Indiana Academic M.A.T.H. Bowl. Invitational February 2012

Indiana Academic M.A.T.H. Bowl Invitational February 2012

Begin Practice Round

2012 MATH Invitational Practice Round 30 seconds a. 18 b. 14 c. 4 d. 28 16 + 12 =?

2012 MATH Invitational Practice Round 16 + 12 =? d. 28

End Practice Round

Begin Round One

M-I-1-1 30 seconds Round to the nearest thousand: 10,764 a. 9,000 b. 10,000 c. 11,000 d. 12,000

M-I-1-1 Round to the nearest thousand: 10,764 c. 11,000

M-I-1-2 30 seconds Which expression has a value of 322? a. 481-129 b. 138 + 194 c. 14 x 23 d. 657 3

M-I-1-2 Which expression has a value of 322? a. 481 129 352 b. 138 + 194 332 c. 14 x 23 322 d. 657 3 219

M-I-1-3 30 seconds Students at Sum Middle School visit the Indianapolis Zoo every 5 years and Space Camp every 2 years. If they are visiting both during the 2011-2012 school year, how many years will it be before both places are visited again during the same school year? a. 4 years b. 6 years c. 8 years d. 10 years

M-I-1-3 Students at Sum Middle School visit the Indianapolis Zoo every 5 years and Space Camp every 2 years. If they are visiting both during the 2011-2012 school year, how many years will it be before both places are visited again during the same school year? a. 4 years b. 6 years c. 8 years d. 10 years LCM(2,5) = 10, count 2, 4, 6, 8, 10, and 5, 10. Ten is the first or least common multiple.

M-I-1-4 45 seconds 5 and 7 are twin primes. Which of the following are also twin primes? a. 7 and 11 b. 13 and 17 c. 17 and 23 d. 59 and 61

M-I-1-4 5 and 7 are twin primes. Which of the following are also twin primes? d. 59 and 61 Twin primes have only one even number between two consecutive primes. 3 & 5 are also twin primes.

M-I-1-5 45 seconds Which expression is equivalent to 3-2 x 0? a. 1 / 9 b. 3 2 c. 1 / 9x d. x / 9

M-I-1-5 Which expression is equivalent to 3-2 x 0? a. 1 / 9 b. 3 2 c. 1 / 9x d. x / 9 3 4 = 81 3 3 = 27 3 2 = 9 3 1 = 3 3 0 = 1 3-1 = 1/3 3-2 = 1/9 X 0 = 1 Divide by 3 Divide by 3 Divide by 3

M-I-1-6 60 seconds Fahrenheit and Celsius temperatures are related by the equation F = 9 / 5 C + 32, where F is the temperature in degrees Fahrenheit and C is the temperature on the Celsius scale. If the temperature is a balmy 77 Fahrenheit, what is the temperature on the Celsius scale? a. 25 b. 33.8 c. 43 d. 45

M-I-1-6 Fahrenheit and Celsius temperatures are related by the equation F = 9 / 5 C + 32, where F is the temperature in degrees Fahrenheit and C is the temperature on the Celsius scale. If the temperature is a balmy 77 Fahrenheit, what is the temperature on the Celsius scale? a. 25 F = 9/5C + 32 77 = 1.8C + 32-32 -32 45 = 1.8C 45 1.8 = C C = 25

M-I-1-7 60 seconds Taylor had a candy bar that was divided into 12 pieces. He gave his brother, Clayton, 2/3 of it. Clayton gave ¼ of his part to his twin, Dalton. What fraction of the original candy bar did Dalton have? a. 1/6 b. 3 pieces c. ¼ d. 4 pieces

M-I-1-7 Taylor had a candy bar that was divided into 12 pieces. He gave his brother, Clayton, 2/3 of it. Clayton gave ¼ of his part to his twin, Dalton. What fraction of the original candy bar did Dalton have? Taylor kept 4/12 a. 1/6 and gave 8/12 to Clayton. Clayton kept 6/12 and gave Dalton 2/12 or 1/6 of the candy bar.

End Round One

Begin Round Two

M-I-2-1 45 seconds Ann, Dan and Van ordered five pizzas. They plan on eating them all and everyone gets the same amount. How much will each person get to eat? a. 1 whole pizza b. 1 ½ pizzas c. 1 2/3 pizzas d. 1 ¾ pizzas

M-I-2-1 Ann, Dan, and Van ordered five pizzas. They plan on eating them all and everyone gets the same amount. How much will each person get to eat? c. 1 ⅔ pizzas Cutting two pizzas in thirds helps each get 5/3.

M-I-2-1 30 seconds Which of the following is equal to one million? a. one hundred thousands b. ten thousands c. one hundred hundreds d. one thousand thousands

M-I-2-2 Which of the following is equal to one million? a. one hundred thousands = 100,000 b. ten thousands = 10,000 c. one hundred hundreds = 10,000 d. one thousand thousands = 1,000,000

M-I-2-3 45 seconds The Bobbles went out to 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? a. $20.60 b. $25.30 c. $15.30 d. $20.40

M-I-2-3 The Bobbles went out to 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? d. $20.40 4($5.10) + 2(0) = $20.40

M-I-2-4 45 seconds What is the next number in the pattern? 64, 81, 100, 121, a. 134 b. 144 c. 142 d. 147

M-I-2-4 What is the next number in the pattern? 64, 81, 100, 121, b. 144 8 2, 9 2, 10 2, 11 2, 12 2 12 2 = 144

M-I-2-5 45 seconds Kyle adds 4 sit-ups to his workout every day. On Wednesday, he did 20 sit-ups. At this rate, how many sit-ups will Kyle be doing by the time he completes his workout next Wednesday? a. 36 sit-ups b. 44 sit-ups c. 48 sit-ups d. 52 sit-ups

M-I-2-5 Kyle adds 4 sit-ups to his workout every day. On Wednesday, he did 20 sit-ups. At this rate, how many sit-ups will Kyle be doing by the time he completes his workout next Wednesday? Wednesday 20 Thursday 24 Friday 28 Saturday 32 Sunday 36 Monday 40 Tuesday 44 Wednesday 48 c. 48 sit-ups

M-I-2-6 60 seconds If Gene E. Us reads 100 words backwards per second, how long would it take Gene to read 40,000 words backwards? a. 6 min 10 sec b. 6 min 20 sec c. 6 min 30 sec d. 6 min 40 sec

M-I-2-6 If Gene E. Us reads 100 words backwards per second, how long would it take Gene to read 40,000 words backwards? dda htam sunim semit tcartbus 100 words = 40,000 words 1 second x seconds d. 6 min 40 sec 100x = 40,000 X = 400 seconds X = 400/60 minutes X = 6 minutes 40 seconds

M-I-2-7 60 seconds The length of a side of a square window in Jessica s bedroom is represented by 2x 1. Which expression represents the area of the window? a. 2x 2 + 1 b. 4x 2 + 1 c. 4x 2 + 4x + 1 d. 4x 2-4x + 1

M-I-2-7 The length of a side of a square window in Jessica s bedroom is represented by 2x 1. Which expression represents the area of the window? X 2 X 2 X 2 X 2 2x -1 d. 4x 2-4x + 1 2x -1

End Round Two

Begin Round Three

M-I-3-1 30 seconds Simplify: 12½ % of 80 a. 10 b. 12 c. 16 d. 100

M-I-3-1 Simplify: 12½% of 80 a. 10 12½% = 1/8 1/8 of 80 is 10

M-I-3-2 45 seconds Of the following, which has the largest least common multiple? a. 3 and 15 b. 6 and 8 c. 6 and 9 d. 5 and 7

M-I-3-2 Of the following, which has the largest least common multiple? a. 3 and 15 LCM(3, 15) = 15 b. 6 and 8 LCM(6, 8) = 24 c. 6 and 9 LCM(6, 9) = 18 d.5 and 7 LCM(5, 7) = 35

M-I-3-3 30 seconds There are 8 girls on the Sum Middle School Volleyball Team. Half of the girls played in the match. Of the girls who played, three-fourths made a point. What fraction of the total number of girls on the team made the points? a. 2 b. 2/8 c. 3 d. 3/8

M-I-3-3 30 seconds There are 8 girls on the Sum Middle School Volleyball Team. Half of the girls played in the match. Of the girls who played, three-fourths made a point. What fraction of the total number of girls on the team made the points? d. 3/8 (½)(8)(¾) = 3 girls

M-I-3-4 45 seconds The Eiffel Tower is 1,063 feet tall. How many 6-foot men, standing on each other s head, will completely fill that height? a. 172 men b. 173 men c. 177 men d. 178 men

M-I-3-4 The Eiffel Tower is 1,063 feet tall. How many 6-foot men, standing on each other s head, will completely fill that height? d. 178 men 6m 1,063 m 177.1666 Must use 178 men to reach top

M-I-3-5 45 seconds Solve 2(x 1) = 3x (x + 2) a. The equation has no solution b. The solution is 1. c. The solution is -1. d. Every number is a solution of the equation.

M-I-3-5 Solve 2(x 1) = 3x (x + 2) 2x 2 = 3x x 2 2x 2 = 2x 2 a. The equation has no solution. b. The solution is 1. Both B & C are true c. The solution is -1. d. Every number is a solution of the equation.

M-I-3-6 60 seconds Your test scores are 79, 95, and 90. You will be taking one more test and you want your average (mean) to round to at least 90. What is the lowest score that will accomplish your goal? a. 91 b. 92 c. 93 d. 94

M-I-3-6 Your test scores are 79, 95, and 90. You will be taking one more test and you want your average (mean) to round to at least 90. What is the lowest score that will accomplish your goal? a. 91 [(79 + 95 + 90) + 91] 4 = 88.75 89 b. 92 [(79 + 95 + 90) + 92] 4 = 89 c. 93 [(79 + 95 + 90) + 93] 4 = 89.25 89 d.94 [(79 + 95 + 90) + 94] 4 = 89.5 90

M-I-3-7 60 seconds Three friends played a game and totaled the points. Kylie had 2/3 of the points, and Kelsie had ¼ of the points. What fractional part of the points did the third player have? a. 1/3 b. ½ c. 3/36 d. 4/9

M-I-3-7 Three friends played a game and totaled the points. Kylie had 2/3 of the points, and Kelsie had ¼ of the points. What fractional part of the points did the third player have? C. 3/36 1 2/3 1/4 1 8/12 3/12 1/12 3/36

End Round Three

Begin Round Four

M-1-4-1 Evaluate the expression (14 + 7) (7-4) 30 seconds a. 1 b. 3 c. -7/2 d. 7

M-I-4-1 Evaluate the expression (14 + 7) (7-4) d. 7 21/3 = 7

M-I-4-2 30 seconds What are all the prime factors of 12? a. 2, 3, 4 b. 2, 3, 7 c. 1, 2, 3 d. 2, 3

M-I-4-2 What are all the prime factors of 12? a. 2, 3, 4 4 is not prime b. 2, 3, 7 7 is not a factor of 12 c. 1, 2, 3 1 is not prime d. 2, 3 2 and 3 are prime factors of 12

M-I-4-3 30 seconds Which number is equal to 2.08? a. 2 2 / 25 b. 2 1 / 8 c. 2 1 / 4 d. 2 8 / 25

M-I-4-3 Which number is equal to 2.08? a. 2 2 / 25 2.08 b. 2 1 / 8 2.125 c. 2 1 / 4 2.25 d. 2 8 / 25 2.32 Will this tool measure 2.08 inches?

M-I-4-4 45 seconds Mr. Smith has 25 students in his third grade class. Only 2/5 of the class made a perfect score on the math test. Only half of those students made a perfect score on the science test. How many students made a perfect score on both tests? a. 5 students b. 10 students c. 15 students d. 20 students

M-I-4-4 Mr. Smith has 25 students in his third grade class. Only of the class made a perfect score on the math test. Only half of those students made a perfect score on the science test. How many students made a perfect score on both tests? a. 5 students 25( )(½) = 5

M-I-4-5 30 seconds Which ordered pair is not a solution set of y > 5x - 1? a. (1, 5) b. (1, 6) c. (1, 8) d. (2, 5)

M-I-4-5 30 seconds Which ordered pair is not a solution set of y > 5x - 1? a. (1, 5) 5 > 5(1) 1 true b. (1, 6) 6 > 5(1) 1 true c. (1, 8) 8 > 5(1) 1 true d. (2, 5) 5 > 5(2) 1 false

M-I-4-6 60 seconds If March 1 falls on a Monday, on what day of the week does April 1 fall? a. Monday b. Tuesday c. Thursday d. Saturday

M-I-4-6 If March 1 falls on a Monday, on what day of the week does April 1 fall? c. Thursday 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3

M-I-4-7 60 seconds Sue walks 9 blocks to school. Each block is 65 feet long. How many yards does she walk to and from school each day? a. 130 yards b. 260 yards c. 390 yards d. 585 yards

M-I-4-7 Sue walks 9 blocks to school. Each block is 65 feet long. How many yards does she walk to and from school each day? c. 390 yards 9(65) = 585 feet one way 2(585 3) = 390 yards to and from

End Round Four

Begin Alternate Round #1

M-I-Alt 1-1 30 seconds Which expression is equivalent to: 4 5 2 3 a. 4 4 4 4 2 2 2 2 2 b. (4 5) + (2 3) c. 5 5 5 5 3 3 d. 20 6

M-I-Alt. 1-1 Which expression is equivalent to: 4 5 2 3 a. 4 4 4 4 2 2 2 2 2 (4 4 4 4 4) (2 2 2) Then write last 4 as 2 2

M-I-Alt. 1-2 30 seconds Which expression is equivalent to 15y 2(y +3)? a. 13y - 6 b. 13y + 3 c. 13y + 6 d. 16y + 1

M-I-Alt. 1-2 Which expression is equivalent to 15y 2(y +3)? a. 13y - 6 15y + (-2)(y + 3) 15y 2y + (-2)(3) 15y 2y - 6

M-I-Alt. 1-3 30 seconds A shirt is on sale for $34.40, which is 20% off the original price. Find the original price of the shirt. a. $36.40 b. $41.28 d. $43.00 d. $54.40

M-I-Alt. 1-3 A shirt is on sale for $34.40, which is 20% off the original price. Find the original price of the shirt. Let p = original price 34.40 = (100-20)% of p 0.80P = 34.40 c. $43.00 0.8P = 34.40 0.8 0.8 P = $43.00

M-I-Alt. 1-4 45 seconds If a car travels at a rate of 30 mph, how far would it travel in one minute? a. 15 miles c. 2 miles c. ½ mile d. 1 mile

M-I-Alt. 1-4 If a car travels at a rate of 30 mph, how far would it travel in one minute? c. ½ mile 30 miles 1 hour 30 miles 60 minutes ½ mile/minute

M-I-Alt. 1-5 45 seconds The Miller s dinner bill came to $73.00. If they left a 15% tip, how much money did the Miller s spend on dinner? a. $80.30 b. $83.95 c. $86.95 d. $87.60

M-I-Alt.1-5 The Miller s dinner bill came to $73.00. If they left a 15% tip, how much money did the Miller s spend on dinner? b. $83.95 10% is $7.30 5% is $3.65 15% is $10.95 So total is $83.95

M-I-Alt. 1-6 45 seconds If 60 ft. of cable weighs 80 lbs, what is the weight of 140 ft. of this cable, to the nearest pound? a. 188 lbs b. 187 lbs c. 186 lbs d. 105 lbs

M-I-Alt. 1-6 If 60 ft of cable weighs 80 lbs, what is the weight of 140 ft of this cable, to the nearest pound? 60 ft = 140 ft 80 lb x lb b. 187 lbs 60x = (80)(140) 60x = (80)(140) 60 60 X = 186.666

M-I-Alt. 1-7 60 seconds Which equation has no solution? a. 4t 8 = 4(t -2) b. 3(r - 1) = -2(2 + r) c. 6p + 2 = 9p - 4 d. 7(s + 1) = -3 + 7s

M-I-Alt. 1-7 Which equation has no solution? a. 4t 8 = 4(t - 2) all real numbers b. 3(r - 1) = -2(2 + r) r = -1/5 c. 6p + 2 = 9p 4 p = 2 d. 7(s + 1) = -3 + 7s 7s + 7 = 7s + -3-7s -7s 7 = -3 has no solution

End Alternate #1 Round

Begin Alternate Round #2

M-I-Alt. 2-1 45 seconds Joe wants to trade in his old lawnmower for a new one that sells for $399. The store owner will allow $95 for Joe s old mower. How much tax will he pay if he pays 7% sales tax on the difference? a. $15.28 b. $21.28 c. $27.93 d. $34.58

M-I-Alt. 2-1 Joe wants to trade in his old lawnmower for a new one that sells for $399. The store owner will allow $95 for Joe s old mower. How much tax will he pay if he pays 7% sales tax on the difference? b. $21.28 Joe pays $399 - $95 = $304 Tax is 0.07($304) = $ 21.28

M-I-Alt. 2-2 30 seconds If Travis saves 25% of the $200 he needs to attend basketball camp, his parents will pay the rest. He has saved $30. How much more does he need to reach his 25% payment portion? a. $10 b. $20 c. $30 d. He has enough.

M-I-Alt. 2-2 If Travis saves 25% of the $200 he needs to attend basketball camp, his parents will pay the rest. He has saved $30. How much more does he need to reach his 25% payment portion? b. $20 0.25(200) 30 = 50 30 or $20

M-I-Alt. 2-3 45 seconds There are 60 students in the 5 th grade and three-fifths of them are girls. How many boys are there in the 5 th grade? a. 12 b. 18 c. 24 d. 36

M-I-Alt. 2-3 There are 60 students in the 5 th grade and three-fifths of them are girls. How many boys are there in the 5 th grade? 3/5 are girls so 2/5 are boys 2/5 of 60 = c. 24 0.4(60) = 24 boys

M-I-Alt. 2-4 45 seconds Of the 32 teams in the National Football League, 4 teams are in the AFC East Division. What percent of the teams are in the AFC East division? a. 4% b. 8% c. 12.5% d. 28%

M-I-Alt. 2-4 Of the 32 teams in the National Football League, 4 teams are in the AFC East Division. What percent of the teams are in the AFC East division? c. 12.5% 4/32 = 1/8 or 12.5/100

M-I-Alt. 2-5 60 seconds Which equation is true? a. 81 (9 2 + 7) = 8 b. (81 9 2 )+ 7 = 8 c. 9 (8 x 2 2 )-1 = 3 d. 36 7 x 2 2 = 116

M-I-Alt. 2-5 Which equation is true? Parentheses, Exponents, Multiply/Divide, Add/Subtract a. 81 (9 2 + 7) = 8 81 (81 + 7) = 81/88 b.(81 9 2 )+ 7 = 8 (81 9 2 ) + 7 (81 81) + 7 = 8 C. 9 (8 x 2 2 ) 1 = 3 9 (8 x 4) 1 9 32 1 = -24 d. 36 7 x 2 2 = 116 36 7 x 2 2 36 28 = 8

M-I-Alt. 2-6 60 seconds The average of 5, 9, 10, 13, and a number n equals 11. Find the value of n. a. 16 b. 17 c. 18 d. 20

M-I-Alt. 2-6 The average of 5, 9, 10, 13, and a number n equals 11. Find the value of n. c. 18 Total will be 11(5 numbers) = 55 5 + 9 + 10 + 13 = 37 So n = 55 37 n = 18

M-I-Alt. 2-7 60 seconds Bob and Greg each have the same amount of money. Bob buys 2 pencils and has 80 left. Greg buys 4 pencils and has 30 left. How much money did each of them have? a. $1.00 b. $1.30 c. $1.50 d. $1.80

M-I-Alt. 2-7 Bob and Greg each have the same amount of money. Bob buys 2 pencils and has 80 left. Greg buys 4 pencils and has 30 left. How much money did each of them have? b. $1.30 Let x = cost of one pencil Bob s cash = Greg s cash 2x + 80 = 4x + 30-2x -2x 80 = 2x + 30-30 -30 50 = 2x X = 25 Since one pencil costs 25, Bob has 2(25) + 80 cents or $1.30