Preliminary notesThis paper presents the achievement in the university entrance examination of secondary school graduates who applied for matriculation in The Faculty of Architecture, Civil Engineering and Geodesy, course Civil Engineering, Banja Luka University, in June 2012. The applicant achievement in the mathematics and physics parts of the examination is analysed with regard to attendance in the preparation courses and academic achievement in secondary school. Based on the findings, the authors make certain conclusions and recommendations intended to help improve the quality of secondary education, especially the teaching of mathematics and physics, through syllabus modification. They also recommended making a comprehensive analysis of university student achievement relative to the type of secondary school completed, and holding thematic meetings with teachers in technical/vocational secondary schools, in order to point to the specific topics or units that students find exceptionally challenging to deal with in university.Keywords: achievement analysis; preparation classes; software support; university entrance examination Efekti pripremne nastave i analiza uspjeha studenata u polaganju kvalifikacijskog ispita -prikaz slučaja studenata građevinarstva Prethodno priopćenje U ovom radu predstavljeni su rezultati kandidata koji su konkurirali na Arhitektonsko-građevinsko-geodetskom fakultetu Univerziteta u Banjoj Luci za upis na studijski program Građevinarstvo tijekom lipnja 2012. Analizirana je uspješnost kandidata iz predmeta matematika i fizika koje su kandidati osvojili tijekom kvalifikacijskog ispita u ovisnosti o pohađanju pripremne nastave, kao i značajnost uspjeha tijekom srednjoškolskog obrazovanja i završenoj srednjoj školi. Na osnovu dobivenih rezultata izvedeni su određeni zaključci i dane preporuke autora za poboljšanje kvalitete srednjoškolske nastave, posebice nastavnih sadržaja iz matematike i fizike. Također je preporučeno da se napravi detaljna analiza uspješnosti studenata na fakultetu prema završenim srednjim školama, kao i da se organiziraju tematski sastanci s nastavnicima koji izvode nastavu u strukovnim srednjim školama kako bi se ukazalo na posebne nastavne cjeline s kojima su studenti imali probleme tijekom studiranja.

Spatial abilities are becoming an increasingly important predictor of success, especially in professions that balance analytical and creative thinking, such as architecture, especially with the increasing presence of digital media and technology, and the importance of the spatial presentation of one’s ideas. There are differing opinions as to whether these abilities can be improved, or whether a spatial thinking strategy can be developed. At the Faculty of Architecture and Geodesy in Banja Luka (FACEG), spatial abilities have long been part of the entrance exam, and this paper will address the analysis of preparatory teaching at FACEG in this area and the success of the entrance exam for two groups of candidates - those who attended preparatory classes and those who prepared independently.

Descriptive geometry is one of the fundamental subjects in the education of future architects, civil engineers and engineers of geodesy. During the course, certain differences in mastering the teaching material have been noticed, as well as the divergence in performance of students in relation to their study program. In order to analyse these differences more closely, we made comparison of the students achievements at the first and second colloquium and final exam, analyzed the differences in relation to the study program, as well as the impact (correlation) of the entrance exam and the success in the secondary school on the final results in the course. Special attention was paid to the analysis of the results of the architecture students in the spatial ability test in order to determine whether the students of the architecture have more success in the subject of Descriptive geometry, considering that they have undergone certain training of spatial abilities through their preparation for the entrance exam.

In this paper we used a new class of special functions and special polynomials which are solutions different Sturm Liouvile differential equations of second order. These functions form a basis of a space of square integrable functions over set of a real numbers. We investigated some properties of these polynomials and established some recurrence formulas. Using a new class of special functions, we obtained some useful summation formulas and recurrence formulas.

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