SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Transcription

1 Review Test 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the number of terms in the sequence or the sum of the sequence as requested. 1) Find the following sum: ) 2) Find the following sum: ) Find the requested term in the sequence. 3) The nth term in 25, 50, 75, 100, 125,... 3) 4) The 10th term in 14, 23, 27, 31, 35,... 4) 5) Given that the sequence 5, x, y, 625, 3125,... is a geometric sequence, find x and y. 5) Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence. 6) 10, 35, 60, 85, 110,... 6) 7) 25, 175, 1225, 8575, 60,025,... 7) 8) 4, 8, 64, 512, 4096,... 8) Solve the problem. 9) A man earned $ 2500 the first year he worked. If he received a raise of $ 400 at the end of each year, what was his salary during the 15 th year? 9) Find the number of terms in the sequence or the sum of the sequence as requested. 10) Find the number of terms in the following arithmetic sequence. 3, 9, 15, 21,..., ) 11) How many terms are there in the sequence 1, 4, 42, 43,..., 427? 11) Draw a valid conclusion from the given premises. 12) If a person is a competition swimmer, then that person can swim continously for one hour or more. Sharon cannot swim for more than 30 minutes. Therefore... 12) 13) Every man with a mind can think. A distracted man canʹt think. A man who is not distracted can apply himself. Therefore... 13) 1

2 14) If itʹs not Saturday, then Dad will shave. If Dad has whiskers, then he did not shave. If itʹs Saturday, then Dad will take us to the game. Therefore... 14) 15) Students who watch television while doing homework jeopardize their grades. Students with grades in jeopardy get grounded. Being grounded includes being barred from watching television. Therefore... 15) 16) If all taxi drivers are on strike, there are no taxis picking up passengers. Some taxis are picking up passengers. Therefore... 16) 17) If I get robbed, I will go to court. I got robbed. Therefore... 17) Given that p and q each represents a simple statement, write the indicated compound statement in its symbolic form. 18) p: They set the alarm. 18) q: They get up on time. They set the alarm or they get up on time. 19) p: This is a brontosaurus. q: This is a dinosaur. If this is not a brontosaurus, then this is not a dinosaur. 19) 20) p: The cone has three scoops. q: The cone costs $1.85. The cone has three scoops if and only if the cone costs $ ) 21) p: The outside humidity is high. q: The basement dehumidifier is running. r: The basement is getting moldy. 21) The outside humidity is high and the basement dehumidifier is running, or the basement is getting moldy. 22) p: The outside humidity is low. q: The central humidifier is running. r: The air in the house is getting dry. 22) If the outside humidity is low or the central humidifier is not running, then the air in the house is getting dry. 2

3 23) p: The outside humidity is low. q: The central humidifier is running. r: The air in the house is getting dry. 23) The air in the house is getting dry, if and only if the outside humidity is low and the central humidifier is not running. Given that p and q each represents a simple statement, write the indicated symbolic statement in words. 24) p: Roger likes Vanessa 24) q: Vanessa likes Roger ~ (p q) 25) p: Roger likes Vanessa q: Vanessa likes Roger ~ (q p) 25) 26) p: The car has been repaired. q: The kids are home. r: We will visit Aunt Tillie. p (q r) 26) 27) p: The car has been repaired. q: The kids are home. r: We will visit Aunt Tillie. (~ r ~ q) p 27) Construct a truth table for the statement. 28) (r q) (~r ~q) 28) 29) ~(~(r p)) 29) 30) ~(q t) ~(t q) 30) 31) ~q (~p q) 31) 32) (p t) (~p ~t) 32) 33) (p q) (p q) 33) 34) ~t (~t p) 34) 35) (q ~p) (q ~p) 35) 36) ~(p q) (p ~q) 36) 3

4 Write the statement indicated. 37) State the converse of the following: If you study hard, then your grades will be good. 37) 38) State the inverse of the following: If you practice, then you will win. 38) 39) State the contrapositive of the following: If it is pouring, then it is raining. 39) 40) State the contrapositive of the following: If he is happy, then he is smiling. 40) Determine the validity of the argument. 41) Football and studying donʹt mix. Don is a football player. Therefore Don does not study. 41) 42) All businessmen wear suits. Aaron wears suits. Therefore Aaron is a businessman. 42) 43) Some TV shows are comedies. All comedies are hits. Therefore some TV shows are hits. 43) 44) Not all cars are considered sporty. Not all cars are safe at high speeds. Therefore sports cars are safe at high speeds. 44) 45) Sailboats need a windy day to sail. Today is a windy day. Therefore today is a good day for sailing sailboats. 45) 46) Martians are green. Roger is not green. Therefore Roger is not a Martian. 46) 47) Martians are green. Frogs are green. Therefore frogs are Martians. 47) Express the symbolic statement ~p in words. 48) p: The Pilgrims did not land in Tahiti. 48) Write the negation of the quantified statement. (The negation should begin with ʺall,ʺ ʺsome,ʺ or ʺno.ʺ) 49) All mathematicians are humans. 49) 50) Some drinks are not liquids. 50) 4

5 51) No South American soccer teams have won a World Cup. 51) 52) All athletes are famous. 52) Write the following as a base-ten numeral. 53) ) 54) ) Convert the base-ten number to a number in the indicated base. 55) 2,874 to base five 55) 56) 329 to base six 56) 57) 13,562 to base eight 57) Write the numeral in base ten. 58) 200six 58) 59) 7,001eight 59) 60) E9twelve (E = 11ten) 60) Write a statement that represents the relationship between the following. 61) M = and N = { } 61) 62) A = {7, 8, 9} and B = {x 7 x 9, x N} 62) 63) A = {a, e, i, o, u} and B = {e, o, i, u, a} 63) 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. 64) Aʹ 64) 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. 65) (A B)ʹ 65) 66) (A B)ʹ 66) 67) Cʹ Aʹ 67) 68) (A B) (A C) 68) 5

6 69) (A B C)ʹ 69) Find n(a) for the set A. 70) A = {800, 801, 802,..., 8000} 70) 71) A = {x x N and 14 x 22} 71) Shade the portion of the diagram that represents the given set. 72) (A B) (A B) 72) 73) (A B) C 73) Use set notation to identify the shaded region. 74) 74) 75) 75) 6

7 76) 76) 77) 77) Find the Cartesian product or cardinal number as requested. 78) n(a B) = 42 n(a) = 6 Find n(b). 78) 79) Write {(k, 3), (k, 4), (j, 3), (j, 4)} as a Cartesian product. 79) Write or in the blank so that the resulting statement is true. 80) {4, 34, 39} {15, 34, 39, 49} 80) Determine whether the statement is true or false. 81) Bob {Bob, Carol, Ted, Alice} 81) Use,,, or both and to make a true statement. 82) {11, 12, 13} {11, 12, 13} 82) List all the subsets of the given set. 83) {Siamese, domestic shorthair} 83) Calculate the number of subsets and the number of proper subsets for the set. 84) {1, 3, 5, 7, 9, 11} 84) 85) {x x is a day of the week} 85) 86) the set of natural numbers less than 10 86) Perform the indicated operation. 87) 34five + 23five 87) 88) 32eight - 13eight 88) 7

8 89) 67eight + 12eight 89) Perform the operation. 90) 101two 111two 90) 91) 14five 21five 91) 92) 112five 4five 92) 93) 11,000two 10two 93) 8

9 Answer Key Testname: FM REVIEW TEST 1 AA 1) 12,628 2) 943 3) 25n 4) 55 5) 25, 125 6) Arithmetic; 135; 160 7) Geometric; 420,175; 2,941,225 8) Neither; 32,768; 262,144 9) $ ) 21 11) 28 12)...Sharon is not a competition swimmer. 13) Every man with a mind can apply himself. 14) If Dad has whiskers, then he will take us to the game. 15) Students who watch TV while doing homework will not be allowed to watch TV. 16)...some taxi drivers are not on strike. 17) I will go to court. 18) p q 19) ~ p ~ q 20) p q 21) (p q) r 22) (p ~ q) r 23) r (p ~ q) 24) It is not true that Roger likes Vanessa and Vanessa likes Roger. 25) It is not true that Vanessa likes Roger or that Roger likes Vanessa. 26) The car has been repaired, and we will visit Aunt Tillie if the kids are home. 27) If we will not visit Aunt Tillie then the kids are not home, or the car has been repaired. 28) r q (r q) (~r ~q) T F F F T F F F T 29) r p ~(~(r p)) T F T F T T F F F 30) q t ~(q t) ~(t q) T T F T F F F T F F F T 31) q p ~q (~p q) T F T F T T F F T 9

10 Answer Key Testname: FM REVIEW TEST 1 AA 32) p t (p t) (~p ~t) T F F F T F F F T 33) p q p q p q (p q) (p q) T T T F F T T F T F T T F F F F T 34) t p ~t (~t p) T F T F T T F F F 35) q p (q ~p) (q ~p) T F T F T F F F F 36) p q ~(p q) (p ~q) T F T F T T F F T 37) If your grades are good, then you studied hard. 38) If you do not practice, then you will not win. 39) If it is not raining, then it is not pouring. 40) If he is not smiling, then he is not happy. 41) Valid 42) Not valid 43) Valid 44) Not valid 45) Not valid 46) Valid 47) Not valid 48) The Pilgrims landed in Tahiti. 49) Some mathematicians are not humans. 50) All drinks are liquids. 51) Some South American soccer teams have won a World Cup. 52) Some athletes are not famous. 53) ) 505,000 55) 42,444five 56) 1305six 57) 32,372eight 10

11 Answer Key Testname: FM REVIEW TEST 1 AA 58) 72 59) ) ) M = N 62) A B 63) A = B 64) Aʹ = {26, 27, 28,..., 40} 65) {r, t, v, x} 66) {r, t, u, v, w, x, z} 67) {q, r, s, t, u, v, x, z} 68) {q, s, u, w, y, z} 69) {r, t} 70) n(a) = ) 9 72) 73) 74) C B A 75) A B 76) (A B) C 77) A C B 78) 7 79) {k, j} {3, 4} 80) 81) False 82) 83) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, { } 84) 64; 63 85) 128; ) 512; ) 112five 88) 17eight 89) 101eight 90) 100,011two 11

12 Answer Key Testname: FM REVIEW TEST 1 AA 91) 344five 92) 13five 93) 1100two 12