Třída: VI. A6 Mgr. Pavla Hamříková VI. B6 RNDr. Karel Pohaněl Schváleno předmětovou komisí dne: Podpis: Šárka Richterková v. r

MATURITNÍ TÉMATA

Školní rok: Ředitel školy: Předmětová komise: Předseda předmětové komise: Předmět: Třída: Schváleno předmětovou komisí dne: Schváleno ředitelem školy dne: Počet výtisků: 6 Výtisk č.:

2016/2017 PhDr. Karel Goš Matematika a deskriptivní geometrie Mgr. Šárka Richterková Matematika VI. A6 Mgr. Pavla Hamříková VI. B6 RNDr. Karel Pohaněl 31. 8. 2016 Podpis: Šárka 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 Tomkova 314/45, 779 00 Olomouc, GPS: Lat: 49° 36' 8.4846", Long: 17° 14' 18.708" tel.: +420 585 711 111, fax: +420 585 711 170, ID datové schránky: gd6fc9p, email: [email protected], https://www.facebook.com/gytool/, www.gytool.cz

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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 Tomkova 314/45, 779 00 Olomouc, GPS: Lat: 49° 36' 8.4846", Long: 17° 14' 18.708" tel.: +420 585 711 111, fax: +420 585 711 170, ID datové schránky: gd6fc9p, email: [email protected], https://www.facebook.com/gytool/, www.gytool.cz

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 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.

Tomkova 314/45, 779 00 Olomouc, GPS: Lat: 49° 36' 8.4846", Long: 17° 14' 18.708" tel.: +420 585 711 111, fax: +420 585 711 170, ID datové schránky: gd6fc9p, email: [email protected], https://www.facebook.com/gytool/, www.gytool.cz

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 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


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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


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Třída: VI. A6 Mgr. Pavla Hamříková VI. B6 RNDr. Karel Pohaněl Schváleno předmětovou komisí dne: Podpis: Šárka Richterková v. r

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