2240

THE NEW ZEALAND GAZETTE.

[No. 72

Algebraic formulæ and symbols may be used. Questions will not be set on present value or “true” discount. The extraction of the cube root and the use and theory of recurring decimals are not required.

Geometry.—The elements of geometrical drawing and practical geometry. Measurement of angles, use of protractor. The substance of Books I to III of Euclid’s Geometry, including application to the measurement of area. A working knowledge of as much of the properties of similar figures and solid figures as is necessary for plan-making and simple problems in mensuration.

Algebra.—To easy quadratic equations. The elementary use of graphs.

The solutions of equations should be worked out to a few significant figures; the candidates should be accustomed to test the accuracy of solutions by substitution. Skill in elaborate analysis, such as the simplification of complicated fractions, will not be looked for.

The questions in Elementary Mathematics will test knowledge of fundamental principles and readiness in application to simple practical problems. Neatness and accuracy of working are expected; and the methods of solution employed must be clearly indicated. In the absence of special instructions that a question is to be answered by a particular method, candidates are at liberty to choose their own method from any branch of Mathematics.

The examination in Elementary Mathematics will include a laboratory test. The laboratory test will carry 400 marks.

• INTERMEDIATE MATHEMATICS. — Includes Elementary Mathematics, together with:—

Arithmetic.—Use of four-figure logarithms will be required, use of slide-rule permitted.

Geometry.—Geometrical drawing and practical geometry of plane figures. The substance of Books I to IV and VI of Euclid’s Geometry. The elements of theoretical solid geometry with application to mensuration of solids.

Proportion may be treated algebraically, and the complications of Euclid’s definitions and nomenclature avoided. The special treatment of incommensurables will not be required.

Algebra.—The meaning and the simplest properties of fractional and negative indices; graphs of the simpler algebraic functions; quadratic equations; use of graphs in solving equations, and in illustrating and solving practical problems; practical applications of gradients and of areas of graphs.

Grasp of elementary principles and readiness in practical application will be looked for, but great skill in analytical transformations will not be demanded.

Trigonometry.—Solution of plane triangles; graphs of trigonometrical functions; use of four-figure tables; formulæ for the trigonometrical ratios of the sum and difference of two angles and for the product forms of the sum and difference of sines and cosines of two angles.

Readiness in straightforward practical applications will be looked for, but no great analytical skill will be demanded. A knowledge of the general expression for all angles which have a given sine or other trigonometrical ratio will not be required.

Statics.—Graphical and analytical methods; simple machines; centre of gravity; friction.

Dynamics.—Accelerated motion in a straight line treated graphically; uniformly accelerated motion in a straight line; composition of velocities and accelerations; uniform circular motion; motion under gravity; elementary illustrations and applications of dynamical principles.

In Intermediate Mathematics, in the absence of special instructions that a question is to be answered by a particular method, candidates are at liberty to choose their method from any branch of Mathematics.

The examination in Intermediate Mathematics will include a laboratory test. The laboratory test will carry 400 marks.

• HIGHER MATHEMATICS.—Includes Elementary and Intermediate Mathematics, together with:—

Geometry.—Elements of solid geometrical drawing.

Algebra.—Elementary knowledge of the use of indeterminate co-efficients, especially with partial fractions.

Co-ordinate Geometry and Infinitesimal Calculus.—Equations to straight line, circle, ellipse, parabola, hyperbola, and other simple curves, in rectangular co-ordinates. The curves referred to will provide illustrations and applications of co-ordinate geometry and infinitesimal calculus, but acquaintance is expected only with the simplest theorems about the curves.

Differentiation and integration of simple standard forms and other forms depending on them; application to easy geometrical properties of plane curves, to easy mechanical and physical problems, to turning values, and to the expansion of simple algebraic and trigonometrical functions. A working knowledge (without rigorous fundamental demonstrations) of the elementary infinite series for (1 + x)ᵐ, eˣ, log (1 + x), and their use in approximate calculations.

Co-ordinate geometry of three dimensions up to the equations to the plane and the straight line.

Polar co-ordinates:—Deduction of the equation of a curve from simple data; drawing a curve from its equation.

Mechanics.—Elementary statics of liquids and gases. Further mechanics of solid bodies—e.g., pendulum and easy questions of moment of inertia.

In Higher Mathematics more analytical skill will be expected than in the earlier stages. In the absence of special instructions that a question is to be answered by a particular method, candidates are at liberty to choose their method from any branch of mathematics.

The examination in Higher Mathematics will include a laboratory test. The laboratory test will carry 400 marks.

• PHYSICS.—The subject will carry about 1,200 marks.—The questions set will be such as may be answered by candidates who have acquired their knowledge by an experimental treatment of the subject.

Heat.—Construction and use of thermometers. Expansion of solids, liquids, and gases. Specific heat. Phenomena of change of state; vapour pressure; latent heat. Simple phenomena of conduction, convection, and radiation of heat. Heat as a form of energy.

Light.—Rectilinear propagation. Reflection and refraction; formation of images by plane and spherical mirrors, and by concave and convex lenses. Telescope and microscope. The dispersion of light by a prism.

Magnetism.—Simple phenomena of magnetism; induction. Lines of force in a magnetic field; terrestrial magnetism. Elementary quantitative notions of strength of pole, magnetic force due to a pole, strength of field.

Static Electricity.—Electrification; induction. The electroscope; electrophorus. Elementary notions of potential and capacity. Distribution of charge on conductors.

Current Electricity.—Meaning of the units volt, ampere, and ohm. The simple voltaic cell; Daniell cell; Leclanche cell; accumulator. Ohm’s law with simple applications; arrangement of cells in series and parallel. Magnetic field due to a current; astatic galvanometer, tangent galvanometer, moving coil galvanometer. Laws of electrolysis; electro-chemical equivalent. Fundamental experiments of electro-magnetic induction.

Practical Work.—The laboratory test will carry about 400 marks.—Simple experiments on the subject-matter of the preceding syllabus, for example:—

Verification of Boyle’s law. Testing the standard points of thermometers. Determination of specific and latent heat by the method of mixtures. Determination of melting and boiling points. Verification of the laws of reflection and refraction. Determination of the positions of images formed by plane and spherical mirrors and by convex lenses. Mapping lines of force in magnetic fields. Comparison of intensities of magnetic fields by the method of oscillations. Comparison of electric currents by the tangent galvanometer and by ammeters. Comparison of potential differences by high-resistance galvanometers and by voltmeters. Comparison of resistances by substitution and by the sliding bridge.

† CHEMISTRY.—The subject will carry about 800 marks.—The questions set will be such as may be answered by candidates who have acquired their knowledge by an experimental treatment of the subject.

Classification of matter into single substances and mixtures, elements and compounds. Quantitative laws of chemical combination, outlines of the explanation of these laws by the atomic theory; Avogadro’s law; general methods of determining chemical equivalents. The chemistry of water and its constituent elements; water as a solvent;

• See footnote on previous column.

† Science.—Credit will be given for lucidity, orderly development, and aptness of language; deductions will be made for incoherence, irrelevance, obscurity, slovenliness of expression, and especially for bad grammar and the incorrect use of words and phrases. Chemical symbols must be restricted to their proper function and not used as a shorthand symbol for the name of the substance.

• MATHEMATICS.—Credit will be given for the clearness and aptness of the language of the answers; deductions will be made for obscurity or slovenliness, and especially for bad grammar and the incorrect use of words or phrases. The use of mathematical symbols and of well-established abbreviations like lb. and cm. is permissible; a calculation can often be exhibited quite clearly without the use of words; and a tabular form is often appropriate; but incomplete sentences such as are customary in telegrams will be punished.