✨ Education Examination Syllabus
(4.) Elementary Mathematics II.—(a.) Algebra: Fundamental operations, factors, fractions, simple equations involving one or two unknown quantities, and easy quadratic equations involving one unknown quantity; easy problems; graphs of simple rational integral algebraic functions; and graphical methods of solving equations.
(b.) Geometry: The paper in geometry will contain questions on practical and on theoretical geometry. Every candidate will be expected to answer questions in both branches of the subject.
The questions on practical geometry will be set on the constructions contained in the annexed Schedule A, together with easy extensions of them. In cases where the validity of a construction is not obvious, the reasoning by which it is justified may be required. Every candidate must provide himself with a ruler graduated in inches and tenths of an inch, and in centimeters and millimeters, set-squares, a protractor, compasses, and a fine pencil. All figures should be drawn accurately. Questions may be set in which the use of the set-square or of the protractor is forbidden.
The questions in theoretical geometry will consist of theorems contained in the annexed Schedule B, together with questions upon these theorems, easy deductions from them, and arithmetical illustrations. Any proof of a proposition will be accepted which appears to the examiners to form part of a systematic treatment of the subject: the order in which the theorems are stated in Schedule B is not imposed as the sequence of their treatment.
In the proof of theorems and deductions from them, the use of hypothetical constructions will be permitted. Proofs which are applicable only to commensurable magnitudes will be accepted.
SCHEDULE A (PRACTICAL).
Bisection of angles and of straight lines.
Construction of perpendiculars to straight lines.
Construction of an angle equal to a given angle.
Construction of parallels to a given straight line.
Simple cases of the construction from sufficient data of triangles and quadrilaterals.
Divisions of straight lines into a given number of equal parts or into parts in any given proportions.
Construction of a triangle equal in area to a given polygon.
Construction of tangents to a circle and of common tangents to two circles.
Simple cases of the construction of circles from sufficient data.
Construction of a fourth proportional to three given straight lines and a mean proportional to two given straight lines.
Construction of regular figures of three, four, six, or eight sides in or about a given circle.
Construction of a square equal in area to a given polygon.
Determination by measurement of the ratio of the circumference of a circle to its diameter.
Approximate determination of the area of a circle.
SCHEDULE B (THEORETICAL).
Angles at a Point.
If a straight line stands on another straight line, the sum of the two angles so formed is equal to two right angles; and the converse.
If two straight lines intersect, the vertically opposite angles are equal.
Parallel Straight Lines.
When a straight line cuts two other straight lines, if—
(i.) A pair of alternate angles are equal; or
(ii.) A pair of corresponding angles are equal; or
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NZ Gazette 1912, No 15
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🎓 Class D Teacher Examination - Elementary Mathematics II. Syllabus
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