MATH DAY 2017 TEAM COMPETITION

Transcription

1 An excursion through mathematics and its history (In no particular order)(and some trivia) MATH DAY 2017 TEAM COMPETITION Made possible by

2 A quick review of the rules History (or trivia) questions alternate with math questions Math questions are numbered by MQ1, MQ2, etc. History questions by HQ1, HQ2, etc. Math answers should be written on the appropriate sheet of the math answers booklet. The answer to every math question will be either an integer (mostly positive) or the square root of a positive integer. Square roots of positive integers MUST be entered in the form m n where m, n are positive integers and n is square free. Examples: 12 should be entered as 2 3, 50 should be entered as 5 2, 3 98 as History questions are multiple choice, answered using the clicker. Math questions are worth the number of points shown on the screen when the runner gets your answer sheet. That equals the number of minutes left to answer the question. Have one team member control the clicker, another one the math answers booklet

3 Rules--Continued All history/trivia questions are worth 1 point. The team with the highest math score is considered first. Next comes the team with the highest overall score, from a school different from the school of the winning math team. Finally, the team with the highest history score from the remaining schools.

4 HQ0-Warm Up, no points Descartes famous phrase Cogito, ergo sum, translates as A. I think I am a man B. I think therefore I am C. I stink therefore I am D. I think my name is Sam E. I drink and eat the ham René Descartes (Cartesius) ( )

5 HQ0-Warm Up, no points Descartes famous phrase Cogito, ergo sum, translates as A. I think I am a man B. I think therefore I am C. I stink therefore I am D. I think my name is Sam E. I drink and eat the ham René Descartes (Cartesius) ( ) 20 seconds

6 HQ0-Warm Up, no points Descartes famous phrase Cogito, ergo sum, translates as A. I think I am a man B. I think therefore I am C. I stink therefore I am D. I think my name is Sam E. I drink and eat the ham René Descartes (Cartesius) ( ) Time s Up!

7 HQ0-Warm Up, no points Descartes famous phrase Cogito, ergo sum, translates as A. I think I am a man B. I think therefore I am C. I stink therefore I am D. I think my name is Sam E. I drink and eat the ham René Descartes (Cartesius) ( )

8 Demonstrating the points system For math questions there will be a number in the lower right corner. It will change every minute. Here I am illustrating with numbers changing every 10 seconds. Try to imagine 10 seconds is a minute. The first number tells you the maximum number of points you can get for the question. Assume a question is on the screen.

9 Demonstrating the point system For math questions there will be a yellow number usually in the lower right corner. It will change every minute. Here I am illustrating with numbers changing every 10 seconds. Try to imagine 10 seconds is a minute. The first number tells you the maximum number of points you can get for the question. Assume a question is on the screen. 4

10 Demonstrating the point system For math questions there will be a yellow number usually in the lower right corner. It will change every minute. Here I am illustrating with numbers changing every 10 seconds. Try to imagine 10 seconds is a minute. The first number tells you the maximum number of points you can get for the question. Assume a question is on the screen. 3

11 Demonstrating the point system For math questions there will be a yellow number usually in the lower right corner. It will change every minute. Here I am illustrating with numbers changing every 10 seconds. Try to imagine 10 seconds is a minute. The first number tells you the maximum number of points you can get for the question. Assume a question is on the screen. 2

12 Demonstrating the point system For math questions there will be a yellow number usually in the lower right corner. It will change every minute. Here I am illustrating with numbers changing every 10 seconds. Try to imagine 10 seconds is a minute. The first number tells you the maximum number of points you can get for the question. Assume a question is on the screen. 1

13 I may/will give less than the allotted time if I see that all teams have answered. TIME s UP!

14 THE CHALLENGE BEGINS VERY IMPORTANT! Put away all electronic devices; including calculators. Mechanical devices invented more than a hundred years ago, are OK.

15 HQ1.Dysfunctional Families The picture shows the first scientifically important members of a Swiss family responsible for some of the most fundamental advances in Mathematics. The family is: A. The Alighieri Family B. The Bernoulli Family C. The Euler Family D. The Leibniz Family E. The Robinson Family

16 HQ1.Dysfunctional Families The picture shows the first scientifically important members of a Swiss family responsible for some of the most fundamental advances in Mathematics. The family is: A. The Alighieri Family B. The Bernoulli Family C. The Euler Family D. The Leibniz Family E. The Robinson Family 20 seconds

17 HQ1.Dysfunctional Families The picture shows the first scientifically important members of a Swiss family responsible for some of the most fundamental advances in Mathematics. The family is: A. The Alighieri Family B. The Bernoulli Family C. The Euler Family D. The Leibniz Family E. The Robinson Family Time s Up!

18 HQ1.Dysfunctional Families The picture shows the first scientifically important members of a Swiss family responsible for some of the most fundamental advances in Mathematics. The family is: A. The Alighieri Family B. The Bernoulli Family C. The Euler Family D. The Leibniz Family E. The Robinson Family Time s Up!

19 MQ1. Adding Numbers Two three digit numbers 6a5 and 3b2 are added together. The result is a multiple of 9. What is the largest possible value of a + b?

20 MQ1. Adding Numbers Two three digit numbers 6a5 and 3b2 are added together. The result is a multiple of 9. What is the largest possible value of a + b? 4

21 MQ1. Adding Numbers Two three digit numbers 6a5 and 3b2 are added together. The result is a multiple of 9. What is the largest possible value of a + b? 3

22 MQ1. Adding Numbers Two three digit numbers 6a5 and 3b2 are added together. The result is a multiple of 9. What is the largest possible value of a + b? 2

23 MQ1. Adding Numbers Two three digit numbers 6a5 and 3b2 are added together. The result is a multiple of 9. What is the largest possible value of a + b? 1

24 TIME s UP!

25 MQ1. Adding Numbers Two three digit numbers 6a5 and 3b2 are added together. The result is a multiple of 9. What is the largest possible value of a + b? 11

26 HQ2. Sophie Germain Marie-Sophie Germain, born April 1, 1776, was a very accomplished Mathematician. But, as a woman, she was afraid not to be taken seriously so she adopted the pseudonym A. M. Le Rouge B. M. Le Vert C. M. Le Bleu D. M. Le Noir E. M. Le Blanc

27 HQ2. Sophie Germain Marie-Sophie Germain, born April 1, 1776, was a very accomplished Mathematician. But, as a woman, she was afraid not to be taken seriously so she adopted the pseudonym A. M. Le Rouge B. M. Le Vert C. M. Le Bleu D. M. Le Noir 20 seconds E. M. Le Blanc

28 HQ2. Sophie Germain Marie-Sophie Germain, born April 1, 1776, was a very accomplished Mathematician. But, as a woman, she was afraid not to be taken seriously so she adopted the pseudonym A. M. Le Rouge B. M. Le Vert C. M. Le Bleu D. M. Le Noir Time s Up! E. M. Le Blanc

29 HQ2. Sophie Germain Marie-Sophie Germain, born April 1, 1776, was a very accomplished Mathematician. But, as a woman, she was afraid not to be taken seriously so she adopted the pseudonym A. M. Le Rouge B. M. Le Vert C. M. Le Bleu D. M. Le Noir E. M. Le Blanc

30 MQ2. The Power of the Year What is the remainder of dividing by 23

31 MQ2. The Power of the Year What is the remainder of dividing by 23 4

32 MQ2. The Power of the Year What is the remainder of dividing by 23 3

33 MQ2. The Power of the Year What is the remainder of dividing by 23 2

34 MQ2. The Power of the Year What is the remainder of dividing by 23 1

35 TIME s UP!

36 MQ2. The Power of the Year What is the remainder of dividing by 23 12

37 HQ3. Wine Barrels He published Nova stereometria doliorum vinariorum (New solid geometry of wine barrels), a book explaining how to measure the volume of wine barrels. He was A. Bonaventura Cavalieri ( ) B. Pierre Fermat ( ) C. Blaise Pascal ( ) D. Johannes Kepler ( ) E. Imbibus Drunkaster ( )

38 HQ3. Wine Barrels He published Nova stereometria doliorum vinariorum (New solid geometry of wine barrels), a book explaining how to measure the volume of wine barrels. He was A. Bonaventura Cavalieri ( ) B. Pierre Fermat ( ) C. Blaise Pascal ( ) D. Johannes Kepler ( ) E. Imbibus Drunkaster ( ) 20 seconds

39 HQ3. Wine Barrels He published Nova stereometria doliorum vinariorum (New solid geometry of wine barrels), a book explaining how to measure the volume of wine barrels. He was A. Bonaventura Cavalieri ( ) B. Pierre Fermat ( ) C. Blaise Pascal ( ) D. Johannes Kepler ( ) E. Imbibus Drunkaster ( ) Time s Up!

40 HQ3. Wine Barrels He published Nova stereometria doliorum vinariorum (New solid geometry of wine barrels), a book explaining how to measure the volume of wine barrels. He was A. Bonaventura Cavalieri ( ) B. Pierre Fermat ( ) C. Blaise Pascal ( ) D. Johannes Kepler ( ) E. Imbibus Drunkaster ( )

41 MQ3. Equations The roots of the equation x 3 9x 2 + 2x + c = 0 are in arithmetic progression. Find c.

42 MQ3. Equations The roots of the equation x 3 9x 2 + 2x + c = 0 are in arithmetic progression. Find c. 4

43 MQ3. Equations The roots of the equation x 3 9x 2 + 2x + c = 0 are in arithmetic progression. Find c. 3

44 MQ3. Equations The roots of the equation x 3 9x 2 + 2x + c = 0 are in arithmetic progression. Find c. 2

45 MQ3. Equations The roots of the equation x 3 9x 2 + 2x + c = 0 are in arithmetic progression. Find c. 1

46 TIME s UP!

47 MQ3. Equations The roots of the equation x 3 9x 2 + 2x + c = 0 are in arithmetic progression. Find c. c = 48

48 HQ4. Hanging Chains One of the things investigated by Jakob Bernoulli was the shape of a hanging chain. He found it could be modeled by the graph of a A. Parabola B. Hyperbolic Cosine C. Semicircle D. Branch of a Hyperbola E. A section of the sine curve

49 HQ4. Hanging Chains One of the things investigated by Jakob Bernoulli was the shape of a hanging chain. He found it could be modeled by the graph of a A. Parabola B. Hyperbolic Cosine C. Semicircle D. Branch of a Hyperbola 20 seconds E. A section of the sine curve

50 HQ4. Hanging Chains One of the things investigated by Jakob Bernoulli was the shape of a hanging chain. He found it could be modeled by the graph of a A. Parabola B. Hyperbolic Cosine C. Semicircle D. Branch of a Hyperbola Time s Up! E. A section of the sine curve

51 HQ4. Hanging Chains One of the things investigated by Jakob Bernoulli was the shape of a hanging chain. He found it could be modeled by the graph of a A. Parabola B. Hyperbolic Cosine C. Semicircle D. Branch of a Hyperbola E. A section of the sine curve

52 MQ4. Trapezoidal Trappings ABCD is a trapezoid, AB CD. If AB = 14 cm, CD = 25 cm, and the area of triangle ABE is 84 cm 2, what is the area of the trapezoid ABCD in square cm?

53 MQ4. Trapezoidal Trappings ABCD is a trapezoid, AB CD. If AB = 14 cm, CD = 25 cm, and the area of triangle ABE is 84 cm 2, what is the area of the trapezoid ABCD in square cm? 4

54 MQ4. Trapezoidal Trappings ABCD is a trapezoid, AB CD. If AB = 14 cm, CD = 25 cm, and the area of triangle ABE is 84 cm 2, what is the area of the trapezoid ABCD in square cm? 3

55 MQ4. Trapezoidal Trappings ABCD is a trapezoid, AB CD. If AB = 14 cm, CD = 25 cm, and the area of triangle ABE is 84 cm 2, what is the area of the trapezoid ABCD in square cm? 2

56 MQ4. Trapezoidal Trappings ABCD is a trapezoid, AB CD. If AB = 14 cm, CD = 25 cm, and the area of triangle ABE is 84 cm 2, what is the area of the trapezoid ABCD in square cm? 1

57 TIME s UP!

58 MQ4. Trapezoidal Trappings ABCD is a trapezoid, AB CD. If AB = 14 cm, CD = 25 cm, and the area of triangle ABE is 84 cm 2, what is the area of the trapezoid ABCD in square cm? ABCD = 234 cm 2

59 HQ5. Rolling Rolling The curve described by a point on the rim of a circle that rolls without slipping is called A. Cycloid B. Circulant C. Cissoid D. Tractrix E. Clockoid

60 HQ5. Rolling Rolling The curve described by a point on the rim of a circle that rolls without slipping is called A. Cycloid B. Circulant C. Cissoid D. Tractrix E. Clockoid 20 seconds

61 HQ5. Rolling Rolling The curve described by a point on the rim of a circle that rolls without slipping is called A. Cycloid B. Circulant C. Cissoid D. Tractrix E. Clockoid Time s Up!

62 HQ5. Rolling Rolling The curve described by a point on the rim of a circle that rolls without slipping is called A. Cycloid B. Circulant C. Cissoid D. Tractrix E. Clockoid

63 MQ5. Tangents Two circles centered at B and A are tangent to each other and to two lines emanating from P. If PA = 15 and the radius of the circle at A is 4, then the radius of the circle at B can be expressed as a fraction a where a, b are positive integers with no common b denominator other than 1. Find: a + b

64 MQ5. Tangents Two circles centered at B and A are tangent to each other and to two lines emanating from P. If PA = 15 and the radius of the circle at A is 4, then the radius of the circle at B can be expressed as a fraction a where a, b are positive integers with no common b denominator other than 1. Find: a + b 4

65 MQ5. Tangents Two circles centered at B and A are tangent to each other and to two lines emanating from P. If PA = 15 and the radius of the circle at A is 4, then the radius of the circle at B can be expressed as a fraction a where a, b are positive integers with no common b denominator other than 1. Find: a + b 3

66 MQ5. Tangents Two circles centered at B and A are tangent to each other and to two lines emanating from P. If PA = 15 and the radius of the circle at A is 4, then the radius of the circle at B can be expressed as a fraction a where a, b are positive integers with no common b denominator other than 1. Find: a + b 2

67 MQ5. Tangents Two circles centered at B and A are tangent to each other and to two lines emanating from P. If PA = 15 and the radius of the circle at A is 4, then the radius of the circle at B can be expressed as a fraction a where a, b are positive integers with no common b denominator other than 1. Find: a + b 1

68 TIME s UP!

69 MQ5. Tangents Two circles centered at B and A are tangent to each other and to two lines emanating from P. If PA = 15 and the radius of the circle at A is 4, then the radius of the circle at B can be expressed as a fraction a where a, b are positive integers with no common b denominator other than 1. Find: a + b = 63

70 HQ6. Pendulum Penduli Because the cycloid is also the tautochrone (don t worry about this name), he devised a pendulum clock in which the bob was forced to describe an inverted cycloidal path. He was A. Galileo Galilei B. Christiaan Huygens C. Isaak Newton D. Evangelista Torricelli E. Leonhard Euler

71 HQ6. Pendulum Penduli Because the cycloid is also the tautochrone (don t worry about this name), he devised a pendulum clock in which the bob was forced to describe an inverted cycloidal path. He was A. Galileo Galilei B. Christiaan Huygens C. Isaak Newton D. Evangelista Torricelli E. Leonhard Euler 20 seconds

72 HQ6. Pendulum Penduli Because the cycloid is also the tautochrone (don t worry about this name), he devised a pendulum clock in which the bob was forced to describe an inverted cycloidal path. He was A. Galileo Galilei B. Christiaan Huygens C. Isaak Newton D. Evangelista Torricelli E. Leonhard Euler Time s Up!

73 HQ6. Pendulum Penduli Because the cycloid is also the tautochrone (don t worry about this name), he devised a pendulum clock in which the bob was forced to describe an inverted cycloidal path. He was A. Galileo Galilei B. Christiaan Huygens C. Isaak Newton D. Evangelista Torricelli E. Leonhard Euler Huygens ( )

74 MQ6. Fenced Fields Farmer Jones wants to fence off a rectangular section of his field, where he wants to plant potatoes. The area of this rectangle should be 1260 square meters and its diagonal should be 53 meters long. What is the dimension, in meters, of its longest side?

75 MQ6. Fenced Fields Farmer Jones wants to fence off a rectangular section of his field, where he wants to plant potatoes. The area of this rectangle should be 1260 square meters and its diagonal should be 53 meters long. What is the dimension, in meters, of its longest side? 4

76 MQ6. Fenced Fields Farmer Jones wants to fence off a rectangular section of his field, where he wants to plant potatoes. The area of this rectangle should be 1260 square meters and its diagonal should be 53 meters long. What is the dimension, in meters, of its longest side? 3

77 MQ6. Fenced Fields Farmer Jones wants to fence off a rectangular section of his field, where he wants to plant potatoes. The area of this rectangle should be 1260 square meters and its diagonal should be 53 meters long. What is the dimension, in meters, of its longest side? 2

78 MQ6. Fenced Fields Farmer Jones wants to fence off a rectangular section of his field, where he wants to plant potatoes. The area of this rectangle should be 1260 square meters and its diagonal should be 53 meters long. What is the dimension, in meters, of its longest side? 1

79 TIME s UP!

80 MQ6. Fenced Fields Farmer Jones wants to fence off a rectangular section of his field, where he wants to plant potatoes. The area of this rectangle should be 1260 square meters and its diagonal should be 53 meters long. What is the dimension, in meters, of its longest side? 45 m

81 HQ7. Under the Tower of Pisa Leonardo Pisano, better known as Fibonacci, published in 1202 the important book titled Liber Abaci. One of its main purposes was, according to the author, to A. Teach the rules of the abacus. B. Teach the basics of arithmetics. C. Teach to operate with Roman numerals. D. Teach farmers how to manage rabbits. E. Introduce the Indian numerals to Europe.

82 HQ7. Under the Tower of Pisa Leonardo Pisano, better known as Fibonacci, published in 1202 the important book titled Liber Abaci. One of its main purposes was, according to the author, to A. Teach the rules of the abacus. B. Teach the basics of arithmetics. C. Teach to operate with Roman numerals. D. Teach farmers how to manage rabbits. E. Introduce the Indian numerals to Europe. 20 seconds

83 HQ7. Under the Tower of Pisa Leonardo Pisano, better known as Fibonacci, published in 1202 the important book titled Liber Abaci. One of its main purposes was, according to the author, to A. Teach the rules of the abacus. B. Teach the basics of arithmetics. C. Teach to operate with Roman numerals. D. Teach farmers how to manage rabbits. E. Introduce the Indian numerals to Europe. Time s Up!

84 HQ7. Under the Tower of Pisa Leonardo Pisano, better known as Fibonacci, published in 1202 the important book titled Liber Abaci. One of its main purposes was, according to the author, to A. Teach the rules of the abacus. B. Teach the basics of arithmetics. C. Teach to operate with Roman numerals. D. Teach farmers how to manage rabbits. E. Introduce the Indian numerals to Europe.

85 MQ7. Fibonacci mod 11 The Fibonacci sequence is the sequence f 1, f 2, f 3, that begins with 1, 1, after which each term is the sum of the two preceding ones. So f 1 = 1, f 2 = 1, f 3 = 2, f 4 = 3, f 5 = 5, f 6 = 8, etc.; in general f n = f n 1 + f n 2 once n 2. We form a new sequence a n by a n = the remainder of dividing f n by 11. This is a periodic sequence; that is, it has the form a 1, a 2,, a p for some p, and then repeats. Find p + a 1 + a a p

86 MQ7. Fibonacci mod 11 The Fibonacci sequence is the sequence f 1, f 2, f 3, that begins with 1, 1, after which each term is the sum of the two preceding ones. So f 1 = 1, f 2 = 1, f 3 = 2, f 4 = 3, f 5 = 5, f 6 = 8, etc.; in general f n = f n 1 + f n 2 once n 2. We form a new sequence a n by a n = the remainder of dividing f n by 11. This is a periodic sequence; that is, it has the form a 1, a 2,, a p for some p, and then repeats. Find p + a 1 + a a p 4

87 MQ7. Fibonacci mod 11 The Fibonacci sequence is the sequence f 1, f 2, f 3, that begins with 1, 1, after which each term is the sum of the two preceding ones. So f 1 = 1, f 2 = 1, f 3 = 2, f 4 = 3, f 5 = 5, f 6 = 8, etc.; in general f n = f n 1 + f n 2 once n 2. We form a new sequence a n by a n = the remainder of dividing f n by 11. This is a periodic sequence; that is, it has the form a 1, a 2,, a p for some p, and then repeats. Find p + a 1 + a a p 3

88 MQ7. Fibonacci mod 11 The Fibonacci sequence is the sequence f 1, f 2, f 3, that begins with 1, 1, after which each term is the sum of the two preceding ones. So f 1 = 1, f 2 = 1, f 3 = 2, f 4 = 3, f 5 = 5, f 6 = 8, etc.; in general f n = f n 1 + f n 2 once n 2. We form a new sequence a n by a n = the remainder of dividing f n by 11. This is a periodic sequence; that is, it has the form a 1, a 2,, a p for some p, and then repeats. Find p + a 1 + a a p 2

89 MQ7. Fibonacci mod 11 The Fibonacci sequence is the sequence f 1, f 2, f 3, that begins with 1, 1, after which each term is the sum of the two preceding ones. So f 1 = 1, f 2 = 1, f 3 = 2, f 4 = 3, f 5 = 5, f 6 = 8, etc.; in general f n = f n 1 + f n 2 once n 2. We form a new sequence a n by a n = the remainder of dividing f n by 11. This is a periodic sequence; that is, it has the form a 1, a 2,, a p for some p, and then repeats. Find p + a 1 + a a p 1

90 TIME s UP!

91 MQ7. Fibonacci mod 11 The Fibonacci sequence is the sequence f 1, f 2, f 3, that begins with 1, 1, after which each term is the sum of the two preceding ones. So f 1 = 1, f 2 = 1, f 3 = 2, f 4 = 3, f 5 = 5, f 6 = 8, etc.; in general f n = f n 1 + f n 2 once n 2. We form a new sequence a n by a n = the remainder of dividing f n by 11. This is a periodic sequence; that is, it has the form a 1, a 2,, a p for some p, and then repeats. Find p + a 1 + a a p = 43

92 HQ8. Archimedes the Great When Archimedes, according to the legend, jumped out of his bathtub running naked through the streets of Syracuse shouting Eureka! (I found it!), what had he discovered? A. A fundamental law of hydrostatics B. A fundamental law of thermodynamics C. A fundamental law of kinetics D. A fundamental law of fluid dynamics E. The place where his bathtub was leaking.

93 HQ8. Archimedes the Great When Archimedes, according to the legend, jumped out of his bathtub running naked through the streets of Syracuse shouting Eureka! (I found it!), what had he discovered? A. A fundamental law of hydrostatics B. A fundamental law of thermodynamics C. A fundamental law of kinetics D. A fundamental law of fluid dynamics E. The place where his bathtub was leaking. 20 seconds

94 HQ8. Archimedes the Great When Archimedes, according to the legend, jumped out of his bathtub running naked through the streets of Syracuse shouting Eureka! (I found it!), what had he discovered? A. A fundamental law of hydrostatics B. A fundamental law of thermodynamics C. A fundamental law of kinetics D. A fundamental law of fluid dynamics E. The place where his bathtub was leaking. Time s Up!

95 HQ8. Archimedes the Great When Archimedes, according to the legend, jumped out of his bathtub running naked through the streets of Syracuse shouting Eureka! (I found it!), what had he discovered? A. A fundamental law of hydrostatics B. A fundamental law of thermodynamics C. A fundamental law of kinetics D. A fundamental law of fluid dynamics E. The place where his bathtub was leaking.

96 MQ8. Lucky Sevens What is the sum of all the multiples of 7 less than 500?

97 MQ8. Lucky Sevens What is the sum of all the multiples of 7 less than 500? 4

98 MQ8. Lucky Sevens What is the sum of all the multiples of 7 less than 500? 3

99 MQ8. Lucky Sevens What is the sum of all the multiples of 7 less than 500? 2

100 MQ8. Lucky Sevens What is the sum of all the multiples of 7 less than 500? 1

101 MQ8. Lucky Sevens What is the sum of all the multiples of 7 less than 500? 2

102 TIME s UP!

103 MQ8. Lucky Sevens What is the sum of all the multiples of 7 less than 500? S = = = 17892

104 HQ9. The End of Alexandria In many ways the death of Hypatia, the first female mathematician of which there is a record, marks the end of one of the most brilliant periods in human history, the Hellenistic era. It happened in A. The year 22 BCE. B. The year 175 of our era C. The year 314 of our era D. The year 415 of our era E. The year 728 of our era

105 HQ9. The End of Alexandria In many ways the death of Hypatia, the first female mathematician of which there is a record, marks the end of one of the most brilliant periods in human history, the Hellenistic era. It happened in A. The year 22 BCE. B. The year 175 of our era C. The year 314 of our era D. The year 415 of our era E. The year 728 of our era 20 seconds

106 HQ9. The End of Alexandria In many ways the death of Hypatia, the first female mathematician of which there is a record, marks the end of one of the most brilliant periods in human history, the Hellenistic era. It happened in A. The year 22 BCE. B. The year 175 of our era C. The year 314 of our era D. The year 415 of our era E. The year 728 of our era Time s Up!

107 HQ9. The End of Alexandria In many ways the death of Hypatia, the first female mathematician of which there is a record, marks the end of one of the most brilliant periods in human history, the Hellenistic era. It happened in A. The year 22 BCE. B. The year 175 of our era C. The year 314 of our era D. The year 415 of our era E. The year 728 of our era

108 MQ9. Trains Chugging Along Train A leaves the town of Utopia going toward the city of Noplacia. At the exact same time, train B leaves Noplacia in direction to Utopia. Train A reaches Noplacia 32 hours after the two trains meet on the way; train B is in Utopia 50 hours after the meeting. How many hours did it take train B to get from Noplacia to Utopia?

109 MQ9. Trains Chugging Along Train A leaves the town of Utopia going toward the city of Noplacia. At the exact same time, train B leaves Noplacia in direction to Utopia. Train A reaches Noplacia 32 hours after the two trains meet on the way; train B is in Utopia 50 hours after the meeting. How many hours did it take train B to get from Noplacia to Utopia? 5

110 MQ9. Trains Chugging Along Train A leaves the town of Utopia going toward the city of Noplacia. At the exact same time, train B leaves Noplacia in direction to Utopia. Train A reaches Noplacia 32 hours after the two trains meet on the way; train B is in Utopia 50 hours after the meeting. How many hours did it take train B to get from Noplacia to Utopia? 4

111 MQ9. Trains Chugging Along Train A leaves the town of Utopia going toward the city of Noplacia. At the exact same time, train B leaves Noplacia in direction to Utopia. Train A reaches Noplacia 32 hours after the two trains meet on the way; train B is in Utopia 50 hours after the meeting. How many hours did it take train B to get from Noplacia to Utopia? 3

112 MQ9. Trains Chugging Along Train A leaves the town of Utopia going toward the city of Noplacia. At the exact same time, train B leaves Noplacia in direction to Utopia. Train A reaches Noplacia 32 hours after the two trains meet on the way; train B is in Utopia 50 hours after the meeting. How many hours did it take train B to get from Noplacia to Utopia? 2

113 MQ9. Trains Chugging Along Train A leaves the town of Utopia going toward the city of Noplacia. At the exact same time, train B leaves Noplacia in direction to Utopia. Train A reaches Noplacia 32 hours after the two trains meet on the way; train B is in Utopia 50 hours after the meeting. How many hours did it take train B to get from Noplacia to Utopia? 1

114 TIME s UP!

115 MQ9. Trains Chugging Along Train A leaves the town of Utopia going toward the city of Noplacia. At the exact same time, train B leaves Noplacia in direction to Utopia. Train A reaches Noplacia 32 hours after the two trains meet on the way; train B is in Utopia 50 hours after the meeting. How many hours did it take train B to get from Noplacia to Utopia? 90 hours

116 HQ10. Apollonius Apollonius of Perga (~ BCE) solved the following problem, known as the problem of Apollonius. A. Draw a circle tangent to three given circles B. Find the solution of quadratic equations C. Construct the regular pentagon. D. Draw the tangent to a parabola from a given point. E. Measure the circumference of the earth.

117 HQ10. Apollonius Apollonius of Perga (~ BCE) solved the following problem, known as the problem of Apollonius. A. Draw a circle tangent to three given circles B. Find the solution of quadratic equations C. Construct the regular pentagon. D. Draw the tangent to a parabola from a given point. E. Measure the circumference of the earth. 20 seconds

118 HQ10. Apollonius Apollonius of Perga (~ BCE) solved the following problem, known as the problem of Apollonius. A. Draw a circle tangent to three given circles B. Find the solution of quadratic equations C. Construct the regular pentagon. D. Draw the tangent to a parabola from a given point. E. Measure the circumference of the earth. Time s Up!

119 HQ10. Apollonius Apollonius of Perga (~ BCE) solved the following problem, known as the problem of Apollonius. A. Draw a circle tangent to three given circles B. Find the solution of quadratic equations C. Construct the regular pentagon. D. Draw the tangent to a parabola from a given point. E. Measure the circumference of the earth.

120 MQ10. Quadrilateral Question The diagonals of quadrilateral ABCD intersect at O. If AO = 8, BO = 4, CO = 3, DO = 6, and AB = 6 what is AD? There could be a square root involved.

121 MQ10. Quadrilateral Question The diagonals of quadrilateral ABCD intersect at O. If AO = 8, BO = 4, CO = 3, DO = 6, and AB = 6 what is AD? There could be a square root involved. 4

122 MQ10. Quadrilateral Question The diagonals of quadrilateral ABCD intersect at O. If AO = 8, BO = 4, CO = 3, DO = 6, and AB = 6 what is AD? There could be a square root involved. 3

123 MQ10. Quadrilateral Question The diagonals of quadrilateral ABCD intersect at O. If AO = 8, BO = 4, CO = 3, DO = 6, and AB = 6 what is AD? There could be a square root involved. 2

124 MQ10. Quadrilateral Question The diagonals of quadrilateral ABCD intersect at O. If AO = 8, BO = 4, CO = 3, DO = 6, and AB = 6 what is AD? There could be a square root involved. 1

125 TIME s UP!

126 MQ10. Quadrilateral Question The diagonals of quadrilateral ABCD intersect at O. If AO = 8, BO = 4, CO = 3, DO = 6, and AB = 6 what is AD? There could be a square root involved. AD = 166

127 HQ11. Abel ( ) Niels Henryk Abel, who died tragically young, is one of the great mathematicians of the 19 th Century. By nationality he was A. Albanian B. Danish C. Finnish D. Norwegian E. Swedish

128 HQ11. Abel ( ) Niels Henryk Abel, who died tragically young, is one of the great mathematicians of the 19 th Century. By nationality he was A. Albanian B. Danish C. Finnish D. Norwegian E. Swedish 20 seconds

129 HQ11. Abel ( ) Niels Henryk Abel, who died tragically young, is one of the great mathematicians of the 19 th Century. By nationality he was A. Albanian B. Danish C. Finnish D. Norwegian E. Swedish Time s Up!

130 HQ11. Abel ( ) Niels Henryk Abel, who died tragically young, is one of the great mathematicians of the 19 th Century. By nationality he was A. Albanian B. Danish C. Finnish D. Norwegian E. Swedish

131 MQ11. Eventful Eleven How many five digit numbers n are there with the following property: If q is the quotient of dividing n by 100 and r is the remainder of that division, then q + r is a multiple of 11.

132 MQ11. Eventful Eleven How many five digit numbers n are there with the following property: If q is the quotient of dividing n by 100 and r is the remainder of that division, then q + r is a multiple of 11. 4

133 MQ11. Eventful Eleven How many five digit numbers n are there with the following property: If q is the quotient of dividing n by 100 and r is the remainder of that division, then q + r is a multiple of 11. 3

134 MQ11. Eventful Eleven How many five digit numbers n are there with the following property: If q is the quotient of dividing n by 100 and r is the remainder of that division, then q + r is a multiple of 11. 2

135 MQ11. Eventful Eleven How many five digit numbers n are there with the following property: If q is the quotient of dividing n by 100 and r is the remainder of that division, then q + r is a multiple of 11. 1

136 TIME s UP!

137 MQ11. Eventful Eleven How many five digit numbers n are there with the following property: If q is the quotient of dividing n by 100 and r is the remainder of that division, then q + r is a multiple of

138 HQ12. How Pi Got Its Name The Greek letter π to denote the ratio of the circumference of a circle to its diameter was first used by A. Diophantus of Alexandria (c ) B. Leonhard Euler of Switzerland ( ) C. Isaak Newton of England ( ) D. Nicola Oresme of France ( ) E. William Jones of Wales ( )

139 HQ12. How Pi Got Its Name The Greek letter π to denote the ratio of the circumference of a circle to its diameter was first used by A. Diophantus of Alexandria (c ) B. Leonhard Euler of Switzerland ( ) C. Isaak Newton of England ( ) D. Nicola Oresme of France ( ) E. William Jones of Wales ( ) 20 seconds

140 HQ12. How Pi Got Its Name The Greek letter π to denote the ratio of the circumference of a circle to its diameter was first used by A. Diophantus of Alexandria (c ) B. Leonhard Euler of Switzerland ( ) C. Isaak Newton of England ( ) D. Nicola Oresme of France ( ) E. William Jones of Wales ( ) Time s Up!

141 HQ12. How Pi Got Its Name The Greek letter π to denote the ratio of the circumference of a circle to its diameter was first used by A. Diophantus of Alexandria (c ) B. Leonhard Euler of Switzerland ( ) C. Isaak Newton of England ( ) D. Nicola Oresme of France ( ) E. William Jones of Wales ( )

142 MQ12. The Chorded Circle Three chords, of respective lengths 6, 8, and 10 just go around a circle. The radius r of the circle satisfies an equation of the form r 3 ar b = 0 where a, b are positive integers. Find them.

143 MQ12. The Chorded Circle Three chords, of respective lengths 6, 8, and 10 just go around a circle. The radius r of the circle satisfies an equation of the form r 3 ar b = 0 where a, b are positive integers. Find a + b. 4

144 MQ12. The Chorded Circle Three chords, of respective lengths 6, 8, and 10 just go around a circle. The radius r of the circle satisfies an equation of the form r 3 ar b = 0 where a, b are positive integers. Find a + b. 3

145 MQ12. The Chorded Circle Three chords, of respective lengths 6, 8, and 10 just go around a circle. The radius r of the circle satisfies an equation of the form r 3 ar b = 0 where a, b are positive integers. Find a + b. 2

146 MQ12. The Chorded Circle Three chords, of respective lengths 6, 8, and 10 just go around a circle. The radius r of the circle satisfies an equation of the form r 3 ar b = 0 where a, b are positive integers. Find a + b. 1

147 TIME s UP!

148 MQ12. The Chorded Circle Three chords, of respective lengths 6, 8, and 10 just go around a circle. The radius r of the circle satisfies an equation of the form r 3 ar b = 0 where a, b are positive integers. Find a + b. a = 50, b = 120, a + b = 170