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Mathematics Workbook 9A Grade
ArchiMath Publishing LLC
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.
• To each topic in the textbook correspond selected problems in the workbook that every student should be able to solve.
• Some of the problems have a solution in the workbook and some have the beginning of a solution, which the students need to complete.
• After working on such problems, students should be able to complete on their own the remaining problems
The workbook:
• highlights the basic knowledge in the textbook;
• has a teaching component;
• helps students learn to organize and correctly write solutions to problems;
• saves time in searching for more problems. The workbooks can be used:
• for independent work by the student;
• to assign homework;
• to conduct tests;
• for practical work with applications.
- 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