MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write a word description of the set. 1) {January, February, March, April, May, June, July, August, September, October, November, December} A) months of the year B) seasons of the year C) days of the week D) days of the year 1) Determine if the set is the empty set. 2) {x x < 6 and x > 10} 2) A) Yes, it is the empty set. B) No, it is not the empty set. Determine whether the statement is true or false. 3) 7 {1, 2, 3,..., 40} 3) A) True B) False Write or in the blank so that the resulting statement is true. 4) {14, 27, 32} {19, 27, 32, 42} 4) A) B) Are the sets equivalent? 5) A = {11, 13, 15, 17, 19} B = {12, 14, 16, 18, 20} A) Yes B) No 5) Calculate the number of subsets and the number of proper subsets for the set. 6) {x x is a day of the week} 6) A) 127; 126 B) 128; 127 C) 64; 65 D) 128; 129 Find the cardinal number for the set. 7) Determine the cardinal number of the set {x x is a letter of the alphabet} 7) A) 25 B) 23 C) 26 D) 30 Are the sets equal? 8) A = {9, 10, 11, 12, 13} B = {8, 9, 10, 11, 12} A) Yes B) No 8) Let U = {21, 22, 23,..., 40}, A = {21, 22, 23, 24, 25}, B = {26, 27, 28, 29}, C = {21, 23, 25, 27,..., 39}, and D = {22, 24, 26, 28,..., 40}. Use the roster method to write the following set. 9) A' 9) A) A' = {26, 28, 30,..., 40} B) A' = {27, 29, 31,..., 39} C) A' = {21, 22, 23,..., 40} D) A' = {26, 27, 28,..., 40} 1

2 Given that p and q each represents a simple statement, write the indicated compound statement in its symbolic form. 10) p: The outside humidity is high. 10) q: The basement dehumidifier is running. r: The basement is getting moldy. If the outside humidity is high, then the basement dehumidifier is running or the basement is not getting moldy. A) p (q r) B) p (q ~ r) C) p (q ~ r) D) p (q ~ r) 11) p: Tosca is an opera. q: Carmen is an opera. Tosca is an opera and Carmen is an opera. A) p q B) p q C) p q D) p ~ q 11) Form the negation of the statement. 12) Copenhagen is not the capital of Brazil. 12) A) It is true that Brazil is not the capital of Copenhagen. B) It is not true that Copenhagen is not the capital of Brazil. C) It is true that Copenhagen is not the capital of Brazil. D) It is not true that Brazil is not the capital of Copenhagen. Use a Venn diagram to answer the question. 13) A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 950 responses with the following results: 285 were interested in an interview show and a documentary, but not reruns; 38 were interested in an interview show and reruns, but not a documentary; 133 were interested in reruns but not documentaries or interviews; 228 were interested in an interview show but not a documentary; 95 were interested in a documentary and reruns; 57 were interested in an interview show and reruns; 76 were interested in none of the three. How many are interested in exactly one kind of show? A) 436 B) 466 C) 446 D) ) 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. 14) (A' B) (A' C') 14) A) {r, s, t, y, z} B) {q, s, u, v, x, y} C) {r, t, z} D) {q, r, t, y, z} 2

3 Complete the truth table by filling in the required columns. 15) ~ (p q) 15) p q p q ~ (p q) T T T F F T F F A) p q p q ~ (p q) T T T F T F F T F T F T F F F T B) p q p q ~ (p q) T T T T T F F F F T F F F F F F C) p q p q ~ (p q) T T T F T F F T F T F T F F T F D) p q p q ~ (p q) T T T F T F F T F T F T F F F F Use the formula for the cardinal number of the union of two sets to solve the problem. 16) 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) 16 B) 14 C) 12 D) 13 16) Use sets to solve the problem. 17) Mrs. Bollo's second grade class of thirty students conducted a pet ownership survey. Results of the survey indicate that 8 students own a cat, 15 students own a dog, and 5 students own both a cat and a dog. How many of the students surveyed own neither a cat nor a dog? A) 25 B) 10 C) 12 D) 3 17) 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. 18) A' B 18) A) {s, u, w} B) {r, s, t, u, v, w, x, z} C) {q, s, t, u, v, w, x, y} D) {q, r, s, t, v, x, y, z} 19) (A B)' 19) A) {s, u, w} B) {r, t, u, v, w, x, z} C) {q, s, t, u, v, w, x, y} D) {t, v, x} 3

4 Construct a truth table for the statement. 20) ~ p ~ q 20) A) B) T T F F T T T F F T T F F T T T F F T F F T T F F F T T F F F F T T T F F T T T C) T T F F F T F F T T F T T F F F F T T T D) T T F T T T F F F T F T T T T F F T F F 21) (p s) (~p ~s) 21) A) p s (p s) (~p ~s) T T T T F F F T F F F T C) p s (p s) (~p ~s) T T T T F T F T T F F F B) p s (p s) (~p ~s) T F F F T F D) p s (p s) (~p ~s) T T F T F F F T T F F T Construct a truth table for the given statement. 22) ~ p ~ q 22) A) B) T T F T F T T F F T T F F T F T F F T F F T T F F F T T F F F F T T T F F T T T C) T T F F T T F F T T F T T F T F F T T T D) T T F F T T F F T F F T T F T F F T T T Express the set using the roster method. 23) {x x N and x is greater than 13} 23) A) {14,15,16,...} B) {14,16,18,...} C) {13,14,15,...} D) {14,15,16} 4

5 Plot the point in the rectangular coordinate system. 24) (1, 3) 24) A) B) C) D) Evaluate the function at the given values of the variable. 25) f(x) = 7x - 8 a. f(9) b. f(4) 25) A) -504, -224 B) 55, 20 C) 504, 224 D) 71, 36 5

6 Use the vertical line test to determine if y is a function of x. 26) 26) A) Function B) Not a function SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate f(x) for the given values for x. Then use the ordered pairs (x, f(x)) from your table to graph the function. 27) f(x) = x 2-2 x f(x) ) 6

7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the x- and y-intercepts to graph the linear equation. 28) x + 2y = 4 28) A) B) C) D) Graph the horizontal or vertical line. 7

8 29) x = -5 29) A) B) C) D) Write the decimal as a percent. 30) 71 30) A) 3550% B) 7100% C) 0.71% D) 7.1% Solve the problem. 31) Suppose that the luxury sales tax rate in a foreign country is 29%. A very wealthy socialite bought a diamond tiara for $185,000. How much tax does she pay? A) $6379 B) $53,650 C) $537 D) $ ) 8

9 32) 21 is 6% of what number? 32) A) 350 B) 35 C) 3500 D) ) A dress regularly sells for $117. The sale price is $95. Find the percent decrease of the sale price from the regular price. A) 431.8% B) 81.2% C) 18.8% D) 23.2% 33) Express the fraction as a percent. 34) ) A) 80% B) 50% C) 40% D) 4% Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate whether the line rises, falls, is horizontal, or is vertical. 35) (2, 8), (5, 6) 35) A) - 2 3, falls B) - 3 2, falls C) 2, rises D) 2, rises 3 The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Find how much money will be in the account after the given number of years (Assume 360 days in a year.), and how much interest was earned. A = P 1 + r n nt P = A 1 + r n nt A = Pe rt Y = 1 + r n n ) Principal: $9000 Rate: 4% Compounded: annually Time: 3 years A) amount in account: $28,080.00; interest earned: $19, B) amount in account: $1,125,000.00; interest earned: $1,116, C) amount in account: $10,146.78; interest earned: $ D) amount in account: $10,123.78; interest earned: $ ) The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year and round answer to the nearest cent. 37) P = $600 37) r = 6.25% t = 5 months A) $15.63 B) $ C) $ D) $17.05 The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total amount due at time t. Round answer to the nearest cent. 38) P = $160, r = 7%, t = 3 years 38) A) $ B) $ C) $ D) $

10 Solve the problem. A = P 1 + r n nt P = A 1 + r n nt A = Pe rt Y = 1 + r n n ) How much money should be deposited today in an account that earns 6% compounded semiannually so that it will accumulate to $9000 in 2 years? A) $ B) $10, C) $ D) $ ) Solve the problem. 40) In how many distinct ways can the letters in MANAGEMENT be arranged? 40) A) 453,600 B) 22,680 C) 3,628,800 D) 226,800 Determine the periodic deposit. Round up to the nearest dollar. How much of the financial goal comes from deposits and how much comes from interest? nt - 1 A = P[(1 + r)t - 1] r A = P 1 + r n r n P = A r n 1 + r n nt ) Periodic Deposit: $? at the end of each year Rate: 8% compounded annually Time: 12 years Financial Goal: $82,000 A) $4321; $51,852 from deposits and $30,148 from interest B) $4926; $59,112 from deposits and $22,888 from interest C) $6667; $80,004 from deposits and $1996 from interest D) $7709; $46,254 from deposits and $35,746 from interest 41) Evaluate the factorial expression. 42) 7! 5! 42) A) 2! B) 7 C) 7 5 D) 42 Solve the problem by applying the Fundamental Counting Principle with two groups of items. 43) A restaurant offers 8 entrees and 9 desserts. In how many ways can a person order a two-course meal? A) 19 B) 144 C) 72 D) 17 43) Use the formula for n P r to solve. 44) A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 9 members and any member can be elected to each position? No person can hold more than one office. A) 168 B) 3024 C) 252 D) ) Graph the equation. Select integers for x, -3 x 3. 10

11 45) y = 1 6 x ) A) B) C) D) Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 46) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 46) 4. A) 4 B) 0 C) 1 6 D)

12 Solve the problem. 47) A group consists of 6 men and 5 women. Three people are selected to attend a conference. In how many ways can 3 people be selected from this group of 11? In how many ways can 3 men be selected from the 6 men? Find the probability that the selected group will consist of all men. A) 165; 20; B) 165; 20; ) C) 165; 20; 4 33 D) 990; 120; 4 33 Use the formula for the number of subsets of a set with n elements to solve the problem. 48) 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) 255 C) 128 D) ) Solve the problem. 49) From 9 names on a ballot, a committee of 3 will be elected to attend a political national convention. How many different committees are possible? A) 504 B) 84 C) 60,480 D) ) In the following exercises, does the problem involve permutations or combinations? Explain your answer. It is not necessary to solve the problem. 50) A record club offers a choice of 7 records from a list of 45. In how many ways can a member make 50) a selection? A) Combinations, because the order of the records selected does not matter. B) Permutations, because the order of the records selected does matter. Find the mean for the group of data items. Round to the nearest hundredth, if necessary. 51) 24, 24, 84, 89, 38, 24 51) A) 56.6 B) C) D) 51.8 Find the median for the group of data items. 52) 11, 9, 4, 0, 2, 1, 2, 0, 0 52) A) 0 B) 2 C) 5 D) 4 Find the mode for the group of data items.if there is no mode, so state. 53) 12, 7, 4, 0, 2, 1, 2 53) A) no mode B) 2 C) 12 D) 7 Find the range for the group of data items. 54) 11, 12, 13, 14, 15 54) A) 15 B) 13 C) 11 D) 4 Find the standard deviation for the group of data items (to the nearest hundredth). 55) 8, 9, 10, 11, 12 55) A) 0 B) 1.58 C) 1.25 D)

13 Answer Key Testname: UNTITLED1 1) A 2) A 3) B 4) B 5) A 6) B 7) C 8) B 9) D 10) C 11) B 12) B 13) D 14) C 15) A 16) D 17) C 18) D 19) B 20) A 21) A 22) B 23) A 24) C 25) B 26) A 27) x f(x) ) B 29) B 30) B 31) B 32) A 33) C 34) C 35) A 36) D 13

14 Answer Key Testname: UNTITLED1 37) A 38) C 39) C 40) D 41) A 42) D 43) C 44) D 45) D 46) C 47) C 48) D 49) B 50) A 51) B 52) B 53) B 54) D 55) B 14