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ARITHMETIC. Three hours allowed for this paper. Candidates are not permitted to answer more than twelve questions.
The solution must in every instance be given at such length as to be intelligible to the Examiner, otherwise the answer will be considered of no value.
1. The collections at different churches for a certain society were 95 sovereigns, 71 half-sovereigns, 1 crownpiece, 713 half-crowns, 893 shillings, 11 fourpenny and 1,000 threepenny pieces, 986 pence, and an equal number of halfpence. What was the total amount collected ?
2. One group of schools consists of 3 main rooms for boys, girls, and infants, each 47. feet long by 22 feet 5 inches wide, and 3 class-rooms, each 23 feet 8 inches by 15 feet 9 inches ;-another group consists of 1 room 53 feet by 24 feet, 2 secondary rooms, each 39 feet 6 inches by 18 feet 6 inches, and 4 class-rooms, each 22 feet by 20 feet. Compare the accommodation of the two groups of schools at 8 square feet per child.
3. Find the difference between 18 times 4 tons 13 cwt. 17 lbs. 10 oz. ;-and 32 times 9 tons 16 cwt. 1 qr. 5 oz.
What is the use of learning the multiplication table ? Explain as you would to children.
4. Divide a sum of £370 7s. 6 d. among 78 claimants, half of which number, being males, are to receive twice as much as the remainder, being females. What will be the share of a male, and what of a female ?
5. Find by practice the cost of 552 articles at 188.71d. each. By what different methods might this sum be worked ? Which method do you prefer, and why?
6. Make out the following bill, showing how the working may,
any case, be abbreviated :173 lbs. of mutton at 9d. 52
beef at 10 d. 7
11}d. bacon at 74d.
what would be left out of a £5 note afuer
the above, the butcher allowing a discount of 10d. in the £?
7. A creditor receives on a debt of £592 a dividend of 12s. 4d. in the pound, and afterwards another dividend of 3s. 9d. in the pound on the remainder of the debt. What does his loss amount to?
Work the sum by practice and by the rule of three.
8. If a farmer pays a rent of £100 198. 10d. for a farm of 53 acres 2 roods 20 poles, and his landlord remits one quarter of the rent, what does the farmer then pay per acre ?
What is meant by the “rule of three direct," and the "rule of three inverse”?
9. Work the following sum by the rule of three and by “first principles” (the method of unity), and show why it is of advantage to be acquainted with both methods:
If the carriage of 10 cwt. 14 lbs. for 794 miles cost £7 178. 6d., what will it cost to have 1 ton 1 cwt. 1 qr. conveyed the same distance ?
10. A merchant receives a consignment of threequarters of a ton of coffee, and a ton and a half of sugar;
;-the cost price of the former, together with freightage, being 7d. per lb., and of the latter 91d. per lb. What is the total amount gained or lost if the coffee and sugar are both sold at 9d. per lb. ?
Is this a sum in simple proportion? Give reasons for your answer.
11. If 20 horses and 196 sheep can be kept for 9 days for £7 158., what sum will keep 15 horses and 72 sheep for 8 days, supposing 5 horses eat as much as 76 sheep?
State and explain the rule for working sums in compound proportion. 12. Arrange in order of magnitude the fractions ja,
; and express the difference of the first two as a fraction of the difference of the last two.
Give, and explain as you would to your class, the rule for the subtraction of vulgar fractions.
13. A woman after spending of her money, shopping, finds that of what she has still remaining is 18.9d. How much money had she to start with ?
Show that if the numerator and the denominator of a fraction be both multiplied by the same number, the value of the fraction remains the same.
106 113 33 34 355
14. Add .275 of a bushel to 725 of a quarter, and find the value of the whole at 13s. 4d. per bushel.
Define a decimal fraction; contrast it with a vulgar fraction; and show how the latter can be converted into the former. Can all vulgar fractions be so converted, and, if not, why?
15. If •2 of an acre of building land fetch •156 of £198, what ought •285714 of 7 acres to fetch, at the same rate ?
Give the proper name to each of the decimal fractions in the last question.
16. Give the rule for ascertaining percentage, making use of the following question as your illustration of it :If the gold of which a cup is made contains 10 per cent. of alloy, what will be the quantity of pure metal in the cup, supposing it to weigh 1 lb. 7 oz. 13 dwt. 13 grs. ?
17. What is meant by “stock !”. If 3} per cent. stock is purchasable at 87}, what annual income can I secure by investing £4,380 168. 8d. in it, after paying} per cent. on the purchase money for brokerage ?
Three hours allowed for this paper. Candidates are not permitted to answer more than one question
in each section. Section I. (Needlework).—1. Explain how you would put on a patch 2 inches square, in (a) a table cloth, and (b) a flannel petticoat ; describe the best method of knitting the toe of a full-sized stocking; give directions for cutting out a shirt for a labouring man's son of 7 years of age, and state the quantity, quality, and price of the most suitable material for the purpose.
2. What stitches would be required in making the sleeve of a man's shirt ? Explain any two of them as you would to children.
SECTION II. (Savings and Investments).-1. Make out a weekly account of expenditure for an artisan, his wife, and four children from 7 to 13 years of age, the man earning 308. a week. How should the surplus, if any remains above the expenditure, be disposed of ?
2. What public encouragements are now offered to saving?. Describe particularly the mode of investment by which you think a schoolmistress can best provide against old age or infirmity.
SECTION III. (Food-its Ingredients).-1. Name the warmth-giving, bone-forming, and Aesh-producing ele. ments of our ordinary food ; give examples of articles of food in which each of these elements is found in the largest proportion.
2. Which are the principal cereals, and what are their ingredients ? What do you know of the nature and properties of sago, arrowroot, and tapioca ?
SECTION IV. (Food-its Preparation).-1. Describe the method of (a) roasting, (6) boiling, and (c) baking, a joint of meat; and state what are the advantages and disadvantages of each method.
2. Name the more common and economical vegetables, and state how each may be cooked to the best advantage.
SECTION V. (Rules for Health).-1. What habits in respect of food, clothing, rest, and recreation are most likely to be conducive to health in the case of a school. mistress (a) in a town, (b) in the country ?
2. What are the symptoms, respectively, of measles, small-pox, scarlatina, whooping cough, and typhus fever? State generally what you believe to be the best precautions and preservatives against infection.
SECTION 6. (Clothing and Washing).-1. Describe the appliances which would be necessary for the week's washing, household and personal, of a working man's family consisting of 6 persons, and state what precautions should be observed in washing (a) muslin, (b) flannel articles.
2. Draw up an estimate for the winter clothing required by a woman of the labouring class, and her daughter of 12 years old. What general directions would you give as to the choice of materials ?
(For the Examiner.) The passages A, B, are to be given alternately if the number of Candidates is large and there is danger of copying. If one is enough, give the first (A).
The passage should be read once distinctly, and then dictated once in portions as marked.
If the room is large, and there is danger of your not being heard at its extremity, you may permit one of the officers of the College to stand half-way down the room, and repeat the words after you, exactly as you give them ont.
It is essential that there be no complaint on the part of the Candidates that they could not hear or understand: you can only prevent this by clearness, accuracy. and audibility.
A. There is a prevalent notion | that sensibility is blunted | or annibilated | by advancing years. But on a calm analysis of the alleged instances, it appears that where fancy is imagined to have decayed | it has not really existed, but that exuberance of youthful spirits has been mistaken for it. Our heroine's impressions
were always as lively, | her sympathies as warm, | her affections as expansive | as in her opening womanhood. | She retained the enviable faculty | of feeling a vivid interest | in all her surroundings, I through sixty years of luxury and flattery, / of political scheming, of alter. nate elation and despondency, I of all that is most fictitious and demoralizing in society.
B. She was rigidly just | in her estimates of character, chary of her preferences, / firm in her disapproval, i warm, but not extravagant, I in praise. / She never indulged | in false enthusiasm, | which often passes current | for amiability and taste. | Her memory will be indissolubly blended | with one of the most brilliant episodes of English social life, I with many a sweet