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Colorful Mathematics
Mathematics 9.
Textbook
Mozaik
MS-6309 - Edition 3,
2024
276 pages
Authors: József Kosztolányi, István Kovács, Klára Pintér, János Urbán István Vincze
Related publications
Combinatorics, sets
Algebra and arithmetics
- 1. Usage of letters in mathematics44
- 2. Exponentiation48
- 3. Exponentiation to integer index52
- 4. Standard index form of numbers55
- 5. Integral expressions (polynomials)58
- 6. Special algebraic products60
- 7. Methods of factorisation66
- 8. Operations with algebraic fractions68
- 9. Divisibility74
- 10. Greatest common divisor (GCD), least common multiple (LCM)80
- 11. Number systems83
Functions
- 1. The Cartesian coordinate system, point sets88
- 2. Linear functions92
- 3. The absolute value function96
- 4. The quadratic function102
- 5. The square root function106
- 6. Linear fractional functions110
- 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 transformations124
Triangles, quadrilaterals, polygons
- 1. Points, straight lines, planes and their mutual position128
- 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 triangle135
- 5. The relation between the sides of a right-angled triangle136
- 6. About the quadrilaterals (reminder)139
- 7. About the polygons143
- 8. Special point sets145
- 9. The inscribed circle of a triangle149
- 10. The circumscribed circle of a triangle151
- 11. Thales’ theorem and some of its applications153
- 12. Circumscribed quadrilaterals, circumscribed polygons (higher level courseware)157
Equations, inequalities, simultaneous equations
- 1. The concept of equation, identity160
- 2. Solving equations graphically164
- 3. Solving equations with examining the domain and the range166
- 4. Solving equations with factorisation169
- 5. Solving equations with elimination, with the “balance method”173
- 6. Inequalities177
- 7. Equations and inequalities containing absolute value182
- 8. Parametric equations (higher level courseware)188
- 9. Solving problems with equations I191
- 10. Solving problems with equations II195
- 11. First-order simultaneous equations (system of equations) in two variables199
- 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 exercises213
Congruent transformations
- Congruent transformations 1. The concept of geometric transformation, examples of geometric transformations216
- 2. Line reflection (reflection about a straight line) in the plane218
- 3. Axially symmetric figures221
- 4. Point reflection in the plane225
- 5. Centrally symmetric figures228
- 6. Applications of point reflection231
- 7. Rotation about a point in the plane236
- 8. Applications of rotation about a point I239
- 9. Applications of rotation about a point II244
- 10. Parallel translation. Vectors246
- 11. Operations with vectors251
- 12. Congruence of figures256
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