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5. Explain what is meant by the diatonic scale. Write it out both in major and minor form.
5. When you pass to the Fa key, what do s, l, r, m, d, become respectively?
Male Candidates. The solution must in all instances be given at full length. A
correct answer, if unaccompanied by the solution, or if not obtained by an intelligible method, will be considered of no value. [This statement was repeated in the Arithmetic Paper for Female Candidates (p. 11), and in the Algebra Paper (p. 13)].
SECTION I. 1. Add together two millions and thirty thousand; one thousand and seventy-four; thirteen hundred and nine; eighty-three thousand and five hundred; one hundred and twenty-three thousand; and take from the sum, five hundred and ninety-eight thousand seven hundred and ninety-nine.
2. Divide six millions seven hundred and twenty-three thousand eight hundred and sixty-four, by fifty-four thousand and eight.
SECTION II. 1. How many farthings in £59 138. 69 d. ?
2. Taking a year as 365 days 6 hours, how many years are there in ten million minutes.
SECTION III. 1. If a pendulum vibrates 5 times in 2 seconds, how many times will it vibrate in 24 hours ?
2. A servant's wages being £10 8s. per annum, how much ought she to receive for 7 weeks ?
SECTION IV. 1. What is the rent of 23 acres 3 roods 16 poles at 2} guineas per acre ?
2. Find the expense of carpeting a room 12ft. 4in. long by 12ft. 6in. broad, with carpet yd. wide, at 48. 6d.
SECTION V. 1. Make out this bill of parcels, and show how it should be receipted. How much change will there be out of a £5 note:
3cwt. of coals at 10 d. a cwt. ; 13 lbs. of cheese at 7 d. per lb.; 27 lbs. of tea at 3s. 4d. per lb. ; 17 lbs. of
sugar at 5£d. per lb.; 3; yds. of flannel at 18. 11 d. per yd ; 29 yds. of calico at 10 d. a yd.
2. A yacht and its fittings cost £1005 128.; the yacht costs 5 times as much as the fittings; how much did the yacht cost ?
SECTION VI. 1. A grocer buys 10 cwt. 3 qrs. 21 lbs. of sugar for £30, and pays 128. 6d. for expenses; at what rate must he sell it per lb. to gain not less than 25 per cent.
2. A merchant expends £1636 5s. on equal quantities of wheat at £2 2s. a quarter; barley at £l ls. a quarter; and oats at 14s. a quarter. What quantity of each will he have ? SECTION VII. 1. Simplify
1+3+1+% 2. Out of a cistern full, 20 gallons are drawn; 70 gallons are then added and it is found to be a full; how much does it hold?
SECTION VIII. 1. Multiply 5.384 by .00723; 20-7 by 500; •072 by 50:34; add them together and take away of 462; what is the result?
2. Divide 500 by 25, the quotient by :025; and the second quotient by 50; what is the result?
SECTION IX. 1. Give the rules for multiplying and dividing vulgar fractions by vulgar fractions, and explain the reason for the rules.
2. Give the reasons for the process of “long division” of numbers.
3. Make notes for a lesson on simple subtraction.
Female Candidates. SECTION I. Add together four millions and ninety; three hundred and one thousand one hundred and nine; twenty-five; eight hundred thousand four hundred and ninety-four; seventy-eight thousand and nine. Take from the sum one million nine hundred and eightyseven thousand and ninety-seven.
SECTIƠN II. 1. Divide £1844 28, 8d. equally among 49 persons.
2. A house and its furniture are worth £6734 58. 9d. and the house is worth eight times as much as the furniture; what is the house worth?
SECTION III. 1. Find by practice the value of 6043 lbs. of tea at 3s. 2 d. per lb.
2. Make out the following bill of parcels in proper form, and show how it should be receipted :
51 stones of flour at 28. 8d. per stone; 8; lbs. of cheese at 8d. per lb.; 114 lbs. of butter at 1s. 9d. per lb.; 2 lbs. of tea at 38. 4d. per lb.; 54 lbs. of coffee at 1s. 5d. per lb. ; 193 lbs. of pork at 9d. per lb.
SECTION IV. 1. A person's weekly income is £14, and he spends £128 10s. per quarter; how much does he save in a year?
2. How many half guineas are there in 537 half crowns ?
SECTION V. 1. If a silver tankard weighing 1 lb. 10 oz. 10 dwts. cost £6 3s. 9d., what is the value of the silver per ounce ?
2. An army is besieging a town in which are 1000 men with provisions for 3 months, how many must leave at once that the rest may be able to subsist for a
SECTION VI. 1. A man spends į of his money, then of the remainder, and then of what was still left. He finally has £25 in hand; how much had he at first ?
2. Which is the greatest and which is the least of the
fractions 15, 17, 25, ži
SECTION VII. 1. A room is 20 ft. 6 in. long, 15 ft. 6 in. wide, and 16 ft. high. It has 2 doors each 8 ft. high by 3 ft. 9 in. wide, and 3 windows, one 5 ft. by 7ft. and the other two 5 ft. by 4 ft. each. What will it cost to paper the room with paper 1 yard wide at 10d. per yard?
2. A man spends every year of his income, and invests the rest in annuities at the rate of £90 for every annuity of £3. His income is £600 to begin with, how much will it be at the end of 4 years?
SECTION VIII. 1. Divide 7.619 by .0019 and multiply the quotient by is of .00011569.
2. Reduce •5 of 168. 4d. to the decimal of £1 98. 101d.
Euclid and Algebra.
SECTION IX. 1. Explain as for a class :-
EUCLID AND ALGEBRA.
EUCLID. Capital letters, and not numbers, must be used in the diagrams.
1. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced the angles on the other side of the base shall be equal to one another.
2. Draw a straight line perpendicular to a given straight line of an unlimited length from a given point without it.
3. If from the ends of the side of a triangle there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
4. Parallelograms upon the same base, and between the same parallels are equal to one another.
5. Describe a parallelogram equal to a given rectilineal figure and having an angle equal to a given rectilineal angle.
6. Find a point in a given straight line, such that its distance from two given points shall be equal.
ALGEBRA. 1. Add together 5w3 — 3x+2y;--23+2x-y; 723—4 +3y.
2. From 2x+11a+105-50–23; take 2c-10+50–36. 3. Multiply 9a2 + 3xy + y2-6x +2y+4 by 3a-4-2.
4. Divide 23—5x2—<+14 by 22—3x—7, and 22—(a+b)x +ab by x-b.
5. Solve these equations :
6 1 (2)
6. A farmer has a number of hurdles, 6 feet long; he finds that by arranging them so as to enclose a given space of ground, if he place them 1 foot distant from each other, he has not enough by 80; but if he place them a yard apart he has 50 hurdles to spare; how many hurdles has he ?
Female Candidates. SECTION I. (Household Work.) 1. Name any household work which you have been accustomed to do, either at home, or in your elementary school; and describe the method in which you have been instructed to do this work.
2. What do you understand by the term “ Domestic Economy”? What instruction have you received upon this subject, either as pupil teacher, or, if not a pupil teacher, from any person previous to this examination ?
3. Describe the duties of an under nursemaid, and show in what way these duties differ from those of a maid of all work.
SECTION II. (Investment.) Describe simply and plainly, as in a letter to a pupil teacher, either,
1. The advantages of the system carried out in the post office savings bank; or,
2. The special benefit to be derived from any other secure mode of investment for persons of small and limited means.
SECTION III. (Cooking.) 1. State briefly the cost, the time required, and the method of cooking three of the following: a mackerel, a poached egg, a potato pie, a rice pudding, a mutton chop, a rasher of bacon.
2. Name six inexpensive and yet nutritious dinners for children attending our elementary schools; state the cost of the same, and the amount of materials required in the preparation of each.
SECTION IV. (Sickness.) 1. In what way have you been taught to relieve any of the school children suffering from the following causes : a burn, a bruise, a severe cut, an attack of fainting, bleeding at the nose, chilblains ?