6. What are the factors of the denominators of those vulgar fractions which are expressible as terminating decimals? Divide 48 by 28800 and by .00288; and find the value of 32 of 10d. + ·032 of 10l. +·03 of 10%. 108. 7. Find, by Practice, the value, at 371. 6s. 8d. the ton, of 9 tons 10 cwt. 19 lbs. 1 oz. 8. If 5 men, 8 women, and II boys can do a piece of work in 4 days, how long would 7 men, 12 women, and 18 boys be in doing double the quantity, the parts done by each in the same time being as 3: 2: I? 9. Find the Compound Interest on 1257. 138. 9d. for 3 years at 4 per cent.? 10. Show that the Simple Interest (at 3 per cent.) of a sum of money for three years: the discount (3 per cent. Simple Interest) of the same sum payable at the end of three years: 109: 100. 11. By transferring his money from 3 per cents. at 1167. 138. 4d. to 3 per cents. at 90, a man increases his income by iol. What money has he? 12. A bankrupt owes his three creditors 16ool., 1400l., and 1000 guineas, his property being worth but 29251. If the law expenses are 10 per cent., how many shillings will he be able to pay in the pound, and what will each creditor receive? TUESDAY, JUNE 10, from 9 to 11.30 A.M. 4 (a). Euclid, I, II. 1. Define-point, straight line, plane, right angle, parallel straight lines, quadrilateral, parallelogram, rectangle; and write down Euclid's 12th axiom, and the axioms on two straight lines and on right angles. 2. Bisect a given rectilineal angle. 3. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other, the base of that which has the greater angle shall be greater than the base of the other. 4. If a straight line be divided into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. 5. If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles. Enunciate the first corollary to this proposition. What number of sides must a rectilineal figure have which has each of its interior angles equal to one and a half right angle? 6. Divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part. 7. The complements of the parallelograms which are about the diameter of any parallelogram, are equal to one another. 8. Describe a square that shall be equal to a given rectilineal figure. TUESDAY, JUNE 10, from 9 to 11.30 A.M. 1. Remove the brackets from 4. Find the quotient and remainder when a64a5b+a1b2 + 12 a2 b4 — ab5 is divided by a-2b. 5. Express in factors (1) 5x1-25x3y —70x2y2; (2) 15x2-34x+15. 6. Find the Greatest Common Measure of 2 x3 −4x2+3x−1 and 6x3-10x2+5×−1. 7. Find the Least Common Multiple of 4xy(x2—y2), 20x3 (x3 —y3) and 15xy3 (x2+2xy+y2). 10. Find the number which exceeds by 100 the sum of its third and its ninth parts. 11. The sum of A's money and B's money is six times the difference between them. If A had 10l. more and B 10l. less then A's money would be five times B's. Find the sum belonging to each. 12. Extract the square root of 4x4-12x3+21x2-18x+9. WEDNESDAY, JUNE 11, from 9 to 11 A.M. A. Latin. (First Paper.) Translate into Latin: 6 Hannibal summoned a meeting of the principal Tarentine citizens, and explained to them all the difficulties that beset him. He saw no way of storming such a strongly fortified citadel, and he had no hope from a blockade as long as the enemy remained masters of the sea. If he had ships with which to stop the import of supplies, the enemy would at once either retire or surrender. The Tarentines concurred, but they maintained that he who gave the advice must help towards carrying it into effect. Carthaginian ships,' they said, 'brought up from Sicily could do this. As for their own, shut in as they were within a confined bay, while the enemy held the entrance to the harbour, in what possible manner could they escape into the open sea?' To this Hannibal replied, Escape they shall, if you follow my advice and carry out what I suggest. Many things which nature surrounds with impediments are easy to accomplish by forethought.' WEDNESDAY, JUNE 11, from 11 A.M. to 1 P.M. A. Latin. (Second Paper.) 1. What is the usual order of words in a simple Latin sentence? Quote or make an example, and show how and why Latin can vary its order more than English can. 2. What is meant by the terms-Adverbial Clause, Adjectival Clause, Ablative Absolute, Impersonal Verb, Dativus Ethicus? Give examples of each. 3. State and illustrate the various uses of the Ablative Case in Latin. Give the equivalent idioms in the other language which you offer for this examination." 4. Explain the use of the following pronouns :-isteullus quisquam-se, suus-ceteri. 5. What is the reason for the use of the Subjunctive Mood in each of the following sentences ?— (1) Sunt qui non habeant, est qui non curat habere. (2) Accusatus est quod socios prodidisset. (3) O felix, qui Homerum virtutis tuae praeconem (the herald) inveneris! (4) Nemo eum laudavit, qui ita dixisset ut ii qui adessent intelligerent, quid diceret. 6. Translate into Latin: (1) I would not have waited to see him, had he not promised to come as soon as he could; but instead of doing this he told a servant to go and see whether I had come. (2) Turning to his friends, he asked them to remember him after he had quitted this life; adding, that he had not deserved to meet such a fate. 7. Translate into English: 6 Itaque is terror in castris ortus, qui si pugnantes cepisset, insignis accepta clades foret. Ubi primum illuxit, abire sine. certamine cupiunt. Sed via una, et ea praeter hostes, erat: qua ingressi, praebuere speciem recta via tendentium ad castra oppugnanda. Consul arma capere milites jubet, et sequi se extra vallum. Legati omnes affirmant, se quidem omnia facturos, sed militum jacere animos. Tota nocte inter vulnera et gemitus morientium vigilatum esse. Si ante lucem ad castra ventum foret, tantum pavoris futurum fuisse, ut relicturi signa fuerint: nunc pudore a fuga contineri: alioquin pro victis esse.' Quae ubi consul accepit, cunctantes arma capere increpabat 'Quid cessarent, tergiversarenturque ?' WEDNESDAY, JUNE 11, from 2.30 to 4.30 P.M. A. Latin. (Third Paper.) 1. Translate: (a) Ventum deinde ad multo angustiorem rupem atque ita rectis saxis, ut aegre expeditus miles tentabundus manibusque retinens virgulta ac stirpes circa eminentes demittere |