Logic and methods of proof | 9 |
1. Logic problems and statements | 10 |
2. Logical operators: negation, conjunction, disjunction | 15 |
3. Logical operators: implication and equivalence | 23 |
4. Induction (higher level courseware) | 28 |
Number sequences | 35 |
1. Definition of a number sequence, examples | 36 |
2. Recursive sequences – examples | 41 |
3. Arithmetic progressions | 48 |
4. Geometric progressions | 54 |
5. Interest calculation, computation of instalments | 61 |
Three-dimensional geometry | 65 |
1. Geometric objects in space | 66 |
2. Division of the plane and the space (extra-curricular topic) | 72 |
3. Classification of solids, Platonic solids | 76 |
4. The concept of area, area of polygons | 82 |
5. The area of the disc and its parts | 87 |
6. Concept of volume, the volume of the prism and the cylinder | 92 |
7. Volume of the pyramid and the cone | 98 |
8. Conical and pyramidal frustum | 103 |
9. The volume and surface of the sphere | 108 |
10. Inscribed solids (extra-curricular topic) | 112 |
11. Applications of three-dimensional geometry | 118 |
Probability theory, statistics | 121 |
1. Geometric probability | 122 |
2. Expected value (higher level courseware) | 128 |
3. Statistics | 134 |
Thematic summary | 145 |
Methods of reasoning | 146 |
1. Sets, statements, events | 146 |
2. Combinatorics, probability | 152 |
Algebra and number theory | 161 |
1. Numbers and operations | 161 |
2. Number theory, divisibility | 164 |
3. Powers, root, logarithm | 167 |
4. Operations with rational expressions | 178 |
5. Equations, inequalities | 183 |
6. Simultaneous equations (systems of equations) | 213 |
Functions | 218 |
1. Definition and graph of a function, simple properties | 218 |
2. Operations on functions (extra-curricular topic) | 221 |
3. Properties of functions | 224 |
Geometry | 230 |
1. Basic concepts | 230 |
2. Geometric transformations | 238 |
Congruent transformations | 238 |
Similarity transformation | 243 |
3. Vectors. Trigonometric functions | 248 |
4. Properties of notable planar objects | 257 |
5. Coordinate geometry | 270 |
Problem sets for intermediate level maturity exam | 276 |
Problem set 1 | 277 |
Problem set 2 | 279 |
Problem set 3 | 281 |
Problem set 4 | 283 |
Problem set 5 | 286 |