Волинський національний університет імені Лесі Українки

Тест ::: 2025 Математика, Математика СО 4 курс (іспит 8 семестр)

Тема :: Текст

1. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
   Computers have become _______ because the modern world is the age of high technologies. Different types, sizes, names of computers _______. They are used for computing in many ways, for example, computer helps us to do _______, to receive, store and transfer any kind of information, to work on the Internet, to communicate with people all over the world... It's really _______ of all usages of the computer.
   We daily deal with different computer systems, as calculators, car electronics, mobile phones, timer in the microwave or the washing machine, the programmer inside the TV set and so on. The impact _______ is felt in every area – government, business, science, medicine, sport, industry, agriculture, entertainment and at home.
   1. of the computer on our society
   2. a part of our everyday life
   3. a unique typewriter
   4. different mathematical and logical operations
   5. find uses throughout our society
   6. computers make us capable of
   7. very hard to finish the enumeration
2. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
   Symbolic language is _______ for it determines its true aspect. With the aid of symbolism _______ in reasoning almost mechanically by the eye and leave their mind free to grasp the fundamental ideas of the subject matter. Just as music uses symbolism _______ so mathematics expresses quantitative relations and spatial forms symbolically. Unlike the common language, which is the product of custom, as well as social and political movements, _______, purposefully and often ingeniously designed. By virtue of its compactness, _______ which when expressed in terms of common language are unmanageable. This compactness makes for efficiency of thought.
   Mathematical language is precise and concise, so that it is often confusing to people unaccustomed to its forms. The symbolism used in mathematical language is essential to distinguish meanings often confused in common speech. Mathematical style aims at brevity and formal perfection.
   1. mathematicians can make transitions
   2. the language of music is carefully
   3. it permits a mathematician to work with ideas
   4. for the representation and communication of sounds
   5. precise and concise
   6. the language of mathematics is carefully
   7. one of the basic characteristics of modern mathematics
3. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
   Trigonometry is a branch of mathematics that deals with triangles, _______ in which one angle has 90 degrees (right triangles). Trigonometry deals with relationships _______ and with the trigonometric functions, which describe those relationships.
   Trigonometry has applications in both _______ where it is essential in many branches of science and technology. It is usually taught in secondary schools _______ part of a precalculus course. Trigonometry is informally called "trig".
   A branch of trigonometry, _______ studies triangles on spheres, and is important in astronomy and navigation.
   1. between the sides and the angles of triangles
   2. between the legs and the hypotenuse
   3. particularly those plane triangles
   4. called spherical trigonometry,
   5. called plane figures
   6. pure mathematics and in applied mathematics,
   7. either as a separate course or as
4. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
   Computers will be embedded or hidden in a variety of items. For example, we’ll have wearable computers that will be embedded in a belt of jewellery, etc.
   ICT devices will be mobile and multimedia: we’ll watch mobile TV programmes on our phones _______.
   We’ll be able to swim _______, a technology that will change the two-dimensional world of the Internet into a 3-D experiences with three-dimensional sound and images and even the sense of touch.
   User interfaces, the systems _______, will resemble human communication. There will be gesture interfaces based on facial-band recognition systems. Computer chips can be injected under the RFID, radio frequency identification tags, might be used to track or identify people or to store information, such as medical data, although there are concerns about privacy and personal safety. There might be intelligent robots, _______. The processing power of computers may have reached 1,000,000,000 MIPS _______ the estimated speed of human thought.
   1. that facilitate communication between people and computers
   2. which will also access the Internet and work as a mobile office
   3. a molecular computer
   4. machines that will be able to think creatively
   5. in the immersive Internet
   6. made with organic material
   7. millions of instructions per second
5. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
   If one angle of a triangle is 90 degrees and _______ the third is thereby fixed, _______ add up to 180 degrees. The two acute angles therefore add up to 90 degrees:_______. The shape of a right triangle is completely determined, up to similarity, by the angles. This means that once one of the other angles is known, _______ regardless of the overall size of the triangle. These ratios are given _______ of the known angle A, where a, b and c refer to the lengths of the sides in the accompanying figure.
   1. the ratios of the various sides are always the same
   2. they are obtuse angles
   3. because the three angles of any triangle
   4. by the following trigonometric functions
   5. they are complementary angles
   6. one of the other angles is known,
   7. the ratios of the various sides are always different
6. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
   Let's try to answer the question: "What makes the computer such an irreplaceable device?" The answer is very simple – _______ doing everything you need. It is a high speed calculating machine which speeds up _______. It is an electronic notebook which manages to collect tremendous quantity of data, _______, which keeps records of students and teachers, studying programs, personal information etc. It is a unique typewriter that allows every user _______, pictures or even photos. It is the greatest electronic entertainment system, so you can relax listening to your favourite music or _______, or playing computer games. And finally, computer is a personal communicator that enables to communicate with other people all over the world without living your house.
   1. computers make us capable of
   2. watching you favourite film
   3. such as databases any school or university
   4. a unique typewriter
   5. a part of our everyday life
   6. to type and to print any kind of written document
   7. your financial calculations
7. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
   I use computers to find information for people. Readers come in with a lot of queries and I use either our own database _______ database that we are connected to to find what we want. They might want to know the name and address of a particular society or last year’s accounts of a company and we can find it for them. On the other hand, they might want to find a particular newspaper article but they do not know the exact date _______ so we can find it for them _______ for anything they can remember: _______. Moreover, we use computers _______ and to record the books that readers borrow.
   1. by checking on our online database
   2. to catalogue the books into the library
   3. a name or the general topic
   4. or the national
   5. to carry out program instructions
   6. it was published
   7. all the instructions and data
8. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
   Three noncollinear points (also knwon as coplanar points) determine a plane, which is yet another undefined term _______ such as a tabletop. Subsets of a plane are called plane shapes or planes figures.
   Another important example of a geometric figure is the concept of an angle. By an angle we mean _______ that have a common endpoint, known as the vertex. The line segments are called _______. If one of the line segments of an angle is horizontal and _______ then we call the angle a right angle. Note that the sides of an angle partition the plane into two regions, _______ of the angle. Two angles with the same opening are said to be congruent.
   1. the sides of the angle
   2. one of the other angles
   3. the other is vertical
   4. between the legs and the hypotenuse
   5. the opening between two line segments
   6. the interior and the exterior
   7. used to describe a flat space
9. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
   A computer system consists of two parts: the software, _______ and the hardware, which consists of all electronic and mechanical parts of the computer. The basic structure of a computer system contains _______: the central processing unit or CPU, the main memory or the internal memory and the peripherals.
   The central processing unit is the brain of the computer. Its function is _______ and to operate the processing of the other computer units. _______ the user can add a specialized expansion cards to the CPU of his computer. The main memory stores all the instructions and data which were currently processed by the CPU. It usually consists of two sections: RAM (random access memory) and ROM (read only memory). RAM is the memory used for creating, loading and running computer programs. ROM is computer memory _______ in the system.
   1. For better video and sound performances or networking
   2. four main hardware sections
   3. to carry out program instructions of the software
   4. that takes in information
   5. three main hardware sections
   6. which holds the programmed instructions
   7. which are instructions and programs of the computer
10. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    Hardware consists of devices composing a computer system: _______, the main memory and the input and output units. The part of the computer _______ is called the input unit. It collects and converts data in the form _______. To be accepted by the machine, information has to be in the form of digits 0, 1, 2, 3, 4,... 9 or signs A, B, C, D, …. So, the input unit makes possible communication _______ and human to the computer. The most common input device is a keyboard, which looks like an electric typewriter. The mouse is a handheld device connected with the computer _______.
    Another type of the input unit is optic-electronic scanner. Video camera and microphone can be also used to take in information into the computer.
    1. from the other data-handling equipment
    2. that takes in information
    3. the central processing unit
    4. suitable for computer processing
    5. by checking on our online database
    6. by means of a small cable or bluetooth
    7. which holds the programmed instructions
11. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    Geometry, a branch of mathematics _______ is a fundamental area of study in the field. Two of the most important concepts in geometry are similarity and congruence. Two figures are said to be similar _______ but not necessarily the same size. This means that one can be a scaled version of the other. The scale factor is _______ of corresponding sides. Two geometric figures are congruent if they have the same size and shape. This means _______ through rotations, translations, or reflections. Similarity and congruence have numerous applications in the real world. Architects and engineers use these concepts when designing and building structures. Artists use them _______. Even in nature, we can find examples of similarity and congruence, such as in the patterns of a snowflake or the symmetry of a butterfly's wings.
    1. that one can be transformed into the other
    2. which are instructions and programs
    3. the ratio of the lengths
    4. to create perspective in their works
    5. that deals with shapes and their properties,
    6. that takes in information
    7. if they have the same shape,
12. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    The part of the computer _______ is called the output unit. The computer can easily put out information _______ – hardcopy or softcopy forms. Hardcopy output can be held in your hands, _______ or pictures printed on it. Softcopy is displayed on a monitor. The output unit is varying _______ of the auxiliary equipment receiving information. But all peripherals are slow as compared with the computer. In this case buffers are used. A buffer is a storage device _______ from the computer and release the information at the proper speed for the peripheral equipment.
    1. that takes in information
    2. which is able to accept information at a very high speed
    3. in the form acceptable to people
    4. which are instructions and programs of the computer
    5. according to the capacity
    6. that puts out information produced by the computer system
    7. such as paper with the text
13. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    The central processing unit (CPU) is the nerve centre of any computer system. It coordinates and controls _______, reads, interprets software instructions and performs all arithmetic and logic processes applied to data. The CPU has three separate sections: an internal or main memory, _______, and a control unit.
    The main memory is the component of the computer which stores information. It stores the numbers to be operated on, intermediate and final results, _______. There are two important features of the memory unit: an access time and a capacity. The more memory has your computer, _______. There are two basic types of the main memory: RAM and ROM. RAM accepts new instructions and information from the peripherals. ROM is used _______ inside of computer permanently.
    1. an arithmetic and logic unit
    2. the more operations you can perform
    3. a name or the general topic
    4. the activities of all other computer units
    5. to carry out program instructions of the software
    6. as well as the instruction themselves
    7. to store data or instruction
14. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    The word polygon _______: Poly and gon. Poly means many and gon means sides. It means that a polygon is a geometrical figure _______. The sides of the polygons are straight line segments _______ with each other. These sides are also referred to as edges of the polygon. Vertex of the polygon refers to a point _______ meet each other. At the vertex, the angle of the polygon is also formed. Some examples of polygons include triangle, square, rectangle, rhombus, and hexagon. All these figures are two-dimensional. A circle is also a two-dimensional figure, but it is not a polygon _______ rather it is a simple curved figure.
    1. if they have the same shape,
    2. where two line segments
    3. that are joined end to end
    4. where the category is derived
    5. is created by combining two words
    6. because it does not have angles or sides,
    7. that has multiple sides
15. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    The final component of any computer system is its Software, _______ for directing all computer operations and electronic data. These computer programs give the hardware _______ to conduct the processing. The computer is merely a general-purpose machine which requires a specific software to execute a given instruction.
    Computers accept information, carry out different calculations – addition, subtraction, multiplication, division, _______ produce logical operations, _______ matching, selecting, etc. and then output data as information. It is exactly _______ which determines the order of operations to be performed.
    1. that unit of the computer
    2. checking on our online database
    3. exact sequence of instructions
    4. such as comparing, sorting,
    5. which includes programs
    6. that takes in information
    7. raising into a power, taking a square root,
16. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    Programs of the software are usually divided into two categories – system software and application software. System software sits directly on top of your
    computer's hardware components (also referred to as its bare metal). It includes the range of software _______ that enables it to function. This include the operating system, _______, linkers and debuggers.
    Systems software can also be used for managing computer resources. Systems software is designed _______, not human users.
    System software controls all standard computer activities: _______, one of the system programs is loaded into its memory, these programs contain information about capacity of the computer's main memory, the processor's model, the disk drivers to be used and so on. System programs are designed for the specific pieces of hardware. _______ For example, if the user wants to activate his peripheral device, such as printer or scanner, he needs to load a specific driver. By installing the driver you start the application of newly attached auxiliary.
    1. These programs are called drivers.
    2. to be used by the computer system itself
    3. that unit of the computer
    4. drivers for your hardware devices
    5. to store data or instruction
    6. you would install to your system
    7. when a computer is first turned on
17. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    A circle is a 2D shape defined as the locus of all points _______ called the 'center'. It is a smooth, curved shape that is perfectly symmetrical all around.
    A polygon is a flat 2D shape with straight sides. It must have at least three sides and could contain many angles. The faces of polygons are made from straight lines, _______ to form a 'closed' shape.
    Circles and polygons differ by their properties. Circles are perfectly _______ they have one continuous curvature. All points on the circle are an equal distance from the center. For a polygon, the sides are straight lines. It has vertices and exhibits individual angles, _______ from all vertices. Thus, circles cannot be classified as polygons _______ these particular characteristics.
    1. round with no sides or vertices,
    2. because they don't share
    3. which connect together
    4. is the perpendicular distance
    5. equidistant from a given point
    6. which includes programs
    7. with no specific point equally distant
18. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    After the system software is loaded, the applications software is acceptable to work. Applications software satisfies user's specific need. The developers of
    application software _______ trying to do their best to attract more users to their software. As the productivity of the hardware has increased greatly in recent years, _______ in one program to make software interface look more attractive to the user.
    Today we find new terms created frequently to classify types of applications software. You have classifications based on usage – _______, office applications, and other categories _______ based on the main use of the software. Unfortunately, we also have a newer group of software related terms that have a negative association. While the applications software itself may be useful, _______ that may cause undesirable effects.
    1. for example games or financial software
    2. where the category is derived
    3. rely mostly on marketing research strategies
    4. it may also carry hidden programs or utilities
    5. which includes programs
    6. the programmers nowadays tend to include all kinds of gimmicks
    7. to be used by the computer system itself
19. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    The Pascal programming language was originally developed by Niklaus Emil Wirth (born February 15, 1934), a member of the International Federation of
    Information Processing Working Group. Professor Niklaus Wirth developed Pascal to provide features _______ of the time. His principle objectives for Pascal _______, allow for the development of well structured and well organized programs, and to serve as a vehicle _______ of computer programming. Pascal, which was named after the mathematician Blaise Pascal, is a direct descendent from ALGOL 60, which Wirth helped to develop. Pascal also draws programming components from ALGOL 68 and ALGOL-W. The original published definition for the Pascal language _______ published in 1973. It was designed _______ to college students and was the language of choice to do so from the late 1960's to the late 1980's.
    1. to be used by the computer system itself
    2. for the teaching of the important concepts
    3. where the category is derived
    4. to teach programming techniques and topics
    5. that were lacking in other languages
    6. appeared in 1971 with latter revisons
    7. were for the language to be efficient to implement and run
20. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    The most popular Internet service is e-mail. Most of the people, _______ use the network only for sending and receiving e-mail messages. However, _______ are available on the Internet: reading USENET News, using the World-Wide Web, telnet, FTP, and Gopher. In many developing countries _______ with a reliable alternative to the expensive and unreliable telecommunication systems of these countries. Commercial users can communicate over the Internet _______ and do it very cheaply. When they send e-mail messages, they only have to pay _______ not for calls across their countries or around the world.
    1. other popular services
    2. for the teaching of the important concepts
    3. having access to the Internet,
    4. the Internet may provide business people
    5. for phone calls to their local service providers,
    6. with the rest of the world
    7. with no specific point equally distant
21. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    A programming language is an artificial language _______ to a computer. In order to distinguish the spectrum of programming languages we divide them according to the convenience of the machine computing or the work of a programmer. Machine language, mnemonic machine language and assembly language are best for machines, _______ PASCAL etc. are best for programmers.
    Sometimes a machine language is called _______ which refers to a computer instructions written in a machine code. This machine code _______ by a computer without translation. The machine code is the coding system adopted in the design of a computer to represent the set of its instructions. The actual machine language _______, but not by the programmer.
    1. whereas such languages as FORTRAN, ALGOL, BASIC,
    2. to be used by the computer system itself
    3. invented to communicate instructions or commands
    4. can be immediately obeyed
    5. where the category is derived
    6. as a basic programming language or autocode
    7. is generated by the software
22. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    High- level programming languages on the contrary _______ to several machine code instructions. Such languages as FORTRAN, ALGOL, BASIC, PASCAL etc. _______, while low-level languages are oriented to the computer's machine code.
    The programming languages are also divided into _______ to their similarity to English: _______ and automatic coding languages. Comparing the convenience of the languages for the computer and the programmer usages we can say _______, while symbolic and automatic coding languages are more similar to English, so they are more convenient for the use of the programmer.
    1. is generated by the software
    2. are oriented to the problem
    3. can be immediately obeyed
    4. that the machine languages are used by the computer directly
    5. use the instruction corresponding
    6. three basic categories according
    7. machine languages, symbolic languages
23. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    The Internet, a global computer network, _______ began in the United States in 1969 as a military experiment. It was designed to survive a nuclear war. Information sent over the Internet _______ from one computer to another. Because of this, any two computers on the Internet will be able _______ as long as there is a single route between them. This technology is called packet switching. Owing to this technology, _______ (by a nuclear explosion, for example), information will just route around them. One such packet-switching network already survived a war. It was the Iraqi computer network, _______ during the Gulf War.
    1. embracing millions of users all over the world,
    2. identifying signs of threats
    3. takes the shortest path available
    4. which was not knocked out
    5. to stay in touch with each other
    6. which is able to accept information
    7. if some computers on the network are knocked out
24. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    A cone is a solid figure formed _______ (the base) and all the lines joining points of the base to a fixed point (the vertex) not in the plane of the base. The closed curve is the directrix of the cone _______ (or elements). The curved area of the cone forms its lateral surface. Cones are named according to the base, e.g. a circular cone or an elliptical cone. If the base has a center of symmetry, _______ is the axis of the cone. A cone that has its axis perpendicular to its base is a right cone; otherwise the cone is an oblique cone. The altitude of a cone (h) _______ from the plane of the base to the vertex. The volume of any cone is l/3hA, where A is the area of the base. A right circular cone _______ has a slant height (s), equal to the distance from the edge of the base to the vertex (the length of a generator). The term "cone" is often used loosely for "conical surface".
    1. and the lines to the vertex are its generators
    2. is the perpendicular distance
    3. by a closed plane curve on a plane
    4. a line from the vertex to the center
    5. which is able to accept information
    6. (circular base with perpendicular axis)
    7. are used by the computer directly
25. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    Bank customers can now download money _______, a smart card, using a specially designed phone _______. To download cash you have to enter your PIN. You can then use your electronic wallet to pay for goods across the Internet, _______.
    Using the Internet, customers can now check their account balance and see their latest statement. One bank has developed a multi-currency payment engine _______ to sell their goods in sixteen countries, with customers paying in their local currency. With these developments, coins and notes _______.
    1. from their account to an electronic wallet
    2. and to transfer money to other card holders
    3. as your sole qualification
    4. equipped with a smart card reader
    5. are likely to disappear
    6. for being a good programmer
    7. which allows on-line retailers
26. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    The hypotenuse is the side opposite to the 90 degree angle _______; it is the longest side of the triangle, _______ adjacent to angle A. The adjacent leg is the other side that is adjacent to angle A. The opposite side is the side that is opposite to angle A. The terms _______ are sometimes used for the opposite and adjacent sides respectively. Many people find it easy to remember _______ are equal to sine, cosine, or tangent, by memorizing the word SOH-CAH-TOA.
    The reciprocals of these functions are named the cosecant (csc or cosec), secant (sec) and cotangent (cot), respectively. The inverse functions are called the arcsine, arccosine, and arctangent, respectively. There are arithmetic relations between these functions, _______.
    1. which are known as trigonometric identities
    2. in an isosceles triangle
    3. and one of the two sides
    4. what sides of the right triangle
    5. what sides of the isosceles triangle
    6. in a right triangle
    7. perpendicular and base
27. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    Nanotechnology, the science of creating and using materials or devices _______, is going to represent a new technological revolution. These devices will fall in the range of 1 nanometre, _______, to 100 nanometres (nm).
    Nanobots, robots formed from molecules or molecular components, will be used in medicine _______. For example, they will be injected and will move through blood vessels destroying cholesterol molecules or cancer.
    Nanocomputers, _______, may have the power of 100 workstations but only be the size of a grain of sand. There will be two main types of molecular computers.
    Quantum computers, based on quantum mechanics, may be millions of items faster than current computers. They will be so fast because _______. This capability is made possible by qbits, quantum bits, which can be 0 or 1, or something in between, simultaneously.
    DNA computers will use DNA biochips to perform the same functions as silicon microchips do today but at a much faster speed.
    1. which is equal to one billionth of a metre
    2. molecule-sized computers
    3. to control and diagnose diseases
    4. they will be able to examine all possible answers to a query at the same time
    5. to revolutionize the way we live
    6. at molecular and atomic sizes
    7. into a test bulb
28. Заповніть пропуски цифрами, які відповідають пропущеному фрагменту у тексті (два фрагменти є зайвими):
    The law of sines and the law of cosines can be used _______ of any triangle as soon as _______ two angles and a side or three sides are known. These laws are useful in all branches of geometry, _______ as a finite combination of triangles.
    The above definitions apply to angles between 0 and 90 degrees (0 and π/2 radians) only. Using the unit circle, one can extend them to all positive and negative
    arguments. The trigonometric functions are periodic, _______ or 2π radians. That means their values repeat at those intervals.
    The trigonometric functions can be defined in other ways besides the geometrical definitions above, _______. With these definitions the trigonometric functions can be defined for complex numbers.
    1. using tools from calculus and infinite series
    2. two sides and an angle or
    3. two legs and an angle
    4. with a period of 360 degrees
    5. to compute the remaining angles and sides
    6. since every polygon may be described
    7. since every square may be described