MATURITNÍ TÉMATA Školní rok: 2016/2017 Ředitel školy: PhDr. Karel Goš Předmětová komise: Matematika a deskriptivní geometrie Předseda předmětové komise: Mgr. Šárka Richterková Předmět: Matematika Třída: VI. A6 Mgr. Pavla Hamříková VI. B6 RNDr. Karel Pohaněl Schváleno předmětovou komisí dne: 31. 8. 2016 Podpis: Šárka Richterková v. r. Schváleno ředitelem školy dne: Podpis a razítko: Počet výtisků: 6 Výtisk č.: 1 Karel Goš v. r. 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 Stránka 1 z 5
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 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 Stránka 2 z 5
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 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. Stránka 3 z 5
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 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 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 Stránka 4 z 5
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 Stránka 5 z 5