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APPENDIX B.

TEXT-BOOKS AND SYLLABUS PRESCRIBED FOR THE EXAMINATIONS OF 1908.

MATRICULATION EXAMINATION.

ENGLISH.

Three papers will be set. One paper will be set from the prescribed course in Prose together with unseen' passages, and questions on Grammar and Idiom on both. A second paper will be set from the prescribed course in Poetry together with unseen' passages, and questions on Grammar and Idiom on both. In the third paper passages in an Indian vernacular (Urdu, Hindi, Mahratti, Gujrati, Bengali, Parbatia, Tamil, Telugu, Uriya) will be set for translation into English; but for such translation there will be substituted English Composition in the case of any candidate whose mother tongue is English.

N.B.-Forty per cent of the marks for each of the first two papers will be allotted to 'unseen' passages.

The following are the Prose and Poetry Courses prescribed :

"A Book of Golden Deeds," by the Author of "The Heir of Redclyffe," omitting the following :-

The cup of water. The devotion of the Decii. The brave brethren of Judah. Withstanding the monarch in his wrath. The Shepherd Girl of Nanterre. Leo the slave. Guzman el Bueno. Faithful till death. What is better than slaying a dragon. The constant Prince. The Crown of St. Stephen. George the Triller. Under Ivan the Terrible. Fort St. Elmo. The volun

tary convict. The housewives of Lowenburg. Gunpowder perils. Heroes of the plague. The second of September. The Vendeens. The petitioners for pardon. The children of Blentarn Ghyll. The mad dog. The Monthyon prizes. The fever at Osmotherly. The chieftainess and the volcano. The children in the wood of the far South.

English Poems, selected by J. G. Jennings (Macmillan & Co.), Part 1, omitting Nos. 12, 13, 15, 18, 22, 24, 35, 37, 39, 44. (The notes are not prescribed.)

MATHEMATICS.

There will be two papers in Mathematics, one paper in Arithmetic and Algebra, and a second paper in Geometry. The courses shall be as follows:

(1) Arithmetic.-The whole of Arithmetic. (The uses of Algebraical symbols and processes shall be permitted.) (2) Algebra.-The four simple rules, Fractions, Greatest Common Measure, Least Common Multiple, Factors, Proportion, Simple Equations of one or more unknown quantities with easy problems, Square Root, Simple questions on Fractional and Negative Indices, Quadratic Equations of one unknown quantity with easy problems. Easy graphs.

(Candidates will be provided with squared paper.)

(3) Geometry.-The course includes both Practical and Theoretical Geometry, and every candidate shall be expected to answer questions in both branches of the subject.

The questions on Practical Geometry shall be set on the constructions contained in the annexed Schedule A, together with easy extensions of them. All figures should be drawn accurately, for which purpose every candidate should provide himself with a graduated scale, a pair of set squares, a protractor, compass and a hard pencil.

The questions on Theoretical Geometry shall consist of Theorems contained in the annexed Schedule B. together with easy extensions and deductions with numeri

cal illustrations. Any proof of a proposition shall 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 the theorems hypothetical constructions shall be permitted.

SCHEDULE A.

Bisections 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.

Division 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 3, 4, 6 or 8 sides in or about a given circle.

Construction of a square equal in area to a given polygon.

SCHEDULE B.

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.

APPENDIX B.

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 (iii) a pair of interior angles on the same side of the cutting line are together equal to two right angles,

then the two straight lines are parallel; and the

converse.

Straight lines which are parallel to the same straight line are parallel to one another.

TRIANGLES AND RECTILINEAL FIGURES.

The sum of the angles of a triangle is equal to two right angles.

If the side of a convex polygon are produced in order the sum of the angles so formed is equal to four right angles.

If two triangles have two sides of the one equal to two sides of the other, each to each, and also the angles contained by these sides equal, the triangles are congruent.

If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

If two sides of a triangle are equal, the angles opposite to these sides are equal; and the converse.

If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.

If two sides of a triangle are unequal, the greater side has the greater angle opposite to it; and the converse.

Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.

The opposite sides and angles of a parallelogram are equal, each diagonal bisects the parallelogram and the diagonals bisect one another.

If there are three or more parallel straight lines and the intercepts made by them on any straight line that cuts then are equal, then the corresponding intercepts on any other straight line that cuts them are also equal.

AREAS.

Parallelograms on the same or equal bases and of the same altitude are equal in area.

Triangles on the same or equal bases and of the same altitude are equal in area.

Equal triangles on the same or equal bases are of the same altitude.

Illustrations and explanations of the geometrical theorems corresponding to the following Algebra indentities:

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The square on a side of a triangle is greater than, equal to, or less than, the sum of the squares on the other two sides, according as the angle contained by those sides is obtuse, right, or acute. The difference in the case of inequality is twice the rectangle contained by one of the two sides and the projection on it of the

other.

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