Maturita topics for Math

Ms. Strupkova (our Math teacher) gave us the maturita question most late of all the teachers (at least those which concerns me). There are fifty questions, but during the maturita, one will draw just one question - combined of two of these fifty. Strupkova said she'd group together always one easier and one harder question...
Some of the questions seem as if Strupkova ran out of topics, so took an original path. Let's see:

1. Sets and logic




2. Algebraic expressions and operations




3. Linear and quadratic equations and inequalities




4. Solving systems of equations and inequalities




5. Word problems leading to an equation or a system of equations - now this is what I call originality :-)




6. Equations solved by consequential modifications (I hope I have the translation right - but I doubt it)




7. Construction of triangles and quadrangles - here begins the planimetry, one of my biggest fears
   




8. Geometric position of points and its use in construction problems




9. Euclid's theorem and Pythagorean theorem




10. Identical images in surface




11. Similar images in surface - homothety!!!!
    




12. Quadratic function




13. Linear rational function




14. Power function




15. Exponential and logarithmic function




16. Exponential equations and inequalities - seems a bit similar to the last topic




17. Logarithmic equations and inequalities - ....




18. Charts of functions with absolute values




19. Goniometric functions




20. Goniometric equations




21. Trigonometry




22. Metric properties of linear formations in space - here begins the stereometry, one of my biggest fears




23. Relative positions of linear formations in space




24. Volumes and surface areas of solid figures




25. Permutations




26. Combinations




27. Sequences




28. Binomial theorem and binomial equations




29. Arithmetic sequence




30. Geometric sequence




31. Usage of geometric sequences (financial mathematics)




32. Infinite geometric progression




33. Vectors - and now the last fear - analytic geometry
    




34. Analytic geometry of linear formations - positional properties




35. Analytic geometry of linear formations - metric properties




36. Analytic expression of circle




37. Analytic expression of ellipse
    




38. Analytic expression of hyperbola
    




39. Analytic expression of parabola




40. Probability




41. Limit of a function




42. Derivative




43. Solving of real situations using extremes of a function - another original topic




44. Examination of function's properties




45. Primitive function




46. Definite integral




47. Complex numbers - I'll have to look at it again
    




48. Quadratic equations in complex domain




49. Mathematical proofs




50. Equations, inequalities and systems of equations with a parameter