This manual is collection of examinations. The first part contains 150 examination papers, the questions for which have been selected mainly from the English, French, and German collections of problems. These papers may be divided into three groups. The first 50 papers are confined to the simple rules, fractions, and weights and measures; the next 50 papers cover all the subjects treated in ordinary text-books except the metric system; the last 50 also include the metric system. In each group the earlier papers will be found somewhat easier than the later ones. The papers are intended to be one-hour papers, but if any of them are thought to be too long for one hour, the time may be increased, or the length of the paper reduced by omitting one or more questions.