Gymnázium Olomouc – Hejčín, Tomkova 45, 779 00, www.gytool.cz, [email protected], 585 711 111
Maturitní témata
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Počet výtisků: 6
Výtisk č.:
2015/2016
PhDr. Karel Goš
Matematika a deskriptivní geometrie
Mgr. Šárka Richterková
Matematika
RNDr. Karel Pohaněl
VI. A6
Mgr. Dana Vojtovičová
VI. B6
28. 8. 2015 Podpis: Š. Richterková v. r.
Podpis a razítko: Karel Goš v. r.
1
1. Sets and Logic.
 Definition of a set and operations with sets including Cartesian product
 Statement and the basic operations with statements
 Tautologies
 Proofs in Mathematics
2. Linear Functions and Solving Linear equations and Inequalities.
 Definition of a linear functions, basic properties and their significance
 The different methods of solving linear equations and inequalities including modulus
3. Quadratic Functions, Equations and Inequalities.
 Definition of quadratic functions, the basic properties and their significance
 The different methods of solving quadratic equations and inequalities including modulus
4. Simultaneous Equations and Inequalities.
 Conditions of solution
 Different methods of solution
 Application of them in different areas of Mathematics
5. Parametric Equations.
 Different methods of solving different types of parametric equations and inequalities
 Examples of the applications of parametric equations and inequalities
6. Isometric Mappings.
 Isometric mappings, their definitions, properties, classification.
 Constructive tasks based on the isometric mappings
7. Similar Mappings.
 Definition of a similar mapping and the basic properties
Gymnázium Olomouc – Hejčín, Tomkova 45, 779 00, www.gytool.cz, [email protected], 585 711 111
 Homothety – definition, basic properties
 Constructive tasks based on the homothety
8. Solving the Right-angled Triangle.
 Definition and basic properties of the right-angled triangle
 Fundamental statements concerning the right-angled triangle
 Metric properties of the right-angled triangle
9. Solving Scalene Triangles.
 Definition and basic properties of scalene triangles
 Fundamental statements concerning the scalene triangle and their metric properties
10. Functions and Their Basic Properties.
 Cartesian product, binary relations and functions
 Definition of function and the basic properties
 Classification of functions
11. Trigonometric Functions and Equations.
 Definition and basic properties of trigonometric functions
 Basic formulae concerning trigonometric functions
 Solving trigonometric equations
12. Exponential Functions, Equations and Inequalities.
 Definition, the graph and basic properties of exponential functions
 Basic methods of solving exponential equations and inequalities
13. Logarithmic Equations and Inequalities.
 Definition, the graph and basic properties of logarithmic functions
 Basic methods of solving logarithmic equations and inequalities
14. Geometry in Space – Configuration of Basic Objects.
 Parallel projection, its basic rules
 Configuration of lines and planes in space
 Section of solids
Gymnázium Olomouc – Hejčín, Tomkova 45, 779 00, www.gytool.cz, [email protected], 585 711 111
15. Geometry in Space – Angles and Distances.
 Angles of lines and planes in space
 Perpendicular distances in space
16. Volumes and Surface Areas of Solids.
 Basic solids
 Volume and Cavalier’s principle
 Surface area of a solid
17. Complex Numbers.
 The set of complex numbers and its geometrical model
 Basic forms of complex numbers
 Moivre’s theorem and binomial equations
18. Vectors.
 Characteristics of vectors, basic operations
 Scalar and vector product of vectors and their applications
19. Coordinate Geometry in the Plane - Lines.
 Equations of lines in the plane
 Configurations of lines in the plane
 Metric properties of lines.
20. Coordinate Geometry in Space.
 Equations of lines and planes in space
 Configurations of lines and planes in space
 Metric properties of lines and planes
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21. Coordinate Geometry in the Plane - Conics.
 Definitions, constructions and equations of conics

Configurations of lines and conics in the plane

Tangents to conics
22. Combinatorics and Probability.
 Permutations, combinations with and without repetition
Gymnázium Olomouc – Hejčín, Tomkova 45, 779 00, www.gytool.cz, [email protected], 585 711 111
 Probability of events, P(AUB), independent events and binomial probability
23. Binomial Theorem.
 Definition of n!, binomial coefficients and their properties
 Binomial theorems and its proofs (different ways)
24. Arithmetical Progression.
 Definition of sequence and its basic properties
 Arithmetical progression and its basic properties and applications
25. Geometrical Progression.
 Definition of sequence and its basic properties
 Geometrical progression and its basic properties and applications
26. Indefinite Geometrical Series.
 Series and their basic properties
 The sum of indefinite geometrical series – proof
27. Differentiation.
 The first principle, basic properties of derivatives, geometrical and physical significance
 Differentiation of composite and implicit functions
28. Curve Sketching.
 Domain, points of discontinuity of f(x)
 The contribution of the derivatives for curve sketching
29. Indefinite Integrals.
 Integration as the operation, necessary and sufficient condition, basic formulae
 Different methods of integration
30. Definite Integrals.
 Riemann’s definition of definite integrals, evaluation of definite integrals
 Geometrical applications of definite integrals