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.3)

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)

4) Slips of paper numbered 1 through 5 are put in a hat. One slip is drawn and called and then asecond slip is drawn without replacing the first. List all possible ways the two numbers couldbe called.

4)

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)

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 1000 6)A) Infinite B) Finite

1

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.

11)

A) Invalid B) Valid

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.

12)

A) Invalid B) Valid

2

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

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, - 13

, 19

, - 127

, 181

, ?

21)

A) 1729

B) 1243

C) -1

243D) -

1729

22) Use inductive reasoning to predict the next term in the sequence of numbers.35, 29, 23, 17, 11, ?

22)

A) 0 B) 2 C) 6 D) 5

Construct a truth table for the statement.23) ~s (~s t) 23)

A) s t ~s (~s t)

T T TT F TF T TF F T

B) s t ~s (~s t)

T T TT F TF T TF F F

C) s t ~s (~s t)

T T FT F FF T TF F F

D) s t ~s (~s t)

T T TT F FF T TF 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, bbaC) 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

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 f2C) 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)28)

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.

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 Maddenknows football well.

33)

A) Inductive B) Deductive

5

Construct a truth table for the given compound statement.34) ~(w t) ~(t w) 34)

A)w t ~(w t) ~(t w) T T F T F F F T T F F F

B)w t ~(w t) ~(t w) T T F T F T F T T F F F

C)w t ~(w t) ~(t w) T T F T F F F T F F F T

D)w t ~(w t) ~(t w) T T F T F F F T F F F F

35) (p ~q) s 35)A)

p q s (p ~q) s T T T F T T F F T F T F T F F T F T T F F T F T F F T T F F F T

B) p q s (p ~q) s T T T F T T F F T F T F T F F F F T T F F T F T F F T T F F F T

C) 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

D) 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}; andD = {all caffeine-free soda pops}. Describe the given set in words.

36) (A B) D 36)A) All soda pops not in cansB) All diet, all cola, and all caffeine-free soda popsC) All soda popsD) All diet, caffeine-free, cola soda pops

Estimate the answer using compatible numbers.37) 7.6% × 193 37)

A) 7 B) 16 C) 70 D) 160

6

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 universityover a four-year period. Solve the problem.

YEAR39) 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.

campinghikingtrails boating swimming

biketrails

visitorcenter

Allaire yes yes no yes no yesParvin yes yes yes yes no yesDelaware and Raritan Canal no yes yes yes yes noCorson's Inlet no yes yes no no noWharton Forest yes yes yes yes no yes

42)

A)B) {Allaire, Parvin, Corson's Inlet, Wharton Forest}C) (Delaware and Raritan Canal)D) {Delaware and Raritan Canal}

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

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.

86× 51

46)

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 7.48)

A) Yes B) No

Determine whether the form represents a valid argument.49) ~p

q ~p~p q

49)

A) Valid B) Invalid

50) rr p(p r) q~p

50)

A) Valid B) Invalid

8

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, tea52)

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}

Illustrate Goldback's conjecture for the following number.53) 32 53)

A) 16 + 16 B) 13 + 19 C) 25 D) 7 + 25

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.

55)

A) Fallacy of the inverse; invalid B) Law of syllogism; validC) Law of contraposition; valid D) Fallacy of the converse; invalid

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

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.

food caloriesprotein(grams)

fat(grams)

calcium(mg)

sodium(mg)

vitamin A(A.U.)

Chow Mein 240 23 16 75 1250 1100Pizza (cheese) 120 15 9 220 694 2720Bean Burrito 340 20 4 185 1230 80Spaghetti & Meatballs 330 19 13 124 1009 1590Pea Soup 250 7 7 158 900 850Chicken Salad 210 33 8 28 360 100Milkshake 270 3 13 145 98 420

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}

61)

A) Foods that provide either 20 or more grams of protein or 150 or more mg of calcium, buthave 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, buthave less than 1000 mg of sodium;

C) Foods that provide both 20 or more grams of protein and 150 or more mg of calcium, andhave 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, andhave 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

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?63)

A) 4; smaller B) 5; larger C) 3; smaller D) 6; larger

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.65)

A) Not equivalent B) Equivalent

Let A and B be sets with cardinal numbers, n(A) = a and n(B) = b, respectively. Decide whether the statement is trueor 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 studentsC) About 108 students D) About 72 students

11

Answer KeyTestname: MLA AT CHCS - UNIT 1 TEST 9-23-2014 TO PCC

1) A2) B3) B4) B5) B6) A7) A8) A9) C

10) A11) B12) A13) D14) D15) B16) A17) B18) A19) A20) A21) C22) D23) B24) C25) B26) B27) D28) C29) A30) B31) A32) B33) B34) C35) D36) B37) B38) C39) C40) A41) D42) D43) {a, b, c}, {a, b, d}, {a, c, d}, {b, c, d}44) B45) C46) A47) A48) B

12

Answer KeyTestname: MLA AT CHCS - UNIT 1 TEST 9-23-2014 TO PCC

49) A50) B51) D52) A53) B54) A55) C56) B57) A58) B59) A60)

61) B62) A63) B64) A65) B66) B67) D

13