Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the set using the roster method. 1) {x x N and x is greater than 7} 1) A) {8,9,10,...} B) {7,8,9,...} {8,10,12,...} D) {8,9,10} 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. 2) A = {12, 13, 14, 15, 16,...} 2) A) {x x N and x 12} B) {x x N and x 12} {x x N and x > 12} D) {x x N and x 16} Are the sets equal? 3) {e, f, g, h} = {f, h, g, e} 3) A) Yes B) No 4) A = {13, 14, 15, 16, 17} B = {12, 13, 14, 15, 16} A) Yes B) No 4) Write or in the blank so that the resulting statement is true. 5) {c, a, n, d, i, d, a, t, e} {a, c, d, e, i, t, a, n, d} 5) A) B) 6) {red, blue, green} {blue, green, yellow, black} 6) A) B) Calculate the number of subsets and the number of proper subsets for the set. 7) {1, 3, 5, 7, 9, 11} 7) A) 64; 63 B) 62; 63 63; 64 D) 63; 62 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. 8) (A ' 8) A) {q, r, s, t, u, v, w, x, y, z} B) {q, s, y, z} {q, r, s, t, u, v, x, z} D) {w, y} 9) A' B 9) A) {s, u, w} B) {q, s, t, u, v, w, x, y} {q, r, s, t, v, x, y, z} D) {r, s, t, u, v, w, x, z} 10) C 10) A) {q, s, y, z} B) {q, s, u, w, y} {v, w, x, y, z} D) { } 1
Place the various elements in the proper regions of the following Venn diagram. 11) Let U = {g, h, j, k, m, n} and A = {g, h, n}. Find A'. Then use a Venn diagram to illustrate the relationship among the sets U, A, and A'. A) A' = {j, k, m} B) A' = 11) A' = {g, h, m} D) A' = {g, h, n} Use set notation to identify the shaded region. 12) 12) A) B A' B) A' B A' B D) (A B)' 2
13) 13) A) (A B' B) (C B') A B' (A D) A C Write the statement in symbolic form to determine the truth value for the statement. 14) 5 3 = 15 or French is a language. 14) A) True B) False Construct a truth table for the statement. Then determine if the statement is a tautology. 15) (q p) (~ p q) 15) A) p q q p ~ p ~ p q (q p) (~ p q) T T T F T T T F T F F F Is not a tautology. F T F T T T F F T T T T B) D) p q q p ~ p ~ p q (q p) (~ p q) T T T T T F T F T F F F Is not a tautology. F T F T T F F F F T T T p q q p ~ p ~ p q (q p) (~ p q) T T T F T T T F F F F T Is a tautology. F T T T T T F F T T T T p q q p ~ p ~ p q (q p) (~ p q) T T T F T T T F T F F F Is not a tautology. F T F T T F F F T T T T Use an Euler diagram to determine whether the argument is valid or invalid. 16) All birds have feathers. No mammal has feathers. Therefore, no mammals are birds. A) valid B) invalid 16) 3
17) All insects have six legs. No spiders are insects. Therefore, no spiders have six legs. A) valid B) invalid 17) Use a truth table to determine whether the symbolic form of the argument is valid or invalid. 18) (p q) (q p) q p q 18) A) B) D) p q p q q p [ (p q) (q p) ] p q [ [( p q) (q p) ] q ] (p q) T T T T T T T T F F T F F T F T T F F F T F F T T T F F Argument is invalid. p q p q q p [ (p q) (q p) ] p q [ [(p q) (q p) ] q ] (p q) T T T T T F T T F F T F F T F T T F F F T F F T T T T F Argument is invalid. p q p q q p [ (p q) (q p) ] p q [ [( p q) (q p) ] q ] (p q) T T T T T T T T F F T F T T F T T F F T T F F T T T F T Argument is valid. p q p q q p [ (p q) (q p) ] p q [ [(p q) (q p) ] q ] (p q) T T T T T T T T F F T F T T F T T F F T T F F T T T F F Argument is valid. Convert the numeral to a numeral in base ten. 19) 54012six 19) A) 32,472 B) 336 1106 D) 7352 Use divisions to convert the base ten numeral to a numeral in the given base. 20) 2,874 to base eight 20) A) 4,572eight B) 5,427eight 4,527eight D) 5,472eight 4
Solve the problem. Round all circumference and area calculations to the nearest whole number. 21) How much fencing is required to enclose a circular garden whose radius is 35 m? 21) A) 220 m B) 55 m 3848 m D) 110 m Find the area of the figure. 22) 29 yd 8 yd 22) 24 yd 7 yd A) 400 yd2 B) 226 yd2 241 yd2 D) 142 yd2 Find the volume of the figure. If necessary, round the answer to the nearest whole number. 23) Cone 23) 2 in. 4 in. A) 50 in.3 B) 67 in.3 17 in.3 D) 34 in.3 24) 12 ft 24) 13 ft A) 490ft3 B) 5881 ft3 1470 ft3 D) 245ft3 Find the measures of the parts of the right triangle that are not given. Round your answers to the nearest whole number. 25) 25) c a 30 b = 57 yd A) a = 37 yd; c = 64 yd; B = 60 B) a = 33 yd; c = 64 yd; B = 60 a = 33 yd; c = 66 yd; B = 60 D) a = 37 yd; c = 66 yd; B = 60 5
Use the inverse trigonometric keys on a calculator to find the measure of angle A, rounded to the nearest whole degree. 26) 26) 16 m 25 m A) 32 B) 33 31 D) 34 Use the formula for n P r to solve. 27) A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 13 members and any member can be elected to each position? No person can hold more than one office. A) 858 B) 572 1716 D) 17,160 27) Use the formula for n C r to evaluate the expression. 28) To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 53 numbers ( one through 53.) The order in which the selections is made does not matter. How many different selections are possible? A) 22,957,480 B) 720 318 D) 20,358,520 28) You randomly select one card from a 52-card deck. Find the probability of selecting: 29) an ace or a 8? 29) 9 2 A) B) 9 D) 13 26 13 2 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),}. 30) Find the probability of getting a sum of 3 or 4. 30) A) 1 18 B) 1 6 1 12 D) 5 36 A single die is rolled. Find the odds: 31) against getting a number less than 4. 31) A) 2:1 B) 1:2 1:1 D) 3:2 Solve the problem involving probabilities with independent events. 32) A single die is rolled twice. Find the probability of getting a 3 the first time and a 5 the second time. 32) A) 1 1 1 B) D) 1 3 36 12 6 6
The table shows the number of employed and unemployed workers in the U.S., in thousands, in 2000. Employed Unemployed Male 67,761 2433 Female 58,655 2285 Assume that one person will be randomly selected from the group described in the table. 33) Find the probability of selecting a person who is employed, given that the person is male. 33) A) 67,761 2433 2285 2433 B) D) 70,194 70,194 70,194 67,761 Find the mean for the data items in the given frequency distribution. Round to the nearest hundredth, if necessary. 34) 34) Score Frequency x f 1 3 2 5 3 4 4 6 5 10 6 7 7 11 8 8 9 12 10 12 A) 5.91 B) 5.15 7.91 D) 6.54 Find the median for the group of data items. 35) 1.1, 2.4, 1.6, 2.5, 1.1, 2.4, 1.1, 8.3, 8.3, 1.9 35) A) 1.9 B) 2.15 2.4 D) 1.1 Find the mode for the group of data items.if there is no mode, so state. 36) 97, 97, 94, 44, 74, 97 36) A) 94 B) 97 no mode D) 44 Find the range for the group of data items. 37) 7, 7, 7, 19, 24, 24, 24 37) A) 31 B) 19 17 D) 12 Find the standard deviation for the group of data items (to the nearest hundredth). 38) 11, 12, 13, 14, 15 38) A) 2.5 B) 0 1.58 D) 1.25 The scores on a driver's test are normally distributed with a mean of 100. Find the score that is: 39) Find the score that is 2 standard deviations below the mean, if the standard deviation is 22. 39) A) 56 B) 78 144 D) 122 7
The correlation coefficient, r is given for a sample of n data points. Use the = 0.05 column in a correlation significance table to determine whether or not we may conclude that a correlation does exist in the population. 40) n = 37 r = -0.395 40) A) Yes, we may conclude that there is a correlation. B) No, we may not conclude that there is a correlation. A set of data items is normally distributed with a mean of 60. Convert the data item to a z-score, if the standard deviation is as given. 41) data item: 80; standard deviation: 5 41) A) 20 B) 5 3 D) 4 Use a table of z-scores and percentiles to find the percentage of data items in a normal distribution that lie between: 42) z = -0.2 and z = 0.2 42) A) 50% B) 42.07% 15.86% D) 57.93% 8