Exercises:

1. Read the following words paying attention to the pronunciation:

algebra, also, double, triangle, quotient, quantity, sign, frequently, twice, meaning, complete, parenthesis, arithmetic, fraction, subtraction, minus.

2. Form nouns of the following words:

to indicate, to add, to operate, to subtract, to mean, to express, to divide, to place, to differ.

3. Make up sentences of your own using the words and expressions given below:

serve to distinguish, to give a zero result, combine with, both plus and minus, either plus or minus.

4. Answer the following questions:

1. What signs are used in algebra?

2. What do signs (+) and (-) indicate?

3. How is the sign (=) read?

4. What is the equality sign?

5. What is the meaning of the multiplication sign?

6. What does the expression (a-b) mean?

5. Translate into Russian:

ab means the same as a x b and 2 x с means the same as 2c, twice c. We cannot write 23, however, for 2 x 3 as 23 has another meaning, namely, the number 23. Therefore, in general, the multiplication sign (x) lay be omitted between algebraic symbols and an ordinary arithmetical umber, but not between two arithmetical numbers.

Another sign which is sometimes used is the inclined fraction line (/); thus 6/3 means the same as 6:3. This form has the advantage of being compact and also allowing both dividend and divisor (or numerator and denominator) to be written n the same line.

6. Translate into English:

В алгебре мы применяем следующие знаки: плюс, минус, знак равенства, знак деления, скобки круглые, квадратные и фигурные, знак "больше, чем", "меньше, чем" и другие. Знак три точки по углам треугольника означает "следовательно" или "поэтому".

TEXT 4

При работе над текстом “Squares and square roots” формируется компетенция ОК-10: владеет одним из иностранных языков на уровне, позволяющем получать и оценивать информацию в области профессиональной деятельности из зарубежных источников.

В рамках формирования компетенции у студентов вырабатываются следующие умения, навыки:

Уметь

• понимать информацию текстов из учебной литературы в соответствии с конкретной целью;

• выступать с подготовленным сообщением.

Владеть

• навыками оформления речевых высказываний в соответствии с грамматическими и лексическими нормами устной и письменной речи, фонетическими нормами (устная речь) и основными правилами орфографии и пунктуации (письменная речь) иностранного языка, не допуская ошибок, препятствующих речевому общению;

• навыком использования двуязычных словарей при чтении различного типа текстов;

• профессиональными основами речевой коммуникации с использованием терминологии данной дисциплины.

Применяются интерактивные технологии: работа малыми группами, решение ситуационных задач.

Squares and square roots

To square a number you must multiply that number by itself. The square root of a number is just the opposite. When you find the square root of a number, you are finding what number multiplied by itself gives you the number you began with. The sign for the square root is √. Thus, the square root of 25 is represented by √25. 25 is a perfect square. That is, a whole number (5) multiplied by itself will five you 25.

A figure or a letter placed a little above and to the right of a number is called an index, or an exponent, of the power thus indicated.

A number a² is read -"a square", or "a second power"; a³ is read "a cube", or "a third power"; a⁴ is read "a fourth power", or "a exponent 4", or "a fourth"; an is read "a nth", "a nth power", or "a exponent n".

When no exponent is written, the exponent is regarded as 1. 5 is regarded as the first power of 5, and a¹ is usu­ally written a.

The terms coefficient and exponent should be distin­guished.

The process of finding a root is known as evolution; it is the inverse of involution, because by the aid of this process we try to find that number which is given only when raising a number to a power. The accuracy of the root taken may always be checked by raising the number to the power. For instance, in order to check the equality: ³√125=5, it is sufficient to cube 5; obtaining the quantity under the radical sign, we conclude that the cube root of 125 has been found correctly.

NOTES:

to square a number - чтобы возвести число в квадрат

number you began with - исходное число

by raising the number to the power - возведением числа в степень