EXAMINATION PAPERS.

NOVEMBER 1864.

MATHEMATICS.

Voluntary Paper, No. I.

REV. W. N. GRIFFIN, M.A.

1. Enumerate the principal books, with their purposes, which are used in keeping accounts by double entry. Why is the name "double entry given to this method? How is a trial balance made from time to time?

2. If a Sovereign is worth 25.3 francs, and a Spanish dollar is worth 50 pence, when 100 dollars are worth 527 francs, is it better to make a payment in Paris by a direct remittance from London, or through the intervention of Spain?

3. A sovereign weighs 123.25 grains, and is 22 carats fine. If a ducat weighing 54 grains is worth 113.2 pence, determine the fineness of the gold of the ducat.

4. If an Exchequer bill for 100l. paying an interest of 1d. per day is purchased at a premium of 40s., what is the yearly interest per cent. on money so invested?

of

5. Prove that the operation of division of numbers may be effected by by subtraction logarithms. Employ logarithms

(1) to divide 86 by 000049372.

(2) to find the amount of 8467. 6s. 8d. in 12 years, at 3 per cent. compound interest.

6. Add together (2a + 3x)3 and (2a—3x)3, and give the numerical value of the result when a=1 and

8. A sum of money is raised by equal contributions from a number of subscribers. If there had been 40 more subscribers, each would have paid 37. less. If there had been 50 fewer subscribers, each would have paid 67. more. How many subscribers were there, and what was the sum of money to be raised? 9. Find the middle term of the expansion of

a

10

(-)" by the Binomial Theorem.

10. There are three white and four black balls. In how many different ways can they be placed in a row so that there is a white ball at each end?

MATHEMATICS.

5

MATHEMATICS.

Voluntary Paper, No. II.

REV. W. N. GRIFFIN, M.A.

1. Any two sides of a triangle are together greater than the third.

2. To divide a given straight line into two parts so that the rectangle contained by the whole and one of the parts shall be equal to the square on the other part.

If the given line be a foot long, compute the lengths of the parts to the nearest hundredth part of an inch.

3. Similar segments of circles upon equal straight lines are equal to one another.

4. To inscribe an equilateral and equiangular pentagon in a given circle.

5. Triangles of the same altitude are to one another as their bases.

6. If a, b, c, be the sides of the triangle ABC, prove that

a2= b2 + c2 - 2bc cos A.

If the sides of a triangle are given, why is this expression unsuitable as a means of computing an angle? add what is the formula adopted?

7. The sides of a right-angled triangle being 827 and 569 feet, find the length of the perpendicular drawn from the right angle on the hypothenuse.

8. The diagonals of a parallelogram being 18 and 34 yards, and the angle between them 47° 18′ 39′′, find the area of the parallelogram in square feet.

9. A thin uniform bar rests with its upper end against a smooth vertical wall, and with its lower end

on a horizontal floor with which its coefficient of friction is 3. Find the greatest slope at which the bar can rest.

10. If a ball is shot vertically upwards with a velocity of 180 feet per second, what time will elapse before it returns to the point of projection, resistance of the air being disregarded?

FRENCH.

M. ESQUIROS.

I.

Traduisez en anglais :

Dans le giron même de la civilisation occidentale, la plupart des colonies se distinguent par ce caractère, qu'elles se consacrent presque absolument à la production des matières premières: ici, comme en Australie, la laine d'innombrables troupeaux, et puis du cuivre, et puis de l'or: là, comme au Canada et dans les provinces attenantes, des spécimens multipliés de bois bruts ou dégrossis, ou façonnés en des formes simples, telles que des manches de haches ou d'autres outils; ailleurs des cuirs et des graisses. D'autres colonies favorisées d'un climat plus chaud, et peuplées en grande partie d'Africains que la traite apporte, sont adonnées à des matières premières d'un autre genre, aux denrées dites coloniales, le sucre et le café principalement. Pendant ce temps, les Etats qui ont des annales plus longues, par conséquent une population plus dense, varient presque à l'infini leurs cultures et leurs fabrications, et se livrent avec un succès toujours croissant aux articles qui réclament

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