**Authors: **Zvezdelina Stankova, Zdravka Paskaleva, Maya Alashka, Raina Alashka

**Pages:** 172

**ISBN: **978-954-779-290-6

**Available**: Paperback & PDF

The fourth year of the Bulgarian Math curriculum solidifies and expands the foundation built in the first three years.

**Overview**

In algebra, students continue their study of functions, master systems of quadratic equations, and learn a crystal clear method for solving inequalities involving polynomials, rational expressions, and/or absolute value. In geometry, students revisit the theorems from prior years and find that they can solve harder problems with less effort.

They move on with a unit on similar triangles, making heavy use of algebra they learned early on and setting the stage for trigonometry, which will be studied in 9B. Finally, students use their combinatorics knowledge from 8B to develop basic probability results.

**Our workbooks are designed to help students strengthen the basic knowledge that they need to master in every grade.**

- Chapter 1. Initial Review

1. Preparation for Entrance Test in Algebra…………. 100

2. Preparation for Entrance Test in Geometry ……… 102

3. Test 1 without Solutions ……………………………….. 104

4. Test 2 without Solutions ……………………………….. 106

5. How Mathematicians Write Solutions…………….. 108

Chapter 2. Functions and Linear Systems

9. Graph of the Quadratic Function…………………… 109

10. Properties of Quadratic Functions…………………. 109

11. Solving Equations Graphically ……………………… 110

13. Solving Linear Systems by Substitution…………. 111

14. Solving Linear Systems by Addition……………… 112

15. Solving Linear Systems via New Variables…….. 114

16. Lines in the Plane. Number of Solutions………… 115

17. Solving Linear Systems Graphically ……………… 116

18. Modeling with Linear Systems……………………… 117

19. Summary of “Linear Systems”……………………… 118

Chapter 3. Systems of Degree 2

21. Systems of Degree 2 with Two Unknowns.

Systems with a Linear Equation……………………. 119

22. Systems with a Linear Equation. Exercises ……. 120

23. Systems with Two Deg 2 Equations………………. 121

24. Systems with Two Deg 2 Equations. Exercises.. 123

25. Solving Systems of Degree 2. Exercises ……….. 124

26. Solving Systems via New Variables………………. 125

27. Solving Systems via New Variables. Exercises.. 126

28. Modeling with Systems of Degree 2 ……………… 127

29. Summary of “Systems of Degree 2”………………. 128

Chapter 4. Review of Geometry

33. Congruent Triangles: Part 1 …………………………… 130

35. Problem Solving with Angles and Triangles………. 130

37. Special Quadrilaterals…………………………………… 132

39. Vectors and Operations…………………………………. 133

40. Midsegments and Centroids…………………………… 134

42. Circles and angles………………………………………… 135

43. Circumcircles and Incircles……………………………. 136

45. Transformations in the Plane, Part I………………… 137

46. Transformations in the Plane, Part II……………….. 137

Chapter 5. Similar Triangles

49. Proportional Segments…………………………………. 138

50. Thales’ Theorem and Its Converse…………………. 138

51. Property of Angle Bisectors in a Triangle ………….138

52. Angle Bisectors in a Triangle. Exercises………… 139

53. Similar Triangles. Definition ………………………… 140

54. 1st Criterion for Similarity of Triangles ……………. 141

55. 1st Criterion for Similarity of Triangles. Exercises142

56. 2nd and 3rd Criteria for Similarity of Triangles…. 143

57. Properties of Similar Triangles………………………. 144

58. Properties of Similar Triangles. Exercises ……….. 145

59. Ratio of the Areas of Similar Triangles………….. 146

60. Summary of “Similar Triangles” …………………… 147

Chapter 6. Rational Inequalities

63. Rational Expressions: Review………………………. 148

65. Union and Intersection of Intervals……………….. 149

66. Inequalities of Type |ax + b| > c, a ≠ 0……………. 150

67. Systems of Linear Inequalities w/ One Unknown 151

68. Systems of Linear Inequalities. Exercises ……….. 152

69. Double Inequalities of Type |ax + b| < c, a ≠ 0… 153

70. Inequalities (ax + b)(cx + d) > 0 and ax b

cx d

+

+

>> 00 . 154

71. Quadratic Inequalities………………………………….. 155

72. Quadratic Inequalities. Exercises ………………….. 155

73. The Method of the Intervals …………………………. 157

74. Applications of the Method of Intervals…………. 158

75. Fractional Inequalities …………………………………. 159

76. The Method of the Intervals. Exercises………….. 160

77. Summary of “Rational Inequalities”………………. 162

Chapter 7. Classical Probability

80. Basic Combinatorial Concepts: Review……….. 163

82. Sets …………………………………………………………. 164

83. Random Events…………………………………………. 164

84. Classical Probability………………………………….. 165

85. Probability of the Sum of Disjoint Events……… 166

86. Probability of the Complement ……………………. 167

87. Probability of an Event. Exercises……………….. 168

88. Probability of Union, Intersection, Difference.. 169

89. Probability of Sum of Compatible Events …….. 171

90. Summary of “Classical Probability” …………….. 172