1. Simplify the following expression completely, leaving no exponents remaining.

Transcription

1 Team 4 GEM

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3 GEMS Team 1. Simplify the following expression completely, leaving no exponents remaining. 2 5! ! 2 "3 2. The number 0. 9 represents a never-ending string of nines after the decimal place. Which one of the following statements is correct? a. 0.9 > 1 b. 0.9 = 1 c. 0.9 < 1 d. Cannot determine 3. You bake a batch of cookies. One ninth of them are burnt and you throw them away. You give away one eighth of the remaining cookies to a friend. Your dog eats one seventh of the remaining cookies. You freeze one sixth of the remaining cookies for later. You bring the rest to school for the other 23 kids on your math class. You have too few, so three of them do not get a cookie. How many cookies did you bake? 4. A cylinder is connected to a cone at a common base to make a giant crayon. The cone has a height of 1.5 feet, the cylinder has a height of 20 feet, and both have a radius of 2 feet. Find the surface area of the crayon in square feet, leaving your answer in terms of π. 5. Estimate the official maximum occupancy of this cafeteria. (Credit will be given to answers that are within ±50 of the actual number.) 6. Find the largest possible distance between two points from the set: {(!2,1),(0, 0),(1,1),(3,!2) }

4 7. A pair of six-sided number dice is thrown. What is the probability that sum of the numbers is less than 11? (Leave your answer as a fraction.) 8. Every element (number) in a data set is doubled. Which one(s) of the following is also doubled? Mean, Median, Mode, Range 9. A car is traveling on I-95 at a constant speed. At 10:00am, the car passes mile marker 123. At 12:30pm, it passes mile marker 298. What mile marker does the car pass at 2:00pm? 10. Container A has 1 gallon of orange juice. Container B has 1 gallon of apple juice. Three pints of orange juice are taken from Container A and poured into Container B. Container B is thoroughly mixed. Three pints are taken from Container B and poured into Container A. Which one of the following is true? a) Container A is more diluted with apple juice. c) Both containers are equally diluted. b) Container B is more diluted with orange juice. d) Not possible to determine.

5 GEMS Team 1. Simplify the following expression completely, leaving no exponents remaining. 2 5! ! 2 "3 2. The number 0. 9 represents a never-ending string of nines after the decimal place. Which one of the following statements is correct? a. 0.9 > 1 b. 0.9 = 1 c. 0.9 < 1 d. Cannot determine 3. You bake a batch of cookies. One ninth of them are burnt and you throw them away. You give away one eighth of the remaining cookies to a friend. Your dog eats one seventh of the remaining cookies. You freeze one sixth of the remaining cookies for later. You bring the rest to school for the other 23 kids on your math class. You have too few, so three of them do not get a cookie. How many cookies did you bake? 4. A cylinder is connected to a cone at a common base to make a giant crayon. The cone has a height of 1.5 feet, the cylinder has a height of 20 feet, and both have a radius of 2 feet. Find the surface area of the crayon in square feet, leaving your answer in terms of π. 5. Estimate the official maximum occupancy of this cafeteria. (Credit will be given to answers that are within ±50 of the actual number.) 6. Find the largest possible distance between two points from the set: (!2,1),(0, 0),(1,1),(3,!2) { }

6 7. A pair of six-sided number dice is thrown. What is the probability that sum of the numbers is less than 11? (Leave your answer as a fraction.) 8. Every element (number) in a data set is doubled. Which one(s) of the following is also doubled? Mean, Median, Mode, Range 9. A car is traveling on I-95 at a constant speed. At 10:00am, the car passes mile marker 123. At 12:30pm, it passes mile marker 298. What mile marker does the car pass at 2:00pm? 10. Container A has 1 gallon of orange juice. Container B has 1 gallon of apple juice. Three pints of orange juice are taken from Container A and poured into Container B. Container B is thoroughly mixed. Three pints are taken from Container B and poured into Container A. Which one of the following is true? a) Container A is more diluted with apple juice. c) Both containers are equally diluted. b) Container B is more diluted with orange juice. d) Not possible to determine.

7 GEMS Team 1. Simplify the following expression completely, leaving no exponents remaining. 2 5! ! 2 "3 2. The number 0. 9 represents a never-ending string of nines after the decimal place. Which one of the following statements is correct? a. 0.9 > 1 b. 0.9 = 1 c. 0.9 < 1 d. Cannot determine 3. You bake a batch of cookies. One ninth of them are burnt and you throw them away. You give away one eighth of the remaining cookies to a friend. Your dog eats one seventh of the remaining cookies. You freeze one sixth of the remaining cookies for later. You bring the rest to school for the other 23 kids on your math class. You have too few, so three of them do not get a cookie. How many cookies did you bake? 4. A cylinder is connected to a cone at a common base to make a giant crayon. The cone has a height of 1.5 feet, the cylinder has a height of 20 feet, and both have a radius of 2 feet. Find the surface area of the crayon in square feet, leaving your answer in terms of π. 5. Estimate the official maximum occupancy of this cafeteria. (Credit will be given to answers that are within ±50 of the actual number.) 6. Find the largest possible distance between two points from the set: (!2,1),(0, 0),(1,1),(3,!2) { }

8 7. A pair of six-sided number dice is thrown. What is the probability that sum of the numbers is less than 11? (Leave your answer as a fraction.) 8. Every element (number) in a data set is doubled. Which one(s) of the following is also doubled? Mean, Median, Mode, Range 9. A car is traveling on I-95 at a constant speed. At 10:00am, the car passes mile marker 123. At 12:30pm, it passes mile marker 298. What mile marker does the car pass at 2:00pm? 10. Container A has 1 gallon of orange juice. Container B has 1 gallon of apple juice. Three pints of orange juice are taken from Container A and poured into Container B. Container B is thoroughly mixed. Three pints are taken from Container B and poured into Container A. Which one of the following is true? a) Container A is more diluted with apple juice. c) Both containers are equally diluted. b) Container B is more diluted with orange juice. d) Not possible to determine.

9 GEMS Team 1. Simplify the following expression completely, leaving no exponents remaining. 2 5! ! 2 "3 2. The number 0. 9 represents a never-ending string of nines after the decimal place. Which one of the following statements is correct? a. 0.9 > 1 b. 0.9 = 1 c. 0.9 < 1 d. Cannot determine 3. You bake a batch of cookies. One ninth of them are burnt and you throw them away. You give away one eighth of the remaining cookies to a friend. Your dog eats one seventh of the remaining cookies. You freeze one sixth of the remaining cookies for later. You bring the rest to school for the other 23 kids on your math class. You have too few, so three of them do not get a cookie. How many cookies did you bake? 4. A cylinder is connected to a cone at a common base to make a giant crayon. The cone has a height of 1.5 feet, the cylinder has a height of 20 feet, and both have a radius of 2 feet. Find the surface area of the crayon in square feet, leaving your answer in terms of π. 5. Estimate the official maximum occupancy of this cafeteria. (Credit will be given to answers that are within ±50 of the actual number.) 6. Find the largest possible distance between two points from the set: (!2,1),(0, 0),(1,1),(3,!2) { }

10 7. A pair of six-sided number dice is thrown. What is the probability that sum of the numbers is less than 11? (Leave your answer as a fraction.) 8. Every element (number) in a data set is doubled. Which one(s) of the following is also doubled? Mean, Median, Mode, Range 9. A car is traveling on I-95 at a constant speed. At 10:00am, the car passes mile marker 123. At 12:30pm, it passes mile marker 298. What mile marker does the car pass at 2:00pm? 10. Container A has 1 gallon of orange juice. Container B has 1 gallon of apple juice. Three pints of orange juice are taken from Container A and poured into Container B. Container B is thoroughly mixed. Three pints are taken from Container B and poured into Container A. Which one of the following is true? a) Container A is more diluted with apple juice. c) Both containers are equally diluted. b) Container B is more diluted with orange juice. d) Not possible to determine.

11 GEMS Team 1. Simplify the following expression completely, leaving no exponents remaining. 2 5! ! 2 "3 2. The number 0. 9 represents a never-ending string of nines after the decimal place. Which one of the following statements is correct? a. 0.9 > 1 b. 0.9 = 1 c. 0.9 < 1 d. Cannot determine 3. You bake a batch of cookies. One ninth of them are burnt and you throw them away. You give away one eighth of the remaining cookies to a friend. Your dog eats one seventh of the remaining cookies. You freeze one sixth of the remaining cookies for later. You bring the rest to school for the other 23 kids on your math class. You have too few, so three of them do not get a cookie. How many cookies did you bake? 4. A cylinder is connected to a cone at a common base to make a giant crayon. The cone has a height of 1.5 feet, the cylinder has a height of 20 feet, and both have a radius of 2 feet. Find the surface area of the crayon in square feet, leaving your answer in terms of π. 5. Estimate the official maximum occupancy of this cafeteria. (Credit will be given to answers that are within ±50 of the actual number.) 6. Find the largest possible distance between two points from the set: (!2,1),(0, 0),(1,1),(3,!2) { }

12 7. A pair of six-sided number dice is thrown. What is the probability that sum of the numbers is less than 11? (Leave your answer as a fraction.) 8. Every element (number) in a data set is doubled. Which one(s) of the following is also doubled? Mean, Median, Mode, Range 9. A car is traveling on I-95 at a constant speed. At 10:00am, the car passes mile marker 123. At 12:30pm, it passes mile marker 298. What mile marker does the car pass at 2:00pm? 10. Container A has 1 gallon of orange juice. Container B has 1 gallon of apple juice. Three pints of orange juice are taken from Container A and poured into Container B. Container B is thoroughly mixed. Three pints are taken from Container B and poured into Container A. Which one of the following is true? a) Container A is more diluted with apple juice. c) Both containers are equally diluted. b) Container B is more diluted with orange juice. d) Not possible to determine.