REVIEW TEST 1

MULTIPLE CHOICE. Choose the one alternative that best completes the 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: 4 + 10 + 16 + . . . + 112 1) A) 1106 B) 1094 C) 1110 D) 1102

2) Find the following sum: 5 + 7 + 9 + . . . + 103 2) A) 2710 B) 2700 C) 2705 D) 2690

3) Find the following sum: 6 + 20 + 34 + . . . + 986 3) A) 35,222 B) 35,216 C) 35,228 D) 35,204

4) Find the following sum: 5 + 405 + 805 + . . . + 4005 4) A) 22,050 B) 22,060 C) 18,045 D) 22,055

5) Find the following sum: 19 + 27 + 35 + . . . + 195 5) A) 2461 B) 2423 C) 2480 D) 2266

Solve the problem. 6) Which is greater, E or P, and by how much? 6) E = 1 + 3 + 5 + 7 + . . . + 95 P = 2 + 4 + 6 + 8 + . . . + 96 A) P is greater by 48 B) E is greater by 47 C) P is greater by 49 D) E is greater by 48

7) Alamo, Brushy, Chet, and Dolly are in an armadillo race. Chet is the slowest. Dolly is faster than 7) Alamo, but slower than Brushy. Name the finishing order of the armadillos. A) Alamo, Brushy, Dolly, Chet B) Brushy, Dolly, Alamo, Chet C) Alamo, Dolly, Brushy, Chet D) Brushy, Alamo, Dolly, Chet

8) A pencil box and a notebook together cost $6.28. The notebook costs $0.50 more than the pencil 8) box. How much does the notebook cost? A) $2.89 B) $3.39 C) $3.89 D) $2.39

9) The temperature rose 7 degrees from 10:00 A.M. to noon. By 3:00 P.M. the temperature had 9) doubled. From 3:00 P.M. to 6:00 P.M. the temperature rose 6 degrees to 94 degrees. What was the temperature at 10:00 A.M. that morning? A) 51 degrees B) 81 degrees C) 43 degrees D) 37 degrees

Find the requested term in the sequence. 10) The 100th term in 8, 13, 18, 23, 28, . . . 10) A) 508 B) 498 C) 503 D) 504

11) The nth term in 15, 30, 45, 60, 75, . . . 11) A) 15n + 15 B) 15n - 15 C) 15n + 2D)15n

1 12) The 10th term in 18, 19, 20, 21, 22, . . . 12) A) 28 B) 27 C) 26 D) 29

13) Given that the sequence 2, 9, x, y, 31, . . . is a Fibonacci sequence, find x and y. 13) A) 13, 22 B) 20, 29 C) 11, 13 D) 11, 20

14) The 10th term in 20, 20.2, 20.4, 20.8, 20.16, . . . 14) A) 20.512 B) 20.1024 C) 20.256 D) 512

Find the number of terms in the sequence or the sum of the sequence as requested. 15) Find the number of terms in the following arithmetic sequence. 15) 1, 3, 5, 7, . . ., 51 A) 51 B) 28 C) 25 D) 26

16) Find the sum of the following arithmetic sequence. 16) 10 + 11 + 12 + . . . + 500 A) 125,214 B) 125,205 C) 124,714 D) 125,250

17) How many terms are there in the sequence 1, 3, 32, 33, . . ., 325? 17) A) 27 B) 26 C) 25 D) 24

Indicate whether the sequence is arithmetic, geometric, or neither. Give the next two terms in the sequence. 18) 1, 8, 15, 22, 29, . . . 18) A) Geometric; 36; 44 B) Neither; 37; 44 C) Arithmetic; 36; 43

19) 15, 75, 375, 1875, 9375, . . . 19) A) Arithmetic; 468,750; 703,125 B) Geometric; 46,875; 234,375 C) Neither; 93,750; 468,750

20) 4, 12, 120, 1200, 12,000, . . . 20) A) Geometric; 120,000; 1,200,000 B) Arithmetic; 120,000; 1,200,000 C) Neither; 120,000; 1,200,000

Solve the problem. 21) A man earned $ 3000 the first year he worked. If he received a raise of $ 400 at the end of each 21) year, what was his salary during the 15 th year? A) None of these B) $ 5600 C) $ 9000 D) $ 8600

22) The population of a town was 33,100 at the beginning of 1970. If the population decreased 300 22) people per year, how many people lived in the town at the beginning of 1985? A) 28,900 B) 28,300 C) 28,600 D) 4500

Find the first five terms in the sequence whose nth term is given. 23) n2 + 2 23) A) 4, 6, 8, 10, 12 B) 3, 6, 11, 14, 22 C) 2, 8, 18, 32, 50 D) 3, 6, 11, 18, 27

2 24) 6n - 4 24) A) 2, 4, 6, 8, 10 B) 2, 8, 14, 20, 26 C) -24, -48, -72, -96, -120 D) 10, 16, 22, 28, 34

Write the statement indicated. 25) Write the negation of the following: 25) The test is difficult. A) The test is not difficult. B) The test is not easy. C) The test is not very easy. D) The test is very difficult.

Write the negation of the quantified statement. (The negation should begin with ʺall,ʺ ʺsome,ʺ or ʺno.ʺ) 26) Some mammals are horses. 26) A) All horses are mammals. B) No mammals are horses. C) No horses are mammals. D) Not all mammals are horses.

27) Some drinks are not liquids. 27) A) All drinks are liquids. B) All liquids are drinks. C) All drinks are not liquids. D) No drinks are liquids.

28) All athletes are famous. 28) A) All athletes are somewhat famous. B) Some athletes are not famous. C) Some athletes are famous. D) All athletes are not famous.

Determine the validity of the argument. 29) Football and studying donʹt mix. 29) Don is a football player. Therefore Don does not study. A) Not valid B) Valid

30) Some investments are risky. 30) Real estate is an investment. Therefore real estate is risky. A) Not valid B) Valid

31) All businessmen wear suits. 31) Aaron wears suits. Therefore Aaron is a businessman. A) Valid B) Not valid

32) Not all cars are considered sporty. 32) Not all cars are safe at high speeds. Therefore sports cars are safe at high speeds. A) Valid B) Not valid

33) Martians are green. 33) Roger is not green. Therefore Roger is not a Martian. A) Not valid B) Valid

3 Write a valid conclusion based on the statements. 34) If I get robbed, I will go to court. 34) I got robbed. A) I will not go to court. B) I will go to court. C) I will get robbed in court. D) I will not get robbed in court.

35) All birds have wings. None of my pets are birds. All animals with wings can flap them. 35) A) No birds can flap their wings. B) None of my pets can flap their wings. C) All my pets can flap their wings. D) All birds can flap their wings.

36) All fish can dream. Any dead animal is unable to dream. All live animals have a heartbeat. 36) A) Any dead fish can dream. B) All fish have a heartbeat. C) Any dead animal has no heartbeat. D) All live animals can dream.

37) Smiling people are happy. Alert people are not happy. Careful drivers are alert. Careless drivers 37) have accidents. A) Careful drivers have accidents. B) People who smile are alert. C) People who smile have accidents. D) Careful drivers are happy.

38) Hard workers sweat. Sweat brings on a chill. Anyone who doesnʹt have a cold never felt a chill. 38) Anyone who works doesnʹt have a cold. A) Anyone who has a cold works hard. B) Anyone who sweats works hard. C) Hard workers donʹt get colds. D) Hard workers donʹt go to work.

Determine whether the statements are logically equivalent. 39) ~p ∨ ~q and ~(p ∧ q) 39) A) Yes B) No

40) ~(~q) and q 40) A) Yes B) No

41) q → p and ~p → ~q 41) A) Yes B) No

Construct a truth table for the statement. 42) ~p ∧ ~s 42) A) p s (~p ∧ ~s) B) p s (~p ∧ ~s) TT F TT F TF F TF F FT F FT F FF T FF F C) p s (~p ∧ ~s) D) p s (~p ∧ ~s) TT F TT T TF T TF F FT T FT F FF T FF T

4 43) ~(~(s ∨ p)) 43) A) s p ~(~(s ∨ p)) B) s p ~(~(s ∨ p)) TT T TT F TF T TF F FT T FT F FF F FF T C) s p ~(~(s ∨ p)) D) s p ~(~(s ∨ p)) TT T TF T TF T FT F FT F FF F

44) ~(s ∨ t) ∧ ~(t ∧ s) 44) A) s t ~(s ∨ t) ∧ ~(t ∧ s) B) s t ~(s ∨ t) ∧ ~(t ∧ s) TT F TT F TF F TF F FT T FT F FF F FF T C) s t ~(s ∨ t) ∧ ~(t ∧ s) D) s t ~(s ∨ t) ∧ ~(t ∧ s) TT F TT F TF T TF F FT T FT F FF F FF F

Letting r stand for ʺThe food is good,ʺ p stand for ʺI eat too much,ʺ and q stand for ʺIʹll exercise,ʺ write the following in symbolic form. 45) If I exercise, then I wonʹt eat too much. 45) A) q → ~pB)~(p → q) C) p → qD)r ∧ p

46) If the food is good or if I eat too much, Iʹll exercise. 46) A) (r ∧ p) → qB)(r ∨ p) → qC)r → (p ∨ q) D) r → p → q

47) If the food is not good, I wonʹt eat too much. 47) A) ~r → ~pB)r → ~pC)~(r → p) D) ~p → ~r

48) The food is good and if I eat too much, then Iʹll exercise. 48) A) (r → p) ∨ qB)r ∧ (p → q) C) (r ∨ p) → qD)(r ∧ p) → q

49) If I exercise, then the food wonʹt be good and I wonʹt eat too much. 49) A) ~(r ∧ p) → qB)(q ∧ ~r) → ~pC)q → (~r ∧ ~p) D) q → ~(r ∧ p)

Write in if-then form. 50) I will lose weight if I diet. 50) A) If I lose weight, then Iʹll diet. B) If I diet, then I gain weight. C) If I donʹt diet, then I wonʹt lose weight. D) If I diet, then Iʹll lose weight.

5 51) Practice is necessary for making the team. 51) A) If you make the team, then you wonʹt have to practice. B) If you make the team, then you must practice. C) If you donʹt practice, then you wonʹt make the team. D) If you practice, then you will make the team.

52) x = 9 if 2x + 9 = 27. 52) A) If x ≠ 9, then 2x + 9 = 27. B) If 2x + 9 = 27, then x = 9. C) If 2x + 9 ≠ 27, then x = 9. D) If x = 9, then 2x + 9 = 9.

53) Showing up at the party is enough to get a door prize. 53) A) If you show up at the party then you will get a door prize. B) If you got a door prize then you showed up at the party. C) If you get a door prize then you donʹt have to show up at the party. D) If you donʹt show up at the party, then you will not get a door prize.

Write the statement indicated. 54) State the inverse of the following: 54) If you practice, then you will win. A) If you do not practice, then you will not win. B) If you practice, then you will not win. C) If you win, then you practiced. D) If you do not win, then you did not practice.

55) State the contrapositive of the following: 55) If it is pouring, then it is raining. A) If it is pouring, then it is not raining. B) If it is raining, then it is pouring. C) If it is not pouring, then it is not raining. D) If it is not raining, then it is not pouring.

Restate in a logically equivalent form. 56) It is not true that both this book is interesting and the book is about stars. 56) A) This book cannot be both interesting and about stars. B) This book is both interesting and about stars. C) Either this book is not interesting or it is not about stars. D) Either this book is interesting or it is about stars.

57) If it is clean, then it was washed. 57) A) If it is clean, then it was not washed. B) If it is clean, then it was washed. C) If it is not clean, then it was not washed. D) If it was not washed, then it is not clean.

58) The flowers are not blooming or it is not winter. 58) A) The flowers are blooming and it is winter. B) It is not true that the flowers are blooming and it is winter. C) It is not true that it is winter and the flowers are not blooming. D) It is not true that both the flowers are blooming and it is winter.

59) It is not tasty or it is not sour. 59) A) It is not true that it is both tasty and sour. B) If it is not tasty, then it is not sour. C) If it is tasty, then it is sour. D) If it is sour, then it is tasty.

6 For the following, write an equivalent numeral in the Hindu -Arabic system. 60) 60) A) 3613 B) 23 C) 4262 D) 722

61) 61) A) 11,011 B) 101,011 C) 110,011 D) 1111

62) MMMCCX 62) A) 32,100 B) 3210 C) 321,000 D) 321

63) 63)

A) 88,360 B) 79,378 C) 88,160 D) 83,479

For the given Hindu-Arabic numeral, write an equivalent numeral in the indicated system. 64) 3063; Egyptian 64)

A) B)

C) D)

Write the following as a base-ten numeral. 65) 8 · 102 + 3 65) A) 703 B) 803 C) 800 D) None of these

66) 3 · 10 + 3 66) A) 303 B) 33 C) 60 D) None of these

67) 8 · 100 67) A) 800 B) 0 C) 8 D) None of these

Convert the base-ten number to a number in the indicated base. 68) 329 to base six 68) A) 135six B) 1530six C) 1305six D) 1350six

69) 68 to base eight 69) A) 120eight B) 104eight C) 102eight D) 140eight

70) 2,874 to base five 70) A) 42,422five B) 42,424five C) 42,222five D) 42,444five

71) 13,562 to base eight 71) A) 23,272eight B) 32,372eight C) 23,227eight D) 32,327eight

7 Write the numeral in base ten. 72) 130five 72) A) 640 B) 60 C) 40 D) 650

73) 42twelve 73) A) 92 B) 29 C) 50 D) 70

74) 25eight 74) A) 21 B) 133 C) 165 D) 33

Convert the following. 75) 74 days to weeks and days 75) A) 10 weeks and 4 days B) 10 weeks and 3 days C) 14 weeks and 5 days D) 9 weeks and 4 days

76) 232 ounces to pounds and ounces 76) A) 14 lb and 8 oz B) 14 lb and 9 oz C) 16 lb and 8 oz D) 15 lb and 8 oz

8 Answer Key Testname: REVIEW TEST 1 FM

1) D 2) B 3) B 4) D 5) A 6) A 7) B 8) B 9) D 10) C 11) D 12) B 13) D 14) A 15) D 16) B 17) B 18) C 19) B 20) C 21) D 22) C 23) D 24) B 25) A 26) B 27) A 28) B 29) B 30) A 31) B 32) B 33) B 34) B 35) D 36) B 37) C 38) D 39) A 40) A 41) A 42) A 43) A 44) B 45) A 46) B 47) A 48) B 49) C 50) D 9 Answer Key Testname: REVIEW TEST 1 FM

51) D 52) B 53) A 54) A 55) D 56) C 57) D 58) D 59) A 60) C 61) B 62) B 63) B 64) D 65) B 66) B 67) C 68) C 69) B 70) D 71) B 72) C 73) C 74) A 75) A 76) A

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