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9. Find the united wages of 27 men working 118 days, if £371 14s. can be earned by 59 men in 36 days.

10. At what rate per cent. would £375 amount to £577 10s. in 12 years?

11. Required the simple interest on £372 17s. 6d. from February 1st to May 31st, 1872, at 3%.

12. What principal would amount to £218 10s. 10.896d. in 3 years, at 3% compound interest?

13. Find the present worth of £392 8s. 8d., due 9 months hence, at 4 per cent.

14. Find the average of 7, 8, 9, 15, 16, 20, 35, 74.

15. If I buy 1 cwt. for £3 5s. 4d., and sell out again at 8d. per lb., what do I gain or lose per cent.?

16. What will be the price of £36,000 stock in the 3 per cents at 85 per cent.? What would be the change in a man's income if he sell out and invest in the 4 per cents at 90?

17. A's share B's share and C's share are in the proportion of,,: what will each receive of yearly profits amounting to £4,860? If these profits are at the rate of 20% on the united capital, what amount of capital did each put into the business?

18. Simplify 16-8216; 751-089429.

19. If 16 cows and 3 horses can be bought for £518, and 9 cows and 10 horses for £707, how many horses could be bought for £600 ?

Geometry.

Junior, Senior, and Higher Local.

Junior Work, Nos. 1-8 inclusive.

Senior Work, Nos. 5-12 inclusive.

Higher Local Work, Nos. 9-16 inclusive.

1. If a straight line falling on two other straight lines makes the alternate angles equal to one another, the two lines are parallel.

2. Parallelograms on equal bases and between the same parallels are equal to one another.

3. If any point be taken within a parallelogram, the sum of the triangles formed by joining the point with the extremities of a pair of opposite sides is half the parallelogram.

4. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.

5. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.

6. The diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less.

7. Define a rhombus, a circle, an angle, a parallelogram, a sector of a circle, a segment of a circle.

8. If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.

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

10. The least square which can be inscribed in a given square is that which is half of the given square.

11. If two circles touch one another internally, the straight line which joins their centres, being produced, shall pass through the point of contact.

12. In equal circles, the angles which stand on equal arcs are equal to one another, whether they be at the centres or circumferences.

13. About a given circle, to describe a triangle equiangular to a given triangle.

14. If the sides of two triangles, about each of their angles, be proportionals, the triangles shall be equiangular to one another, and shall have these angles equal which are opposite to the homologous sides.

15. Rectilineal figures which are similar to the same rectilineal figure, are also similar to each other.

16. From the same point in a given plane, there cannot be two straight lines at right angles to the plane, on the same side of it; and there can be but one perpendicular to a plane from a point without the plane.

Algebra.

Junior, Senior, and Higher Local.

Junior Work, Nos. 1-9 inclusive.
Senior Work, Nos. 3-13 inclusive.

Higher Local Work, Nos. 4-13 inclusive.

1. Show that the sum of the cubes of three consecutive numbers is greater than three times their product by nine times the middle number.

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5. Show that a quadratic equation has two, and only two, roots. For what value of m will the equation 2x2+ 8x+m=0 have equal roots?

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7. Define ratio. Show that a ratio of greater inequality is diminished by adding equal quantities to both its terms. If the ratio be a b, and it becomes a pb, find what is the quantity added to each term.

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There are n arithmetical means between 1 and 31, and the 7th mean: (n − 1)th mean :: 5 : 9. Find the number of means.

9. The first term in a G.P. is 1, and any one term is equal to the sum to infinity of all that follow it. Find the series.

10. Solve the equation 1 + x3 − 4x2 + x + 1 = 0.

11. Given 10 consonants and 5 vowels, find the number of words that can be formed, each containing 3 consonants and 2 vowels.

12. Prove the Binomial Theorem for any positive or negative index. Find the co-efficient of " in the expansion of (1 + x)2 (1 x) 4°

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13. If the number of births in a year be of the population at the beginning of the year, and the number of deaths, find in what time the population will be doubled, having

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