Higher mathematics test VK1

Task 1

Question 1. Where was the birth of mathematics as a science?

1. in a primitive society;

2. in Egypt and Babylonia;

3. in Ancient Greece;

4. in the countries of Asia and the Arab world;

5. in ancient India.

Question 2. What book is rightfully considered the first textbook in mathematics?

1. "Beginnings" of Euclid;

2. "Ars Magna" by D. Cardano;

3. "Mathematical Principles of Natural Philosophy" by I. Newton;

4. "Arithmetic" by LF Magnitsky;

5. "Calculus of grains of sand" by Archimedes.

Question 3. Which of the numbers is not valid?

1;

2. -3;

3. √3;

4. √-3;

5. -√3.

Question 4. Which of the numbers is not rational?

1;

2. -2;

3. √2;

4. 1/2;

5. all numbers are rational.

Question 5. For the numbers a and b, find the true statements if a = 3,2712821 ..., b = 2,272727 ...

1.a ¹ b;

2. a - an irrational number, b - a rational number;

3. a and b belong to the set of real numbers;

4. a and b are not imaginary numbers;

5. all previous statements are correct.



Task 2

Question 1. How can you formulate the main directions of mathematical research in the social sciences?

1. Research in the part of an accurate description of the functioning of social systems and their parts and research into the influence of conscious influence (management) on the functioning of social structures and the course of social processes;

2. Research in the field of economics;

3. Research in the field of linear programming;

4. Research in the field of nonlinear programming;

5. Research in the field of cybernetics.

Question 2. What is the assumption underlying the use of the matrix of survival rates and fertility rates?

1. Assumption of the absence of wars;

2. Assumption of the absence of natural disasters;

3. Assumption of the invariability of survival and fertility;

4. Assumption of a homogeneous age structure;

5. Assumption of the cessation of epidemics in the considered time interval;

Question 3. How is it most often advisable to solve the problem that arises when it is necessary to take into account additional factors in a very large and complex economic model?

1. Take into account all the available information in the model;

2. Simplify the model, then take into account additional factors;

3. Introduce new categories and dependencies into the model;

4. Try to highlight (develop) sub-models, which will take into account additional factors;

5. Develop the model again taking into account additional factors;

Question 4. Which of the formulations is the definition?

1. There are at least two points;

2. Each segment can be continued for each of its ends;

3. Two segments equal to the same segment are equal;

4. Line AB is a figure that is the union of all segments containing points A and B;

5. Each straight line divides the plane into two half-planes;

Question 5. Find the false statement: Two triangles are equal if they have correspondingly equal

1.three sides;

2. side and two adjacent corners;

3. two sides and the angle between them;

4. three corners;

5. hypotenuse and leg.



Task 3

Question 1. What statement contradicts the V postulate of Euclid?

1. The sum of the angles of the triangle is 180 °;

2. There are similar unequal triangles;

3. The sum of the angles of any quadrangle is less than 360 °;

4. The set of points lying on one side of a given straight line at the same distance from it is a straight line;

5. Two parallel straight lines at the intersection of their third straight line form equal corresponding angles.

Question 2. Which of the statements is Lobachevsky's axiom of parallelism?

1. Two lines parallel to the third line are parallel to each other;

2. Two straight lines perpendicular to the third straight line are parallel;

3. Lines not having common points on