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Ex. 13. Give the proper English equivalents for the Russian expressions.

Ex. 13. Give the proper English equivalents for the Russian expressions. - раздел Образование, Grammar: verb “to be”, there is/are. Possessive and Personal Pronouns Computed, Instead Of, Simpler, Ordinary Letters, Re...

computed, instead of, simpler, ordinary letters, replace, hold, generalization, relations, concerning, multinomials

1. Algebra is обобщение of arithmetic. 2. In order to state the general rule we write symbols, обычные буквы, instead of particular numbers. 3. These signs have been introduced to denote отношения between numbers. 4. Algebra is the system of rules относительно the operations with numbers. 5. Particular numbers may замещать the symbols a and b. 6. All the laws of arithmetic верны for operations with letters. 7. We write symbols вместо particular numbers. 8. The square of the sum of any two numbers c and d can be вычислен by the rule (c + d)2 = c2 + 2c•d2. 9. Algebraic expressions may be given a более простая form by combining similar terms. 10. Algebraic expressions consisting of more than one term are called полиномами.

 

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Эта тема принадлежит разделу:

Grammar: verb “to be”, there is/are. Possessive and Personal Pronouns

Grammar verb to be there is are Possessive and Personal Pronouns... Pronouns...

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Ex. 1. Analyze the following sentences and translate them into Russian.
1. They live together with their parents. 2. Oxford is famous for its University. 3. I didn’t have an

C) Preparatory “it”.
  It is was will be easy/difficult/impossible/dangerous/safe/ expensive/interesting/nice/wonderful/ terrible/a pleasure

Ex. 4. Make the following sentences interrogative and negative.
a) 1. Twenty miles is a long way to walk. 2. My native city is very large. 3. The pair of black trousers is cheap.4. Phonetics is a branch of linguistics. 5. The family are fond of their house. 6.

Ex. 6. Analyze the following sentences and translate them into Russian.
a) 1. There are some big trees in the garden. 2. There is a seminar on philosophy today. 3. There are comfortable apartments in this block of flats. 4. There are a lot of accidents on this road. 5.

Read and learn the basic vocabulary terms.
sense (n) [sens] ощущение, чувство support (v, n) [sq'pLt] содержать (семью); поддержка seem (v)

About My Family and Myself
I believe that everything has its beginning in the family. Family is very important for every person, because it gives you a sense of stability and tradition, a feeling of having support and unders

Looks and Appearance
beautiful (adj) ['bjHtIful] красивый (о женщинах) blond/fair [feq]/ginger [GInGq]/ dark hair светлые/русые/рыжие/черные в

Features of Character
be in good/bad mood [mu:d] быть в хорошем (плохом) настроении brave (adj) [breIv] смелый devoted

Interests and Ambitions
ambition (n) [xm'bISqn] стремление be keen [kJn] on smth увлекаться чем-либо desire (n), (v) [di'

Family Members and Relations in the Family
average ['xvqrIG] /small/large family средняя/маленькая/большая семья   consist of (v) [kqn'sIst] состоят

Ex. 12. Translate into English making use of the words from the box.
slender beard shy short fat hazel eyes pale skin kind-hearted plump cheeks honest ginger-haired curly hair broad shoulders

Ex. 1. Make the sentences interrogative and negative.
a) 1. I usually have a sandwich for my lunch. 2. Students have one English class a week. 3. We have a shop next to the post office. 4. Most cars have got four wheels. 5. An insect has got six legs.

Present Simple
  Positive   Negative   Interrogative I we you they

Ex. 4 . Make the following sentences interrogative and negative.
1. We do a lot of things in our free time. 2. The shops open at 9 o’clock and close at 5.30. 3. It costs a lot of money to stay in luxury hotels. 4. The Moon goes round the Earth. 5. They usually s

Past Simple
  Positive   Negative   Interrogative I we you they he she

Future Simple
Positive / Negative   Interrogative I/we you/they he/she/it (shall(‘ll)/shall not/shan’t) will(‘ll)/wil

General
Auxiliary verb Subject Predicate or part of it Obje

Read and learn the basic vocabulary terms.
delay (n) [dI`leI] задержка recent (adj) [`rJs(q)nt] последний, недавний manage (v) [`mxnIG]

Memorise the following word combinations.
to be busy быть занятым the students’ hall of residence студенческое общежитие as a matter of fac

A Letter to a Friend
Dear Linda, I’m very sorry for the delay in answering your recent letter. I was so awfully busy. In the spring I passed my A-Level examinations and tests at school and managed to get good

Ex. 10. Find the Russian equivalents for the following English word combinations.
1. to belong to a group 2. to describe the routine 3. to depend on the weather 4. to have a late night 5. on the other hand

Pronouns some, any, no
Affirmative sentences Examples Some and its compounds (somebody, something, somewhere, someone) is used with the meaning “small amo

Read and learn the basic vocabulary terms.
number (n) [`nAmbq]- число, количество, номер date back to (v) [`deIt] – датироваться, относиться к определенному времени antiquity (n) [xn`tIkwItI]- древность, античность

Numbers
The beginning of our number system dates back to antiquity where symbols, which we call positive integers, were used as an aid in counting, and only in the nineteenth century the system, which we k

Ex. 8. Answer the following questions.
1. What were positive integers used for? 2. When was the number system completed? 3. Are the first numbers which we use the positive integers or the negative ones? 4. Is unity a first or a last int

Ex. 1. Analyze the following sentences and translate them into Russian.
1. She could do sums in her head when she was 6 years old. 2. Peter was able to carry out the experiment successfully, but Nick couldn’t finish it without any help.

Read and learn the basic vocabulary terms.
number (n) [`nAmbq] число, количество; v перечислять numeral (n) [`nju:mqrql] цифра, символ, число digit (n) [`dIGIt] цифра value (n) [`vxlju:] величина, значение; (v) це

Four Basic Operations of Arithmetic
Many thousands of years ago this was a world without numbers. Today, using the same numbers in many different ways, man can build bridges, skyscrapers, fly off the Earth like a bird, even measure t

Ex. 14. Choose the phrase closest in meaning to the given statement.
1. Dan can’t be a teacher. a) I’m sure Dan isn’t a teacher. b) I think Dan isn’t a teacher. 2. Need I take the tablets every day? a) Is it a good idea to take th

Ex. 4. Translate the following sentences into Russian.
1. Mathematicians have used mathematical formulas in solving these problems. 2. By the end of the lesson we’ll have been able to obtain the modified definition of the function. 3. Scientific theori

Read and learn the basic vocabulary terms.
part [pa:t] n часть proper ['prOpq] a правильный improper [im'prOpq] a неправильный

Rational numbers and decimal numerals
In mathematics, a fraction is a concept of a proportional relation between a part and a whole. In other words, it is an example of a specific type of ratio, in which the two number

Ex.7. Give the proper English equivalents for the Russian expressions.
the greatest common factor; to invert; the quotient; performed operations; the numerator and denominator; decimal numerals; proper fractions; the minuend, subtrahend and r

Ex. 10. Choose the correct tense form.
1. (Have you ever heard/ Did you ever hear) about continued fractions? 2. We (have started/ started) learning fractions when we were at school. 3. By the end of the lecture the st

Ex. 11. Ask special questions.
1. By 5 o’clock the experiment will have been over. (by what time) 2. By the age of 41 Sophia Kovalevskaya had won recognition of mathematicians all over the world. (whose) 3. Zero concept has got

Ex. 12. Translate into English.
1. Дробь представляет часть целого. Она показывает, что что-то раздели­ли на несколько равных частей. 2. В дроби число, стоящее над чертой называется числителем, число, стоящее под чертой называетс

Degrees of Comparison
short words: -er, -est big – bigger – the biggest thin – thinner – the thinnest short – shorter – the shortest

Ex. 1. Analyze these sentences and compare the adjectives given there. Translate them into Russian.
1. He has a difficult test. I have a more difficult test. Her test is the most difficult of all. 2. Your problem is easy. His problem is easier than yours. That student’s problem is the easiest. 3.

Types of Comparisons
There are a number of different sentence patterns with comparative and superlative forms:   Than чем This book is more interesting

Ex. 5. Give the proper English equivalents for the Russian expressions.
the best, greater, as difficult as, less, longer… that one, as interesting as, not so important as, the youngest, better, not so famous as, the sooner… the better, the old

Facts to be remembered
  a. Present Perfect Continuous is used: For actions started and finished in the past and lasted for some time. The result of the actions is visible

Note the difference in translation between the Present Perfect Continuous and the Present Perfect Tenses.
1. – You look hot. – I’ve been running all the way. Я бежала всю дорогу.   2. I’ve been learning irregular verbs all afternoon. Я учил неправильные глаголы ве

Read and learn the basic vocabulary terms.
compute [kqm`pjHt] вычислять deal (dealt) with [dJl] иметь дело с; рассматривать apply [q`plaI]

The Nature of Algebra
Algebra is a generalization of arithmetic. Each statement of arithmetic has been dealing with particular numbers for years: the statement (20 + 4)2 = 202 + 2 • 20 • 4 + 4

Monomials and Polynomials
1. Algebraic expressions are divided into two groups according to the last operation indicated. 2. A monomial is an algebraic expression whose last operation is neither addition not subtraction. 3.

Ex. 1. Read these sentences. Compare the predicates in these pairs of sentences
a 1. I attend all lectures at the University. 2. We often use the Internet. 3. He applies a new method in his research.   &n

Read and learn the basic vocabulary terms.
equation (n) [i`kweiSqn] – уравнение statement (n) [`steItmqnt] – утверждение, формулировка finite (a) [`faInaIt] – конечный variable (a) [`vFqriqbl] – переменная

Equations and Identities
An equation is a statement of equality between two algebraic expressions. The two expressions are called members, or sides of the equation. If the two members of an equation are finite and are exac

Ex. 5. Give the proper English equivalents for the Russian expressions.
to solve, the unknown quantity, substituted into the expression, the value, roots, have been transposed, the Least Common Denominator, is checked, clearing, to satisfy

Ex. 9. Translate the sentences from English into Russian.
1. In solving problems by means of algebraic equations, the first and the most difficult step which must be done is to translate the words into the algebraic language. 2. Definite rules cannot be g

Ex. 10. Translate the sentences from Russian into English.
1. Уравнение – это утверждение, выражающее равенство двух алгебраических выражений. 2. Корень уравнения остаётся прежним, если к обеим частям уравнения прибавить или от обеих частей уравнения вычес

Ex.1. Analyze these pairs of sentences and compare the predicates given there.
1. They are solving the equation at the moment. 2. He was dividing these numerals at 2 o’clock yesterday. 3. We have already reduced the fr

Guess the meaning of the following words.
Algebraic adj. ["xlGI`breIIk]; polynomial n. ["pOlI`nqumIql]; integral adj. [`IntIgr(q)l]; constant n. [`kOnstqnt]; coefficient n. ["kquI`fISqnt]; exponent n. [eks`pqunqnt]; fundamen

Polynomials
A number represented by algebraic symbols is referred to as an algebraic expression. An algebraic expression whose parts are not separated by + or – is called a term; as 2

Ex. 6. Give the proper English equivalents for the Russian expressions.
a trinomial, descending, subtraction, obtain, a fraction, coefficients, terms, exponents, sum, remainder, fractional 1. Each of these polynomi

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