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Mathematics 9.

Table of contents
Combinatorics, sets
1. The meaning of expressions in the mathematical language
2. Let us count up!
3. Sets
4. Set operations
5. Order of sets, inclusion-exclusion principle
6. Number lines, intervals
7. Graphs
Algebra and arithmetics
Functions
Triangles, quadrilaterals, polygons
Equations, inequalities, simultaneous equations
Congruent transformations
Statistics

Combinatorics, sets

1. The meaning of expressions in the mathematical language
2. Let us count up!
3. Sets
4. Set operations
5. Order of sets, inclusion-exclusion principle
6. Number lines, intervals
7. Graphs

Algebra and arithmetics

1. Usage of letters in mathematics
2. Exponentiation
3. Exponentiation to integer index
4. Standard index form of numbers
5. Integral expressions (polynomials)
6. Special algebraic products
7. Methods of factorisation
8. Operations with algebraic fractions
9. Divisibility
10. Greatest common divisor (GCD), least common multiple (LCM)
11. Number systems

Functions

1. The Cartesian coordinate system, point sets
2. Linear functions
3. The absolute value function
4. The quadratic function
5. The square root function
6. Linear fractional functions
7. The integral part, the fractional part and the algebraic sign function (higher level courseware)
8. More examples of functions (higher level courseware)
9. Systematization of function transformations

Triangles, quadrilaterals, polygons

1. Points, straight lines, planes and their mutual position
2. A few basic geometric concepts (reminder)
3. About the triangles (reminder)
4. The relation between the sides and the angles of the triangle
5. The relation between the sides of a right-angled triangle
6. About the quadrilaterals (reminder)
7. About the polygons
8. Special point sets
9. The inscribed circle of a triangle
10. The circumscribed circle of a triangle
11. Thales’ theorem and some of its applications
12. Circumscribed quadrilaterals, circumscribed polygons (higher level courseware)

Equations, inequalities, simultaneous equations

1. The concept of equation, identity
2. Solving equations graphically
3. Solving equations with examining the domain and the range
4. Solving equations with factorisation
5. Solving equations with elimination, with the “balance method”
6. Inequalities
7. Equations and inequalities containing absolute value
8. Parametric equations (higher level courseware)
9. Solving problems with equations I
10. Solving problems with equations II
11. First-order simultaneous equations (system of equations) in two variables
12. Solving problems with simultaneous equations (systems of equations)
13. Linear systems of equations in more than two unknowns (higher level courseware)
14. Practical exercises

Congruent transformations

Congruent transformations 1. The concept of geometric transformation, examples of geometric transformations
2. Line reflection (reflection about a straight line) in the plane
3. Axially symmetric figures
4. Point reflection in the plane
5. Centrally symmetric figures
6. Applications of point reflection
7. Rotation about a point in the plane
8. Applications of rotation about a point I
9. Applications of rotation about a point II
10. Parallel translation. Vectors
11. Operations with vectors
12. Congruence of figures

Statistics

1. The representation of data
2. The description of data
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