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# Subject Mathematics Algebra Total 108hours

Kazakh-American University

Subject Mathematics Algebra Total 102 hours

Theme of the lecture Rational/Irrational numbers 3 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Lesson 7, 8

Set of numbers

Real numbers {x| x is a coordinate of a point on a number line}

Natural numbers or counting numbers {1,2,3,4,5,6,7,8,…}

Whole numbers {0,1,2,3,4,5,6,7,…}

Integers {…,-3,-2,-1,0,1,2,3,…}

Rational numbers { | p and q are integers, with q≠ 0}

Irrational numbers {x| x is a real number that is not rational}

Examples of irrational numbers include most square roots, such as and (Some square roots are rational: and so on.) Another irrational number is π, the ratio of the length of circumference of a circle to its diameter. All irrational numbers are real numbers.

Real numbers can also be defined in terms of decimals. By repeated subdivisions, any decimal can be located (at least in theory) as a point on a number line. Because of this, the set of real numbers can be defined as the set of all decimals. Also, the set of rational numbers can be shown to be the set of all repeating or terminating decimals. For example, and so on. The set of irrational numbers is the set of decimals that do not repeat and do not terminate.

Glossary

 English Russian Kazakh Square root Квадратный корень Квадраттық түбір Rational expressions Рациональные выражения Рационал өрнек Multiplication Умножение Көбейту Positive Положительный Оң

Home task: Lesson 1 ex 6, Lesson 2 ex 12, 13

Individual work of student: Collection for preparing to examination Group1 (1A11 –1A15).

Office–hours Algebra 8 grade Абылкасымов А.Е., 2012.ex 14, 15

Literature: Algebra 8 grade Абылкасымов А.Е., 2012, [24-27], Collection for preparing to examination Group1

Additional literature Tulebaeve S.K. Collection of problems. Algebra., 2012,

Notes

Kazakh-American University

Subject Mathematics Algebra Total 108 hours

Theme of the lecture Square root 3 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Lesson 9 - 11

You know that 52 = 5 5 = 25, so that 5 squared is 25. The opposite of squaring a number is called taking its square root. For example, a square root of 25 is 5. Another square root of 25 is -5, since (-5)2=25. Thus, 25 have two square roots, 5 and -5. The symbol is used to write the positive square root of a number. With this symbol, the positive square root of 25 is written Example.

a) since 6 is positive and 62=36

b) since 122=144

c) since 02=0

d) The symbol is used only for the positive square root, except that Find the meaning of the square root if:  Glossary

 English Russian Kazakh Square root Квадратный корень Квадраттық түбір Rational expressions Рациональные выражения Рационал өрнек Multiplication Умножение Көбейту Positive Положительный Оң

Home task: Lesson 1 ex 29, 31, 32 Lesson 2 Ex 37, 38 Lesson 2 Ex 44, 45

Individual work of student: Collection for preparing to examination Group1 (1A01 –1A10).

Office–hours Algebra 8 grade Абылкасымов А.Е., 2012 ex 32, 33

Literature: Algebra 8 grade Абылкасымов А.Е., 2012, [24-27], Collection for preparing to examination Group1

Additional literature Tulebaeve S.K. Collection of problems. Algebra., 2012,

Notes

Kazakh-American University

Subject Mathematics Algebra Total 108 hours

Theme of the lecture Properties of square roots 3 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Lesson 13 – 18

Lesson 18 – control work

For any a it means if a≥0 |a|=a. If a<0 |a|=-a

so: For example: Theorem: If a>b>0 then For example:

Simplify the given expression: . As 3<4, , it means , then Calculate: Glossary

 English Russian Kazakh Square root Квадратный корень Квадраттық түбір Rational expressions Рациональные выражения Рационал өрнек Multiplication Умножение Көбейту Positive Положительный Оң

Home task: Lesson 1 ex 56, 58 Lesson 2 ex 60 Lesson 3 ex 64, 65 Lesson 4 ex 67

Individual work of student: Collection for preparing to examination Group1 (1B16 –1B20).

Office–hours Algebra 8 grade Абылкасымов А.Е., 2012, ex 57, 61

Literature: Algebra 8 grade Абылкасымов А.Е., 2012, [31-35], Collection for preparing to examination Group1

Additional literature Tulebaeve S.K. Collection of problems. Algebra., 2012,

Notes

Kazakh-American University

Subject Mathematics Algebra Total 108hours

Theme of the lecture Properties of square roots 3 hours/ week

Lecturer Grachyova Svetlana Semenovna. Profile Economics

Lesson 19,20

Theorem:If a≥0 and b≥0then Theorem:If a≥0 and b>0then For example: For example: Calculate:  Glossary

 English Russian Kazakh Square root Квадратный корень Квадраттық түбір Rational expressions Рациональные выражения Рационал өрнек Multiplication Умножение Көбейту Positive Положительный Оң

Home task: Lesson 1 ex 70, 71, 74,75

Lesson 2 ex 77, 78.

Individual work of student: Collection for preparing to examination Group1 (1B21 –1B25).

Office–hours Algebra 8 grade Абылкасымов А.Е., 2012, ex 89, 90

Literature: Algebra 8 grade Абылкасымов А.Е., 2012, [35-37], Collection for preparing to examination Group1

Additional literature Tulebaeve S.K. Collection of problems. Algebra., 2008,

Notes

Kazakh-American University

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