Arithmetic. —The principles and processes of arithmetic applied to whole numbers and vulgar and decimal fractions. The metric system. Approximations to a specified degree of accuracy. Contracted methods of multiplication and division of decimals. Ratio and proportion. Percentage. Averages. Practical applications of arithmetic. Algebra.—Symbolical expressions. Equations of the first or second degree (and problems leading thereto). Square root. Graphs of simple rational integral algebraic functions. Arithmetic and harmonic progression. Geometric progression. Theory of indices. Logarithms. Theory and use of the slide rule. Binomial theorem for a positive integral index. Geometry.— The subjects covered by Euclid I.-IV. with simple deductions, including easy loci and the areas of triangles and parallelograms of which the bases and altitudes are given commensurable lengths. (Euclid proofs will not be insisted upon.) Trigonometry.—Up to and including the solution of triangles, together with the practical solutions of triangles and applications, and numerical examples involving the use of logarithmic and other tables.