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Colorful Mathematics
Mathematics 10.
Textbook
Mozaik
MS-6310 - Edition 3,
2021
256 pages
Authors: József Kosztolányi, István Kovács, Klára Pintér, János Urbán, István Vincze
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Mathematical reasoning
Computing the root
The quadratic equation
- 1. The quadratic equation and function60
- 2. The quadratic formula64
- 3. The zero product form. The relation between the roots and the coefficients69
- 4. Equations of higher degree which can be reduced to quadratic equations74
- 5. Quadratic inequalities80
- 6. Parametric quadratic equations (higher level courseware)84
- 7. Equations involving square roots90
- 8. Quadratic simultaneous equations96
- 9. Arithmetic and geometric mean101
- 10. Extreme value exercises (higher level courseware)106
- 11. Problems leading to quadratic equations110
Geometry
- Widening the knowledge about circles116
- 1. Reminder116
- 2. The theorem of the central and inscribed/tangent-chord angles117
- 3. The theorem of inscribed angles; the arc of viewing angles121
- 4. The theorem of inscribed quadrilaterals (higher level courseware)125
- The similarity transformation and its applications129
- 1. Parallel intercepting lines, parallel intercepting line segments (higher level courseware)129
- 2. The angle bisector theorem (higher level courseware)135
- 3. The transformation of central dilation (or homothety)137
- 4. The similarity transformation141
- 5. Similarity of figures; the simple cases of similar triangles143
- 6. A few applications of similarity147
- 7. The ratio of the area of similar planar figures154
- 8. The ratio of the volume of similar solids158
- Trigonometric functions of acute angles161
- 1. Determining distances with the help of similarity161
- 2. Trigonometric functions of acute angles164
- 3. Relations between the trigonometric functions of acute angles168
- 4. Trigonometric functions of special angles172
- 5. Determining several data of a triangle with the help of trigonometric functions175
- 6. Calculations in the plane and in space with the help of trigonometric functions180
- Vectors184
- 1. The concept of a vector; the sum and the difference of vectors; scalar multiplication of vectors (reminder)184
- 2. Expressing vectors as the sum of components in different directions188
- 3. Applying vectors in the plane and in space194
- 4. Vectors in the coordinate system, the coordinates of a vector, operations with vectors given with coordinates199
Trigonometric functions
Calculation of probability