- •Pronouns
- •Pronoun “it”
- •The verb “to be”
- •Pre-reading activity
- •Reading Activity About My Family and Myself
- •Additional Vocabulary
- •Looks and Appearance
- •Features of Character
- •Interests and Ambitions
- •Family Members and Relations in the Family
- •Post-reading Activity
- •The verb “to have”
- •Present, Past, Future Simple Present Simple
- •The Present Simple tense denotes:
- •Past Simple
- •The Past Simple tense describes:
- •Future Simple
- •The Future Simple tense denotes:
- •Facts to be remembered
- •Types of Questions
- •Reading Activity a Letter to a Friend
- •Post-Reading Activity
- •Continuous tenses
- •Present Continuous Tense
- •Past Continuous Tense
- •Future Continuous Tense
- •Pronouns some, any, no
- •Pre-Reading Activity
- •Reading Activity Numbers
- •Post-Reading Activity
- •To have to
- •To be to
- •Should, ought to
- •Pre-Reading Activity
- •Reading Activity Four Basic Operations of Arithmetic
- •Post-Reading Activity
- •Grammar Rules Patterns.
- •Pre-Reading Activity
- •Reading Activity Rational numbers and decimal numerals
- •Post-Reading Activity
- •Degrees of Comparison
- •Irregular Comparatives and Superlatives:
- •Types of Comparisons
- •Perfect Continuous
- •Facts to be remembered
- •Pre-reading activity
- •Reading Activity The Nature of Algebra
- •Post-Reading Activity
- •Monomials and Polynomials
- •Unit 7
- •Pre-Reading Activity
- •Reading Activity Equations and Identities
- •Post-Reading Activity
- •Unit 8
- •Pre-Reading Activity
- •Reading Activity Polynomials
- •Post-Reading Activity
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.
a trinomial, descending, subtraction, obtain, a fraction, coefficients, terms, exponents, sum, remainder, fractional |
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 коэффициенты. 3. In the polynomial 2x³+ 5x²+9 the upper numbers 3 and 2 are called показателями степени. 4. A polynomial consisting of three terms is called трёхчлен. 5. One of the fundamental operations that had been applied to those polynomials before other operations was вычитанием. 6. The algebraic expression 2y³-3y²+2y is arranged in убывающим powers of the letter y. 7. Multiplying two polynomials we получаем a product. 8. If the остаток of division is zero, it is exact. 9. An expression, any term of which is дробь, is called a дробным expression. 10. Adding two polynomials we obtain a сумму.
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.
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 |