CCHS Math Unit Exam (Ch 1,2,3) Name: Math for Luiberal Arts (200 Points) 9/23/2014

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1 CCHS Math Unit Exam (Ch 1,2,3) Name: Math for Luiberal Arts (200 Points) 9/23/2014 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 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. 1) A - C 1) A) {q, s, u} B) {w, y} C) {q, s, u, v, x, z} D) {v, x, z} 2) (A B)' 2) A) {q, s, t, u, v, w, x, y} B) {r, t, u, v, w, x, z} C) {t, v, x} D) {s, u, w} List the items mentioned. Try to organize your list in a systematic way. 3) A coin is flipped and a 6-sided number cube is rolled. Use H for heads and T for tails, and list all possible outcomes. A) (H, 1), (T, 2), (H, 3), (T, 4), (H, 5), (T, 6) B) (1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T) C) (H, 1), (H, 2), (H, 3), (H,4), (H, 5), (H, 6) D) (1, H), (H, 1), (1, T), (T, 1), (2, H), (H, 2), (2, T), (3, H), (H, 3), (3, T), (T, 3), (4, H), (H, 4). (4, T), (T, 4). (5, H), (H, 5), (5, T), (T, 5), (6, H), (H, T), (6, T), (T, 6) 3) 4) Slips of paper numbered 1 through 5 are put in a hat. One slip is drawn and called and then a second slip is drawn without replacing the first. List all possible ways the two numbers could be called. A) (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2,2), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5) B) (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 4), (3, 5), (4, 1), (4, 2), (4, 3), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4) C) (1, 2), (2, 1), (3, 2), (2, 3), (3, 1), (4, 2), (2, 4), (4, 1), (4, 3), (3, 4), (5, 1), (1, 5), (4, 5), (5, 4), (1, 4), (1, 3), (3, 5) D) (1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 1), (4, 2), (4, 3), (4, 5) 4) Identify the set as finite or infinite. 5) The set of fractions that are less than 1 but greater than 0 5) A) Finite B) Infinite 6) The set of odd numbers greater than ) A) Infinite B) Finite 1

2 Shade the Venn diagram to represent the set. 7) (A B) (A B)' 7) A) B) Rephrase the statement in the requested symbolic form. 8) contrapositive of a b 8) A) ~b ~a B) ~a ~b C) b a D) a ~b 9) converse of ~a ~b 9) A) a b B) b a C) ~b ~a D) ~a b 10) converse of a ~(b c) 10) A) ~(b c) a B) ~a ~(b c) C) (b c) ~a D) ~a (b c) Determine whether the argument is valid or invalid. 11) If your father fixes the car, then you will go to the museum. Your father will buy a wrench or you will not go to the museum. Your father fixes the car. Therefore, your father will buy a wrench and you will go to the museum. A) Invalid B) Valid 11) 12) The boat has a new battery. If the boat has a new battery, then you can go fishing by the bridge. The boat does not have gasoline or you will not go fishing by the bridge. Therefore, the boat has gasoline. A) Invalid B) Valid 12) 2

3 Use the Venn diagram below to find the number of elements in the region. 13) n(a B C) 13) A) 16 B) 18 C) 44 D) 8 14) n(c - A) 14) A) 11 B) 13 C) 15 D) 20 Use the following definitions to determine if the statement is true or false. N = {x : x is a natural number} I = {x : x is an integer} R = {x : x is a real number} W = {x : x is a whole number} Q = {x : x is a rational number} 15) W is a proper subset of I, Q, N, and R. 15) A) True B) False 16) W is a proper subset of I, Q, and R. 16) A) True B) False 17) Q is a proper subset of N, I, and W. 17) A) True B) False Represent the circuit with a logical form. 18) 18) A) (p q) (r s) B) (p q) (r s) C) p (q r) s D) (p q) (r s) 3

4 Write a description of the shaded region using the symbols A, B, C,,, -, and as needed. 19) 19) A) (A B) C B) (A B) C C) (A B C) D) A B C Replace the # with either or to express a true statement. 20) -5.1 # {n : n is a whole number} 20) A) B) Use inductive reasoning. 21) Use inductive reasoning to predict the next term in the sequence of numbers. 1, - 1 3, 1 9, , 1 81,? 21) A) B) C) D) ) Use inductive reasoning to predict the next term in the sequence of numbers. 35, 29, 23, 17, 11,? A) 0 B) 2 C) 6 D) 5 22) Construct a truth table for the statement. 23) ~s (~s t) 23) A) s t ~s (~s t) T T T T F T F T T F F T C) s t ~s (~s t) T T F T F F F T T F F F B) s t ~s (~s t) T T T T F T F T T F F F D) s t ~s (~s t) T T T T F F F T T F F F Continue the pattern for five more items in the list. 24) aaa, aab, aba,... 24) A) baa, aba, abb, bbb, baa B) bab, baa, aba, bbb, bba C) baa, abb, bab, bba, bbb D) abc, acb, cab, caa, cba Decide whether the sets are equivalent. 25) { } and {x : x is a state in the U.S. with a minimum voting age of 51} 25) A) Yes B) No 4

5 Use DeMorgan's Laws to rewrite the negation of the statement. 26) The number x is not less than 7 and y is not greater than 0. 26) A) The number x is less than 7 and y is greater than 0. B) The number x is less than 7 or y is greater than 0. C) The number x is less than 7 and y is not greater than 0. D) The number x is not less than 7 or y is not greater than 0. Decide which set of names would be most meaningful for the indicated items. 27) Ramon and Christy are sharing servings of root beer and cake. 27) A) x, w, z, and w B) p1, p2, f1, and f2 C) r, c, r, and c D) R, C, b, and k Write, as indicated, the converse, inverse, or contrapositive for the statement. 28) If the sum of the interior angles of a geometric figure is 180 degrees, then the figure is a triangle. (contrapositive) A) If a geometric figure is not a triangle, then the sum of the interior angles is 180 degrees. B) If the sum of the interior angles of a geometric figure is not 180 degrees, then the figure is not a triangle. C) If a geometric figure is not a triangle, then the sum of the interior angles is not 180 degrees. D) If a geometric figure is a triangle, then the sum of the interior angles is 180 degrees. 28) Decide whether the statement is true or false. 29) {a : a is an odd integer} {b : b is a positive integer} 29) A) False B) True 30) {6, 12, 18, 24, 30} 30) A) False B) True Decide whether the argument is an example of inductive or deductive reasoning. 31) If (-p)2 = p2, then (-7)2 = 49 31) A) Deductive B) Inductive 32) The last four stoplights were green, therefore the next will be green. 32) A) Deductive B) Inductive 33) Every coach must know his sport well. John Madden was a football coach. John Madden knows football well. A) Inductive B) Deductive 33) 5

6 Construct a truth table for the given compound statement. 34) ~(w t) ~(t w) 34) A) B) w t ~(w t) ~(t w) w t ~(w t) ~(t w) T T F T T F T F F T F T F T T F T T F F F F F F C) D) w t ~(w t) ~(t w) T T F T F F F T F F F T w t ~(w t) ~(t w) T T F T F F F T F F F F 35) (p ~q) s 35) A) B) p q s (p ~q) s p q s (p ~q) s T T T F T T T F T T F F T T F F T F T F T F T F T F F T T F F F F T T F F T T F F T F T F T F T F F T T F F T T F F F T F F F T C) D) p q s (p ~q) s T T T F T T F T T F T F T F F F F T T F F T F T F F T T F F F T p q s (p ~q) s T T T F T T F F T F T T T F F F F T T F F T F F F F T F F F F F Let U = {all soda pops}; A = {all diet soda pops}; B = {all cola soda pops}; C = {all soda pops in cans}; and D = {all caffeine-free soda pops}. Describe the given set in words. 36) (A B) D 36) A) All soda pops not in cans B) All diet, all cola, and all caffeine-free soda pops C) All soda pops D) All diet, caffeine-free, cola soda pops Estimate the answer using compatible numbers. 37) 7.6% ) A) 7 B) 16 C) 70 D) 160 6

7 Determine how many lines will be in the truth table for the following statement. 38) (p q) (~r s) ~t 38) A) 8 B) 10 C) 32 D) 25 Refer to the double-bar graph below which shows the number of male (M) and female (F) athletes at a university over a four-year period. Solve the problem. YEAR 39) In which year was the number of male athletes equal to 375? 39) A) 1986 B) 1987 C) 1988 D) 1989 Find n(a) for the set. 40) A = {, 0} 40) A) n(a) = 2 B) n(a) = 1 C) n(a) = 0 D) n(a) = 41) A = {{a, b}, {c, d}, {e, b}} 41) A) n(a) = 5 B) n(a) = 6 C) n(a) = 2 D) n(a) = 3 Use an alternative method to express the set. 42) {x: x has bike trails} The table shows some of the facilities available at selected State Parks in New Jersey. hiking bike visitor camping trails boating swimming trails center Allaire yes yes no yes no yes Parvin yes yes yes yes no yes Delaware and Raritan Canal no yes yes yes yes no Corson's Inlet no yes yes no no no Wharton Forest yes yes yes yes no yes A) B) {Allaire, Parvin, Corson's Inlet, Wharton Forest} C) (Delaware and Raritan Canal) D) {Delaware and Raritan Canal} 42) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. List the subsets. 43) List all of the three element subsets of the set {a, b, c, d}. 43) 7

8 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the set is well defined or not. 44) {x : x is an expensive boat on the Great Lakes} 44) A) Well defined B) Not well defined Use the following definitions to translate the statement into words. p: The monitor is included. q: The color printer is optional. r: The zip drive is extra. 45) ~(p q) (r ~q) 45) A) It is not true that if the monitor is included or the color printer is optional, then the zip drive is extra and the color printer is not optional. B) If the monitor is included and the color printer is optional, then the zip drive is extra or the color printer is not optional. C) It is not true that if the monitor is included and the color printer is optional, then the zip drive is extra or the color printer is not optional. D) If the monitor is included and the color printer is optional, then it is not true that the zip drive is extra or the color printer is not optional. Estimate the answer by rounding as indicated. 46) Estimate by rounding to the nearest ten ) A) 4500 B) 4390 C) 4386 D) 140 Decide whether the sets are equal. 47) {4, 8, 12, 16, 32} and {4, 8, 12, 16,..., 32} 47) A) No B) Yes Decide whether the two sequences of operations give the same result. 48) Dividing r by 7, then dividing s by 7, then multiplying the quotients; multiplying r and s, then dividing by 7. A) Yes B) No 48) Determine whether the form represents a valid argument. 49) ~p q ~p ~p q A) Valid B) Invalid 49) 50) r r p (p r) q ~p A) Valid B) Invalid 50) 8

9 Round the number to the place value indicated. 51) 98,549 51) A) 98,510 B) 98,400 C) 98,600 D) 98,500 Use set notation to list all the elements of the set. 52) The letters needed to spell these words: tear, rate, rat, tea A) {a,e,r,t} B) {r,a,t} C) {t,t,t,t,r,r,r,a,a,a,a,e,e,e} D) {t,t,a,a,r,r,e} 52) Illustrate Goldback's conjecture for the following number. 53) 32 53) A) B) C) 2 5 D) Find the number of subsets of the set. 54) {1, 2, 3,..., 9} 54) A) 512 B) 16 C) 1024 D) 508 Identify the form of the argument and state whether the argument is valid or invalid. 55) If it is cold, then you need a coat. You do not need a coat. Therefore, it is not cold. A) Fallacy of the inverse; invalid B) Law of syllogism; valid C) Law of contraposition; valid D) Fallacy of the converse; invalid 55) Negate each quantified statement and rewrite it in English in an alternative way. 56) Some citizens obey traffic laws. 56) A) All citizens obey traffic laws. B) All citizens do not obey traffic laws. C) No citizens obey traffic laws. D) Some citizens do not obey traffic laws. Identify the statement as simple or compound. 57) It is false that whales are fish and bats are birds. 57) A) Compound B) Simple Decide whether or not the following is a statement. 58) My favorite baseball team will win the pennant. 58) A) Statement B) Not a statement Rewrite the statement in the form "if p, then q". 59) I won't go until it's 2 pm. 59) A) If it's 2 pm, then I'll go. B) If I don't go, then it's not 2 pm. C) If I go, then it's 2 pm. D) If it's not 2 pm, then I won't go. 9

10 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Represent the logical form by a circuit. 60) (p ~r) q 60) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Describe the indicated set in words and find the set. 61) (P L) - S, given the following information: The table gives the approximate nutritional value per serving of foods at a certain restaurant. protein fat calcium sodium vitamin A food calories (grams) (grams) (mg) (mg) (A.U.) Chow Mein Pizza (cheese) Bean Burrito Spaghetti & Meatballs Pea Soup Chicken Salad Milkshake ) Let: C = {m : m provides 251 or more calories} P = {m : m provides 20 or more grams of protein} F = {m : m provides 10 or more grams of fat} L = {m : m provides 150 or more mg of calcium} S = {m : m provides 1000 or more mg of sodium} A = {m : m provides 1000 or more A.U. of vitamin A} A) Foods that provide either 20 or more grams of protein or 150 or more mg of calcium, but have less than 1000 mg of sodium; {Pizza, Pea Soup, Chicken Salad} B) Foods that provide both 20 or more grams of protein and 150 or more mg of calcium, but have less than 1000 mg of sodium; C) Foods that provide both 20 or more grams of protein and 150 or more mg of calcium, and have 1000 or more mg of sodium; {Chow Mein, Bean Burrito} D) Foods that provide either 20 or more grams of protein or 150 or more mg of calcium, and have 1000 or more mg of sodium; {Chow Mein, Bean Burrito} Write the statement in symbolic form. 62) Press the Enter key if the screen is black or the Tab key if it is not. 62) A) (p q) (r ~q) B) (p q) (r ~p) C) (p q) (r ~s) D) (p q) (r ~s) 10

11 Estimate the answer. State whether the estimate is larger or smaller than the exact answer. 63) Each gallon of porch and deck paint covers 200 square feet. How many gallons are needed to cover 939 square feet? A) 4; smaller B) 5; larger C) 3; smaller D) 6; larger 63) Assume that p represents a true statement, q represents a true statement, and r represents a false statement. Determine the truth value of the following. 64) (q ~r) (~p r) 64) A) False B) True Determine whether the statements are equivalent. 65) If the wind speed is over 70 miles per hour, then the tree will be uprooted. If the tree is not uprooted, then the wind speed is not over 70 miles per hour. A) Not equivalent B) Equivalent 65) Let A and B be sets with cardinal numbers, n(a) = a and n(b) = b, respectively. Decide whether the statement is true or false. 66) n(a - B) = n(b - A) 66) A) True B) False In a school survey, students showed these preferences for instructional materials. Answer the question. 67) About how many students would you expect to prefer TV in a school of 600 students? 67) A) About 12 students B) About 120 students C) About 108 students D) About 72 students 11

12 Answer Key Testname: MLA AT CHCS - UNIT 1 TEST TO PCC 1) A 2) B 3) B 4) B 5) B 6) A 7) A 8) A 9) C 10) A 11) B 12) A 13) D 14) D 15) B 16) A 17) B 18) A 19) A 20) A 21) C 22) D 23) B 24) C 25) B 26) B 27) D 28) C 29) A 30) B 31) A 32) B 33) B 34) C 35) D 36) B 37) B 38) C 39) C 40) A 41) D 42) D 43) {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d} 44) B 45) C 46) A 47) A 48) B 12

13 Answer Key Testname: MLA AT CHCS - UNIT 1 TEST TO PCC 49) A 50) B 51) D 52) A 53) B 54) A 55) C 56) B 57) A 58) B 59) A 60) 61) B 62) A 63) B 64) A 65) B 66) B 67) D 13