Final exam RFEI Mathematics 100 questions
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Final exam RFEI Mathematics 100 questions.
1. Who is considered to be the founder of modern mathematics?
2.What does geometry mean in translation from Greek?
3. What is the ratio of the areas of similar circular segments according to Hippocrates?
4. By whom were the axioms of planimetry laid down?
5. Which of the listed geometric bodies is Plato's body?
6. What is the number of faces (planes) of the hexahedron?
7. What does Euclid's algorithm determine?
8. Which of the following works is called the most famous work of Euclid?
9. What did Euclid understand by the expression A?
10. In what ratio are the medians of the triangle divided when they intersect at a point?
11. What is depicted on the tombstone of Archimedes?
12. What was the name of the first textbook on geometry published in Russia?
13. Which scientist is credited with creating analytical geometry?
14.What does analytic geometry do?
15. Sections of which of the bodies was considered by Apollonius of Perga: to obtain a hyperbola or an ellipse, or a parabola?
16. What is the Cavalieri Principle?
17. Which of the curves is given by the equation xy = k2?
18 In the works of which of the mathematicians, such concepts of projective
geometry, as perspective, projectivity, etc.?
19. Which of the three famous problems of antiquity did Archimedes solve with the help of the spiral he discovered?
20. What kind of curve is called a “hard character” curve?
21. What discovery of Moebius reminds us that he is one of the founders of our modern topology?
22. What is Newton's contribution to the development of analytic geometry?
23. Which of the great mathematicians belongs to the primacy in the idea that the postulate of parallel Euclid is an independent axiom?
24. What was the name of the geometry constructed by N.I. Lobachevsky?
25. What is the name of the surface on which many of the axioms and theorems of Lobachevsky's geometry hold?
26. What does topology do?
27. Which of the great mathematicians showed that Lobachevsky's geometries can be interpreted as projective geometries with the Keli metric?
28. What is a model in Riemann planimetry?
29. What is the main contribution of Henri Poincaré to the development of mathematics?
30. Who owns the statement: "Everything is number"?
31. How did Euclid consider the theory of quadratic equations in the "Elements"?
32. Three people must be transported across the river: a wolf, a goat and a head of cabbage; the boat, apart from the carrier, can only fit one of the three. How to transport them so that the goat cannot eat the cabbage, and the wolf cannot eat the goat?
33. What is the Ferrari Method?
34. Who Invented Logarithms?
35. How was the class of complex numbers obtained?
36. What property does an imaginary unit have?
37. Who established Vieta's theorem in general terms?
38. Without solving the quadratic equation, determine which of them has roots (-3) and 2?
39. Who proved Fermat's Last Theorem for the case n = 3?
40. In what year was the proof of Fermat's Last Theorem published in full?
1. Who is considered to be the founder of modern mathematics?
2.What does geometry mean in translation from Greek?
3. What is the ratio of the areas of similar circular segments according to Hippocrates?
4. By whom were the axioms of planimetry laid down?
5. Which of the listed geometric bodies is Plato's body?
6. What is the number of faces (planes) of the hexahedron?
7. What does Euclid's algorithm determine?
8. Which of the following works is called the most famous work of Euclid?
9. What did Euclid understand by the expression A?
10. In what ratio are the medians of the triangle divided when they intersect at a point?
11. What is depicted on the tombstone of Archimedes?
12. What was the name of the first textbook on geometry published in Russia?
13. Which scientist is credited with creating analytical geometry?
14.What does analytic geometry do?
15. Sections of which of the bodies was considered by Apollonius of Perga: to obtain a hyperbola or an ellipse, or a parabola?
16. What is the Cavalieri Principle?
17. Which of the curves is given by the equation xy = k2?
18 In the works of which of the mathematicians, such concepts of projective
geometry, as perspective, projectivity, etc.?
19. Which of the three famous problems of antiquity did Archimedes solve with the help of the spiral he discovered?
20. What kind of curve is called a “hard character” curve?
21. What discovery of Moebius reminds us that he is one of the founders of our modern topology?
22. What is Newton's contribution to the development of analytic geometry?
23. Which of the great mathematicians belongs to the primacy in the idea that the postulate of parallel Euclid is an independent axiom?
24. What was the name of the geometry constructed by N.I. Lobachevsky?
25. What is the name of the surface on which many of the axioms and theorems of Lobachevsky's geometry hold?
26. What does topology do?
27. Which of the great mathematicians showed that Lobachevsky's geometries can be interpreted as projective geometries with the Keli metric?
28. What is a model in Riemann planimetry?
29. What is the main contribution of Henri Poincaré to the development of mathematics?
30. Who owns the statement: "Everything is number"?
31. How did Euclid consider the theory of quadratic equations in the "Elements"?
32. Three people must be transported across the river: a wolf, a goat and a head of cabbage; the boat, apart from the carrier, can only fit one of the three. How to transport them so that the goat cannot eat the cabbage, and the wolf cannot eat the goat?
33. What is the Ferrari Method?
34. Who Invented Logarithms?
35. How was the class of complex numbers obtained?
36. What property does an imaginary unit have?
37. Who established Vieta's theorem in general terms?
38. Without solving the quadratic equation, determine which of them has roots (-3) and 2?
39. Who proved Fermat's Last Theorem for the case n = 3?
40. In what year was the proof of Fermat's Last Theorem published in full?
Additional Information
80 There are only 20 balls in the drawing box. Of these, 5 are green, 5 are red, the rest are white. What is the probability of removing the white ball from the urn?81. The probability of the occurrence of some event cannot be equal?
82. What is the theory of probability often called?
83. What is the origin of the theory of probability?
84. Which mathematician is the author of the axiomatics of probability theory?
85. What events are called impossible?
86. Which mathematician is the founders of the theory of probability?
87. What will be the product of events A and B, if event A = [all students of the institute], event B = [students of the institute doing pop dancing]?
88. What will be the sum of two events in the condition of the previous problem?
89 The dice is rolled once. What is the probability that the number of points equal to 7 will fall on the upper edge?
90. How can you characterize the falling heads or tails on a coin toss?
91.For this shooter, the probability of hitting the target is 0,7. What is the probability of a miss for a given shooter?
92. Which of the equalities corresponds to the formula for multiplying the probabilities of independent events?
93. What is the probability of getting an even number on a toss of a die?
94. Which mathematician is the leader in the introduction of the term "mathematical expectation"?
95. Find the mathematical expectation of the number of defective items in a batch of 10 items, if each item can be defective with a probability of 000?
96. What is the mathematical expectation of some random variable, if it takes its first value x1 = -2 with probability p1 = 1/3, and the second value x2 = 4 it takes with probability p2 = 2/3?
97. What is the variance in the condition of the previous problem?
98. Who was the first to establish the law of large numbers?
99. "Life is beautiful thanks to only two things - studying mathematics and teaching mathematics." Which mathematician does this saying belong to?
100. What is the highest international award for achievement in mathematics?