1054
THE NEW ZEALAND GAZETTE.
No. 29

(10.) Arithmetic and Algebra.—(a.) Arithmetic: Contracted and approximate methods of multiplying and dividing numbers, so as to omit all unnecessary figures; use of rough checks, especially with regard to the position of the decimal point; use of such expressions as 1·732 × 10⁴ for 17320, and 1·732 × 10⁻³ for ·001732. Meaning of a common logarithm; use of logarithmic tables of four or five figures. Calculation of numerical values from formulae. Working of problems in practice, interest, &c., by decimals; use of squared paper, and application of graphical methods to arithmetical problems.

A knowledge of the arithmetic and mensuration included in the programme of the Civil Service Junior Examination will be assumed. Tables of logarithms will be supplied.

(b.) Algebra: Definitions and explanations of algebraical signs and terms; addition, subtraction, multiplication, and division of algebraical quantities, including easy fractions and easy surds (the candidate will not be expected to show skill in the manipulation of complicated formulae, but he may be required to ascertain accurately the numerical value of any quantity or expression given to him); square root; the elementary rules of ratio and proportion; easy equations of a degree not higher than the second, and questions producing such equations; easy arithmetical and geometrical series; graphs of simple algebraic functions within the limits of the foregoing work, and graphical methods of solving equations. Very easy permutations and combinations; binomial theorem (the candidate may be expected to explain the case in which the exponent is a positive integer, but a rigid proof will not be required); the use of approximate formulae, such as (1 + x)³ = 1 + 3x, (1 − x)⁻¹ = 1 + ½x, when x is small compared with 1.

(11.) Geometry and Trigonometry.—Every candidate must be provided with a ruler graduated in inches and tenths and in centimeters and millimeters, a small set-square, a protractor or scale of chords, compasses with pencil-point, and a fine pencil. Tables of logarithms will be supplied.

(a.) Geometry: Sections A and B (practical and theoretical geometry) as in the Civil Service Junior Examination, together with the following:—

SECTION C (PRACTICAL).

To draw a normal to a plane from an external point.

Projections of a point on three planes at right angles.

Determination of a point by means of its co-ordinates (x, y, z), referred to three rectangular axes and by means of its polar co-ordinates.

Projection of a straight line on a plane making a given angle with it.

Projection of a plane figure on a plane making a given angle with it.

Development of the right prism, and of the right pyramid.

Determination of the surface, the base being a regular polygon, of the right prism and right pyramid.

Volume of the prism and pyramid.

The generation of the right circular cylinder, right circular cone, and sphere by revolution.

Development of the right circular cylinder, and right circular cone; the surface of each.

Volume of the cylinder, cone, and sphere.

SECTION D (THEORETICAL).

If a straight line is drawn parallel to one side of a triangle, the other sides are divided proportionally; and the converse.