Макарычев Ю.Н., Миндюк Н.Г., Алгебра 8-сынып, 1989
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Макарычев Ю.Н.
Миндюк Н.Г.
8-сынып
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Макарычев Ю.Н., Миндюк Н.Г., Алгебра 8-сынып, 1989
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66
Chapter I. Rational fractions
Theory
Page 5
§1. Rational fractions and their properties
Theory
Page 5
1. Rational expressions
Theory
Page 5
2. Fundamental property of fractions. Reducing fractions
Theory
Page 10
§2. Addition and subtraction of fractions
Theory
Page 17
3. Addition and subtraction of fractions with like denominators
Theory
Page 17
4. Addition and subtraction of fractions with unlike denominators
Theory
Page 21
§3. Multiplication and division of fractions
Theory
Page 28
5. Multiplication of fractions. Raising a fraction to a power
Theory
Page 28
6. Division of fractions
Theory
Page 34
7. Transforming rational expressions
Theory
Page 38
8. The function y = k/x and its graph
Theory
Page 44
Additional exercises for Chapter I
Problem
Page 50
Chapter II. Square roots
Theory
Page 56
§4. Real numbers
Theory
Page 60
9. Rational numbers
Theory
Page 60
10. Irrational numbers
Theory
Page 62
§5. Arithmetic square root
Theory
Page 71
11. Square roots. Arithmetic square root
Theory
Page 71
12. The equation x² = a
Theory
Page 75
13. Finding approximate values of square roots
Theory
Page 78
14. The function y = √x and its graph
Theory
Page 82
§6. Properties of the arithmetic square root
Theory
Page 87
15. Square root of a product and a fraction
Theory
Page 87
16. Square root of a power
Theory
Page 92
§7. Applying properties of the arithmetic square root
Theory
Page 96
17. Taking a factor out of a radical. Bringing a factor under a radical
Theory
Page 96
18. Transforming expressions containing square roots
Theory
Page 100
Additional exercises for Chapter II
Problem
Page 105
Chapter III. Quadratic equations
Theory
Page 114
§8. Quadratic equation and its roots
Theory
Page 114
19. Definition of a quadratic equation. Incomplete quadratic equations
Theory
Page 114
20. Solving quadratic equations by completing the square
Theory
Page 119
§9. Quadratic formula
Theory
Page 122
21. Solving quadratic equations using the formula
Theory
Page 122
22. Solving problems using quadratic equations
Problem
Page 128
23. Vieta’s theorem
Theory
Page 132
§10. Rational equations
Theory
Page 137
24. Solving rational equations
Theory
Page 137
25. Solving problems using rational equations
Problem
Page 141
26. Graphical method for solving equations
Theory
Page 144
Additional exercises for Chapter III
Problem
Page 147
Chapter IV. Inequalities
Theory
Page 158
§11. Numerical inequalities and their properties
Theory
Page 158
27. Numerical inequalities
Theory
Page 158
28. Properties of numerical inequalities
Theory
Page 162
29. Addition and subtraction of numerical inequalities
Theory
Page 166
§12. Inequalities in one variable and their systems
Theory
Page 170
30. Numerical intervals
Theory
Page 170
31. Solving inequalities in one variable
Theory
Page 175
32. Solving systems of inequalities in one variable
Theory
Page 183
Additional exercises for Chapter IV
Problem
Page 190
Chapter V. Powers with integer exponents
Theory
Page 198
§13. Powers with integer exponents and their properties
Theory
Page 198
33. Definition of a power with a negative integer exponent
Theory
Page 198
34. Properties of powers with integer exponents
Theory
Page 202
35. Scientific notation
Theory
Page 207
§14. Approximate calculations
Theory
Page 211
36. Writing approximate values
Theory
Page 211
37. Operations with approximate values
Theory
Page 216
38. Calculator computations with approximate values
Theory
Page 222
39. Information on approximate calculations
Theory
Page 230
More difficult problems
Problem
Page 231
Review of the Grade 7 algebra course
Theory
Page 242
Subject index
Other
Page 248
Answers
Answer
Page 249
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