Grammar Rules Patterns.

Я решил эти задачи ...

I solved the problems yesterday. (Past Ind.) I have already solved the problems. (Pr. Perf.) I had solved the problems before he came. (Past Perf.)

Я решу эти задачи …

I shall solve the problems tomorrow. (Fut. Ind.) I shall have solved the problems when he comes. (Fut. Perf.) If I solve the problems, will we obtain the required result of the experiment? (Pr. Ind.)

Ex. 2. Read and compare the following sentences. Explain the use of the English Tense forms. (Present Perfect, Past Indefinite, Past Perfect, Future Perfect, Future Indefinite, Future Continuous, Present Continuous).

1. a) He has enlarged his English vocabulary lately.

b) He enlarged his English vocabulary when he was in Great Britain.

c) Before he went to Great Britain he had enlarged his English vocabulary.

2. a) How long have you been here?

b) How long ago were you there?

c) He wondered how long I had been there.

3. a) Since when have you started working as a teacher?

b) When did you start working as a teacher?

c) By that time she had started working as a teacher.

4. a) The scientists have just changed the order of the whole process.

b) The scientists changed the order of the whole process just now (a moment ago).

c) He said that the scientists had just changed the order of the whole process.

5. a) Perhaps man will improve the devices used in calculations.

b) By the end of this century man will have radically improved the devices used in calculations.

c) Man is going to improve the devices used in calculations radically in the near future.

6. a) Our students will translate this article next week.

b) Our students will be translating the article this time tomorrow.

c) Our students will have translated this article by the time you come.

7. a) I promise I shall find a proper solution of the problem soon.

b) By the middle of the lesson I shall have found a proper solution of the problem.

c) Don’t phone now. I shall be looking for a proper solution of the problem.

8. a) In the future she will try to enter the faculty of Cybernetics.

b) She is going to enter the faculty of Cybernetics after she finishes school.

c) When we meet again, I am sure, she will have become a student of the faculty of Cybernetics.

9. a) They will take part in the international conference on mechanics in a year.

b) They will already have taken part in the international conference on mechanics by the time you come there.

c) This time next week they will be taking part in the international conference on mechanics.

Ex. 3. Make the following sentences interrogative and negative.

1. By the middle of the 21^st century we’ll have built a lot of space stations. 2. The teacher has just spoken about rational and irrational numbers. 3. By that time natural scientists had learnt to use the parallelogram as a means of addition. 4. A young mathematician has found a better proof of the theorem recently. 5. By the end of the week I’ll have written the second chapter of my dissertation. 6. He has already taken his exam in differential equations. 7. They had done their laboratory work by 2 o’clock. 8. We have just replaced the terms in the equation. 9. This week the students have learnt to perform operations on complex fractions. 10. I had simplified the fractions before multiplying them.

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 theories have often suggested directions for mathematical investigations. 4. Physical objects and observed facts had often served as a source of the postulates in Maths. 5. Einstein was able to achieve some of his results after Maths had suggested new ways of thinking about space and time. 6. Abel had hardly reached the age of 22 when he made two of his most famous discoveries. 7. Algebra has become the science that can deal effectively with anything. 8. By the end of June the students will have passed their exams and gone on holiday. 9. Throughout the centuries people have improved their ability to record, process and communicate information. 10. When you come, I will have solved these equations with fractions. 11. This century scientists have made a lot of discoveries about the universe.

Pre-Reading Activity

Guess the meaning of the following words.

Fraction ['frxkS(q)n] n, fractional ['frxkSqnl] a, equivalent [i'kwivqlqnt] a, rational ['rxSqnl] a, process ['prquses] n, concept ['kOnsept] n, arithmetic [q'riTmqtik] n, operation [Opq'reiSn] n, horizontal [,hOri'zontl] a, separate ['sepqreit] v ['seprit] a, decimal ['desiml] a, type ['taip] n.

Read and learn the basic vocabulary terms.

part [pa:t] n	часть
proper ['prOpq] a	правильный
improper [im'prOpq] a	неправильный
change [tSeindZ] n	замена, заменять
proportional [prq'pLSnl] a	пропорциональный
equal ['i:kw(q)l] a	равный
reduce [ri'dju:s] v	сокращать
relation [rI'leISn] n	отношение
ratio ['reISIqu] n	пропорция, отношение
numerator ['nju:mqreitq] n	числитель (дроби)
denominator [di'nOmineitq] n	знаменатель (дроби)
slanting ['slRntIN] a	наклонный
define [dI'faIn] v	определять
quantity ['kwOntiti] n	величина, количество
mixed [mikst] a	смешанный
imply [Im'plaI] v	значить
point [pOint] n	точка
repeat [ri'pi:t] v	повторять
repeating (fraction) [ri'pi:tiN] a	периодическая (дробь)
terminating [,tWmi'neitiN] a	конечная (дробь)
agreement [q'gri:mqnt] n	соглашение
produce [prq'djHs] v	производить
consider [kqn'sidq] v	рассматривать, полагать, считать
the former (of) ['fLmq] adj	первый (из)
compare [kqm'pFq] v	сравнивать
irreducible [iri'dju:sqbl] a	несократимая (дробь)
nought [nO:t] n	ноль
whole ['hqul] a	весь, целый
power ['pauq] n	степень

Memorize the following word combinations.

1. over and over again – многократно

2. may be changed to – может бы превращена

3. in full agreement with – в полном соответствии с

4. a part – to – whole relationship – отношение части к целому

5. by a slanting line – наклонной линией

6. the absolute value of the entire fraction – абсолютное значение всей дроби

7. in its lowest or simplest terms – в своем простейшем виде

8. to the left of (to the right of) – налево, направо

9. leaving out the decimal point – пропуская десятичную точку

10. to have in common – иметь что-то общее (сходное)

11. rather than – скорее чем, вернее чем