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SECTION V. 1. The sides AB, AC of a triangle are bisected in DE respectively, and BE, CD are produced till EF=EB, and GD=DC; show that the line GF passes through A.
2. From the angles C, B of a parallelogram ABCD, CE, BE are drawn parallel to the diagonals, which EA, ED intersect in H.K. Show that HK is half BC.
3. On AC the hypothenuse of a right-angled isosceles triangle ABC a square ACED is described, and BE meets AC in F. Join DF, and show that the square on BE is five times the square on a side of the triangle. Show also that nine times the square on DF is thirteen times the square on the hypothenuse.
SECTION VI. 1. Circles are described on the sides of a right angled triangle. Shew that the square on their common tangent is equal to the area of the triangle.
2. Given the perpendiculars from any point on the three sides of a triangle and two of the angles, construct the triangle.
3. ACB is a diameter of a circle, CD a radius perpendicular to it. The chord AD is bisected in E; BE
. meets CD in F and the circle in G. Show that three times the rectangle contained by BF, EG is equal to the
square on the radius.
POLITICAL ECONOMY. Candidates are not permitted to answer more than six
1. Detail the functions of money, and explain the difference between money and capital.
2. What do you understand by the value of money? Discuss the effects of recent gold discoveries upon it.
3. Examine the consequences of the conversion of circulating into fixed capital.
4. Distinguish between productive and unproductive consumption, and show whether the latter is beneficial to society or not.
5. Tell how wealth is divided, and discuss the relations of landlord, labourer and capitalist.
6. Discuss the causes and consequences of strikes and lock-outs.
7. Examine the effects of foreign commerce on the countries concerned, and discuss the relative importance of imports and exports.
8. Enumerate the received canons of taxation, and classify the legitimate objects of national expenditure.
9. Investigate the various modes of investing small savings, with their comparative advantages.
1o. Write a short essay on the conditions under which popular education promotes national wealth.
11. Write Notes of a Lesson, such as you would give to an intelligent first class of children on one of the following subjects:
(a). A Savings Bank.
.) left for it after each question.
С 5. 6 „12 + 2 −147 – 13 – 5 175
many miles an hour ?
present value being £2405. what is the amount of the bill? ...
5) + 63 (18 - 4)
among the Candidates.
FEMALE CANDIDATES. FIRST YEAR.
Two hours and a HALF allowed for this paper.
*1. Multiply nine million four hundred and seventy thousand eight hundred and sixty-two by seven hundred and nineteen, and divide the product by two thousand one hundred and fifty-seven.
2. Find the difference between 58 miles 5 furlongs 10 poles 3 yards and 811 miles 4 furlongs 2 yards, and explain the steps of the process as you would to a class.
*3. Divide £39517. 18. 9d. by 108. Explain as you would to a class each step of the process, as well as your reason for the method which you adopt.
4. How many articles worth £57. 3 florins 1 cent. 4 mils. each can be bought for £974:338?
• 1. Find, by Practice, the value of 7496 articles at £13. 183. 74d. each.
2. If tea is sold wholesale at 18. 9d. per lb. and retail at 3d. per oz.; rock-oil wholesale at 11d. per gall
, and retail at 4d. per pt.; soap wholesale at 48. per stone and retail at 5 d. per Ib.; rice wholesale at 11s.6d. per cwt. and retail at 31d. per lb. ; what will be the annual saving by buying at wholesale prices upon a consumption of 40 lbs. of tea, 13 galls. of rock-oil
, 65 lbs. soap and 56 lbs. of rice
*3. Find the difference between the cost of 30 tons 15 cwt. 2 qr. 21 lbs. 8 oz. at 88. 9d. per quarter and 176 gallons 3 qts. 1 pt. at 78. 101d. per pint.
* See infrá, p. 81.
SECTION III. *1. In papering the walls of a room 624 yds. of paper are used at 28. 9d. per dozen yds., and the labour is charged at 78. 6d. ; find the whole expense.
.; *2. A parish with a rental of £13740. has to raise £143. 28. 6d. for the support of the school ; what is the rate per £1?
3. The painting of a hall 10 yds. long, 74 broad, 4 yds. high cost £38. ; what will be the cost of painting another hall 12 yds, long, 8 yds. broad, and 5 yds. high?
2. Divide by 1 of 4 the product of £936. 178. 11d. x 1 of 5??
3. The income of a family is earned by a father and three children. The father earns of the whole and the children earn on the average £12.168. 8d. each. They spend of their income on rent and rates, d on clothes and books, on food and other necessaries, and the remainder they deposit in the Post Office Savings Bank. Find their income, their expenditure upon (a) rent and rates, (1) clothes and books, (c) food and other necessaries, and (d) the amount of their deposit.
SECTION V. 1. Divide 97.6237 by .031, and 13.72 by 4:196. 2. Reduce 5 fur. 3 per. 31 yds. to the decimal of
3 a mile.
3. What is a recurring decimal ? Reduce •63 and •14356 to vulgar fractions, and 48and ff to decimals.
money that she had not enough by 10d. to give 1s. 8d. to each of a certain number of poor. So she gave them 18. 31. each, and then had 2s. Id. left. Find the number of poor.
2. Three men built 165 yds. of wall. The second built 7 yds. more than the first, and the third 16 yds. more than the second. How many yds. did each of the three build ?
3. Two numbers are to one another as 3 to 5, and their product is 1425931, Find the numbers.