Indiana Academic M.A.T.H. Bowl. Invitational February, 2011

Transcription

1 Indiana Academic M.A.T.H. Bowl Invitational February, 2011

2 Begin Round One

3 2011 MATH Invitational Round 1 Number 1 30 seconds Which is greater 12 ¼ or 12 ¼? A. 12 ¼ B. 12 ¼ C. They are equal D. It can not be determined

4 2011 MATH Invitational Round 1 Number 1 Which is greater 12 ¼ or 12 ¼? B. 12 ¼ 12 ¼ = 12/4 or 3 12 ¼ = 12(4) or 48

5 2011 MATH Invitational Round 1 Number 2 30 Seconds Convert 125% to an improper fraction. A. 1 ¼ B. 5/4 C. 3/2 D. 1 2/5

6 2011 MATH Invitational Round 1 Number 2 Convert 125% to an improper fraction. B. 5/4 125% = 125/100

7 2011 MATH Invitational Round 1 Number 3 30 second A number cube is rolled. What is the chance of rolling composite numbers? A. 17% B. 33% C. 50% D. 67%

8 2011 MATH Invitational Round 1 Number 3 A number cube is rolled. What is the chance of rolling composite numbers? B.33% 4 and 6 are composite 2/6 = 33 1/3%

9 2011 MATH Invitational Round 1 Number 4 30 seconds How many strips of wallpaper 4/45 m long can be cut from a strip 2/5 m long? A. 2 strips B. 2 ½ strips C. 4 strips D. 4 ½ strips

10 2011 MATH Invitational Round 1 Number 4 How many strips of wallpaper 4/45 m long can be cut from a strip 2/5 m long? D. 4 ½ strips 2/5 4/45 = 2/5 * 45/4 = 90/20 or 4.5

11 2011 MATH Invitational Round 1 Number 5 30 seconds Taylor bought 5 tickets for a bike raffle. Fifty tickets were sold. What are Taylor s chances of winning the bike? A. ½ B. 1/3 C. 1/10 D. 1/4

12 2011 MATH Invitational Round 1 Number 5 Taylor bought 5 tickets for a bike raffle. Fifty tickets were sold. What are Taylor s chances of winning the bike? C. 1/10 5/50 = 1/10

13 2011 MATH Invitational Round 1 Number 6 45 seconds Sally and Sarah work in the school bookstore Monday through Friday. Sally works every second day. Sarah works every third day. If they both work on the first day of school, how many days will they work together during the first 2 weeks of school? A. 1 day C. 3 days B. 2 days D. 4 days

14 2011 MATH Invitational Round 1 Number 6 Sally and Sarah work in the school bookstore Monday through Friday. Sally works every second day. Sarah works every third day. If they both work on the first day of school, how many days will they work together during the first 2 weeks of school? B. 2 days Sally works M, W, F, Tu, Th. Sarah works M, Th, Tu, Fr. So they work together the first Monday and the second Tuesday.

15 2011 MATH Round 1 Number 7 45 Seconds What numbers will the next or sixth row contain? A. 1, 4, 6, 4, 1 B. 1, 5, 10, 10, 5, 1 C. 1, 5, 10,15, 5, 1 D. 1, 7, 21, 21, 7, 1

16 2011 MATH Invitational Round 1 Number 7 What numbers will the next or sixth row contain? B. 1, 5, 10, 10, 5, 1 Add adjacent numbers to find the number in the box centered below them.

17 End Round One

18 Begin Round Two

19 2011 MATH Invitational Round 2 Number 1 30 seconds Which decimal has the same value as 7/8? A B C D

20 2011 MATH Invitational Round 2 Number 1 Which decimal has the same value as 7/8? C

21 2011 MATH Invitational Round 2 Number 2 30 seconds What is the probability of choosing a green gem that is not a smiley face? A. 2/11 C. 1/11 B. 1/5 D. 1/10

22 2011 MATH Invitational Round 2 Number 2 What is the probability of choosing a green gem that is not a smiley face? C. 1/11

23 2011 MATH Invitational Round 2 Number 3 30 Seconds Find the sum of one and sixteen thousandths and seventeen and nineteen hundredths. A B C D

24 2011 MATH Invitational Round 2 Number 3 Find the sum of one and sixteen thousandths and seventeen and nineteen hundredths. B

25 2011 MATH Invitational Round 2 Number 4 30 Seconds What percent of 140 is 56? A. 40% B. 56% C. 84% D. 250%

26 2011 MATH Invitational Round 2 Number 4 What percent of 140 is 56? A. 40% P = P = 5600 P = 5600/140 P = 0.4

27 2011 MATH Invitational Round 2 Number 5 30 Seconds Which of the following ratios is greater than 5:12? A. 3 to 4 B. 7:18 C. 15 out of 36 D. 6:15

28 2011 MATH Invitational Round 2 Number 5 Which of the following ratios is greater than 5:12? A. 3 to 4 Whether written as 3 to 4, 3/4, 3 out of 4, they are all /12 is

29 2011 MATH Invitational Round 2 Number 6 60 seconds If the spinner is spun twice, how many ways can it get a sum of 11? A. 1 way B. 2 ways C. 3 ways D. 4 ways

30 2011 MATH Invitational Round 2 Number 6 60 seconds If the spinner is spun twice, how many ways can it get a sum of 11? D. 4 ways 4 then 7, 5 then 6, 6 then 5, and 7 then 4

31 2011 MATH Invitational Round 2 Number 7 45 seconds A wagon wheel has 12 spaces between spokes. How many spokes does the wagon wheel have? A. 10 spokes B. 11 spokes C. 12 spokes D. 13 spokes

32 2011 MATH Invitational Round 2 Number 7 A wagon wheel has 12 spaces between spokes. How many spokes does the wagon wheel have? B. 12 spokes Simplify first: 1 spoke one space 2 spokes two spaces 3 spokes three spaces N spokes N spaces

33 End Round Two

34 Begin Round Three

35 2011 MATH Invitational Round 3 Number 1 30 seconds The bookstore makes a profit of 5 for each pencil sold. Which expression best shows the profit in dollars for 50 pencils? A x 50 B. 5 x 0.50 C D. 50-5

36 2011 MATH Invitational Round 3 Number 1 The bookstore makes a profit of 5 for each pencil sold. Which expression best shows the profit in dollars for 50 pencils? A x 50 $0.05(50) = $2.50 total profit, in dollars

37 2011 Invitational Round 3 Number 2 30 seconds What is the value of 8 in the number 814,635,702? A. Hundred thousands B. Millions C. Ten millions D. Hundred millions

38 2011 Invitational Round 3 Number 2 What is the value of 8 in the number 814,635,702? D. Hundred millions We normally read as : 8 hundred fourteen million, 635 thousand, 702.

39 2011 MATH Invitational Round 3 Number 3 45 seconds Mrs. Triple bought 3 toys, one for each of her triplets. She walked into the store with $35.30 and walked out with $4.10 in change. What was the average toy cost? A. $10.40 B. $11.60 C. $15.20 D. $35.20

40 2011 MATH Invitational Round 3 Number 3 Mrs. Triple bought 3 toys, one for each of her triplets. She walked into the store with $35.30 and walked out with $4.10 in change. What was the average toy cost? A. $10.40 $ $4.10 = $31.20 $31.20 / 3 = $10.40

41 2011 MATH Invitational Round 3 Number 4 30 seconds Seven eighths of what number is 21? A. 24 B. 3/8 C. 18 ⅜ D. 32

42 2011 MATH Invitational Round 3 Number 4 Seven eighths of what number is 21? A. 24 7/8(24)=21 by simply checking each answer Or 21 / (7/8) = 21(8) 7

43 2011 MATH Invitational Round 3 Number 5 45 seconds Name three distinct factors of 12 whose sum is 11. A. 3, 4, 4 B. 1, 2, 8 C. 2, 4, 5 D. 1, 4, 6

44 2011 MATH Invitational Round 3 Number 5 Name 3 distinct factors of 12 whose sum is 11. A. 3, 4, 4 are not distinct B. 1, 2, 8 eight is not a factor C. 2, 4, 5 five is not a factor D. 1, 4, 6

45 2011 MATH Invitational Round 3 Number 6 45 seconds The Browns went out for dinner. For every 2 meals they buy, they get one free. If one meal costs $5.10, how much will it cost for all 6 family members to eat? A. $30.60 B.$25.50 C.$20.40 D.$30.00

46 2011 MATH Invitational Round 3 Number 6 The Browns went out for dinner. For every 2 meals they buy, they get the next one free. If one meal costs $5.10, how much will it cost for all 6 family members to eat? C. $20.40 Buy 2, get 3. Buy 4, get 6. 4($5.10) = $20.40

47 2011 MATH Invitational Round 3 Number 7 45 Seconds Half of the books Heath owns are mysteries. One third are historical fiction. The other four books are science fiction. How many of Heath s books are mysteries? A. 4 B. 8 C. 12 D. 24

48 2011 MATH Invitational Round 3 Number 7 Half of the books Heath owns are mysteries. One third are historical fiction. The other four books are science fiction. How many of Heath s books are mysteries? C. 12 1/2 + 1/3 = 5/6 so the 4 is 1/6 of his books. If he owns 24 books, 12 are mysteries, 8 are historical fiction and 4 are science fiction.

49 End Round Three

50 Begin Round Four

51 2011 MATH Invitational Round 4 Number 1 30 seconds Use the proper symbol. 14/19 15/16 Emcee will NOT read answers. A. < B. > C. = D.

52 2011 MATH Invitational Round 4 Number 1 Use the proper symbol. 14/19 15/16 A. 14/19 < 15/16 14/19 = and 15/16 = or use estimation: 14/19 is about 3/4 and 15/16 is closer to one whole

53 2011 MATH Invitational Round 4 Number 2 30 seconds What is the LCM of 8, 9, and 12? A. 36 B. 72 C. 96 D. 864

54 2011 MATH Invitational Round 4 Number 2 30 seconds What is the LCM of 8, 9, and 12? B. 72 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99 12, 24, 36, 48, 60, 72, 84, 96, is Least Common Multiple of 8, 9 and 12.

55 2011 MATH Invitational Round 4 Number 3 30 Seconds Write 64% as a decimal and a fraction. A. 6.4; 16/25 B. 0.64; 16/25 C. 0.64; 4/5 D. 6.4; 4/5

56 2011 MATH Invitational Round 4 Number 3 30 Seconds Write 64% as a decimal and a fraction. B. 0.64; 16/25 64 =

57 2011 MATH Invitational Round 4 Number 4 30 seconds What is the probability of drawing out a ball that has a composite number on it? A. 1/3 B. 3/7 C. 1/2 D. 4/7

58 2011 MATH Invitational Round 4 Number 4 What is the probability of drawing out a ball that has a composite number on it? B. 3/7 2, 7, 13 and 97 are prime. 63 is divisible by 3, 7, 9, and is divisible by 2, 3, 6, 7, 14, and is divisible by 2, 5, 7, 10, 14, and 35.

59 2011 MATH Invitational Round 4 Number 5 60 seconds Yourtown, USA 2011 Length of daylight savings time: 210 days Number of homes: 10,000 A. $5,700 B. $39,900 C. $1,197,000 Money saved each day during daylight saving time: about $0.57 per house. How much money will the town save each week? D. $1,235,400

60 2011 MATH Invitational Round 4 Number 5 Yourtown, USA 2011 Length of daylight savings time: 210 days Number of homes: 10,000 Money saved each day during daylight saving time: about $0.57 per house. B. $39,900 How much money will the town save each week? (7 days)(10,000 homes)($0.57/house)

61 2011 MATH Invitational Round 4 Number 6 45 seconds Phil is buying a used sports car that costs $29,748. If he buys 4 new tires for $125 each, which place values in the car s cost will change? A. Ones, tens, hundreds B. Tens, hundreds, thousands C. Hundreds, thousands D. Hundreds, thousands, and ten thousands

62 2011 MATH Invitational Round 4 Number 6 Phil is buying a used sports car that costs $29,748. If he buys 4 new tires for $125 each, which place values in the car s cost will change? $29, $30,248 D. Hundreds, thousands, and ten thousands

63 2011 MATH Invitational Round 4 Number 7 60 seconds Student Start Time Finish Time Bob Brown 10:20 10:22:48 Ola Orange 10:25 10:27:10 Brian Blue 10:28 10:29:38 Rally Red 10:30 10:32:50 List the runners from first through fourth place. A. Bob Brown, Ola Orange, Brian Blue, Rally Red B. Brian Blue, Ola Orange, Bob Brown, Rally Red C. Ola Orange, Brian Blue, Bob Brown, Rally Red D. Rally Red, Brian Blue, Bob Brown, Ola Orange

64 2011 MATH Invitational Round 4 Number 7 Student Start Time Finish Time Times Bob Brown 10:20 10:22:48 2:48 Ola Orange 10:25 10:27:10 2:10 Brian Blue 10:28 10:29:38 1:38 Rally Red 10:30 10:32:50 2:50 List the runners from first through fourth place. B. Brian Blue, Ola Orange, Bob Brown, Rally Red

65 End Round Four

66 Begin Alternate Round

67 2011 Invitational Alternate 1 Number 1 30 seconds Simplify 5 1/2-2 5/14 A. 3 4/12 B. 3 1/3 C. 3 1/14 D. 3 1/7

68 2011 Invitational Alternate 1 Number 1 Simplify 5 1/2-2 5/14 5 7/14 2 5/14 3 2/14 then simplify D. 3 1/7

69 2011 MATH Invitational Alternate #1 Number 2 30 seconds When finding a measure of central tendency, we may get a number that is NOT one of the data items, except when finding which of the following? A. mean B. mode C. median D. all the above

70 2011 MATH Invitational Alternate #1 Number 2 When finding a measure of central tendency, we may get a number that is NOT one of the data items, except when finding which of the following? B. Mode There may be no mode or more than one mode, but if there is a mode, it must be one of the data items. The mean and sometimes the median result from calculations that may result in a number that is NOT one of the items from the data list.

71 2011 MATH Invitational Alternate 1 Number 3 30 seconds Add 5 3/ /9 A. 7 5/27 B. 7 5/9 C. 7 6/27 D. 7 2/9

72 2011 MATH Invitational Alternate 1 Number 3 Add 5 3/ /9 D.

73 2011 MATH Invitational Alternate 1 Number 4 30 Seconds How many acres? 74,052 square feet = acres (43,560 square feet = 1 acre) A. 1.7 B. 1 1/2 C. 1.8 D. 1 2/3

74 2011 MATH Invitational Alternate 1 Number 4 How many acres? 74,052 square feet = acres (43,560 square feet = 1 acre) A ,052/43, This is a calculator problem!

75 2011 MATH Invitational Alternate 1 Number 5 30 Seconds Which pair of ratios do not form a proportion? A. B. C. D.

76 2011 MATH Invitational Alternate 1 Number 5 Which pair of ratios do not form a proportion? 8*36 = 9*32 8*27 = 18*12 C. 25*6 = 150 but 36*5 = 180 6*13 = 31.5*2.5

77 2011 MATH Invitational Alternate 1 Number 6 45 Seconds Sarah babysits each week and gets paid $4.50 per hour for each child. Next week, Sarah will babysit Lauren for 3.5 hours, Jake for 6 hours, and Jeremiah for 11 hours. How much should Sarah get paid at the end of next week? A. $87.75 B. $92.25 C. $78.00 D. $82.00

78 2011 MATH Invitational Alternate 1 Number 6 Sarah babysits each week and gets paid $4.50 per hour for each child. Next week, Sarah will babysit Lauren for 3.5 hours, Jake for 6 hours, and Jeremiah for 11 hours. How much should Sarah get paid at the end of next week? B. $92.25 $4.50( ) = $92.25

79 2011 MATH Invitational Alternate 1 Number 7 45 seconds Beth s check stub is smudged. She earned $ before taxes by working 30 hours last week. If she works 35 hours next week, how much will she earn, before taxes? A. $ B. $ C. $ D. $257.75

80 2011 MATH Invitational Alternate 1 Number 7 Beth s check stub is smudged. She earned $ before taxes by working 30 hours last week. If she works 35 hours next week, how much will she earn, before taxes? A. $ ($ / 35) * 30 = $ B. ($ / 35) * 30 = $ C. ($ / 35) * 30 = $ D. ($ / 35) * 30 = $220.93

81 End Alternate Round 1

82 Begin Alternate Round 2

83 2011 Invitational Alternate 2 Number 1 30 seconds Every royal carriage needs 6 horses to pull it. There are 28 horses. How many carriages can be used? A. 4 carriages C. 6 carriages B. 5 carriages D. 7 carriages

84 2011 Invitational Alternate 2 Number 1 Every royal carriage needs 6 horses to pull it. There are 28 horses. How many carriages can be used? A. 4 carriages 28 / 6 = 4 carriages with 4 horses left over

85 2011 MATH Invitational Alternate 2 Number 2 30 Seconds Convert 67/80 to a percent. A. 67.8% B % C. 32.2% D. 83.6%

86 2011 MATH Invitational Alternate #2 Number 2 Convert 67/80 to a percent. B % 67 / 80 = or 83.75% when decimal is moved two places to the right to change decimal to percent

87 2011 MATH Invitational Alternate 2 Number 3 30 seconds Which of these fractions and/or mixed numbers is not equal to 4/3? 8/6 1 3/6 1 1/3 1 9/27 A. 8/6 B. 1 3/6 C. 1 1/3 D. 1 9/27

88 2011 MATH Invitational Alternate 2 Number 3 Which of these fractions and/or mixed numbers is not equal to 4/3? 8/6 1 3/6 1 1/3 1 9/27 B. 1 3/6

89 2011 MATH Invitational Alternate 2 Number 4 45 Seconds Colby s sock drawer consists of 12 pair of white socks, 3 pair of blue socks, and 5 pair of black socks, each pair neatly folded together. If Colby reaches in his sock drawer and chooses a pair of socks without looking, what is the probability that the pair of socks will be blue or black? A. 1/3 B. 2/3 C. 2/5 D. 3/5

90 2011 MATH Invitational Alternate 2 Number 4 Colby s sock drawer consists of 12 pairs of white socks, 3 pairs of blue socks, and 5 pairs of black socks, all neatly folded together. If Colby reaches in his sock drawer and chooses a pair of socks without looking, what is the probability that the pair of socks will be blue or black? C. 2/5 (3+5) / (12+3+5) = 8/20

91 2011 MATH Invitational Alternate 2 Number 5 30 Seconds Simplify the fraction: 2/3 A. 3/8 1/4 B. 1/6 C. 2 1/3 D. 2 2/3

92 2011 MATH Invitational Alternate 2 Number 5 Simplify the fraction: 2/3 1/4 D. 2 2/3

93 2011 MATH Invitational Alternate 2 Number 6 45 Seconds A shirt costs $29.96 after a 30% discount is applied and 7% sales tax is added. What was the shirt s original price? A. $8.40 B. $36.40 C. $40.00 D. $58.00

94 2011 MATH Invitational Alternate 2 Number 6 A shirt costs $29.96 after a 30% discount is applied and 7% sales tax is added. What was the shirt s original price? C. $40.00 Working backward from answer: $40(0.70)(1.07) = $29.96

95 2011 MATH Invitational Alternate 2 Number 7 60 seconds Molly has 24 coins in her pocket. How much money does she have? 1/2 are nickels 1/4 are quarters 1/6 are dimes A. $1.79 B. $2.52 C. $2.79 D. $3.52 1/12 are pennies

96 2011 MATH Invitational Alternate 2 Number 7 Molly has 24 coins in her pocket. How much money does she have? 1/2 are nickels 1/4 are quarters 1/6 are dimes B. $ * 0.05 = * 0.25 = * 0.10 = * 0.01 = /12 are pennies

97 End Alternate Round 2