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Combinatorics, sets
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Algebra and arithmetics
- 1. Usage of letters in mathematics 44
- 2. Exponentiation 48
- 3. Exponentiation to integer index 52
- 4. Standard index form of numbers 55
- 5. Integral expressions (polynomials) 58
- 6. Special algebraic products 60
- 7. Methods of factorisation 66
- 8. Operations with algebraic fractions 68
- 9. Divisibility 74
- 10. Greatest common divisor (GCD), least common multiple (LCM) 80
- 11. Number systems 83
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Functions
- 1. The Cartesian coordinate system, point sets 88
- 2. Linear functions 92
- 3. The absolute value function 96
- 4. The quadratic function 102
- 5. The square root function 106
- 6. Linear fractional functions 110
- 7. The integral part, the fractional part and the algebraic sign function (higher level courseware) 116
- 8. More examples of functions (higher level courseware) 120
- 9. Systematization of function transformations 124
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Triangles, quadrilaterals, polygons
- 1. Points, straight lines, planes and their mutual position 128
- 2. A few basic geometric concepts (reminder) 129
- 3. About the triangles (reminder) 133
- 4. The relation between the sides and the angles of the triangle 135
- 5. The relation between the sides of a right-angled triangle 136
- 6. About the quadrilaterals (reminder) 139
- 7. About the polygons 143
- 8. Special point sets 145
- 9. The inscribed circle of a triangle 149
- 10. The circumscribed circle of a triangle 151
- 11. Thales’ theorem and some of its applications 153
- 12. Circumscribed quadrilaterals, circumscribed polygons (higher level courseware) 157
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Equations, inequalities, simultaneous equations
- 1. The concept of equation, identity 160
- 2. Solving equations graphically 164
- 3. Solving equations with examining the domain and the range 166
- 4. Solving equations with factorisation 169
- 5. Solving equations with elimination, with the “balance method” 173
- 6. Inequalities 177
- 7. Equations and inequalities containing absolute value 182
- 8. Parametric equations (higher level courseware) 188
- 9. Solving problems with equations I 191
- 10. Solving problems with equations II 195
- 11. First-order simultaneous equations (system of equations) in two variables 199
- 12. Solving problems with simultaneous equations (systems of equations) 204
- 13. Linear systems of equations in more than two unknowns (higher level courseware) 209
- 14. Practical exercises 213
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Congruent transformations
- Congruent transformations 1. The concept of geometric transformation, examples of geometric transformations 216
- 2. Line reflection (reflection about a straight line) in the plane 218
- 3. Axially symmetric figures 221
- 4. Point reflection in the plane 225
- 5. Centrally symmetric figures 228
- 6. Applications of point reflection 231
- 7. Rotation about a point in the plane 236
- 8. Applications of rotation about a point I 239
- 9. Applications of rotation about a point II 244
- 10. Parallel translation. Vectors 246
- 11. Operations with vectors 251
- 12. Congruence of figures 256
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Statistics