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# The final exam of 100 questions RFEI Mathematics

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**09.06.2011**

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# Description

Final exam RFEI Mathematics 100 questions.

1.Kogo considered the ancestor of modern mathematics?

2. What is the geometry in the Greek language?

3.Chemu is the ratio of the areas of such circular segments Hippocrates?

4.Kem laid axioms of plane geometry?

5. As of the above geometrical bodies is body Plato?

6.Chemu equal to the number of faces (planes) hexahedron?

7. What determines the Euclidean algorithm?

8. As of the listed products is called the most famous work of Euclid?

9. What Euclid understood the expression A?

10. In what respect are divided medians of a triangle intersect at a point?

11. What is depicted on the tombstone of Archimedes?

12. How it is called the first textbook on geometry published in Russia?

13.Komu of the scientists credited with the creation of analytic geometry?

14.Chem engaged in analytic geometry?

15.Secheniya some of the bodies examined Apollonius of Perga: for hyperbole or an ellipse, or a parabola?

16. In what is the "principle of Cavalieri"?

17.Kakaya of the curves defined by the equation xy = k2?

18. In the writings of mathematicians for the first time there are such concepts projective

geometry as promising, projective, etc..?

19.Kakuyu of the three famous problems of antiquity Archimedes decided to open them using a spiral?

20. As the curve called the curve "with a strong character"?

21. As the opening Moebius reminds us that it is one of the founders of our modern topology?

22. In what is the contribution of Newton in the development of analytic geometry?

23.Komu of the great mathematicians of the primacy belongs to the thought that the parallel postulate of Euclid is an independent axiom?

24. As called geometry, NI Lobachevsky?

25.Kak is a surface on which the many axioms and theorems of geometry Lobachevsky?

26.Chem engaged topology?

27.Kto of the great mathematicians showed that Lobachevsky geometry can be interpreted as a projective geometry with the metric Keli?

28.Chto is a model of plane geometry in Rome?

29. In what is a major contribution of Henri Poincare in the development of mathematics?

30.Komu belongs statement: "Everything is a number"?

31. As Euclid considered the theory of quadratic equations in the "Elements"?

32.Cherez river need to carry three: wolf, goat and cabbage; on a boat, except for the carrier can fit only one of the three. How to transport them to the goat could not eat cabbage, the wolf could not eat the goat?

33. In what is the method of Ferrari?

34.Kem were invented logarithms?

35.Kakim way was obtained class of complex numbers?

36.Kakim property has imaginary unit?

37.Kem generally installed Vieta theorem?

38.Ne solving the quadratic equation, determine which of them has the roots (3) and 2?

39.Kem proved Fermat's Last Theorem for the case n = 3?

40. In what year was completely published proof of Fermat's Last Theorem?

# Additional information

80. In rozygryshnoy urn just 20 balls. Of these, 5 green, 5 red, the other white. What is the probability of drawing a white ball from the urn?

81.Veroyatnost occurrence of an event can not be equal?

82.Kak often called the theory of probability?

83.S what has caused the emergence of the theory of probability?

84.Kto mathematicians is the author of the axioms of probability theory?

85.Kakie event called the impossible?

86.Kto mathematician is the founder of the theory of probability?

87.Chto will be the product of events A and B, if the event is A = [all the students of the institute], the event B = [students of the institute dealing with variety dances]?

88.Chto will be the sum of the two events in the previous problem?

89.Igralny dice thrown once. What is the probability that the top face fall the number of points equal to 7?

90.Kak loss can be characterized by an eagle or tails at the coin toss?

91.Dlya of the arrow hit probability is 0.7. What is the probability of a miss for the shooter?

92.Kakoe equality corresponds to the formula of probabilities independent events?

93.Kakova probability of getting an even number when tossing dice?

94.Komu mathematicians belongs championship in the Introduction of the term "expectation"?

95.Nayti expected number of defective items in a batch of 10,000 items, if each product may be defective with a probability of 0.005?

96.Chemu equal to the expectation of a random variable if its first value x1 = -2 she accepts with probability p1 = 1/3, and the second value x2 = 4 it accepts with probability p2 = 2/3.

97.Chemu equal to the variance in the previous problem?

98.Kem was first set law of large numbers?

99. "Life is beautiful only because of two things - the study of mathematics and teaching mathematics." To mathematicians owns this saying?

100. As the highest international award is given for achievements in the field of mathematics?