7. At what time between the hours of 3 and 4 will the hands of a watch be at right angles to each other? 8. Find the squares of 7380481 and 1905632, and divide the greater result by the less, to the first significant digit in the decimal places. 9. Two persons set off to walk from different points in opposite directions along the line joining them; when they meet, the quicker turns back, and on arriving at the point from which he started, again sets off; they arrive simultaneously, each at the point from which the other started. At what point do they first meet? 11. If the sum of £1200 be put out at 10 per cent. per annum compound interest, and interest paid half yearly, to what will it amount in a year and a half? What would it amount to in 4 years at the same rate at simple interest? 12. Find the thickness of a solid whose length is 2 yards, breadth a yard and a half, and solid content 1 cub. yd., 6 cub. ft. and 1296 cub. in. 13. Give the algebraical definition of proportion and prove that if a b c d then a + b: a :: c + d : c. 14. What sum must a person invest in the 3 per cents. at 90, in order that by selling out £1000 stock, when they have risen to 93, and the remainder when they have fallen to 841, he may gain £6. 5s. by the transaction? If he invest the produce in 4 per cents. at par, what will be the difference in his income? THURSDAY, January 10, 1856. 9 to 12. FIRST DIVISION.—(A.) 1. TWELVE rupees, three florins, and six half-crowns amount to £2.8s. What is the value of a rupee? 2. The tenth, hundredth, and thousandth parts of a pound sterling being called florins, cents, and mils respectively, subtract 1 florin 4 cents from 7 florins 1 cent 5 mils, and shew that eight times the difference equals £4. 12s. 3. State the rules for the multiplication and division of vulgar fractions. Multiply and divide by 1-3. Find which result is the + greater, and express their difference in its lowest terms. 4. What fraction of 10s. is 2s. 9d.? Reduce the result to a decimal. 5. What sum must be invested in the 3 per cents. at 92, in order to derive an income of £150 per annum? What will be the amount of stock? 6. Define present value. What sum will amount to £820. 16s. in 3 years at 4 per cent. simple interest? 7. The distance between two stations A and B is 65 miles. A train starts from A to go to B at the rate of 15 miles an hour, and is delayed 10 minutes on the way: another train starts from A two hours after the former at the rate of 25 miles an hour, find the interval between their times of arrival at B. 8. Remove the brackets from the expression, 3a - [b - {a + (b − 3a) } ]. Find the value of ( √x2 + y2+z) ( √√x2 + y2 − z), when x=4, y = 5, 2 = 6. 9. Reduce to their simplest forms the expressions 11. When is one quantity said to vary directly and when inversely as another? One horse takes 6 strides while another takes 5, but 7 strides of the latter horse are equal to 8 strides of the former; which is the swifter horse? 12. Divide x − xy3 — x3y + ya by x2 + xy + y2, and extract the square root of the quotient. 13. The expense of carpeting a room 18 feet long was £7. 4s, but if the breadth of the room had been 4 feet less than it was, the expense would have been £5. 8s, what was the breadth of the room? 14. A merchant has teas worth 4s. 6d. and 3s. 6d. per lb. respectively, which he mixes in the proportion of 2 lbs. of the former to 1lb. of the latter and sells the mixture at 4s. 4d. per lb.; what does he gain or lose per cent? FIRST DIVISION.—(B.) 1. NINE rupees, six crown-pieces, and eleven threepenny-pieces amount to £2. 13s. What is the value of a rupee? 2. The tenth, hundredth, and thousandth parts of a pound sterling being called florins, cents, and mils respectively, subtract 5 florins 3 cents 5 mils from 9 florins 6 cents, and shew that eight times the difference equals £3. 8s. 3. State the rules for the multiplication and division of vulgar fractions. Multiply and divide by 1-4. Find which result is the greater, and reduce their difference to a decimal. 5. 4. What fraction of 5s. is 2s. 3d.? Reduce the result to a decimal. What sum must be invested in the derive an income of £120 per annum? stock? 3 per cents. at 96, in order to What will be the amount of present value of £402. 12s. due per cent. per annum. 6. Define present value. Find the 3 years hence, simple interest being at 4 7. The distance between two stations A and B is 75 miles. A train starts from A to go to B at the rate of 20 miles an hour, and is delayed 6 minutes on the way; another train starts from A an hour after the former, at the rate of 24 miles an hour; find the interval between their times of arrival at B. 8. Prove that a − (b − c) = a − b + c, specifying the limitations to the values of a, b, c necessary to your proof. Shew that (a2 + b2) (c2 + d2) = (ac + bd)2 + (ad − bc)2. 9. Reduce to their simplest forms the expressions, 11. When is one quantity said to vary directly, and when inversely as another? One horse takes 5 strides while another takes 4, but 6 strides of the latter horse are equal to 7 strides of the former; which is the swifter horse? 12. Divide x + xy3 + x3y + y2 by x2 - xy + y2, and extract the square root of the quotient. 13. The expense of carpeting a room 20 feet long was £7. 10s, but if the breadth had been 3 feet less than it was, the expense would have been £6; what was the breadth of the room? 14. A merchant has teas worth 5s. and 3s. 6d. per lb. respectively, which he mixes in the proportion of 2lbs. of the latter to one of the former. How much will he gain or lose per cent. by selling the mixture at 4s. 6d. per lb.? 1. TRANSLATE into literal ENGLISH PROSE, X. 56—107: Beginning, Quosdam præcipitat subjecta potentia magnæ... Write a succinct life of Sejanus (with dates). What English poet has made Sejanus the subject of a piece? v. 74. Nortia. Where lies the point of introducing her? v. 77. Ex quo &c. What is the political change alluded to? What were the Consules suffecti under the empire? v. 84. Ajax. Explain the mythological allusion, and thence shew how the present passage must be understood. v. 100. potestas. Illustrate this use of the abstract word by corresponding instances in ancient and modern languages. v. 102. Cite a similar passage from Persius. What were the offices of the ædiles? What were the two kinds of ædiles? 2. Translate, XIII. 71-105: Beginning, Intercepta decem quereris sestertia fraude... Ending, Ille crucem sceleris pretium tulit, hic diadema. v. 71. What is the value of the sestertius? What of the sestertium? How much would decies centena be in English money? v. 79. framea : What language is this word? v. 82. Herculeos arcus: What was this? v. 97. eget Anticyra: Explain this, and illustrate the expression. Explain briefly the allusions in the words, Tarpeiaque, 1. 78; Cirrhæi, 1. 79; Ægæi, 1. 81; nati, 1. 84; Pharioque, 1. 85; qui, l. 86; Ladas, 1. 97; Archigene, 1. 98; Pisææ, 1. 99. 3. Quote Juvenal's description of the Canal of Xerxes. What have you to remark on the justice of his sneer? At whom was it aimed? 4. What are the usages of the future exact and perfect subjunctive in Latin? What have you to remark on the quantity of each? How can the Greeks express the future exact? . 5. Give the perfects of cado, cædo, occido, traho, frango, quæro; and the nominative and genitive of the participle of eo. Derive induperator, prudens. FIRST DIVISION.—(B.) 1. TRANSLATE into literal ENGLISH PROSE, X. 7—32 : Beginning, Evertere domos totas optantibus ipsis... Ending, Mirandum est, unde ille oculis suffecerit humor. v. 7. Domus totas. Give any example of this. v. 10. Ille. Give some account of him: when did he live? What remarkable events took place at Crotona in his time? v. 16. What were the grounds (real or pretended) of the proceedings against Longinus and Seneca ? v. 28. Sapientibus. Who were they? By what Greek epithets were they known? State their views on Physics and the Universe. Point out a metrical license in a line of the above passage, and illustrate it by similar examples. 2. Translate, XIII. 13-70: Beginning, Tu quamvis levium minimam exiguamque malorum... Determine the date of this satire. v. 28. Enumerate the ages of mankind, according to Hesiod. What other poets follow him, and how far? v. 31. Produce similar instances of this use of fides. v. 33. bulla dignissime explain this distinctly. v. 62. Tuscis libellis. What were these? Explain briefly the mythological allusions in the words, Idæis, 1. 41; Iliacus, uxor, 1. 43; Liparæa, 1. 45; Sicula, 1. 50; rota, Furiæ, vulturis, 1. 51. What are the significations of quamvis, and dies in Latin? Do their different senses affect other words in the sentence? 3. Quote Juvenal's account of Alexander's ambition and decease. When and where did Alexander die? Who succeeded him? 4. What are the principal usages of the subjunctive mood (and especially when joined with qui) in Latin? Compare the Greek and Latin use of this mood. 5. Give the genitive of iter, also the nominative plural, and the perfect of sequor, suesco, nosco, jubeo, sono, soleo. Derive sinciput, consul. |