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5. Find the cost of 11 tons 3 cwts. 3 qrs. 16 lbs. at 37. 128. IId. per cwt.
6. Multiply 25.3125 by 2.56; divide 648 by 0256; and from the sum of 2.6 and 3.583 subtract 5.05.
7. Reduce 57. 188. 10d. to the decimal of 257.; and find the value of
025 of 17.+35 of 178. 6d. +2 of 24d.
8. If the food of 11 persons for 13 weeks costs 1127. 128. 3d., what will it cost to feed 26 persons for 11 wks. 5 days?
9. At what rate per cent. per annum will 407. 10s. be the simple interest on 4327. for 2 years?
10. A grocer buys 6 cwts. of tea for 70%, and sells 4 cwts. at 2s. 6d. per lb. at what price per lb. must he sell the remainder to bring his profit on the whole to exactly 20 per cent.?
11. A person, who had 2 sons and 4 daughters, left an estate of 2800 acres to be divided between them so that each son might have twice as much as each daughter if one of his sons has a family of 4 sons and 2 daughters, and leaves his share to be divided in the same manner, how many acres will each of his daughters inherit ?
12. From a cask of wine, worth 28. 3d. per gallon, a sixth part is drawn and replaced by wine worth only 18. 3d. per gallon what is now the value per gallon of the wine in the cask?
TUESDAY, JUNE 5, from 9.30 A.м. to 12.
4 (a). Euclid, I, II.
1. Define-a plane rectilineal angle, a plane superficies, a right angle, an oblong, a rectangle, a gnomon.
Can a trapezium be correctly defined as any irregular four-sided figure'? If not, why not?
2. If two triangles have two sides of the one equal to two sides of the other, each to each, and have also the angles contained by those sides equal to one another, they shall also have their bases or third sides equal; and the two triangles
shall be equal; and their other angles shall be equal, each to each, namely those to which the equal sides are opposite.
By what other propositions of Euclid, Book I, are triangles proved to be equal?
3. If one side of a triangle be produced, the exterior angle shall be greater than either of the interior opposite angles.
4. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts.
5. Make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
6. If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
7. Parallelograms on equal bases, and between the same parallels, are equal to one another.
8. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.
TUESDAY, JUNE 5, from 9.30 A.M. to 12.
4 (6). Algebra.
1. Evaluate (x-y)2 + ( y − z)2 + (z−x)2 when x=31, y=21, 2=11.
2. From the sum of 3 (2x-3y+4%) and 11⁄2 (4x + 3y −112) subtract (8-9y+6x).
x2 + y2+a(x-y) by xy-a (x+y) + a2.
x3 +8y3 — 12523 +30xyz by ∞ + 2y − 52.
5. Express in factors
(2) 20x4-60x3y+45x2 y2.
6. Find the greatest common measure of
7. Find the least common multiple of
15 x2 (a2 — 2 ax+x2), 21 a2 (a2 +2 ax+x2), 35ax (a2 — x2).
9. Solve the equations :
(1) 2 (x − 1) + 3 (— − 9 ) − (≈—13) =
10. The sum of three consecutive whole numbers exceeds the greatest of them by 19: what are the numbers?
11. Find the fraction which is such that if 3 be subtracted from the numerator and 5 added to the denominator, the value is ; but if 5 be subtracted from the numerator and 3 added to the denominator, the value is .
12. Extract the square root of
36x2-120 ax-12 a2x + 100 a2 + 20 a3 + aa.
THE SECOND EXAMINATION. PASS.
WEDNESDAY, JUNE 6, from 9 to 11 A.M.
A. Latin. (First Paper.)
1. Translate, with explanations of personal or historical allusions:
(1) Possum persequi multa oblectamenta rerum_rusticarum; sed ea ipsa, quae dixi, fuisse sentio longiora. Ignoscetis autem; nam et studio rerum rusticarum provectus sum, et senectus est natura loquacior: ne ab omnibus eam vitiis videar vindicare. Ergo in hac vita M'. Curius, quum de Samnitibus, de Sabinis, de Pyrrho triumphasset, consumpsit extremum tempus aetatis: cuius quidem ego villam contemplans, (abest enim non longe a me), admirari satis non possum vel hominis ipsius continentiam vel temporum disciplinam.
(2) Te autem alio quodam modo, non solum natura et moribus, verum etiam studio et doctrina esse sapientem, nec sicut vulgus, sed ut eruditi solent appellare sapientem, qualem in Graecia neminem. Nam qui septem appellantur, eos, qui ista subtilius quaerunt, in numero sapientium non habent. Athenis unum accepimus, et eum quidem etiam Apollinis oraculo sapientissimum iudicatum.
(3) Nae tu, Eruci, accusator esses ridiculus, si illis temporibus natus esses, quum ab aratro arcessebantur, qui consules fierent. Etenim, qui praeesse agro colendo flagitium putes, profecto illum Attilium, quem sua manu spargentem semen, qui missi erant, convenerunt, hominem turpissimum atque inhonestissimum iudicares.
2. Translate and explain (noting particularly the words italicised):
(1) Nobis senibus ex lusionibus multis talos relinquant et tesseras.
(2) Qui clamores tota cavea nuper in hospitis et amici mei M. Pacuvi nova fabula, cum ignorante rege uter Orestes esset, Pylades Orestem se esse diceret, ut pro illo necaretur.
(3) Intellego me prope modum errare qui, cum capiti Sex. Roscii mederi debeam, reduviam curem.
(1) Truditur dies die,
Novaeque pergunt interire Lunae.
Locas sub ipsum funus, et sepulchri
Marisque Baiis obstrepentis urges
Parum locuples continente ripa.
(2) Tu, quid ego et populus mecum desideret, audi :
4. Translate, and explain the construction of the genitive case in each of the following:
(1) Notus in fratres animi paterni.
(2) Desine mollium tandem querelarum.
(3) Damnatus longi Sisyphus Aeolides laboris.
5. Translate and explain :
(1) Versibus impariter iunctis querimonia primum, Post etiam inclusa est voti sententia compos. (2) Scriptor cyclicus-Plautini sales-meret aera liber Sosiis.
6. Answer briefly one only of the following questions:(1) An account of the interlocutors in the dialogue De Amicitia.
(2) The political circumstances under which the speech Pro Roscio Amerino was delivered.
(3) The position assigned by Horace to the Chorus in drama.
WEDNESDAY, JUNE 6, from 11 A.M. to 1 P.M.
A. Latin. (Second Paper.)
Translate into Latin:
So far as to the crimes: so far as to the criminal.
I shall say a few words about the evidence which we have