E.—la.

11

Class D. —Latin (Optional). 1. Give the dative singular of unus, idem, alter, respublica. Give the first person singular of the perfect indicative active, the present infinitive active, and the supine in torn, of each of the following verbs : — Scindo, quaro,pasco, sepelio, gigno, cogo, adolesco. Give the first person future indicative of pereo, memini, prosum. 2. What are the so-called supines, and how are they used? Is the supine in u dative or ablative ? Give reasons. Express in Latin in two w*ays, using (1) the supine, (2) the gerundive, Ambassadors came to sue for peace. 3. Explain the use of ut and ne after verbs of fearing. How is quin used (1) in independent, (2) in dependent sentences ? 4. Explain the use of the cases in the words printed in italics in the following sentences:— Permulta nobis facienda sunt. Exitio est avidis mare nautis. Atrox discordia fuit domi forisqua. Est mihi tanti Quirites hanc invidiam subire. Paucis post cliebus fit certior. In the last sentence what part of speech is post ? 5. Translate : —Et manu fortis et belli peritus fuit, et, id quod in tyranno non facile reperitur, non luxuriosus, non avarus, nullius denique rei cupidus nisi singularis perpetuique imperii, ob eamque rem crudelis: nam, dum id studuit munire, nullius pepercit vitae, quern ejus insidiatorem putaret. Hie cum virtute tyrannidem sibi peperisset, magna retinuit felicitate : major enim annos sexaginta natus decessit florente regno. Neque in tarn multis annis cujusquam ex sua stirpe funus vidit, cum ex tribus uxoribus liberos procreasset multique ei nati essent nepotes. 6. Translate into Latin :— Socrates used to inquire what things were just, what unjust. Dionysius, having been expelled from Syracuse, opened a school at Corinth. Cassar, having overcome the Gauls, waged war with Pompey. He could easily have done this, and he ought to have done it.

Class D.—Algebra (Optional). 1. Explain fully the meaning of the expression— [a+ */W+c*]*- [(&+c) 2-a 2], and calculate its value when a=s, &==4, c = 7. x+ —;) ■+-{%— —-)■ x-3/ \ x+ 3J 2. Find the continued product olpx-\-qy, qx—py,p' ix 2—pqxy+q iy' i, and q 2x^—pqxy-{-p 2y9. Arrange your answer in ascending powers of y, collecting co-efficients of like powers in a bracket. 3. Simplifva--2?/-(-30+ [(2a; —^ +2) — (3a;-22)] -x). %(3,-%)-{-^-i[^-(3,-f)](. 4. Eesolve into elementary factors x d — 8y 3; V2ix" — 2xy — 2y^; (sa—lb — c)' 2 — (ia— 2&+c) 9; a?+V i-c i-2ab; 2 (uv+xy)+ti 2+v 2-x 2—y\ 5. Find the highest common divisor and the lowest common multiple of 36a° —18a 5 —27a 4-)-9a a; 27aW-V6ai^-9aW. r. TV 1 r.l 1 A + 37-1 1 «+ l a(b +l) 6. Find the value of , when x = , y=~ '; x-y + 1 ab + 1 a ab+l , . ' • 6x SOxt+ix 4x and simplify 1 . * J 3<B-2 9x*+4 3.C + 2 7. Solve the equations — 2z + l 402-3X' 471-6K "29 12 2 ' c— x a— x b— x 1- 1 =1. a+ b b+c c+ a 8. A steamer can travel x miles an hour with engines alone in calm weather, and her speed is increased by y miles an hour when she uses her sails with a favourable wind, and diminished by y' miles an hour when the wind is contrary. If she have a current flowing at the rate of z miles an hour, (a) in her favour, (/3) against her, how fast can she travel in each case, supposing (1) that the wind is favourable, and (2) that it is contrary? 9. The areas of two adjacent countries are as ato b ; in a war between them the latter takes from the former p square miles of territory, and then their areas are in the ratio of mto n : find the area of both countries at first.

Class D.—Euclid (Optional.) 1. Define a plane surface, a plane angle, and a circle. Is Euclid's use of the word "circle," for example in the First Proposition of the First Book, in accordance with the definition ? Quote the axioms which are exclusively geometrical. 2. From a given point to draw a straight line equal to a given straight line. In the construction of the figure, the sides of the equilateral triangle may be produced, not beyond the base, but through the vertex. Construct the diagram in this manner, and show how the proof must be modified. 3. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angles contained by those sides unequal, the base of that which has the greater angle shall be greater than the base of the other.