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- Grammar: verb “to be”, there is/are. Possessive and Personal Pronouns
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Grammar: verb “to be”, there is/are. Possessive and Personal Pronouns
Grammar: verb “to be”, there is/are. Possessive and Personal Pronouns - раздел Образование, Unit 1 ...
UNIT 1
| Grammar: verb “to be”, there is/are. Possessive and Personal Pronouns. |
Pronouns
| Personal | Possessive | ||
| Nominative | Objective | Dependent | Independent |
| I you he she it we they | me you him her it us them |  my
your
his
her noun
its
our
their
| mine yours his hers its ours theirs |
Ex. 1. Analyze the following sentences and translate them into Russian.
Ex. 2. Put in my/our/your/his/her/their/its/mine/yours/ours. 1. We want to go to the cinema after the exam. Do you like … idea?Ex. 3. a) We use a personal pronoun “it” as a subject or an object
1. Where is your pen? – It is in the bag. 2. Your translation is good. I like it. 3. This is our classroom. It is large. 4. Where is my ticket? I can’t find it. 5. Your new car is nice. Is it expensive? 6. I want that book. Please give it to me.
b) We use “it” as a subject with expressions that refer to time, weather, day temperature or distance.
1. It is ten miles to the nearest petrol station. 2. It is Monday again. 3. It is thirty degrees. 4. It is half past ten. 5. It is a nice day today. 6. It was very windy yesterday. 7. It was my birthday yesterday. 8. How far is it to the nearest restaurant?
C) Preparatory “it”.
the verb “to be” Present Past Future …Analyze the interrogative and negative forms.
1. Jane is at home at the moment, but her mother isn’t. Where is Jane’s mother? Is her brother at home?
2. When I was a child, I was afraid of dogs and my sister wasn’t. Why were you afraid of that little dog yesterday?
3. Today Sue is in Madrid. Tomorrow she will be in Rome. She won’t be in Tokyo on Friday. Where will Sue be on Saturday?
Ex. 4. Make the following sentences interrogative and negative.
b) 1. The boy was at home three days ago. 2. My lessons were over at 2…Ex. 5. a) Say the following sentences in the past.
1. The facts from the newspaper article are old. 2. The boy’s family is at home. 3. The students from group 2 are in the next room. 4. He is ready to read this text. 5. Their plans are simple and short. 6. The weather is good at this time of the year. 7. Bob and James are foreign students. 8. A city is a place with big industry and busy streets. 9. The article in the newspaper is interesting. 10. Sport is an essential part of Mike’s life.
B) Say the following sentences in the future.
1. Our street is very green in spring. 2. Children are already in bed at 9 o’clock. 3. Saturday morning is a very busy time for shopping. 4. It is not hot in winter. 5. The chief method of teaching is the lecture method. 6. Travelling by sea is very interesting. 7. The leaves are not green in autumn. 8. Our trip to Moscow is very tiring. 9. The workers are at the meeting at this time of the day. 10. At the end of the lecture she is very tired.
The Constructionthere is … , there are …
Read the sentences and compare the information given.
| 1. The teacher’s desk is in the room. Стол учителя стоит в комнате. 2. The film on TV was very interesting last night. Фильм по телевизору был вчера интересный. 3. A lot of people will be present at the party on Saturday. Много людей придет на вечеринку в субботу. | There is a teacher’s desk in the room. В комнате стоит стол учителя. There was an interesting film on TV last night. Вчера по телевизору шел интересный фильм. There will be a lot of people at the party on Saturday. В субботу на вечеринке будет много людей. |
Ex. 6. Analyze the following sentences and translate them into Russian.
b) 1. There were a lot of children in the yard an hour ago. 2. There was an…Ex. 7. Make the sentences interrogative and negative. Follow the models.
A) Are there any new messages for me today?
Yes, there are. / No, there aren’t.
There are no (not any) new messages for you today.
How many new messages are there for me today?
1. There are twelve students in my group. 2. There are twenty six letters in the English alphabet. 3. There is only one chair in this room. 4. There are thirty days in September. 5. There is one button on my jacket.
B) Was there little time for this work?
Yes, there was. / No, there wasn’t.
There wasn’t much time for this work.
How much time was there for this work?
1. There was little water in the bottle. 2. There was only one circus in the city 50 years ago. 3. There were a lot of lights in my Christmas-tree last year. 4. There was a shop at the end of the street. 5. There were seven flowers in the vase. 6. There were three pictures on the wall near the door. 7. There was little food in the fridge.
C) Will there be a new tube station in our street?
Yes, there will. / No, there won’t.
There won’t (will not) be a new tube station in our street.
What will there be in your street?
1. There will be a meeting in the hall. 2. There will be a bridge across the river. 3. There will be one more flight to London next month. 4. There will be four seatbelts in my car. 5. There will be a traffic jam in your area.
Pre-reading activity
Read and learn the basic vocabulary terms.
Memorise the following word combinations
1. I believe – полагаю...
2. to go in for trade – заняться торговлей
3. to look for a better paid job – искать лучше оплачиваемую работу
4. to try one’s luck – попытать счастья
5. to be similar in character – иметь похожие характеры
6. in appearance – по внешнему виду
7. to devote to the children – посвящать детям
8. a grown-up person – взрослый человек
9. to give up working – бросить работу
10. to enjoy respect from – пользоваться уважением у
11. to keep the house – вести хозяйство
12. to be concerned about – беспокоиться о
13. to be in good shape – быть в хорошей форме
14. according to the latest vogue – согласно последней моде
15. to do well at school – хорошо учиться в школе
16. to make a hell of the house – превратить дом в ад кромешный
17. to be of a strong built – быть крепкого телосложения
Reading Activity
About My Family and Myself
I think I'd better start my story with my dad. His name is Ivan Petrovich. He is in his late forties, but he looks powerful and impressive. He is… My mother's name is Larisa Ivanovna. She has turned 40 this year. But if you… My younger brother Sasha is only 7 years old. He studies at school. He does well at school, which makes all of us…Additional Vocabulary
Ex. 8. Look through the vocabulary below that may be useful when speaking about your family.
Looks and Appearance
Features of Character
Interests and Ambitions
Family Members and Relations in the Family
Post-reading Activity
Ex. 9. Answer the following questions.
1. How old are you? 2. Where are you from? 3. Where and when were you born? 4. What are your good habits? 5. Who do you most take after? 6. Do you easily make friends? 7. Are you on friendly terms with all your group mates? 8. What talents do you think you have? 9. Is it necessary to have a hobby? Why? 10. What is the right age for young people to get married? 11. Are you for small or large families? 12. What do you do if your parents are not right (in your opinion)? 13. What do your parents make you do that you don't like doing? 14. What is your parents' attitude to your friends? 15. Why does the fathers-and-sons problem always exist? 16. What is your idea of a good husband (wife)? 17. What does family happiness depend on?
Ex. 10. Arrange the following words in pairs of antonyms and translate them.
1. hard-working
2. generous
3. cheerful
4. strong
5. clever
6. relaxed
7. nice
8. optimistic
9. honest
10. reserved
11. sensitive
12. reliable
a. miserable
b. tense
c. horrible
d. pessimistic
e. dishonest
f. emotional
g. lazy
h. insensitive
i. unreliable
j. mean
k. weak
l. stupid
Ex. 11. Study the list of professions in the box and guess the profession of each person.
| vet, plumber, accountant, lawyer, engineer, architect, lecturers, firefighter |
1. My uncle Jim is an … , he designs buildings.
2. An … is someone who controls the financial situation of people and companies.
3. There are a lot of … at our faculty.
4. The person who is afraid of dogs cannot be a … .
5. It is impossible to imagine our life without a … who fits and repairs water pipes, bathrooms.
6. My father’s friend is a … , he advises people on legal problems.
7. The man over there plans the construction of roads and bridges, he is an ….
8. I am very proud of my grandfather, he works in the fire brigade. He is a ….
Ex. 12. Translate into English making use of the words from the box.
1. У ее брата очень широкие плечи. 2. Она симпатичная, а вот сестра ее…Ex. 15. Fill in the blanks with the necessary form of the verb to be.
1. I … at home now. My room … small. 2. He … at the University yesterday. 3. We … in the man’s house last week. 4. Our work … over tomorrow. 5. The girls … in the next room now. 6. Next year she … a teacher of English. 7. The children … at home at this time of the day. 8. My friend … in bed tomorrow because he is ill. 9. My brother … at school at 2 o’clock yesterday. 10. This time last year Jack … in Paris. 11. Today the weather … nice, but yesterday it … very cold. 12. It … a public holiday yesterday. 13. When I was a child, I … afraid of dogs.
Ex. 16. Ask special questions.
1. Her desk is in the room (what, where). 2. These houses are old (what). 3. We are in the classroom (who, where). 4. They will be ready soon (who, when). 5. She was a post-graduate last year (who, when). 6. The work will be over tomorrow (what, when). 7. They were ready to begin the work (who, what). 8. I was at the University last week (where, when). 9. The next text is in the note-book (what, where). 10. They will be students next year (when). 11. This ancient monastery is a museum now (what).
Ex. 17. Translate into English.
1. Завтра будет урок английского языка. 2. Эта книга моя или твоя? 3. Сегодня солнечно, но не тепло. 4. Это не мой пиджак, мой черный. 5. Десять минут назад дети были в саду. 6. Было приятно послушать ее рассказ. 7. В этом тексте для меня нет новых слов. 8. Двух студентов не было на уроке английского языка в прошлую пятницу. 9. Сейчас это их проблема, а не наша. 10. До ближайшего почтового отделения 500 метров. 11. Будет интересно увидеть ее в этом новом фильме. 12. Сколько страниц в этой книге?
Ex. 18. Writing. Using the words given in the list for the text do the following assignments.
1. Describe the student sitting next to you.
2. Write a description of someone you know well and like a lot (you may bring a photo of that person).
3. Describe someone from your group but do not say who the person is. Other students listen to your description and must guess the name of the person.
UNIT 2
| Grammar: The verb “to have” Present, Past, Future Simple; Types of questions |
The verb “to have”
| Present | Past | Future | ||||||
| I we you they | have | have got | I you he she it we they | had | I we | shall have/ will have | ||
| he she it | has | has got | you he she it they | will have |
In questions and negative sentences the following forms are used.
| Present | Have you got any money? Do you have any money? Have you any money? (less usual) | I haven't got any money. I don't have any money. I haven't any money, (less usual) |
| Has she got a car? Does she have a car? Has she a car? (less usual) | She hasn't got a car. She doesn't have a car. She hasn't a car. (less usual) | |
| Past | Did they have a car last year? | They didn’t have a car last year. |
| Future | Will the students have a seminar tomorrow? | The students won’t have a seminar tomorrow. |
The verb to HAVE is also used for many actions and experiences.
| have | breakfast / dinner / a cup of coffee / a cigarette/a drink / a meal. a bath / a shower / a swim / a rest / a party / a holiday / a nice time / a good journey / a good flight / a good trip an accident / an experience / a dream/ a sleep / a lie-down / a look (at something) / a chat (with somebody) / a talk / a fight a baby (= give birth to a baby) difficulty / trouble / fun |
| I don’t usually have a big breakfast. What time does Ann have lunch? Did you have any difficulty at the exam yesterday? |
Ex. 1. Make the sentences interrogative and negative.
b) 1. You had a good teacher of English at school. 2. They had two English… 8. The boy had his father’s blue eyes.Ex. 2. Say the following sentences in the past.
1. They have a few lectures this week. 2. He has much work to do this summer. 3. You have an interesting seminar today. 4. He has good ideas how to spend the weekend. 5. My parents have a nice little dog. 6. My friend has a reasonable answer. 7. They have lots of visitors in the Art museum. 8. Pete has many bookshelves in his room. 9. Olga has got a black leather bag. 10. Our students haven’t got much free time in winter.
Ex. 3. Say the following sentences in the future.
1. On Sunday my brother has breakfast at 9. 2. We have special seminars on Wednesday and Friday. 3. He has got a lot of publications. 4. Students have examinations in winter and in summer. 5. She has 3 hours at her disposal. 6. Our city has many green parks. 7. They haven’t got any money to pay their bills. 8. Our paper usually has much information about science. 9. First-year students have English classes two times a week. 10. My friend’s father has got a fine collection of pictures.
Present, Past, Future Simple
Present Simple
The Present Simple tense denotes: 1. Repeated actions indicated by adverbials of frequency such as often, always, usually, seldom,…Ex. 4 . Make the following sentences interrogative and negative.
Ex. 5. Write sentences using these words. Put the verb in the right form… 1. (always / early / Sue / arrive).Past Simple
The Past Simple tense describes: 1. A single action or a state, or a succession of single past actions with time adverbials such as…Ex. 6. Make the following sentences interrogative and negative.
1. Caroline went to the cinema three times last week.
2. We did a lot of work yesterday.
3. The police stopped him on the way home last night.
4. She passed her examinations successfully in January.
5. Mozart wrote more than 600 pieces of music.
6. Peter broke a window last night.
7. I lived in London for ten years while I was a child.
8. Janet used to have long hair when she was young.
9. He gave up his job as a journalist the other day.
10. Liz used to play tennis a lot when she was a student.
Ex. 7. Write sentences about the past (yesterday / last week etc.).
1. Jim always goes to work by car. Yesterday … .
2. Rachel often loses her keys. She … last week.
3. Kate meets her friends every evening. She … yesterday evening.
4. I usually buy two newspapers every day. Yesterday I … .
5. We usually go to the cinema on Sundays. Last Sunday we … .
6. I eat an orange every day. Yesterday I … .
7. Tom always has a shower in the morning. This morning he … .
8. Our friends come to see us every Friday. They … last Friday.
9. Pupils pass their A-Level exams every summer. Ann … last June.
10. Our faculty holds the Olympiads in mathematics in spring. Last spring our faculty … .
Future Simple
The Future Simple tense denotes: 1. A predicted future action, a happening which is inevitable…Facts to be remembered
| 1. We use shall I … ? / shall we … ? to ask somebody’s opinion (especially in offers or suggestions) | Shall I open the window? I’ve got no money. What shall I do? Where shall we go this evening? |
| 2. You can use won’t to say that somebody / something refuses to do something | The car won’t start. I wonder what’s wrong with it. |
Ex. 8. Make the following sentences interrogative and negative.
1. They will know the results in a week. 2. Clothes will be different in many years. 3. Sally will phone you when she gets home from work. 4. The weather will be much warmer tomorrow. 5. Everybody will have a computer in the year 2100. 6. I will remember this day all my life. 7. You will become a well-qualified specialist in 5 years. 8. Jack will be back in a minute. 9. He will like our new house when he sees it. 10. I will pay him a lot if he works well. 11. Helen will stay in bed till the clock strikes seven.
Types of Questions
General
Special (to the subject) …Pre-Reading Activity
Guess the meaning of the following words.
Mathematician [,mxTImq`tIS(q)n], founder [`faundq], progress [`prqugres]
information [Infq`meIS(q)n], privilege [`prIvIlIG], union [`jHnIqn], especially [I`speS(q)lI], comfortable [`kAmf(q)tqbl].
Read and learn the basic vocabulary terms.
Memorise the following word combinations.
Reading Activity
A Letter to a Friend
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… I have so much to tell you about my life in Minsk. I live in the students’… And now I would like to describe the routine I more or less follow everyday. During the week I usually wake up at 6.30…Post-Reading Activity
Ex. 9. Answer the following questions.
1. Do you take a cold or a hot shower in the morning? 2. What time do you leave home to get to university? 3. Have you ever been late for classes? 4. How many classes do you have every day? 5. Eating is such a waste of time and effort, isn’t it? It would be better if we could simply take pills. 6. What is your idea of a good rest after classes? 7. How long does it take you to prepare your homework? 8. What sports are you good at? 9. Do you take part in any organized sporting activities? 10. Do you prefer to stay in or go out in the evening? 11. What is your favourite pastime? 12. Do you make any plans for the weekend? 13. Do you like to spend your free time with your friends or on your own? 14. How often do you go to the cinema (to the theatre)? 15. Why do some people prefer to watch films at the cinema instead of relaxing in front of their TV sets? 16. Are theatres as popular now as they used to be? 17. What is the best time for you to go to bed?
Ex. 10. Find the Russian equivalents for the following English word combinations.
2. to describe the routine 3. to depend on the weather 4. to have a late nightEx. 13. Write sentences beginning I think... or I don't think... .
| 1 (Diana will pass the exam) 2 (Diana won't pass the exam) 3 (we'll win the game) 4 (I won't be here tomorrow) 5 (Sue will like her present) | 6 (they won't get married) 7 (you won't enjoy the film) 8 (it won’t rain this afternoon) 9 (the exam will be difficult) 10 (she won’t be up to her neck in work) |
Ex. 14. Ask special questions.
1. They had an important paper in the desk. (what, where) 2. Five girls from our group live in the hall of residence. (how many) 3. Paul and Jim played tennis yesterday. (when) 4. This student has got three lectures today. (how many) 5. His friends work hard all day. (whose) 6. Professor Smirnov will hold a seminar tomorrow. (what, when) 7. These men have a logical plan. (who) 8. It took me two hours to do my homework yesterday. (how long) 9. We will probably go to Scotland for our holiday. (where) 10. We usually have our meals in the kitchen. (where) 11. I like a big breakfast in the morning. (who, when) 12. Sally goes to the theatre once a month. (how often) 13. My cousin won one million rubles in the lottery. (how much)
Ex. 15. Translate into Russian.
1. I overslept this morning because I had a late night yesterday. 2. Helen will stay in this evening. 3. Did you go out last Sunday? 4. At the end of each term students are always up to their neck in work. 5. Jennifer and her room-mate get on well because they respect each other. 6. Jack left his house a bit late in the morning, missed the bus and was late for classes. 7. We have a long lunch break but I never go to the University canteen. 8. At times there are other things to do like going shopping, doing sports and so on. 9. Later in the evening Kate does a bit of painting which is a sort of a hobby for her. 10. I used to go fishing when at school, but now I haven’t got any time to do that.
Ex. 16. Translate into English.
1. Летом я принимаю душ по утрам, а зимой я часто принимаю ванну. 2. В Минске есть много мест отдыха и развлечений. 3. Твоя квартира выходит окнами на юг или на север? 4. Я занимаюсь английским в выходные дни, так как я по горло загружен работой в течение недели. 5. К сожалению, у меня очень мало времени на отдых. 6. Моя подруга никогда не опаздывает на первую лекцию. 7. В наше время не так уж легко поступить в университет. 8. Если вечером я ложусь поздно спать, то на следующий день я стараюсь поспать немного днём. 9. Здесь у меня есть возможность играть в теннис два раза в неделю. 10. Как правило, рабочая неделя пролетает очень быстро. 11. Катя живёт в студенческом общежитии №7, и с ней в комнате живут ещё две девушки.
Ex. 17. Writing.
1. Write a letter to your mother describing your weekdays at the University.
2. Write a letter to your friend in which you tell him/her how you enjoy your life at weekends.
UNIT 3
| Grammar: Continuous tenses. Pronouns: some, any, no |
Continuous tenses
| Present Continuous | Past Continuous | Future Continuous | |||
| I He/She/It We/You/ They | am working is working are working | I/He/She/It | was working | I He/She/It We/You They | will be working |
| We/You/ They | were working |
Present Continuous Tense
| The Present Continuous Tense is used: | Examples |
| For an action happening at the moment of speaking usually with time expressions: at this moment at the time, now, at present, just now | The younger children are sleeping now, but the elder children are not sleeping. They are watching TV. What aretheir parents doing? |
| For a temporary action | Jack is studying at Oxford University. Is his friend Bill studying there too? No, he is not studyingat Oxford. He is working for a company in London. |
| For a pre-arranged, planned and intended action | My father is leaving for Paris tonight. My mother is not going with him. Is she staying at home? |
Ex. 1. Compare and analyze the usage of Present Simple Tense and Present Continuous Tense.
1. I usually watch TV in the evenings. I am watching TV now. 2. Are you looking for a key now? You always look very smart. 3. Why are you not wearing your new dress now? She usually wears fashionable clothes. 4. Today it is raining heavily outside. It rains heavily in autumn in this part of the country. 5. He walks very slowly as a rule but now he is walking fast. 6. I usually don’t rest after university, but today I’m very tired and I am having a rest. 7. I think I will be on holiday next month. I am going on holiday next month. 8. We live in Washington, though we are staying in London at the moment. 9. I play tennis every week. Where are the children? – They are playing tennis on the court now. 10. The foreign scientists are flying back to Europe tomorrow. Some passenger planes fly faster than sound.
Past Continuous Tense
| The Past Continuous Tense is used: | Examples |
| For an action in progress at a definite moment in the past usually with time expressions at five o’clock yesterday ,all day yesterday, the whole evening, all day long, when he came, while | 1. What were you doing at one o’clock yesterday? – At one o’clock yesterday I was having lunch. 2. Were you waiting for a bus when I noticed you at the bus stop? – No, I wasn’t. I was just passing by it. |
| For a temporary action in the past | 1. When Alex met Mary in Minsk last year, she was not having preparatory courses for University. 2. Was she already studying at BSU? Yes, she was studying at the faculty of Mechanics and Mathematics. |
Ex. 2. Compare and analyze the usage of the Past Simple Tense and the Past Continuous Tense.
1. I dropped my bag when I was running for a bus. 2. I played computer games yesterday. I was playing computer games at 3 o’clock yesterday. I was playing computer games the whole evening yesterday. 3. When I came into the kitchen, mother was cooking. 4. Did you do your homework yesterday? – I was doing my homework from 6 till 9 o’clock yesterday. 5. She always looked very smart. When I met her in Rome, she was wearing a long beautiful dress. 6. Father came home at 5 o’clock yesterday. Then he was reading a newspaper while mother was watching TV.
Future Continuous Tense
| The future Continuous Tense is used: | Examples |
| For an action which will be going on at a definite moment in the future: at 6 o’clock tomorrow, the whole day tomorrow, at this time tomorrow | I will be working in the library at 10 o’clock tomorrow. And you? What will you be doing at this time? I will not (won’t) be working in the library, I’ll be preparingfor my exams. |
| For an action which will be going on during a certain period of time in the future: when he comes | The children will not (won’t) be sleeping when I come home from work. Will they be having a party? No, they won’t. They will be havingsupper. |
Ex. 3. Compare and analyze the usage of the Future Simple Tense and the Future Continuous Tense.
1.Tomorrow I will begin decorating my flat as soon as I come home from the market. I’ll be decorating it from 2 till 6 o’clock. 2. I think I’ll use a bike to get to school tomorrow. Will you be using your bike this evening? 3. Richard will be cleaning the house while Sue is cooking dinner. 4. This time tomorrow evening my friends will be flying over France. They’ll probably go to the UK too. 5. I think I’ll take an umbrella because it is still raining. They say it will be raining the whole week-end.
Ex. 4. Make the following sentences interrogative and negative.
1. This time next month I will be sitting on the beach. 2. Mr. Molden was driving a car at the time of the accident. 3. Peter will be working the whole evening tomorrow. 4. The little boy was swimming in the sea the whole morning. 5. Yesterday the teams were playing football from 2 till 5 o’clock. 6. It is getting cooler and cooler day by day. 7. Mr. Pitt is talking on the phone at the moment. 8. The Browns are moving house next week. 9. In two years’ time he will be living in the country.
Pronouns some, any, no
Ex. 5. Analyze the following sentences and translate them into Russian.
1. Are there any English books in the library? 2. I can’t find any mistakes in your dictation. 3. I’d like to have some more jam. 4. Can you give me some more information? 5. There is some sugar in the cake but there is no salt. 6. What book shall I take? – Any you like. 7. Take some juice, please. It’s very tasty. 8. Would you like some time to finish your work? 9. I know some funny jokes. 10. No students are happy to have extra seminars. 11. I can do it without anybody’s help. 12. Once I ate some ten ice-creams a day. 13. I want to know if you have done anything good in your life. 14. Can I have some of these books?
Ex. 6. Chose the right word.
1. He left without saying something/anything to somebody/anybody. 2. Suddenly anyone/someone entered the room. 3. Is there something/ anything good on TV tonight? 4. Do you want anything/something to eat? 5. Is there any/some coffee in the coffee-pot? 6. Someone/anyone can take part in the competition. 7. There is anything/nothing in the bag. 8. There are any/no matches left. 9. Will you have any/some more jam? 10. I can’t find the pen nowhere/anywhere.
Ex. 7. Answer the following questions using the pattern below.
Have you got any sisters?
Yes, I have some.
No, I have no sisters.
No, I haven’t any sisters.
1. Do you want something to eat? 2. Have you got any news? 3. Do you know anybody in the village? 4. Have you invited anybody to the party? 5. Do you understand anything? 6. Was there anything interesting at the exhibition? 7. Do you have any energy left? 8. Have you seen John anywhere? 9. Is there any coffee in the coffee-pot?
Pre-Reading Activity
Guess the meaning of the following words.
system n. ['sIstqm], symbol n. [sImbl], positive adj. ['pOzItIv], diagram n. ['daIqgrxm], complex adj. ['kOmpleks], rational adj. ['rxSqnl], fundamental adj. [ֽfAndq'mentl], fact n. [fxkt], express v. [Iks'pres], negative adj. ['negqtiv], start n. [sta:t], position n. [pq'zISn], direction n. [dI'rekSn], occupy v. [`OkjupaI], zero n. [`ziqrou], different adj. ['dIfrent], basic adj. [`beIsIk].
Read and learn the basic vocabulary terms.
date back to (v) [`deIt] – датироваться, относиться к определенному времени antiquity (n) [xn`tIkwItI]- древность, античность integer (n) [`IntIGq]- целое числоMemorize the following word combinations
1. zero is neither positive nor negative-ноль не является ни положительным, ни отрицательным
2. to label a point on the line- отметить точку на прямой
3. to each point on the line we assign a number-каждой точке на кривой мы ставим в соответствие число
Reading Activity
Numbers
The first numbers we use are the positive integers, and the fundamental fact… The positive integers are often written without the plus sign, thus we may write 789 instead of + 789. Since zero is…Post-Reading Activity
Ex. 8. Answer the following questions.
Ex. 9. Find the Russian equivalents for the following English word… 1. in either direction; 2. imaginaries; 3. is composed of; 4. real and imaginary parts; 5. a quotient of two integers;…Ex. 10. Give the proper English equivalents for the Russian expressions.
| Древность, соотношение, разделительная точка, делитель, рациональные и иррациональные числа, частное двух чисел, мнимые числа, запись, действительная и мнимая части. |
1. … is occupied by the number zero. 2. The irrationals can not be expressed as …. 3. Positive fractions or numbers can be expressed as…of two of these integers. 4. We are not allowed to use the number zero as… 5. The beginning of our number system dates back to… 6. The real number system is formed of… 7. Numbers √-2, -√-1 are called… 8. The expression 2+√-3 is composed of… 9. To denote the real part of a complex number we use…
Ex. 11. Open the brackets putting the verbs in the correct form.
1. Why you (look at) me like that? 2. We (read) a book while he (cook) lunch at that time yesterday. 3. This time next month I (to cross) the Pacific Ocean. 4. I (wait) for you when you come out. 5. He (sit) in a café when I saw him. 6. I (go) to the cinema tonight. 7. Look! She (wear) the same dress as me. 8. Yesterday at 8 o’clock we (watch) the football match. 9. He (drive) his car himself today. 10. Great news! Jack (come) in a week.
Ex. 12. Fill in the blanks with the pronouns from the box.
| any, anything, no, some, nobody, anyone, anything, any, some, anybody, anywhere, something, anyone |
1. Is there … juice left in the fridge? 2. Could I have … coffee? 3. Has … called me? 4. Is there … I can do for you? 5. She said … very interesting. 6. Don’t go … tonight. 7. When I came home there was … there. 8. Does … know … funny jokes? 9. Would you like ... more tea? 10. Did you notice … strange about him? 11. There is … time left at all. 12. We can rarely meet … as brave as he is.
Ex. 13. Ask special questions.
1. The students are applying irrationals in the given mathematical problems. (Who?) 2. The teacher is explaining how to mark off the line with numbers. (What?) 3. There are some positive numbers in the expression. (What?) 4. He was trying to find the common ratio of the three fractions from 3 until 5 o’clock. (How much time?) 5. We will be using this notation to introduce imaginaries next term. (When?) 6. The students are doing the research now. (Who?) 7. At 4 o’clock yesterday Professor Clarkson was delivering a lecture. (When?) 8. This time next month we will be having a winter session. (What?) 9. They are solving some mathematical problems at the moment. (Who?) 10. We are going on a summer holiday in a couple of days. (When?)
Ex. 14. Translate from English into Russian.
1. We will be considering complex numbers next term. 2. They are trying to find the quotient of these two numbers. 3. This time last week we were having a holiday. 4. We are substituting unknowns for irrationals to get a right result. 5. The researchers were using this equipment all month long. 6. Are there any irrational numbers in this system? 7. The students were finishing the test on mathematics when the bell rang. 8. The delegation of scientists is coming to Minsk in a week. 9. This time next term the students of MMF will be celebrating the birthday of the faculty. 10. I don’t see any other ways to arrange this matter. 11. I can do it without anybody’s help. 12. You can take any of these books.
Ex. 15. Translate from Russian into English.
1. Студенты выполняют контрольную работу сейчас. 2. Группа аспирантов отправляется в Германию в декабре. 3. Мы будем использовать комплексные числа в следующем семестре. 4. В это время через неделю мы будем сдавать экзамены. 5. Мы решали эту задачу целый урок вчера. 6. Мы стараемся найти частное этих целых чисел. 7. Что ты делаешь завтра после занятий? 8. В это время вчера мы обедали в столовой. 9. Что ты делал, когда я позвонил тебе? 10. Некоторые из этих числовых систем сложны. 11. Студенты выбирают мнимые и иррациональные числа из данных выше.
UNIT 4
| Grammar: Modal verbs and their equivalents |
CAN
| Present Can, cannot (can’t); am/are/is (not) able to | Future Can; shall/will (not) be able to | Past Could, could not (couldn’t); Was/were (not) able to |
| Mental, physical or circumstancial ability to do something знать как сделать, уметь, мочь, иметь право сделать что-либо; to be able to – быть способным к чему-либо, быть в состоянии, иметь силу, власть, ум, возможность что-либо сделать | ||
| He can swim. I am able to help you now. (particular situation) I can’t hear anything. | I can do it tomorrow. I shall be able to help you. | He could speak three languages before he was twelve. (repeated action, ability in the past) He was able to win the game. (managed to do; past single action) |
| Request | ||
| Can you tell me the time? (informal) Could you give me a lift? (polite) | ||
| Permission/Asking for permission(informal) | ||
| You can take the book now. Can I go to the party too, Mother? | ||
| Prohibitionнельзя (in informal speech or writing) | ||
| You can’t cross the street here. | ||
| Offer | ||
| Can I help you? (informal) | ||
| Strong doubtне может быть, чтобы; вряд ли, неужели | ||
| You can’t be cold. It’s very hot here. She can’t be Sam’s sister. She is in Kiev now. | ||
| Possibility | ||
| This road can get very busy. (general possibility) The roads could get very busy tomorrow because there is a demonstration. (specific situation) |
Ex. 1. Analyze the following sentences and translate them into Russian.
MAY
| Present May, may not | Future May; Shall/will (not) be allowed to | Past Might, might not; Was/were (not) allowed |
| Permission/Asking for permission можно, можете | ||
| You may answer the questions later. (formal) May I come in? (polite) | You may call me tomorrow. (formal) They will be allowed to go to the concert. | He said that I might borrow his pen. He was allowed to enter the country. |
| Prohibitionнельзя (in formal speech and writing) | ||
| You may not talk during the test. (formal) | You will not be allowed to take the exam. | We were not allowed to tell her everything. |
| Doubt/Uncertaintyможет быть, возможно | ||
| The rain may (might) stop later in the day. He may come tomorrow. | ||
| Possibility | ||
| In the museum you may(can) see some interesting things. |
Ex. 2. Analyze the following sentences and translate them into Russian.
1. The students may not use the calculator at the exam. 2. Professor, may I take the exam next week? 3. Were students allowed to visit the laboratory? 4. The answer may give the key to the whole problem. 5. Will he be allowed to take part in the conference? 6. The teacher may ask you to stay after the lessons and copy the text. 7. You are not allowed to use the machine without permission. 8. You may do the rest of the work tomorrow. 9. May I smoke here? – No, you mustn’t. 10. May I take this map? – No, you may not. 11. May he wait for us in the hall? – Yes, he may.
MUST
| Present Must, must not (mustn’t) | Future Shall/will (not )have to | Past Had to, did not have to; Did you have to…? |
| Necessity, duty, obligationдолжен, нужно, надо | ||
| You must obey these rules. I’m afraid I must go now. | She will have to come later. | We had to get more exercise last week. |
| Near certainty, logical assumptionвероятно, должно быть | ||
| She must be about twenty. BUT:Probably, he doesn’t know English. | BUT:The weather is likely to change. | BUT:Evidently, she didn’t know my address. |
| Prohibition | ||
| You mustn’t walk on the grass. | ||
| Order, strong advice | ||
| You must revise for your test. |
Ex. 3. Analyze the following sentences and translate them into Russian.
1. As a postgraduate student you must obtain some new scientific results. 2. Must we send them the results of our work immediately? – Yes, do please. 3. You must pay more attention to details. 4. The door to the laboratory must not be left open. 5. The meeting is at 10 o’clock sharp and you mustn’t be late. 6. He must be at the library now. 7. You must let him know about it. 8. You must be tired after your hard work. 9. Must I type the document? – No, you needn’t. 10. People must not cross the border without passports. 11. Everyone must go to school. 12. Must we measure the perimeter? – Yes, you must. 13. Must I really help him with the translation?
TO HAVE TO
| Present Have/has to, do/does not have to; Do you have to…? | Future Shall/will (not) have to; Will you have to…? | Past Had to, did not have to Did you have to…? |
| Necessity, duty, obligationдолжен, нужно, надо, приходится, вынужден | ||
| She has to find a new job. They’ve got to sell their car. | I shall have to speak to them about this plan. | He had to return home. |
| Absence of necessityне нужно, не надо | ||
| We don’t have to attend classes on Sunday. | Sam won’t have to come back till April. | She didn’t have to take a taxi. |
Ex. 4. Analyze the following sentences and translate them into Russian.
1. Do I have to present another schedule? 2. I had to explain the rule twice to make it perfectly clear. 3. They didn’t have to change the date of the conference. 4. You‘ve got to study the relation between these two discoveries. 5. Does she have to wear glasses? – Yes, she does. 6. They will have to arrange everything for the meeting. 7. Did you have to walk all the distance to the station yesterday? 8. Do we have to define prime numbers? – No, you needn’t. 9. Have I got to make another drawing? – Yes, you have.
TO BE TO
| Present Am/is/are (not) to do… | Future Am/is/are (not) to do… | Past Was/were (not) to do… |
| Necessity, an expected, planned action, a predestined event должен, предстоит, суждено | ||
| What am I to do? The train is to come at 7. | You were to stay here. He was never to see her again. | |
| Order, formal instructionsне делай, не смей делать | ||
| You are not to say a word to anyone. No-one is to live the room. |
Ex. 5. Analyze the following sentences and translate them into Russian.
1. The students are not to take the books out of the reading-room. 2. Were they to meet at four o’clock at the University? 3. You are to write an abstract of your thesis. 4. Am I to follow you? 5. We are to have six lessons of English this week. 6. You are to give the books back to the library at the end of the year. 7. The concert was to take place yesterday. 8. Who is to meet Jack? 9. She was to finish school last year. 10. The lessons are to begin at eight o’clock. 11. Is she to make a speech? – Yes, she is.
NEED
| Present Need, needn’t | Future Need, needn’t | Past |
| Necessityнужно, надо | ||
| Need I call the doctor tomorrow? (Also: Do I need to call the doctor?) | (Also: The plants needed to be watered.) | |
| Absence of necessityне нужно, не надо | ||
| I needn’t speak to her about it. (Also: She didn’t need to work as hard as me.) | (Also: He didn’t need to stay in a hotel.) |
Ex. 6. Analyze the following sentences and translate them into Russian.
1. Need we continue working by this plan? 2. You needn’t do all this in written form, you know. 3. He didn’t need to read his paper at the seminar. 4. Do you need to write sentences about numbers in all branches of mathematics? 5. Need you worry about the man who always deceives you? 6. They needn’t hurry now. They will have to wait for another train. 7. Need I come myself? – Yes, you must. 8. Need we perform any other construction? – No, you needn’t.
SHOULD, OUGHT TO
| Present Should (not), ought (not) to | Future Should (not), ought (not) to | Past |
| Should (general advice) следует, должен | ||
| You should try again. Why should I go there? | ||
| Ought to (moral obligation, laws, rules) следует, должен | ||
| You ought to tell your parents the truth. You ought to keep to the speed limit. | ||
| Probability | ||
| It’s 10 o’clock. He should/ought to be at work. It shouldn’t be difficult to get there. |
Ex. 7. Analyze the following sentences and translate them into Russian.
1. You shouldn’t miss lectures and seminars if you want to pass the exams. 2. If you want to know mathematics you should work hard at it. 3. Doctor, what should I do? 4. You ought to go further with this investigation. 5. Ought you to tell everybody what has happened? 6. You ought not to participate in their useless argument. 7. You should switch off your mobile in class. 8. They ought to ban smoking in public places.
Pre-Reading Activity
Guess the meaning of the following words.
Decimal [`desIm(q)l] adj, combination [,kOmbI`neISqn] n, positive [`pozItIv] adj, negative [`negqtIv] adj, symbol [`sImbql] n, plus [plAs] n, minus [`maInqs] n, indicate [`IndIkeIt] v, sum [sAm] n, product [`prodqct] n, numeration [,nju:mq`reISqn] n, base [beIs] n, arithmetic [q`rITmqtIk] n, system [`sIstIm] n, represent [,reprI`zent] v
Read and learn the basic vocabulary terms.
numeral (n) [`nju:mqrql] цифра, символ, число digit (n) [`dIGIt] цифра value (n) [`vxlju:] величина, значение; (v) ценитьMemorize the following word combinations
1. (the former)/ the latter – (первый из вышеупомянутых)/ последний (из вышеупомянутых)
2. no matter how great – неважно, насколько большое
3. ten times as great – в десять раз больше
4. the number to be made smaller – число, которое должно быть уменьшено
5. since – так как
6. the number resulting from multiplication – число, являющееся результатом умножения
7. therefore - следовательно
8. what is left over – то, что осталось
9. whenever – всегда, когда бы ни
10. except – за исключением
Reading Activity
Four Basic Operations of Arithmetic
Until XVI century people in Europe used Roman numerals. The Roman system of numbers is based upon the letters I, V, X, L, C, D, and M. These letters… The invention of our present notation for the decimal number system made… There are special signs to indicate operations with numbers. They are plus (+), minus (-), multiplication (x) and…Post-Reading Activity
Ex. 8. Answer the following questions.
1. What numerals were used in Europe until XVI century? 2. Who introduced the symbol 0? 3. Is the Hindu-Arabic system a decimal system or a binary one? 4. What does the value which a digit represents depend on? 5. What are the signs most used in arithmetic? 6. What are the fundamental operations of arithmetic? 7. Are division and multiplication inverse operations? 8. Are subtraction and multiplication inverse operations? 9. What must you remember about multiplication? 10. What important facts about division must be remembered?
Ex. 9. Find the Russian equivalents for the following English word combinations.
1. to use the same numbers; 2. to represent numbers; 3. present notation; 4. numeration system; 5. decimal system; 6. to be based on tens; 7. inverse operation; 8. capital letters; 9. arithmetic sentence; 10. to measure the distance
a. основываться на десятках; b. обратная операция; c. заглавные буквы; d. измерять расстояние; e. десятичная система; f. представить числа; g. использовать одни и те же числа; h.система счисления; i. арифметическое выражение; j. современная система записи
Ex. 10. Mark the following as True or False.
1. People used numbers thousands of years ago. 2. The decimal number system was invented by the Romans. 3. The Roman system of numbers is based upon the letters A, B, C, D, E, F and G. 4. The symbol 0 was introduced by the Arabs. 5. The work of a zero is to keep the other nine symbols in their proper place. 6. Our decimal number system is positional. 7. We go from right to left in forming larger and larger units of ten, hundred, thousand and so on. 8. We work both with positive and negative numbers in arithmetic. 9. The product of any number multiplied by one is the same number. 10. The quotient is 0 whenever the divisor is 0.
Ex. 11. Fill in the blanks with necessary words and word combinations from the box.
| the sum, the quotient, the multiplication sign, to divide, the difference, subtraction, factors, addends, the subtrahend, a remainder, to be added, a numeral, division |
1. We get … as a result of addition. 2. The numbers to be added are called …. 3. You may check … by multiplication. 4. Will there be … if you divide 25 by 7? 5. If you are … two numbers, you must remember that division by 0 is meaningless. 6. To find the minuend … and the subtrahend must be known. 7. Addition and … are inverse operations. 8. The multiplicand and multiplier are the names for the … . 9. The result of division is known as …. 10. The difference is the number that when added to the … gives the minuend. 11. The plus sign between two numbers means that these numbers are … . 12. A dot placed between two numbers is used as … . 13. A symbol used to represent a number is called … .
Ex. 12. Make the sentences negative and interrogative.
1. We can add numbers in any order. 2. You should discuss the rules of multiplication at the next lesson. 3. Mathematicians were able to discover another fundamental law of nature. 4. The result must be checked immediately. 5. You have to decide on the subject of your thesis. 6. They may misunderstand the theoretical character of the problem. 7. We were allowed to work on our experiment out of class. 8. They will be able to use some symbols instead of words. 9. We need to use special methods to obtain necessary results. 10. You ought to study carefully the definitions given above.
Ex. 13. Ask special questions.
1. Scientists should develop this important branch of mathematics. (What) 2. In antiquity people could count using positive integers. (When) 3. We are not allowed to use zero as a divisor. (Who) 4. Natural numbers may be divided into two classes: even and odd. (How many) 5. She was able to obtain the solution by multiplying two numbers. (How) 6. He had to speak English at the international conference. (Where) 7. I must discuss the details of my dissertation with the science adviser. (Who(m)) 8. You need to follow your teacher’s instructions during the test. (Whose) 9. You ought to do your best and fulfil the task. (What) 10. First you are to perform the operation of division and then multiply the quotients. (Which)
Ex. 14. Choose the phrase closest in meaning to the given statement.
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?Ex. 15. Choose the correct modal verb or its equivalent.
1. You (may/ought to/are to) take care of your parents. 2. My sight is getting worse. Next year, I’m afraid I (cannot/may not/won’t be able to) read without glasses. 3. Twelve delegates from several countries (can/have to/are to) meet at the end of February. 4. Excuse me, (could/may/must) you tell me the way to the Houses of Parliament? 5. The weather is getting worse. It (must/is likely/may) rain. 6. There are no people in the hall, we (must/can/need) have a talk there. 7. Although he felt ill, he (could/was able to/may) finish all the paperwork. 8. You (can/must/ought to) go and see that movie. It’s very interesting. 9. Don’t worry, you (don’t have to/mustn’t/may not) pay now.10 When we were at school, we (had to/ought to/must) wear a uniform.
Ex. 16. Give the proper English equivalents for the Russian expressions.
1. Нам пришлось perform the operation of addition to find the answer. 2. Ему предстоит specify the conditions of the experiment. 3. Им разрешают use a dictionary if necessary. 4. Я в состоянии solve this difficult problem myself. 5. Вам следует remember that multiplication is associative. 6. Ей не надо use this theorem. 7. Они могут apply their theories in practice. 8. Вы обязаны remember several rules about division. 9. Можно мне start the calculations now? 10. Вам следует to accept everything your parents say as an axiom.
Ex. 17. Translate from English into Russian.
1. Everyone studying mathematics must have a good understanding of the meaning of each symbol. 2. These expressions may contain numbers and letters. 3. Multiplication can be distributed over addition, e.g. 14x12 = (14x10)+(14x2) 4. A prime number is a number that can be divided evenly by only 1 and itself. 5. No multiplication sign is to be used between two letters or a letter and a number written side by side. 6. The plus sign should be understood when there is no sign before the number. 7. Will you be able to name other factors of 18 except nine and two? 8. In some cases, when we have to name a whole number in a factored form, more than two factors can be used. 9. A positive number can be indicated by placing a plus sign (+) before the number. 10. When the minus sign is placed between any two numbers, it indicates that the difference of the two numbers is to be found. 11. Division may be indicated also by writing the dividend above the divisor with a line between them.
Ex. 18. Translate from Russian into English.
1. Числа, которые нужно сложить, называются слагаемыми, а результат сложения называется суммой. 2. Эти числа предстоит перемножить. 3. Мы должны записывать результат справа от знака равно. 4. Число можно поделить на два без остатка (точно), если это четное число. 5. Деление обратно умножению. 6. Произведение любого числа, умноженного на ноль, равно нулю. 7. Никто не может сказать, когда люди начали считать. 8. Они обозначили (указали) операцию сложения знаком плюс. 9. Ни один студент не мог решить задачу, заданную профессором. 10. Им придется использовать двоичную систему счисления. 11. Данный элемент может быть обозначен тем же символом.
UNIT 5
| Grammar: Present, Past, Future Perfect (Active Voice) |
| The Present Perfect Tense | The Past Perfect Tense | The Future Perfect Tense |
| have/ haven’t + V3 has/ hasn’t + V3 | had/ hadn’t + V3 | shall/ will have + V3 shan’t/ won’t have + V3 |
| a) Resultative Perfect just, yet, already, ever, never, lately, recently, today, this week, this month, etc. They have not done it yet. Они еще это не сделали. b) Durative Perfect (to be, to have, to know) for, since, how long How long have you known him? Как давно ты его знаешь? | by 6 o’clock yesterday, by that time, by the end of last year, before he came They had done it by the time we came. Они сделали это к нашему приходу. They hadn’t done it by the time he came. Had they done it by the time you came? | by 6 o’clock tomorrow, by this time tomorrow, by the end of next year, before he comes They will have done it by 6 o’clock tomorrow. Они сделают это завтра к шести часам. They won’t have done it by 6 o’clock tomorrow. Will they have done it by 6 o’clock tomorrow? |
Ex. 1. Compare Russian and English Tense forms.
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 longago 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 21st 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.
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.
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
Reading Activity
Rational numbers and decimal numerals
A fraction is a quotient of numbers, the quantity obtained when the numerator is divided by the denominator. Thus, ¾ represents three divided… The denominator represents the number of equal parts that an object is divided… Fractions are rational numbers and that means that the denominator and the numerator are integers. Any rational number…Post-Reading Activity
Ex. 5. Answer the following questions.
1. What’s a fraction in mathematics? 2. In what form is a common fraction generally written? 3. What does the denominator (the numerator) represent? 4. How can a rational number be defined? 5. What types of fractions do you know in algebra? 6. What is an equivalent (mixed) fraction? 7. Is it possible to change a mixed number to an improper fraction? 8. What happens to a common fraction when we multiply it by one? 9. In what way can we reduce a fraction? 10. What is a decimal fraction?
Ex.6. Find the English equivalents for the Russian words and word combinations.
1. часть целого; 2. числитель дроби; 3. знаменатель дроби; 4. должны быть превращены; 5. в десятичной форме; 6. наименьший общий знаменатель; 7. полученная дробь; 8. неправильная дробь; 9. сократить дробь; 10. часть целого; 11. члены дроби; 12. представлено дробью; 13. искомая дробь; 14. иметь что-либо общее
a. the fraction sought for; b. a proper fraction; c. to reduce a fraction; d. a part of the whole; e. to have in common; f. in decimal form; g. the resulting fraction; h. the terms of a fraction; i. the denominator of a fraction; j. an improper fraction; k. the least common denominator (LCD); l. the numerator of a fraction; m. must be changed to; n. is represented by the fraction
Ex.7. Give the proper English equivalents for the Russian expressions.
1. A rational number is частное (divisor is not zero) of two integers. 2. Fractions which represent values less than one are called правильными…Ex. 8. Mark the following as True or False.
1. Every fraction has a numerator and a denominator. 2. A rational number can’t be another name for a fraction. 3. In the proper fraction the denominator is less than the numerator. 4. In the improper fraction the denominator is greater than the numerator. 5. A mixed fraction contains an integer and a proper fraction. 6. We change a fraction if we multiply it by 1. 7. If we multiply the numerator and the denominator by the same whole number we produce another name for the fractional number. 8. Principles of arithmetic are valid in the case of mathematics. 9. It’s impossible to express rational numbers as decimal numerals. 10. The digits to the right of the decimal point represent whole numbers. 11. The name given to a decimal like 0.1313 is terminating. 12. We obtain a tenth by dividing 1 by 10.
Ex. 9. Fill in a suitable verb in the Present Perfect Tense.
| to give, to become, to show, to draw, to learn, to find, to be, to make, to take, to rewrite |
1 They … an attempt to overcome difficulties of this complicated procedure.
2 The science adviser … the whole situation under control.
3 They … not all the examination material yet.
4 I … this article on Maths very helpful.
5 In the given example he … the validity of these principles.
6 The post-graduate … the previous chapter of his report.
7 He … a first-year student of the Mechanics and Mathematics faculty this year.
8 My friend … already the diagram which has certain advantages.
9 The teacher … an example of an algorithm.
10 … you … able to name these rational numbers by decimal numerals?
Ex. 10. Choose the correct tense form.
2. We (have started/ started) learning fractions when we were at school. 3. By the end of the lecture the students (had learnt/ has learnt) that in… 4. I (have looked up/ looked up) in a dictionary just now the meaning of the word ‘a solidus’(a slanting line).Ex. 11. Ask special questions.
Ex. 12. Translate into English.
UNIT 6
| Grammar: Degrees of Comparison; Perfect Continuous Tenses |
Degrees of Comparison
Ex. 1. Analyze these sentences and compare the adjectives given there. Translate them into Russian.
Irregular Comparatives and Superlatives: good / well – хороший/хорошо bad / badly – плохой/плохо much / many - много …Ex. 2. Analyze these sentences and compare the adjectives given there. Translate them into Russian.
1. This example is not quite good. You ought to find a better one. I do not think it is the best example that you can give. 2. The result of their exam is bad. It is much worse than we expected. In fact, it is the worst in many years. 3. I have little free time. Mary has less free time than me. Jane has the least free time. 4. My house is far from the University. The hostel is farther from the University. I saw them in the farthest corner of the park. Please, send the books back without further delay. 5. Peter has 5 notebooks. Mary has more notebooks. She has 10. John has the most books. He has 15. 6. He came home later than usual. Have you heard the latest news? The last train leaves in half an hour. 7. My elder brother is 5 years older than me. My grandmother is the oldest in our family. Her eldest son is my father. 8. The nearest café is in a five - minute walk from here. The next news bulletin comes in 10 minutes.
Types of Comparisons
Than чем This book is more interesting thanthat one. Today is warmer thanit was yesterday. The chair is less comfortable…Ex. 3. Follow the model and make the sentences in which comparison is expressed.
Model 1: This problem is … (difficult) … the first problem.
This problem is as difficult as the first problem.
1. This text is … (interesting) … that one. 2. This sentence is … (long) … the second one. 3. This definition is … (exact) … the definition given in the text-book. 4. His answer is … (good) … that girl’s answer. 5. English classes are … (important) … lectures on mathematics.
Model 2: This theorem is … (famous) … people may think.
This theorem is not so famous as people may think.
1. This system is … (reliable) … the one we studied. 2. That dictation is … (easy) … we’ll write next lesson. 3. The proof is … (valid) … he supposed at first. 4. This story is … (boring) … he thought about it before. 5. This solution is … (good) … she suggested at the conference.
Model 3: (Big) the plan (long) they will work.
The bigger the plan the longer they will work.
1. (Soon) the problem is solved, (good). 2. (Long) the student refuses to learn the words, (bad) for him. 3. (Hard) they work, (good) is for their salary. 4. (Much) she practices, (healthy) she becomes. 5. (Convincing) the lecturer speaks, (attentive) the audience listens.
Ex. 4. Open the parentheses and use the correct form.
1. Our sitting-room is (light) room in our flat. 2. There are (many) students in our group than in yours. 3. The railway station is (far) from here than the airport. 4. My suit is much (expensive) than yours. 5. Betty is a little (short) than her brother. 6. Who was (late) person to leave the building yesterday? 7. Her (old) brother is a well-known Belarusian mathematician. 8. Who is (old) in your group? 9. Her translation is (bad) than his. 10. You will get (far) instructions in a few days. 11. His equation is (difficult) than hers. 12. Silver is (heavy) than copper. 13. There were (few) problems than we expected. 14. It is (successful) experiment we have ever made. 15. (Long) the days, (short) are the nights. 16. He has to work a lot (hard) in his new job than he used to (early). 17. The (carefully) you do it, the (well) it will be. 18. The (much) I get to know you, the (little) I understand you.
Ex. 5. Give the proper English equivalents for the Russian expressions.
1. In the improper fraction the denominator is меньше than the numerator. 2. If you want to say that six is больше than 5, we write: 6>5. 3. Чем…Ex. 6. Translate into English.
1. Эта статья – самая трудная из всех, которые мы когда-либо переводили. 2. Сегодня намного холоднее, чем вчера. 3. Его книга гораздо интереснее вашей. 4. Эта аудитория меньше той. 5. Мое пальто такое же теплое, как его. 6. «Ваша сестра старше вас?» - «Нет, она немного моложе меня». 7. Этот студент самый младший в своей группе. 8. Сегодня ветер не такой сильный, как вчера. 9. Моя ручка гораздо хуже вашей. 10. Ее перевод значительно лучше того, который она сделала вчера. 11. Какой язык труднее: немецкий или английский? 12. В пятой группе больше студентов, чем в во второй.13. У меня меньше книг, чем у Кати. 14. Мария гораздо красивее своей сестры. 15. Я получил дальнейшую (добавочную) информацию по этому делу. 16. У мамы меньше времени, чем у отца.17. Этот текст намного больше, чем предыдущий. 18. Он не так молод, как мой брат.
Perfect Continuous
| Present | Past | Future | ||||||
| I you we they | have | been working | I you he she it we they | had been working | I we | shall will | have been working | |
| he she it | has | he/she it/you they | will | |||||
| 1) for a long time 2) for 5 years 3) since 2 o’clock 4) all morning/day/week | 1) for 2 hours when he came. 2) since 2 o’clock when you came | 1) for two hours by the time he comes 2) next year for five years already 3) for forty minutes when you ring us up |
Ex. 7. Analize the following sentences and translate them. Compare the predicates in these pairs of sentences.
A) Affirmative
| 1. I am studying English now. 2. They were discussing the definition in class yesterday. 3. He will be speaking at the conference next month. | - I have been studying it since September. - They had been discussing the definition for some time, when the teacher came. - He will have been speaking at the conference for half an hour, when his scientific adviser comes. |
B) Negative
| 1. He is not doing any experiments right now. 2. She wasn’t watching TV yesterday. 3. Next year they will not be living here as they are moving to another house. | - He has not been doing any experiments since last year. - She had not been watching TV for some time when her mother came. - Next year they will not have been living here for 5 years but for 6 years already. |
C) Interrogative
| 1. Are they working in the garden now? 2. Was he translating the text in class yesterday? 3. Will she be doing her research next week? | - Have they been working for a long time? - Had he been translating this text for an hour when his mother came? - Will she have been doing her research for five years by the end of this year? |
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… b. Past Perfect Continuous is used: For certain duration with visible results in the past. They were…Note the difference in translation between the Present Perfect Continuous and the Present Perfect Tenses.
Ex. 8. Choose the correct variant: 1. For how long (have they discussed, have they been discussing) the…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 1st 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.
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
Reading Activity
The Nature of Algebra
This is a general rule which remains true no matter what particular numbers may replace the symbols a and b. A rule of this kind is often called a… Algebra is the system of rules concerning the operations with numbers. These… The outstanding characteristic of algebra is the use of letters to represent numbers. Since the letters used represent…Post-Reading Activity
Ex. 11. Answer the following questions.
1. What is the relationship between arithmetic and algebra? 2. In what arithmetic operations do we use numbers? 3. What do we use in algebra to represent numbers? 4. What examples of the close relationship between arithmetic and algebra can you give? 5. What is algebra? 6. What is the outstanding characteristic of algebra? 7. Name algebraic expressions you know. 8. When are two terms called similar? 9. What signs are used in algebra and what do they indicate? 10. How is the sign (
) read? 11. What is the meaning of the multiplication sign, the equality sign and the division sign? 12. What does the expression (a + b) mean?
Ex. 12. Find the English equivalents for the following Russian words and word combinations.
1. утверждение; 2. иметь дело; 3. рассматривать; на языке; 4. вычислять; 5. подобно, таким же образом; 6. алгебраические выражения; 7. полином; 8. для удобства; 9. член; 10. трехчлен; 11. возведение в степень; 12. тогда утверждение справедливо; 13. представлять
a. then the statement is true; b. trinomial; c. raising to a power; d. deal with; e. for convenience; f. term; g. compute; h. likewise; i. in terms of; j. algebraic expressions; k. statement; l. represent; m. polynomial
Ex. 13. Give the proper English equivalents for the Russian expressions.
Ex. 14. Mark the following as True or False.
1. Algebra is a generalization of geometry. 2. In order to state the general rule, we write numbers instead of particular letters. 3. Algebra is the system of rules concerning the operations with numbers. 4. Since the letters used represent numbers, all the laws of arithmetic fail to hold in operations with letters. 5. The operations of addition, subtraction, multiplication, division, raising to a power and extracting roots are called algebraic expressions. 6. An expression of two terms is a trinomial. 7. As in arithmetic, the equality sign means “not equal to”.8. In finding the product of multinomials we make use of commutative law. 9. These rules cannot be easily stated as formulas in terms of letters, like the rule given above for squaring the product of two numbers. 10. The outstanding characteristic of algebra is the use of numbers to represent letters.
Ex. 15. Ask special questions.
1. A polynomial is an algebraic expression composed of one or more terms (what, how many) 2. Algebraic expressions are divided into two groups. (how many) 3. An expression 6x6 + 4x3 + 8 is of the fifth degree in x. (what) 4. If a polynomial contains but one term, it is called a monomial. (when) 5. The fundamental operations with polynomials are addition, subtraction, multiplication and division. (what) 6. If the remainder is zero, the division is exact. (when) 7. The so-called “double sign” () is sometimes used. (what) 8. The equality sign (=) means “equals” or “is equal to”. (what) 9. In the operation + 10 - 10 = 0, the minus sign means that 10 is subtracted from 10 to give a zero remainder. (what) 10. We use the signs plus (+) and minus (-) to indicate addition and subtraction. (why, what for) 11. There are three requirements for an equation. (how many)
Ex. 16. Translate into Russian.
Monomials and Polynomials
Ex. 17. Translate into English.
1. Алгебра – это система правил, касающихся действий с числами. 2. В алгебре числа обозначаются буквами, а не цифрами. 3. Поскольку буквы обозначают числа, все законы арифметики годны для действий с буквами. 4. Знаки, которые обозначают действия с цифрами, также употребляются для букв. 5. Операции сложения, вычитания, умножения, деления, возведения в степень и извлечения корней называются алгебраическими операциями. 6. В алгебре мы применяем следующие знаки: плюс, минус, знак равенства, знак умножения, знак деления, скобки круглые, квадратные и фигурные, знак «больше, чем», знак «меньше, чем» и другие. 7. Алгебраическому выражению можно придать более простую форму путём приведения подобных членов. 8. Алгебраическая сумма нескольких одночленов называется многочленом. 9. Двучлен – это алгебраическое выражение, состоящее из двух членов, трёхчлен – алгебраическое выражение, состоящее из трёх членов.
UNIT 7
| Grammar: Present, Past, Future Indefinite, Passive Voice |
 Present Indefinite Passive
|  Past Indefinite Passive
| Future Indefinite
 Passive
|
| I am He/She/It is asked We/You/They are | I/He/She/It was We/You/They were asked | I/We shall/will be He/She/It will be asked You/They will be |
| Universal truths, repeated actions indicated by adverbials of frequency usually, always, often, sometimes, seldom, rarely, never, as a rule, every (day, month, etc.), once (a week, a month, etc.). | A single action or a state with time adverbials such as yesterday, ago, last (time, week, month, year), the other day, in 2008. | A predicted future action, an action which the speaker regards as possible to happen in future with the adverbials of time tomorrow, the day after tomorrow, in (a week, month, year), next (week, month, etc.), in 2015. |
| 1. She is often asked at the lessons. – Ее часто спрашивают на уроках. 2. Computers are used everywhere. – Компьютеры используются везде. | 1. He was asked at the lesson yesterday. – Его спросили на уроке вчера. 2. A computer was used to solve a difficult problem last week. – Компьютер был использован для решения трудной задачи на прошлой неделе. | 1. You will be asked at the lesson tomorrow. – Вас спросят на уроке завтра. 2. This new computer will be used in our laboratory next week. – Этот новый компьютер будет использоваться в нашей лаборатории на следующей неделе. |
Ex. 1. Read these sentences. Compare the predicates in these pairs of sentences
Ex. 2. State the voice of the verb in the following sentences. Translate these sentences.
1. The students left the experiment unfinished. 2. Algebraic language is used to express mathematical ideas. 3. The members of the equality are connected by the equality sign. 4. The result will be checked immediately. 5. We shall study higher mathematics next term. 6. This property was discussed in the previous chapter. 7. All the facts are summarized in this statement. 8. Will the test be written on Monday? 9. The student showed me his graduation paper a few days ago. 10. She will be told about their recent investigations in the field of algebra. 11. They told the foreign scientists about their studies in the theory of programming. 12. Their calculations will not be used in his work.
Pre-Reading Activity
Guess the meaning of the following words.
Expression [Iks`preS(q)n], identical [aI`dentik(q)l], conditional [kqn`dIS(q)nl], accuracy [`xkjurqsI], classify [`klxsifaI], linear [`lInIq], transformation [,trxnsfq`meiS(q)n], original [q`rIGqnl], reduce [rI`djHs].
Read and learn the basic vocabulary terms.
statement (n) [`steItmqnt] – утверждение, формулировка finite (a) [`faInaIt] – конечный variable (a) [`vFqriqbl] – переменнаяMemorize the following word combinations.
1. other than – кроме;
2. in question – рассматриваемый;
3. to check the accuracy – проверить точность;
4. for convenience – для удобства;
5. regardless of the form – независимо от формы;
6. when applied to an equation – в применении к уравнению;
7. is said to be equivalent with respect to – считается эквивалентным относительно;
8. can readily be recognized and discarded – можно легко распознать и отбросить.
Reading Activity
Equations and Identities
(x - 2)2 = x2 - 4х + 4, (x + 3) (x - 2) = x2 + x - 6 If the two members of an equation are equal for certain particular values of… The following rules aid in finding the root.Post-Reading Activity
Ex. 3. Answer the following questions.
1. What is an equation? 2. What are the members or expressions on the either side of the sign of equality called? 3. What must we do to solve the equation? 4. What do we call the solution of the equation? 5. In what way are the equations classified? 6. How do we check the equation? 7. In what types are equations classified according to the degree? 8. In what types are equations classified according to their form? 9. In what way can one solve an equation containing fractions? 10. What operation must one do when solving an equation by the combination of rules?
Ex. 4. Find the Russian equivalents for the following English words and word combinations.
1. may be true for 2. in finding 3. a linear equation 4. the Least Common Denominator 5. for every value of the variables involved 6. to be equal for certain particular values 7. the expression in question 8. to satisfy the equation upon substitution 9. regardless of the form 10.by substituting
a. независимо от формы; b. линейное уравнение; c. равный для некоторых определенных величин; d. рассматриваемое выражение; e. путем подстановки; f. наименьший общий знаменатель; g. для каждого значения включенной переменной; h. при нахождении; i. может быть верным для; j. удовлетворять уравнению при подстановке
Ex. 5. Give the proper English equivalents for the Russian expressions.
1. No rule can be given чтобы решить the given problem. 2. We must write out a definite description of what the letter selected for неизвестная…Ex. 6. Make the following sentences interrogative and negative.
1. This relation is expressed symbolically. 2. Such numbers are easily multiplied. 3. These problems are discussed at the seminars. 4. Various examples were given at the last lesson. 5. I was told to solve another equation. 6. All the facts were summarized in that expression. 7. The line will be divided into several parts. 8. The conference will be held next week. 9. This exercise was done in the classroom yesterday. 10. The common solution will be examined tomorrow.
Ex. 7. Ask special questions.
1. All the students will be examined next week. (When) 2. This equation is called linear. (What) 3. The Latin alphabet is used in algebra. (Where) 4. They were told about the scientific conference. (Who) 5. Some new rules were given at the last lesson. (What, when) 6. The necessary equation will be written on the blackboard. (What) 7. This algebraic expression was discussed in the previous chapter. (Where) 8. Terms are usually written with the signs before them. (How) 9. The concept of an equation was explained yesterday. (When) 10. The values of the unknowns are called the roots. (What)
Ex. 8. Translate from English into Russian. Mind the use of Modal Verbs.
1. This equation can be solved easily. 2. This algebraic expression can be evaluated. 3. The result must be obtained today. 4. One or more numbers can be described by stating a condition. 5. The following condition must be satisfied. 6. The result must be checked by division. 7. A fractional equation may be changed into an integral equation. 8. Like terms must always be combined. 9. The results of the research can be sent tomorrow. 10. Some interesting information on the system of equations can be given at the next lecture.
Ex. 9. Translate the sentences from English into Russian.
Ex. 10. Translate the sentences from Russian into English.
UNIT 8
| Grammar: Present, Past Continuous. Present, Past, Future Perfect. Passive Voice |
| Present Continuous Passive | Past Continuous Passive | Future Conti-nuous Passive |
 I am
He/She/It is being asked
We/You/They are
|  I/He/She/It was
being asked
We/You/They were
| -------- |
| now, at this moment, while (в то время как, пока), at present | at 6 o’clock, when she came, from 6 till 7 o’clock, the whole evening | |
| 1. He is being asked by a teacher now. Его сейчас опрашивает учитель. 2. These natural numbers are beingmultiplied at the moment. – Эти натуральные числа умножают в данный момент. | 1. He was being asked by a teacher at 7. Его опрашивал учитель в 7ч. 2. The problems were beingdiscussed at 3 o’clock yesterday. – Проблемы обсуждали вчера в 3 часа. |
| Present Perfect Passive | Past Perfect Passive | Future Perfect Passive |
 I have
 He
She has
It been asked
 We
You have
They
|  I
He
She
It had been asked
We
You
They
|   I shall/
We will
 He
She have been
It will asked
You
They
|
| already, yet – уже (в вопро-се), ещё (в отриц. предл.), this month, recently, for along time, just | by (к), before | already, yet, by, before |
| 1. He has already been asked by a teacher. Учитель его уже опросил. 2. The axiom hasjust been accepted. – Аксиома только что была принята. | 1. He had been asked by a teacher by 6. Учитель его опросил к 6ч. 2. The whole chapter had been studied by the end of the semester. – Вся глава была изучена к концу семестра. | 1. He will have been askedby a teacher by 4. Учитель его опросит к 6ч. 2. A new method will have been introduced by the end of the month. – Новый метод будет представлен к концу месяца. |
Ex.1. Analyze these pairs of sentences and compare the predicates given there.
Ex. 2. State the voice and the tense-form of the verbs in the following sentences and translate them into Russian.
1. The students are being given a lecture now. 2. The students were being asked about mathematical sentences the whole lesson. 3. The given quantity hasn’t been divided yet. 4. All the data had been obtained by that time. 5. The algorithm will have been carefully worked out by tomorrow. 6. Have any of these articles on mathematics been translated recently? 7. All the digits have already been aligned as appropriate. 8. The conference is being held at the moment. 9. Are the numbers being added without a calculator right now? 10. His graduation paper hasn’t been presented yet.
Ex. 3. Open the parentheses and give the correct form of the verb in the Passive Voice.
1. Don’t enter the room! A student (to examine) there just now. 2. The letter (to type) by the typist when I came in. 3. I am sure that his work (to complete) by the end of the month. 4. A lot of new words (to learn) already by the students. 5. All the dinner (to eat) before they finished the conversation. 6. The question (not to answer) yet. 7. The proposal (to consider) by 9 o’clock yesterday. 8. The papers (to sign) just by the dean of the faculty. 9. The results of the test (to discuss) by the students at the moment. 10. The article (to translate) by the time you return.
Pre-Reading Activity
Guess the meaning of the following words.
Read and learn the basic vocabulary terms: term n. [tE:m] …Memorize the following word combinations.
1. such as – такой как
2. in other words – другими словами
3. is known as a polynomial – известен как многочлен, называется многочленом
4. thus – таким образом
5. either … or – либо … либо, или … или
6. in order to – для того, чтобы
7. by the aid of – с помощью (чего-либо)
Reading Activity
Polynomials
An algebraic expression whose parts are not separated by + or – is called a term; as 2×3, –5×yz, and xy/z. In the expression 2×3 – xyz – xy/z there are three terms. The expression… An algebraic expression of one term is known as a monomial or a simple expression. (xy and 3ab are monomials).Post-Reading Activity
Ex. 4. Answer the following questions.
1. What is an algebraic expression? 2. What algebraic expression is called polynomial (monomial, binomial)? 3. What are the terms of a polynomial? 4. What numbers in a polynomial are called coefficients (exponents, the constant term)? 5. How do we define the degree of a polynomial? 6. What are the fundamental operations of polynomials? 7. How is the sum of two polynomials obtained? 8. How is subtraction of polynomials performed? 9. How is the product of two polynomials obtained? 10. What is the rule of polynomial division?
Ex. 5. Find the English equivalents for the following Russian word combinations.
1. состоять из нескольких одночленов; 2. алгебраическое выражение; 3. образовывать многочлен; 4. знаки, предшествующие им; 5. состоять из одного или нескольких членов; 6. разместить таким образом; 7. сложить коэффициенты; 8. разместить делимое по возрастающим или убывающим показателям степени; 9. касающееся операции деления; 10. сложить произведения
a. to form a polynomial; b. to be compose of one or more terms; с. to consist of several monomials; d. to place in such a way; e. an algebraic expression; f. to add the products; g. signs preceding them; h. to arrange the dividend in ascending or descending powers; i. to add the coefficients; j. concerning the operation of division
Ex. 6. Give the proper English equivalents for the Russian expressions.
1. Each of these polynomials is composed of членов. 2. In the algebraic expression 3x³+ 2x²+5 the constant multipliers 3, 2, 5 are called…Ex. 7. Make the following sentences negative and interrogative.
1. The result of the subtraction is being checked now. 2. Polynomials and their fundamental operations were being studied by the students the whole day yesterday. 3. These polynomials are being multiplied at the moment. 4. Each step of the process has already been carefully studied. 5. The necessary information has just been obtained. 6. The whole material about polynomials has been learned by the student recently. 7. Those algebraic expressions have been carefully arranged in descending powers. 8. The report on four operations of polynomials is being discussed during the meeting. 9. The remainder in this expression will have been found by the end of the lesson. 10. The experiment was being conducted when you came in.
Ex. 8. Mark the following as True or False.
1. A polynomial is composed of one term only. 2. A number represented by algebraic symbols is called a fractional expression. 3. Each term of a polynomial is either an integral power of x multiplied by a constant or a constant free of x. 4. The division isn’t exact if the remainder is zero. 5. Division of one polynomial by another is rather a long process. 6. A monomial consists of several terms. 7. All algebraic expressions are divided into different groups. 8. When subtracting we change the signs of the terms of the subtrahend. 9. The polynomial 3x²y²+2xy+5 is of the fifth degree. 10. A polynomial of three terms is called a binomial.
Ex. 9. Ask special questions.
1. A polynomial is an algebraic expression composed of one or more terms. (What) 2. In the expression 2×3 – xyz – xy/z there are three terms. (How many) 3. A polynomial of two terms is called a binomial. (How) 4. The polynomial 3x³+4x²+5 is of the third degree in x. (What) 5. The whole material has already been learned by the students. (By whom) 6. All the trinomials were being subtracted when we came. (What) 7. If the remainder of division is zero it is exact. (When) 8. You should divide the leading term of the dividend by the leading term of the divisor. (What, how) 9. The remainder found in the result of the subtraction is used as the dividend. (How) 10. The subtraction with those polynomials hadn’t been done correctly by the end of the class yesterday. (What)
Ex. 10. Translate these sentences from English into Russian.
1. An algebraic expression of one term is called a monomial or simple expression. 2. An algebraic expression of more than one term is called a polynomial. 3. The terms of a polynomial are taken with the signs preceding them. 4. The polynomial is of the third degree in x since 3 is the highest exponent appearing in the expression. 5. You have been given two polynomials and have been asked to multiply one of them by the other. 6. We place the terms of the subtrahend under like terms of the minuend. 7. The fractional numerals are being written as the corresponding decimal numerals by the students right now. 8. In dividing polynomials both the dividend and the divisor must be arranged in ascending or descending power of the letter common to both. 9. To add or to subtract polynomials we must place them so that like terms fall under each other. 10. The remainder is of lower degree than the divisor.
Ex. 11. Translate these sentences from Russian into English.
1. Многочлен состоит из двух и более членов. 2. Алгебраическое выражение, которое содержит только действия умножения, деления и возведения в степень, называется одночленом. 3. Алгебраическая сумма нескольких одночленов называется многочленом. 4. Трёхчлен – алгебраическое выражение, состоящее из трёх членов. 5. Числа при неизвестных х, у, называются коэффициентами многочлена. 6. Многочлены можно складывать, вычитать, умножать и делить. 7. Чтобы разделить многочлен на одночлен, нужно делимое и делитель разместить в убывающем или возрастающем порядке общего неизвестного. 8. Правило, касающееся деления, может быть сформулировано определенным образом. 9. Деление продолжается до тех пор, пока не будет найден остаток с числовым значением меньшим,чем делитель. 10. Если остаток при делении равен нулю, то деление называют точным или без остатка.
Таблица нестандартных глаголов
| Infinitive | Past Indefinite | Past Participle | Перевод |
| arise | arose | arisen | возникать |
| be | was, were | been | быть |
| bear | bore | borne | носить, выносить |
| become | became | become | становиться |
| begin | began | begun | начинать(ся) |
| bend | bent | bent | гнуть(ся) |
| bind | bound | bound | связывать |
| break | broke | broken | ломать |
| build | built | built | строить |
| choose | chose | chosen | выбирать |
| come | came | come | приходить |
| cost | cost | cost | стоить |
| cut | cut | cut | пересекать, резать |
| deal | dealt | dealt | иметь дело (с) |
| do | did | done | делать |
| draw | drew | drawn | чертить, тащить |
| fall | fell | fallen | падать |
| feel | felt | felt | чувствовать |
| find | found | found | находить |
| fight | fought | fought | бороться |
| fly | flew | flown | летать |
| foresee | foresaw | foreseen | предвидеть |
| forget | forgot | forgotten | забывать |
| get | got | got | получать, становиться |
| give | gave | given | давать |
| grow | grew | grown | расти, выращивать |
| have | had | had | иметь |
| hear | heard | heard | слышать |
| hold | held | held | иметь силу, держать |
| keep | kept | kept | держать, хранить |
| know | knew | known | знать |
| lay | laid | laid | класть |
| lead | led | led | вести |
| learn | learnt (learned) | learnt (learned) | узнавать, учиться |
| leave | left | left | оставлять |
| let | let | let | позволять |
| lose | lost | lost | терять |
| make | made | made | делать, заставлять |
| mean | meant | meant | значить, подразумевать |
| meet | met | met | встречать |
| put | put | put | класть |
| read | read | read | читать |
| run | ran | run | приводить в движение, бежать |
| say | said | said | говорить, сказать |
| see | saw | seen | видеть |
| send | sent | sent | посылать |
| set | set | set | помещать, ставить |
| show | showed | shown | показывать |
| sit | sat | sat | сидеть |
| speak | spoke | spoken | говорить, разговаривать |
| spend | spent | spent | тратить |
| spread | spread | spread | распространяться) |
| stand | stood | stood | стоять |
| strike | struck | struck(stricken) | ударять, бастовать |
| swing | swung | swung | качать(ся) |
| tear | tore | torn | разрывать |
| tell | told | told | рассказывать, сказать |
| think | thought | thought | думать |
| throw | threw | thrown | бросать |
| understand | understood | understood | понимать |
| wear | wore | worn | носить |
| win | won | won | выигрывать |
| write | wrote | written | писать |
– Конец работы –
Используемые теги: Grammar, Verb, There, is/are, Possessive, and, personal, Pronouns0.106
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