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Mathematical reasoning
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Computing the root
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The quadratic equation
- 1. The quadratic equation and function 60
- 2. The quadratic formula 64
- 3. The zero product form. The relation between the roots and the coefficients 69
- 4. Equations of higher degree which can be reduced to quadratic equations 74
- 5. Quadratic inequalities 80
- 6. Parametric quadratic equations (higher level courseware) 84
- 7. Equations involving square roots 90
- 8. Quadratic simultaneous equations 96
- 9. Arithmetic and geometric mean 101
- 10. Extreme value exercises (higher level courseware) 106
- 11. Problems leading to quadratic equations 110
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Geometry
- Widening the knowledge about circles 116
- 1. Reminder 116
- 2. The theorem of the central and inscribed/tangent-chord angles 117
- 3. The theorem of inscribed angles; the arc of viewing angles 121
- 4. The theorem of inscribed quadrilaterals (higher level courseware) 125
- The similarity transformation and its applications 129
- 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 transformation 141
- 5. Similarity of figures; the simple cases of similar triangles 143
- 6. A few applications of similarity 147
- 7. The ratio of the area of similar planar figures 154
- 8. The ratio of the volume of similar solids 158
- Trigonometric functions of acute angles 161
- 1. Determining distances with the help of similarity 161
- 2. Trigonometric functions of acute angles 164
- 3. Relations between the trigonometric functions of acute angles 168
- 4. Trigonometric functions of special angles 172
- 5. Determining several data of a triangle with the help of trigonometric functions 175
- 6. Calculations in the plane and in space with the help of trigonometric functions 180
- Vectors 184
- 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 directions 188
- 3. Applying vectors in the plane and in space 194
- 4. Vectors in the coordinate system, the coordinates of a vector, operations with vectors given with coordinates 199
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Trigonometric functions
- 1. The definition and the simple properties of the sine and the cosine function 204
- 2. The graph of the sine function 209
- 3. The graph of the cosine function, equations, inequalities 214
- 4. The tangent and the cotangent function 221
- 5. Compound exercises and applications 228
- 6. Geometric applications 232
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Calculation of probability