1. 18; 53157376;; 525; 0016384. 2. 004115226; 012345679; f. 5. (1) 1414213 with remainder '000001590631. (2) 2.6457513 with remainder 00000003834831. (6) 29 68164 with remainder '0002469104. APPENDIX, CONTAINING EXAMINATION PAPERS. I. Winchester College. Election, 1868. Boys under Thirteen years. Arithmetic for 1. Write down the tables of linear and of superficial measure, and shew how the number of yards in a pole of the latter may be deduced from that of the former. 2. Multiply £3764, 18s. „, 6d. by 95; and divide 55 tons 19 cwt.,, 3 qrs.,, 27 lbs. by 96. 99 3. Four new houses are to be built: the estimated cost of (1) is £4949,, 158. 8d., of (2) £4798,, 88.,, 1d., of (3) £4501, 19s. „, 9d., and of (4) £5129, 11s. „ 11d.; what will be their total amount? and what, if the estimates be exceeded 10 per cent.? 4. How many shillings in a continuous straight line would reach from Winchester to London, 64 miles, the diameter of a shilling being of an inch? and what would be their total value in pounds? 5. A yard, 63 feet long and 18 feet broad, is paved with bricks, each measuring 9 in. by 4 in.; required the number of bricks. 6. If 15 men, working 13 hours a day, earn £95,, 18.,, 3d. in 26 days; how many hours a day must 17 men work, that their wages may amount to £84,, 3s. in 24 days? 7. Find the sum, difference, product, and quotient of 33 and 23. 8. How long will an 18-gallon cask of beer last if 4 pints be drawn from it daily? 9. Brown can run 10 yards whilst Green runs 11; what start ought Green to give Brown in a half-mile course in order to make an even race? 10. How far may a boy ride with his father, who leaves Winchester at 12:30, and will drive to Romsey (12 miles) in 2 hours, so that he may, by walking at the rate of 3 miles an hour, be back by a quarter before 3,-in good time for school? II. Winchester College. Election, 1868. Arithmetic for Boys of Thirteen years and over. 1. Write down the tables of linear and of superficial measure, and shew how the number of yards in a pole of the latter may be deduced from that of the former. 2. Multiply £3764, 188.,, 63d. by 954; and divide 55 tons,, 19 cwt.,, 3 qrs.,, 27 lbs. by 96. 3. A cistern is to be made 4 ft. 9 in. long, 3 ft. „ 6 in. wide, 2 ft.,, 4 in. deep; how many square feet of lead will line it, and how many cubic feet of water will fill it? 4. What is a gentleman's income who, after paying sixpence out of every pound of it, has £962, 16s.„, 3d. left ? 5. If a boy can paddle his own canoe three quarters of a mile down the river in ten minutes, but without the aid of the stream would take a quarter of an hour; what is the rate of the stream per hour? and how long will it take him to return against it? 6. Find the sum and the difference of the fractions 213 and 16: also divide their sum by their difference, and their difference by their sum. and 7. Reduce of a guinea to the fraction of 15 shillings: of a crown to the decimal of 12s. 6d. 8. In latitude 51° the length of a degree of longitude is about 37.76 geographical miles: how many miles is Winchester from Dresden-both nearly in that latitude-the longitude of the former being 1° 20′ west, and of the latter 13° 40′ east? 9. How many small cubes, whose edges are 2 inches, may be cut out of a large cube whose edge is 12 inches? 10. At what rate simple interest would a sum of money amount in 2 years to the same, as at 4 per cent. compound interest? 11. A poor fellow, ignorant of arithmetic, had 6s.,, 6d. in his purse; he talked of spending of it on cakes, of it on fruit, and of it on a knife: shew (1) his mistake, and (2) how he might have spent his money in proportion to the fractions he intended. III. Winchester College. Duncan Prize. Easter, 1869. 1. Write down in words 7392586044001; and in figures five billions, twenty-one millions and thirty. 2. Multiply 174550613 by 600417; and divide 5. Reduce 4. Multiply 5678 by '08765; and divide 75445 by '00625. 747 " 960 2 7 11 and of of of 2 to decimal frac12 21 tions. 6. From 261 times £35,, 4s.,, 2d. take £9089 divide the remainder by 89. 625 7. Extract the square root of 30712.5625 of ; and of 2401 000000133225. 8. Find the interest of 125 guineas for 23 years at 4 per cent. and the discount of £63, 15s. for 15 months at 5 per |