The article is the first chapter of an extensive study about the preparedness of apprentices in mathematics, physics (by the author) and in the Czech language (by Z. Skoupil) compiled in the Research Institute of Vocational Schooling in Prague in the years 1966 and 1967. The aim of the research in mathematics was to find out about changes in grading at the Basic School, U/study the influence of the extension of compulsory school attendance from eight to nine years, to find out what differences there are in the preparedness of apprentices as to the knowledge and skills. The necessary material was provided in the main by a written examination taken by about one per cent of all apprentices in the Czech lands in the years 1960, 1962 and 1965. The selection of the apprentices was stratified. Partial tests were set and some observations were carried out with the aim of verifying certain hypotheses. In evaluating the results a number of statistical methods were used, especially that of non-parametric tests. In the first chapter we came to the conclusion that knowledge and skills of the apprentices received for training in 1965 were better than in previous years. We found that Basic School teachers had become more strict in grading the pupils. About 1962 the grades on school reports in the last year of the Basic School improved, but the knowledge of the newly received apprentices was worse than in any other year. Deterioration of knowledge is conspicuous especially among those pupils whose general results at school were above average. The knowledge of those below average did improve slightly, but not significantly from the statistical viewpoint. This improvement may have been brought about by the special care for the so-called backward pupils, which culminated about 1962. During the whole period of research the number of apprentices who had been graded ≫excellent≪ in mathematics systematically declined. This may be accounted for by the greater possibilities of continued attendance at selective schools as well as by a greater interest of excellent pupils in higher studies. It was confirmed that according to the attractiveness of a particular trade there are classes of apprentices, formed at Trade Schools, which differ from one another both in the pupils basic school results and in their knowledge. This differentiation does not result from the difficulty of the trade at all, 'but from the number of applicants interested in the trade. We did not succeed in assessing the overall influence of the extension of compulsory school attendance because with the transition from the eight-year to the nine-year school attendance the total number of lessons in mathematics in the new curriculum was unexpectedly reduced. This reduction makes itself felt especially in the first five years where pupils learn the fundamentals of numerical arithmetic. It will not be possible to draw conclusions earlier than in about 1970 when Trade Schools will be receiving apprentices who have gone through the whole Basic School according to the new curricula.