Facts to be remembered

1. 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 in the present.	He looks so tired. He has been studying for his exam.
To express anger, annoyance or irritation.	Who has been using my cup?
We can use the Present Perfect Continuous to talk about longer repeated actions that have finished.	“You look tired.” – “I have been running.”

2. Past Perfect Continuous is used:

For certain duration with visible results in the past.	They were wet because they had been walking in the rain.
As past equivalent to the Present Perfect Continuous.	(She is going to the doctor. Her leg has been aching for two days). She went to the doctor. Her leg had been aching for two days.

Note the difference in translation between the Present Perfect Continuous and the Present Perfect Tenses.

– You look hot. – I’ve been running all the way. Я бежала всю дорогу. I’ve been learning irregular verbs all afternoon. Я учил неправильные глаголы весь день. Sorry about the mess – I’ve been painting the house. Извините за беспорядок – я крашу дом.

He’s run all the distance to the finish fairly well. Он пробежал всю дистанцию до финиша довольно хорошо. I’ve learnt irregular verbs. (= I know them.) Я выучил неправильные глаголы. I’ve painted two rooms since lunchtime. Я покрасил две комнаты с обеда.

Ex. 8. Choose the correct variant:

1. For how long (have they discussed, have they been discussing) the situation? 2. Why (have you repeated, have you been repeating) these English words over and over again? 3. The students (have taken, have been taking) the examination for more than 5 hours. 4. They (were discussing, have been discussing) the situation for three hours. 5. She (has been answering, has answered) the lesson already. 6. She (has worn, has been wearing) glasses for two years. 7. Peter’s English is getting much better. He (is practising, has practised, has been practising) a lot this year. 8. I (have written, am writing, have been writing) my course paper for three months, but I (am not finishing, haven’t been finishing, haven’t finished) it yet. 9. “… you (are defending, have defended, have been defending) your course paper?” – “No, I (haven’t done, am not doing, haven’t been doing) it yet.” 10. Tom (is having, has been having, has had) a toothache for nearly a week. He (is going, has been going, has gone) to the doctor today and I’m waiting for him. 11. What you (are doing, have been doing, have done) with my cassette-recorder? I can’t find it anywhere. 12. You look tired! – Yes, I (am dancing, have danced, have been dancing) and I (haven’t danced, am not dancing, haven’t been dancing) for years, so I’m not used to it. 13. Everybody (is looking, has looked, has been looking) forward to this holiday for months. 14. Recently this scientific theory (is being proved, has been proved, has been proving) to be false.

Ex. 9. Match the beginnings and the ends of the sentences.

1. Tom had been working for two hours a. as if he had been running for several hours without a rest.

2. “You look tired.” b. she will have been working at the department for 35 years.

3. “Aren’t you hungry?” c. I decided to have a cup of tea.

4. By the 1^st of August, 2009 d. because she has been painting the ceiling.

5. He was out of breath e. “I have been writing my course paper for more than a month”.

6. “Why are my books all over the floor?” f. because she had been cleaning the flat the whole day.

7. After I had been walking for an hour g. “No, I’ve been eating all day”.

8. Her hair is white h. “He has been walking in the rain”.

9. “Why is his coat wet?” i. when his brother came

10. She looked very dirty j. “Your little sister has been playing with them”.

Ex. 10. Translate into English.

1. Они учат эти правила больше года. 2. Как долго этот студент переводит эту статью? 3. Весь день идет снег. 4. Она преподаватель английского языка. Она преподает с тех пор, как закончила университет. 5. Ты выглядишь усталой. – Я стирала белье весь день. 6. Я вымыл свою машину. – Разве она не выглядит чудесно? 7. Сейчас она учит испанский язык, но она еще не очень говорит. 8. Он часами играет эту музыку на фортепьяно. Пусть он перестанет играть. 9. Студенты пишут этот тест уже 20 минут. Только один студент уже написал его. 10. На этой неделе я написала несколько писем своим друзьям. 11. Как долго вы будете писать контрольную работу перед тем, как сдадите ее преподавателю? 12. Мой друг ждет вас уже с двух часов. Почему вы не пришли вовремя?

Pre-reading activity

Guess the meaning of the following words.

generalization [GenqrqlaI`zeIS(q)n] n, arithmetic [q`rITmetik] n, procedure [prq`sJGq] n, symbol [`sImbql] n, formula [fLmjulq] n, characteristic [,kxrIktq`ristik] n, coefficient [,kouI`fISqnt] n, zero [`zIqrou] n

Read and learn the basic vocabulary terms.

compute [kqm`pjHt]	вычислять
deal (dealt) with [dJl]	иметь дело с; рассматривать
apply [q`plaI]	использовать, применять
instead of [In`sted]	вместо
particular [pq`tIkjulq]	определенный
concerning [kqn`sWnIN]	относительно, касательно
replace [rI`pleIs]	заменять, замещать
hold (held) for [hould]	годится для
to be true [trH]	быть верным, справедливым; удовлетворять
likewise [laIkwaIz]	подобно, так же, таким же образом
raising to a power [reIzIN tq q `pauq]	возведение в степень
term [tWm]	член
in terms of	на языке... , в переводе на... , с точки зрения
multinomial [mAltI`noumjql]	многочлен, полином
binomial [baI`noumjql]	двучлен, бином
trinomial [traI`noumjql]	трехчлен
monomial	одночлен

Memorize the following word combinations.

1. let the number 20 be replaced – давайте заменим число 20

2. then the statement is true – тогда утверждение справедливо

3. no matter what – независимо от того, какие

4. for convenience – для удобства

5. serve to distinguish – служат для того, чтобы различить

6. both plus and minus – как плюс, так и минус

7. is to be treated as – следует рассматривать как