Euclid and Algebra.

EUCLID AND ALGEBRA.

Male Candidates.

EUCLID.

27

Capital letters, and not numbers, must be used in the diagrams. Not more than ten questions to be answered.

1. On the same straight line, and on the same side of it, there cannot be two triangles which have their sides terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.

2. Show how to bisect a given finite straight line. How would you practically do this?

3. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the sides of the one greater than the angle contained by the two sides equal to them of the other, the base of that which has the greater angle shall be greater than the base of the other.

4. Triangles upon equal bases and between the same parallels are equal to one another.

5. To a given straight line apply a parallelogram that shall be equal to a given rectilineal figure, and have an angle equal to a given rectilineal angle.

6. Construct a square equal to the sum of three given

squares.

ALGEBRA.

1. Add together 8ax — 7by + 3y2; 9ax +4y2 — 2; 7 + 3by − 2y2 + 4ax;

2. From 4-7x+10a - 126 take -15x+20.

away 7a + 2b

3. Multiply Say-3ya-4xy by 7xy-8x+6y.

4. Divide a + 3x2y2 + 2y1 by x2 + 2y2 and x + (q − x)l

— qb2 by b-1.

6. A goods train travels at the rate of 8 miles an

hour on a railway, at the end of 12 hours it meets a passenger train travelling in the opposite direction, which arrives at the original starting station 16 hours after the goods train left. At what rate is the passenger train travelling?

DOMESTIC ECONOMY.

Female Candidates.

SECTION I. (Household Work.) 1. State the industrial work which devolves on a young person day by day, who has charge of her own bedroom; the time such work should occupy; and the method she should adopt.

2. What special subjects are included under the term "Domestic Economy"? Describe the duties of a "child's maid," as you would to an elder girl on leaving school for such a place.

3. Describe, as clearly as you can, the "household work" which a mother of a family has to do day by day in her home, where she has no servant of any kind to assist her.

SECTION II. (Investment.) 1. What are the particular benefits offered to the wage-earning classes by the Post Office Savings' Banks ?

2. Give reasons why an elementary school teacher should of necessity lay by some sum of money year by year; and mention safe investments for such savings.

SECTION III. (Cooking.) 1. What are the special purposes accomplished by food ?

2. Give recipes for three of the following :— An Irish stew,

A fried sole,

A grilled mackerel,
A suet pudding,
An apple dumpling,
Eggs and bacon.

SECTION IV. (Sickness.) 1. What special care should be taken by those attending in a sick room, both as regards themselves and the sick person?

2. Name the common vegetable poisons against which school children should be specially warned; and what

Dictation and Penmanship.

29

treatment have you been recommended to adopt in the case of a child suffering accidentally from such poisons?

SECTION V. (Clothing and Washing.) 1. What would be the cost of an outfit for a girl of 13 years of age? What amount of materials would be required? Make a bill for the same.

2. Write out a receipt for making a baby's sock.

3. What method should be followed in washing woollen articles ? What difference should be made with coloured prints ?

DICTATION AND PENMANSHIP.

TWENTY MINUTES allowed for these Exercises.

You are not to paint your letters in the Copy-setting Exercises, but to take care that the copy is clean and without erasures. Omissions and erasures in the Dictation Exercise will be counted as mistakes.

The words must not be divided between two lines; there is plenty of room for the passage to be written.

Write in large hand, as a specimen of Penmanship, the word Sufficiently.

Write in small hand, as a specimen of Penmanship, the sentence

"The mountains of their native land."

DICTATION.

You are to write the passage* dictated to you by the Examiner, and punctuate it correctly.

For Male Candidates.

(A1.)

"Gratitude is properly a virtue disposing the mind to an inward sense and an outward acknowledgment of a benefit received, together with a readiness to return the same or the like, as the occasions of the doer of it shall require, and the abilities of the receiver extend to." -SOUTH.

The passages A1, A2, were given alternately where the number of Candidates was large, and there was danger of copying.

"His abilities as a statesman are glorious; yet surprise us still more when they are observed in the ablest scholar and philosopher of his age; but a union of both these characters exhibits that sublime specimen of perfection to which the best parts with the best culture can exalt human nature.”—MIDDLETON's Life of Cicero.

66

(A2.)

"Of all the glories of science, none equals that of a well-directed and successful attempt at diminishing the risk of danger to human life; yet, while we owe much to the labours of those who have discovered its important truths, let it not be forgotten that we owe all to that great Being who, from time to time, permits His creatures to obtain a view of those mighty governing principles with which He orders and directs the course of natural events. Should the inquiry be made as to the immediate connection between the chemistry of nature and the movements of the air, the reply must be, that the connection is most intimate. The irregular, capricious winds which constantly agitate the air of temperate regions, fulfil a most important office in the operations of nature."-Chemistry of Creation.

For Female Candidates.

(A1.)

"You are so little accustomed to receive any marks of respect or esteem from the public, that if, in the following lines, a compliment or expression of applause should escape me, I fear you would consider it as a mockery of your established character, and perhaps an insult to your understanding."-JUNIUS.

"In general, then, we should be understood to maintain that the beauty and grandeur so much admired in the Greek statues were not a voluntary fiction of the brain of the artist, but existed substantially in the forms from which they were copied, and by which the artist was surrounded."-HAZLITT.

(A2.)

"The mind of man naturally hates everything that looks like a restraint upon it, and is apt to fancy itself under a sort of confinement, when the sight is pent up

Dictation and Penmanship.

31

in a narrow compass, and shortened on every side by the neighbourhood of walls and mountains. On the contrary, a spacious horizon is an image of liberty, where the eye has room to range abroad, to expatiate at large on the immensity of its views, and to lose itself amidst the variety of objects that offer themselves to its observation. Such wide and undetermined prospects are as pleasing to the fancy as the speculations of eternity or infinitude are to the understanding."-ADDISON.