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.

to solve, the unknown quantity, substituted into the expression, the value, roots, have been transposed, the Least Common Denominator, is checked, clearing, to satisfy

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 величина represents. 3. There is an indefinite number of pairs that can be подставлены в это выражение. 4. Check the величину obtained in the solution of the equation. 5. The derived equation may have fewer number of корней than the original one. 6. All the terms containing the unknowns были перенесены to the left member. 7. Each member of the equation is multiplied by the наименьший общий знаменатель. 8. The result проверяется by the given formula. 9. The process of multiplying each member by the Least Common Denominator is called устранение the equation of any fractions. 10. The statement of condition may be such that no number can be found to удовлетворить it.

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.

1. In solving problems by means of algebraic equations, the first and the most difficult step which must be done is to translate the words into the algebraic language. 2. Definite rules cannot be given to enable the student to solve mechanically the given problem. 3. The following suggestions may be helpful for the students of mathematics. 4. The difficult problem must be read over and over again until it is clearly understood. 5. A full and definite description of the unknown quantity represented by the letter is written out. 6. The expressions for all quantities in the example involving this unknown will be given afterwards. 7. Expressions, which, according to the statement of the problem, represent the same number, are found and set equal to each other. 8. An equation in one unknown has a finite number of solutions, or values of this unknown, which will satisfy the equation. 9. Any term of one side of an equation may be transposed to the other side if its sign is changed. 10. An equation which can be reduced to the form ax + b = 0 is called a linear equation in x.

Ex. 10. Translate the sentences from Russian into English.

1. Уравнение – это утверждение, выражающее равенство двух алгебраических выражений. 2. Корень уравнения остаётся прежним, если к обеим частям уравнения прибавить или от обеих частей уравнения вычесть одно и то же выражение. 3. Корень уравнения остаётся прежним, если обе части уравнения умножить или разделить на одно и то же выражение. 4. Решить уравнение – значит найти те значения неизвестного, при которых обе части уравнения равны одному и тому же числу (другими словами, все те значения неизвестного, при которых равенство будет верным). 5. После подстановки эти значения неизвестного удовлетворяют уравнению. 6. Значения неизвестного, которые удовлетворяют уравнению, называют корнями или решениями уравнения. 7. Величина, обозна-ченная через х, является неизвестной. 8. Такие задачи обычно решаются алгебраически, и используются определённые правила. 9. Выражение, написанное слева от знака равенства, называется левым членом уравнения. 10. Результат обычно проверяется по данной формуле. 11. В этом случае будет получено новое уравне-ние. 12. Оба члена умножаются на выражение, содержащее неиз-вестную. 13. Как называется система линейных уравнений?