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E.—la

2. Find the value of 375 ac. 2 ro. 17 pr. at £75 15s. 6d. an acre. 3. (a.) Simplify 1| x X |-| 4J+ 3 (6.) Find the value of 0-246 of 9s. 3d. + 0259 of 255. + 0-02 of £3 7s. 6d., and reduce the result to the decimal of £3. 4. Apply a short method to find the product of 375-76843 and 3-14159 correct to four places of decimals. 5. A bankrupt estate pays 6s. 6d. in the pound, and a creditor is paid £350 ss. 6d. : what was his full claim ? 6. If a meter contains 39-37 inches, find the number of meters in a mile, to three places of decimals. 7. Find the length of the side of a square which is equal in area to a rectangle whose sides are 513 yards 1 foot 11 inches and 1,628 yards 11 inches. 8. At what time between 10.30 and 11.30 will the angle between the hands of a watch be equal to the angle through which the long hand turns in 25 minutes ? 9. Find the compound interest on £2,350 ss. 9d. for 2 years at 3J per cent, per annum, interest accruing quarterly. 10. A person invests £14,970, part in the three-per-cents at 90 and the rest in the three-and-a-quarter-per-cents at 97 : if his total income is £500 a year, how much of each stock did he buy ? 11. (a.) When multiplying a number by 9 the digits.carried were successively 7, 2, 3, 0, 6, 6, 2, 4 : what was the number ? (b.) Supply the missing digits in the following multiplication sum :— •* 9 * 6_* 18• * 9 + ***** 1 "7 3 " * * 12. The diameter of a tree at the base is 6 feet, and at 25 feet from the ground it is 5 feet: find the number of cubic feet in this part of the tree, considering it as a part of a right circular cone. [The volume of a right circular cone is one-third of the product of the height and the area of the base.]

No. 32. — Arithmetic and Algebra. — For Class C and for Civil Service Senior. Time allowed: Three hours. [Algebraic symbols and methods may be used throughout.] 1. The solar year contains 365-242218 mean solar days : show that it would be more nearly correct to add 8 days in 33 years than to continue the present arrangement of leap year. With this correction, what would the accumulated errors amount to in 5,000 years ? 2. Discuss briefly the advantages and disadvantages of introducing a decimal system of measures. Make out the following bills :— (a.) 23 tons 7 cwt. 3 qr. 14 lb., at lls. sd. a pound. 18 yd. 2 ft. 1£ in., at s£d. an inch. 107 gallons 1 quart, at 10s. 4d. a pint. (b.) 1278-35 grams, at 11-23 francs a gram. 17-26 meters, at 5-22 francs a meter. 236-13 liters, at 15-35 francs a liter. 3. Prove the identity ~ = 26 ; and hence, or otherwise, simplify (* + ***) X 0 + " ***) * (* ~ ***) 0 + iota) + i 1 - ioTa) 4. A and B enter into a speculation. A puts in £50 and B puts in £125; at the end of 5 months A withdraws \ of his capital, and at the end of 6 months B withdraws \of his; C then enters with a capital of £85. At the end of 15 months the profits of the concern are £364. How ought this to be divided, allowance being made for capital and for the time during which it remains invested. 5. A merchant insures a ship and cargo for £65,250 at a premium of 2J% to cover the value of the ship and cargo and the cost of insurance : find the premium paid, and the value of the ship and cargo. 6. Simplify (i.) — - — - - ... . / a*\ (a c\ 7. Prove that a m xa n = a m+n where m and n are positive integers. What meaning is ascribed to the symbols a*, a- 2 , a O , and why ? Multiply +1 + a-id by aic- -l + a~*c*. 8. Draw graphs of y=£ + 2, and y— 3 — 2x—x*; and hence solve the equations x+2 = 0, 3_2<b—x 2 =0, and the simultaneous equations y = x+% and y= 3 — 2a; — x*.

5—E. IA.