SECTION III.-1. Compare the fractions 15, 38,

117 31 8507 88,

, and find the product of the sum and difference of the greatest and least of them.

2. What number multiplied by 35 will be less by 511 than the sum of 3 and 511?

SECTION IV.-1. Reduce of 4 of £1 1s. 8. to the decimal of £1 7s. 1d.

2. A man possesses 765 of an estate; he sells '19 of his share for £612: find the value of the whole estate.

SECTION V.-Write out clearly and concisely the rules for

(a) Finding mentally the value of dozens of articles at a given price per article;

(b) Division of fractions;

The pointing in the extraction of a cube root, when the number is partly decimal.

(These form one question.)

SECTION VI.-1. Find (by Practice) the value of 13 tons 1344 lb., at £39 10s. 6d. per ton.

2. Make out the following bill (deducting 5 per cent. for ready money)—

307 dozens of buttons at 24d. per dozen.

57 pieces of tape at 3 for 24d.

180 reels of cotton at 94d. per score.
89 yards of ribbon at 3 d. per yard.

71 yards of cloth at 1s. 14d. per yard.

SECTION VII.-1. How many hours a day must 16 Englishmen and 72 Frenchmen work for 34 days to do a piece of work that 24 Englishmen and 12 Frenchmen can do in 95 days of 6 hours each, if 5 Englishmen can do as much in a day as 6 Frenchmen?

2. Find the saving in carpeting a room 18 feet long and 15 feet wide, if, instead of carpeting the whole floor, a width of 3 feet from each wall is stained. The carpet, 18 inches wide, costs 3s. 9d. per yard, and staining costs 4d. per square foot.

SECTION VIII.-1. If a cube containing 31-255875 cubic feet can be exactly contained in a cubical box, whose

outer edge is 14 yard, find the thickness of a side of the tox.

2. The gross profits of a railway are £450,000, and the working expenses are 45 of the gross profits: find the capital of the railway if an annual dividend of 33 is paid.

SECTION IX.-1. Goods are bought for £250, and one quarter of them are sold at a profit of 15 per cent.: at what profit per cent. must the remainder be sold to obtain a profit of 20 per cent. on the whole?

2. If the price of land fall 30 per cent., so that 15 of an estate becomes worth £1,400, find the original value of the whole estate.

SECTION X.-1. What sum of money at 5 per cent. per annum, simple interest, will produce in 15 years the same amount of interest that £500 will produce in 3 years at 5 per cent. per annum compound interest?

2. If I transfer £1,000 from 3 per cent. stock at 92 to a 4 per cent. stock, and gain £1 5s. in income, find the price of the latter stock.

EUCLID, ALGEBRA, AND MENSURATION.
Three hours allowed for this paper.

Males.

Candidates in Scotland may answer two questions out of Section IV. if they omit Section IX. With this exception Candidates are not permitted to answer more than one question in each section. (Marks are given for portions of questions.)

EUCLID.

N.B.-Capital letters, not numbers, must be used in the diagrams. The only signs allowed are + and . The square on AB may be written "sq. on AB," and the rectangle contained by AB and CD, "rect. AB CD." Other abbreviations (if employed) must not be ambiguous.

SECTION I.-Complete the following definitions::"A diameter of a circle is a straight line terminated by the circumference."

"A square is a figure which has all its sides equal."

State the exceptions to the following rule: If in two triangles three of their parts, i.e. of their three angles and three sides, be equal, each to each, the other three parts will also be equal, each to each.

Write out the axiom concerning parallel straight lines.

(These form one question.)

SECTION II.-1. The angles at the base of an isosceles triangle are equal to each other.

2. To bisect a given rectilineal angle.

The three lines which bisect the angles of an equilateral triangle meet in a point.

3. If a straight line, falling on two other straight lines, make the alternate angles equal to one another, these two straight lines will be parallel.

A line, drawn through the vertex of an isosceles triangle parallel to its base, will make equal angles with the two sides of the triangle.

SECTION III.-1. To describe a parallelogram equal to a given square, and having one of its angles equal to half a right angle.

2. To describe a square upon a given straight line.

If the square be described upon the semi-diameter of another square, compare the areas of the two squares.

3. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by those parts.

SECTION IV.-1. If a straight line be divided into two equal and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.

2. The angle in that segment of a circle which is less than a semicircle is greater than a right angle.

If the angle in a segment of a circle be double of the angle in the other segment, compare the arcs.

3. Two circles have the same centre; show that if a Ichord of the outer circle touch the inner circle all chords that are equal to it will touch the same circle.

ALGEBRA.

SECTION V.-Multiply 1-x2 + x1 − x by 1 + x2

6

2 4

Find the value of √ a2 b3 + ✔ a3 b3 + °/ a2 b2,

when a = 5, b = 25.

(These form one question.)

SECTION VI.-1. Find the G. C. M. of x + 7x3 + 6x2 - 32x 32 and x2+9x + 20.

2. Find the L. C. M. of x2 y2, x2 + xy - 2y2, and x2 + 3xy + 2y2.

3. What is the condition that x2 + px + q may be divided by x

1'?

(3) √x2 + 16x + 7 = 3x-5.

(These form one question.)

SECTION VIII. (a) The breadth of an oblong space is four yards less than its length; the area of the space is 252 square yards: find the length of its sides.

(b) A regiment has sufficient food for m days; but if it were reinforced by p men, would have food enough for n days only: find the number of men in the regiment. (These form one question.)

MENSURATION.

SECTION IX.-1. A triangular space whose sides are in the ratio, 5 5 6 contains 588 square yards: find the length of its sides.

:

2. A cottage which stands on a square plot of 729 feet, contains four rooms of equal size on the ground floor, and is divided into two equal parts by a passage four feet wide, having two rooms on each side: allowing one foot for the thickness of each wall, find the area of each of the four rooms.

DOMESTIC ECONOMY.

Females.

Three hours allowed for this paper.

Candidates are not permitted to answer more than one Question in each Section.

SECTION I. (Needlework.)—1. Describe fully the different stages of instruction by which a child would advance from her first lesson in knitting to making a stocking for a full-grown man.

2. State the amount of material required, and the kind of material best suited, for making a shirt for a boy of twelve, and give accurate measurements of its different parts.

SECTION II. (Investment.) 1. An agricultural labourer makes 15s. a week, and has a wife, and five children between the ages of two and ten. State clearly how much per annum he ought to spend (a) on bread, (b) animal food, (c) clothing, (d) house-rent, and (e) fuel, and what contribution he could make to a benefit club to support him in sickness and old age.

2. Describe the amount of savings that unmarried school-teachers (male or female), could make per annum out of a salary of £80 a year, and the best modes of investment for their money.

SECTION III. (Food.) 1. State what ingredients in food produce (a) bone, (b) fat, (c) warmth, in the human system, and describe the principal articles in common consumption that contain the ingredients of bone and fat, separately or combined.

2. Mention the kinds of animal food in common use in England, and state the position which each holds as regards nutrition and easiness of digestion, and give your

reasons.

SECTION IV. (Food.) 1. Describe very fully the process of making bread, and the differences of method necessary to suit the kind of oven used in the process.

2. Say what you consider to be (a) the most wholesome, and (b) the cheapest method of using a shoulder of mutton