12, 3, 4, 7, 11, 12 A) 9.14 B) 6.5 C) 7.43 D) 8 12) Find the median for the group of data items. 13) 10, 6, 4, 0, 1, 1, 1, 0, 0 A) 1 B) 5 C) 0 D) 4 13) Find the midrange for the group of data items. 14) 99, 99, 94, 38, 74, 99 A) 96.5 B) 66 C) 68.5 D) 86.5 14) 3
Find the mode for the group of data items.if there is no mode, so state. 15) 98, 98, 93, 41, 79, 98 A) 98 B) 93 C) 41 D) no mode 15) Given that p and q each represents a simple statement, write the indicated compound statement in its symbolic form. 16) p: 1984 is a novel. 16) q: Persuasion is a novel. 1984 is a novel and Persuasion is a novel. A) p q B) p q C) p ~ q D) p q Given that p and q each represents a simple statement, write the indicated symbolic statement in words. 17) p: Darren admires Zoe q: Zoe admires Darren ~ (p q) A) Darren does not admire Zoe, but Zoe admires Darren. B) Darren admires Zoe but Zoe does not admire Darren. C) Darren admires Zoe and Zoe admires Darren. D) It is not true that Darren admires Zoe and Zoe admires Darren. 17) Let U = {1, 2, 4, 5, a, b, c, d, e}. Use the roster method to write the complement of the set. 18) T = {2, 4, b, d} A) {1, 5, a, e} B) {1, 3, 5, a, c, e} C) {1, 5, a, c, e} D) {1, 2, 4, 5, a, b, c, d, e} 18) Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. 19) A' B A) {q, s, t, u, v, w, x, y} B) {s, u, w} C) {r, s, t, u, v, w, x, z} D) {q, r, s, t, v, x, y, z} 19) 4
Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement. 20) ~(p ~q) 20) A) True B) False Provide an appropriate response. 21) A conditional statement is false only when the, the statement before the connective, is true and the, the statement after the connective, is false. A) consequent; antecedent B) implication; tautology C) tautology; implication D) antecedent; consequent 21) Solve the problem by applying the Fundamental Counting Principle with two groups of items. 22) In how many ways can a girl choose a two-piece outfit from 6 blouses and 8 skirts? A) 14 B) 16 C) 96 D) 48 22) Solve the problem. 23) A group consists of 6 men and 5 women. Four people are selected to attend a conference. In how many ways can 4 people be selected from this group of 11? In how many ways can 4 men be selected from the 6 men? Find the probability that the selected group will consist of all men. 23) A) 330; 15; 1 22 C) 330; 15; 1 1814400 B) 7920; 360; 1 22 D) 330; 15; 1 15840 24) Six students, A, B, C, D, E, F, are to give speeches to the class. The order of speaking is determined by random selection. Find the probability that (a) E will speak first (b) that C will speak fifth and B will speak last (c) that the students will speak in the following order: DECABF (d) that A or B will speak first. A) 1 6 ; 1 36 ; 1 720 ; 1 12 B) 1 6 ; 1 24 ; 1 720 ; 1 3 C) 1 6 ; 1 36 ; 1 360 ; 1 3 D) 1 6 ; 1 12 ; 1 720 ; 1 3 24) 5
25) Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1 through 6, and 5 yellow disks numbered 7 through 11, find the probability of selecting a disk numbered 3, given that a red disk is selected. A) 6 B) 1 1 C) D) 5 11 6 11 11 25) 26) 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) 56 B) 336 C) 6720 D) 168 26) Subtract in the indicated base. 27) 42five -13five 27) A) 12five B) 22five C) 24five D) 14five 6
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% 28) With which model was the greatest percentage satisfied? Estimate the empirical probability that a person with this model is very satisfied with the experience. Express the answer as a fraction with a denominator of 100. A) Model F; 0.57 100 B) Model A: 0.81 100 C) Model F; 57 100 D) Model A; 81 100 28) Use an Euler diagram to determine whether the argument is valid or invalid. 29) All doctors have studied chemistry. All surgeons are doctors. Therefore, all surgeons have studied chemistry. A) valid B) invalid 29) 30) All birds have feathers. No mammal has feathers. Therefore, no mammals are birds. A) valid B) invalid 30) 7
Use divisions to convert the base ten numeral to a numeral in the given base. 31) 89 to base seven A) 152seven B) 1520seven C) 155seven D) 66seven 31) Use the De Morgan law that states: ~(p q) is equivalent to ~ p ~ q to write an equivalent English statement for the statement. 32) It is not the case that a piano and a tattoo are both musical instruments. A) A piano is not a musical instrument or a tattoo is not a musical instrument. B) A piano is a musical instrument but a tattoo is not. C) A piano is not a musical instrument and a tattoo is not a musical instrument. D) pianos are not tattoos. 32) Use the Venn diagram to list the elements of the set in roster form. 33) List the elements of A. 33) A) {13, 17} B) {12, 15, 16} C) {11, 12, 13} D) {11, 13, 14, 17} 8
Use the Venn diagram to list the elements of the set in roster form. 34) The set of students who studied Saturday or Sunday A) {Karen, Charly, Vijay} B) {Karen, Charley, Sam, Sophia, Kenneth, Miguel, Kavita} C) {Sam, Sophia} D) {Karen, Charley, Sam, Sophia, Kenneth, Miguel, Kavita, Vijay} 34) Use the formula for n P r to evaluate the expression. 35) 8 P 3 A) 336 B) 6720 C) 40,320 D) 13,440 35) Use the formula for n C r to evaluate the expression. 36) 12 C 7 A) 240 B) 95,040 C) 1,995,840 D) 792 36) Use the formula for the cardinal number of the union of two sets to solve the problem. 37) Set A contains 35 elements and set B contains 22 elements. If there are 40 elements in (A B) then how many elements are in (A B)? A) 13 B) 5 C) 8 D) 17 37) 9
Use the table below to write the Mayan numeral as a Hindu-Arabic numeral. 38) 38) A) 5,406 B) 5046 C) 100,806 D) 286 10
Use the table below to write the traditional Chinese numeral as a Hindu-Arabic numeral. Hindu-Arabic Numerals 1 Traditional Chinese Numerals 2 3 4 5 6 7 8 9 10 100 1000 11
39) 39) A) 417 B) 413 C) 4137 D) 437 Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 40) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of 40) getting a 10. A) 10 B) 1 C) 10 D) 0 6 41) This problem deals with eye color, an inherited trait. For purposes of this problem, assume that only two eye colors are possible, brown and blue. We use b to represent a blue eye gene and B a brown eye gene. If any B genes are present, the person will have brown eyes. The table shows the four possibilities for the children of two Bb (brown-eyed) parents, where each parent has one of each eye color gene. 41) Second Parent B b First Parent B BB Bb b Bb bb Find the probability that these parents give birth to a child who has blue eyes. A) 1 4 B) 1 2 C) 1 D) 0 12
Use,,, or both and to make a true statement. 42) {a, b} {z, a, y, b, x, c} A) B) and C) D) 42) Write a word description of the set. 43) {January, February, March, April, May, June, July, August, September, October, November, December} A) months of the year B) days of the year C) days of the week D) seasons of the year 43) Write the Roman numeral as a Hindu-Arabic numeral. 44) MIX A) 1009 B) 910 C) 1110 D) 109 44) Write the contrapositive of the statement. 45) If I am in the city of Grominia, then I am on the planet Plochus. A) If I am not on the planet Plochus, then I am not in the city of Grominia. B) If I am not in the city of Grominia, then I am on the planet Plochus. C) If I am not in the city of Grominia, then I am not on the planet Plochus. D) If I am not on the planet Plochus, then I am in the city of Grominia. 45) Write the converse and inverse of the statement. 46) If you watch too much TV, then you get bleary-eyed. A) converse: If you get bleary-eyed, then you are watching too much TV. inverse: If you don't get bleary-eyed, then you are watching too much TV. B) converse: If you don't watch too much TV, you don't get bleary-eyed. inverse: If you get bleary-eyed, then you are watching too much TV. C) converse: If you get bleary-eyed, then you are watching too much TV. inverse: If you don't get bleary-eyed, then you are not watching too much TV. D) converse: If you get bleary-eyed, then you are watching too much TV. inverse: If you don't watch too much TV, you don't get bleary-eyed. 46) Write the negation of the conditional statement. 47) If I am in Acapulco, then I am in Mexico. A) I am not in Acapulco and I am in Mexico. B) I am in Acapulco and I am not in Mexico. C) If I am in Acapulco, then I am not in Mexico. D) If I am not in Acapulco, then I am not in Mexico. 47) 13
Write the negation of the quantified statement. (The negation should begin with "all," "some," or "no.") 48) Some eagles are not birds. A) All eagles are birds. B) All eagles are not birds. C) All birds are eagles. D) No eagles are birds. 48) You are dealt one card from a 52-card deck. Find the probability that you are not dealt: 49) a 9. A) 12 B) 1 9 C) D) 1 13 13 10 10 49) You randomly select one card from a 52-card deck. Find the probability of selecting: 50) an ace or a 8? A) 13 B) 9 C) 9 D) 2 2 26 13 50) 14
Answer Key Testname: LIBARTFINALSPRING2011PRACTICE 1) C Objective: (11.8) Compute Expected Value 2) C Objective: (2.2) Determine the Number of Subsets of a Set 3) A Objective: (3.4) Construct Truth Tables for Conditional Statements 4) D Objective: (3.3) Construct Truth Tables 5) A Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten 6) A Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments 7) D Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments 8) D Objective: (11.2) Evaluate Factorial Expressions 9) A Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral 10) A Objective: (3.1) Express Quantified Statements in Two Ways 11) C Objective: (2.1) Determine a Set's Cardinal Number 12) D Objective: (12.2) Determine the Mean for a Data Set 13) A Objective: (12.2) Determine the Median for a Data Set 14) C Objective: (12.2) Determine the Midrange for a Data Set 15) A Objective: (12.2) Determine the Mode for a Data Set 16) B Objective: (3.2) Express Compound Statements in Symbolic Form 17) D Objective: (3.2) Express Symbolic Statements with Parentheses in English 18) C Objective: (2.3) Find the Complement of a Set 19) D Objective: (2.3) Find the Union of Two Sets 20) B Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case 21) D Objective: (3.4) Understand the Logic Behind the Definition of the Conditional 22) D Objective: (11.1) Use the Fundamental Counting Principle to Determine the Number of Possible Outcomes in a Given Situation 23) A Objective: (11.5) Compute Probabilities with Combinations 15
Answer Key Testname: LIBARTFINALSPRING2011PRACTICE 24) B Objective: (11.5) Compute Probabilities with Permutations 25) B Objective: (11.7) Compute Conditional Probabilities 26) A Objective: (11.3) Solve Problems Involving Combinations Using the Combinations Formula 27) C Objective: (4.3) Subtract in Bases Other Than Ten 28) D Objective: (11.4) Compute Empirical Probability 29) A Objective: (3.8) Use Euler Diagrams to Determine Validity 30) A Objective: (3.8) Use Euler Diagrams to Determine Validity 31) C Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases 32) A Objective: (3.6) Use De Morgan s Laws 33) D Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets 34) B Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets 35) A Objective: (11.2) Use the Permutations Formula 36) D Objective: (11.3) Solve Problems Involving Combinations Using the Combinations Formula 37) D Objective: (2.3) Use the Formula for n(a B) 38) B Objective: (4.1) Understand and Use the Mayan Numeration System 39) D Objective: (4.4) Understand and Use the Traditional Chinese System 40) D Objective: (11.4) Compute Theoretical Probability 41) A Objective: (11.4) Compute Theoretical Probability 42) B Objective: (2.2) Recognize Proper Subsets and Use the Notation 43) A Objective: (2.1) Use Three Methods to Represent Sets 44) A Objective: (4.4) Understand and Use the Roman System 45) A Objective: (3.5) Write the Contrapositive for a Conditional Statement 46) D Objective: (3.5) Write the Converse and Inverse of a Conditional Statement 16
Answer Key Testname: LIBARTFINALSPRING2011PRACTICE 47) B Objective: (3.6) Write the Negation of a Conditional Statement 48) A Objective: (3.1) Write Negations of Quantified Statements 49) A Objective: (11.6) Find the Probability that an Event Will Not Occur 50) D Objective: (11.6) Find the Probability of One Event or a Second Event Occurring 17