| Combinatorics, sets |
10 |
| 1. The meaning of expressions in the mathematical language |
10 |
| 2. Let us count up! |
15 |
| 3. Sets |
21 |
| 4. Set operations |
26 |
| 5. Order of sets, inclusion-exclusion principle |
32 |
| 6. Number lines, intervals |
36 |
| 7. Graphs |
38 |
| Algebra and arithmetics |
44 |
| 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 |
| Functions |
88 |
| 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 |
| Triangles, quadrilaterals, polygons |
128 |
| 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 |
| Equations, inequalities, simultaneous equations |
160 |
| 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 |
| Congruent transformations |
216 |
| 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 |
| Statistics |
260 |
| 1. The representation of data |
260 |
| 2. The description of data |
264 |
