H.—3.

AKITHMETIC. 1. What number is that which, being increased by 26, and then multiplied by 26, gives a product which is greater by 2314 than the product found by multiplying 26 by one-half of itself P 2. Make out the following bill, and deduct 10 per cent, as discount for cash:—3o Ib. butter, at Is. s|d. per lb.; 9 tins coffee, at 2s. Gd.; 1 cwt. sugar, at sd. per lb.; 54 lb. tea, at 3s. 3d. per lb.; 23 lb. cheese, at 13d. per lb. 3. Of the fractions of 2-j, -^ of 3r, and of 41, divide the sum of the greatest and least by the intermediate one. 4. Find the sum, difference, and product of 8625 and 39625, and divide the sum of the three results by 625. 5. Find product of square root of 1444 multiplied by square root of zwr6. How much will an income-tax of sd. in the pound bring in if a tax of 10 per cent, on the income of a country brings in £578,900 ? 7. What is the difference between the simple and compound interest on £168 15s. for 3 years at 3| per cent, per annum ? 8. The rent of an estate is £45 a year. What must I pay for it if I buy it at 20 years' purchase at a rent which is to the above rent as 5 is to 4 ? 9. 12 a=29 b ; 15 b—2s c; 17 c = 3d ; 8d = 13 e : how many e = 340 b ? 10. What are Bankers' Discount and True Discount ? What is the difference between the two discounts on a bill for £612 17s. 6d. drawn July 12th at -4 months, and discounted September 3rd, at 5 per cent. ? 11. What will it cost to paper a room of the following dimensions, with paper at 7s. 6d. a piece of 12 yards, the width of the paper being 22 inches: —Length of room, 17 feet 6 inches ; breadth, 15 feet; height, 10 feet 6 inches (there is a bay-window, 9 feet 6 inches by 9 feet; another window, 9 feet 6 inches by 5 feet; a fireplace, 4 feet 6 inches by 6 feet; and a door 7 feet 6 inches by 3 feet 6 inches) ? 12. What will the alteration in my income be if I transfer £2,500 Stock from the Three per Cents at 93| to Four per Cents at 98! ? GEOGRAPHY. 1. Describe fully the routes you would follow if you went from Auckland to London with the mails via San Francisco, and came back from Southampton to Dunedin with the mails via. the Suez Canal. 2. What influence does the ocean exert upon climate ? Give examples. 8. Through what Arctic straits and channels does the " North-west passage" go ? 4. Name the islands which constitute Australasia, and say to whom they severally belong. 5. On what rivers are Cork, York, Glasgow, Moscow, Benares, Ottawa, New York, Hobart Town, Christenureh (N.Z.), Nganiawahia, Kaitangata, Westport (N.Z.) ? 6. Under what kind of government are the United States ? FRENCH. 1. Translate— '" La ceremonie semblait terininee, et le nouveau comte allait se retirer, lorsque les Francais lui dirent, ' II esfc convenable que celui qui rec,oit un paroil don s'aqenouille devant le roi, et lui baise le pied.' Mais le Normand repondit, ' Jauiais je ne plierai le genou devant aucun homme, ni ne baiserai le pied d'aucun homme.' Les seigneurs insisterent sur cette formalite, qui etait un dernier reste do l'utiquette observee jadis a la cour des empereuvs franks; et Roll, avec une simplicity malicieuse, fit signe uun de ses gens de venir et de baiser pour lui le pied du roi. Le soldat norwegien, se courbant sans plier le genou, prit le pied du roi, et le leva si haut, pour le porter asa bouche, que le roi tomba ala renverse. Peu habitues aux convenances du ceremonial, les pirates firent de grands eclats de rire, et il y eut un moment de tumulte; mais ce bizarre incident ne prodnisit rien de facheux."—Ara. Thieeet. 2. Parse the words in italics. 3. Write the feminine of the following:— brave, vif, peureux, aigu, ancien, rouqe, doux, amer, bleu, pareil, poltron, vertueux. 4. Translate — (a) What is the matter with you ? Nothing. Then why are you making that noise ? I cut my little finger, and it is bleeding. (b) Ne causez pas avec votre voisin ; je vous ai averti une fois, je ne vous avertirai plus. (V) Avez-vous recu ee matin la lettre que vous attendiez hier soir ? Oui, Monsieur, je l'ai re^ue. 5. Account for regu and regue in passage (c). 6. Write throughout the present indicative of venir, and the future of vouloir; the present subjunctive of aimer, and the imperfect of fctire. TRIGONOMETRY. 1. The value (positive) of the sine of an angle less than aright angle is ./3a, and of its cosine -/a: What is the angle, and what is the value of a ? What are the angles whose cosecants are —p- t i. Q ~ , ... ~ respectively, the values being positive, and the angles less than a right angle ? \/yofi) and \/y±fl) 2. What is the general value of 0 when sin3o + cos 3# =0? What ambiguity attaches to the expression sin3 #, and what expression would be more strictly accurate ? _ Tin ■ i , • COS a COS 8« , 7T „ 3. What is the value ot .-—. - a - when a = r=-f cos 4a + cos ba 13

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