E.—la.

Arithmetic. — For Class E. Time allowed : Three hours. 1. Multiply 10 ac. 4 po. 27 sq. yd. by 423. 2, Seduce to a single fraction—s§§f + 2|§f - 7|f| 8. Express § of £4 + 4f of 17s. 6d. + If of ss. as the decimal of £12 7s. 6d. 4. A bucket filled with water weighs 55 lb. ; when one-third of the water is emptied out the bucket and the remaining water together weigh 37 lb. 8 oz. Find the weight of the bucket when empty. 5. Find the number of feet in a side of a square piece of ground which contains three-quarters of an acre. 6. Find the compound interest on £3,715 for three years at 4 per cent, per annum, to the nearest penny. 7. The two temperatures known as " freezing-point " and " boiling-point " are denoted in the Fahrenheit scale by 32° and 212°, in the Centigrade scale by 0° and 100°, and in Beaumur scale by 0° and 80° respectively. Express the temperature of 98-2° Fahrenheit in the other two scales. 8. What weight of alloy must one melt down with 3 oz. 5 dwt. of pure gold and 2 oz. 8 dwt. of twenty-two-carat gold in order to produce a mass of eighteen-carat gold? 9. If the amount of wool exported in a certain year shows an increase of 7 per cent, on the export of the preceding year, and if the average price has risen from 9d. a pound to lid., find the percentage of increase in the total value of the exported wool. 10. Explain by means of examples, as you would to a class of children, the two methods of subtraction known respectively as the method of " equal additions " (or " borrowing " and " paying back "') and the method of " complementary addition."

Arithmetic. — For Glass D. Time allowed : Three hours. 1. Find the cost of 231 lb. 9 oz. 17 dwt. 20 gr. at £3 17s. 9d. an ounce. 2. Besolve 693, 686, 504, and 847 into their prime factors, and write down their L.C.M. 3. (a.) Prove that a fraction is not altered in value if a common factor is removed from numerator and denominator. (b.) Investigate a rule for turning a circulating decimal into a vulgar fraction, using as an example 0-2619047. , D . ~, 3-25 , 0-325 x 0-39 .4. Simplify W2 + 0 , 14 a x 8 , 2 5. Taking the metre as 39-37 square inches, find the number of square metres in an acre. 6. What is the present value of £730 due at the end of five years, compound interest at 4 per cent, per annum being reckoned ? Give the answer to the nearest penny. 7. A man bought an article and resold it, losing 3 per cent, on the transaction. If he had obtained £14 more he would have gained 4 per cent. What was the cost of the article? 8. A vessel, A, contains a certain volume of spirit, and another vessel, B, contains an equal volume of water. A is half emptied into B, and, after mixing, Bis half emptied into A. This is done three times. Find the ratio of spirit to water in A. 9. Extract the square root of 1-7 to six places of decimals. Show how to find the last three figures by simple division. 10. A room three times as long as it is broad is carpeted at 4s. 6d. a square yard, and the walls are coloured at 9d. a square yard, the respective costs being £8 ss. 4Jd. and 4 guineas. Find the dimensions of the room. 11. Explain by means of a diagram the principles involved in multiplying a vulgar fraction by a vulgar fraction— e.g., £Xf,orf of f. . 12. Give short methods for the following operations, and explain them briefly as you would to a class of children in Standard VI. : — (a.) Multiplication of a number by 995. (b.) Division by 125. (c.) Division by 1-25. (ii.) Value (by practice) of 893 lb. at 17s. lOd. a pound.

Arithmetic. — For Civil Service Junior. Time allowed: Three hours. A. All the work by which a result is obtained must be clearly shown, as no credit can be allowed for any result, however correct it may be, unless the method of obtaining it is given. B. Take the ratio of the circumference of a circle to its diameter as 3-1416, and 1 yard as equivalent to 0-914 metre. 1. What is the greatest number by which 18407 and 10090 can be divided so as to leave remainders 16 and 27 respectively ? 2. Beduce to its simplest form :— (a) 2x+3£ Bfof4 A _ (a -> l2fofff-6A + ' (b.) (by decimals only, and to six places,) V 0-625 x 0-1875 x 0-005 0-016025-11-75 X 0-0003 3. Find the value of 18±i. yards - l_ poles + f of 5| acres, and reduce the result to the fraction of 5f acres.

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