16 Express 378216 as a vulgar fraction in its lowest terms. 17 Express 78. 10d. as the decimal of a pound, and find the value of 03234 of a guinea.

18 Extract the square root of 49660209; also that of 7·0032 to four places of decimals.

19 Find by any rule with which you are acquainted the sum which paid one year hence will be an equivalent for 2007. due now and 6007. due at the end of two years, the rate of interest being 5l. per cent.

20 Reduce to their simplest form the expressions,

x + y

(b) (x-3y) (x + y) — (x — 2 y) (x + 3 y) + (x — y) (x + 5 y) - x2 + 2 y2.

21 Find the greatest common measure of x + x3y

-

2 x2 y2

+ x y3 — y1, and x3

6 x2 y 11 xy2

6 ყ3.

22 Write down the expansion of

(x + y). How

many terms

3 x 22

17

are there in the expansion of (x + y) 100?

23 Extract the square roots of 14 + 6 √ 5 and 1 + 4 √ — 3.

24 Solve the equations

25 A traveller sets out to walk from A to B at 4 miles an hour. One hour later another traveller sets out from B towards A

at 3 miles an hour; when they meet the first has walked 6 miles more than the second. Find the distance from A to B. 26 Sum the Arithmetical Progression 1+5+9+ to 15 terms; and the Geometric Progression 1 + + √2 + ... to n terms and ad infinitum.

...

It is important the addition should be quite correct.

It is important the addition should be quite correct.

3 In

4 In

furlongs, poles,

yards, how many

lbs. avoirdupois weight, how many tons, cwts.,

many grains?

dwts., grs., troy weight, how

5 In a table, the sides of which are ft. in., and

ft.

in, how many square yards, feet, and inches?

PART IV.

Departmental Examination Papers, previous to the Order in Council.

WAR OFFICE.

ENGLISH GRAMMAR AND COMPOSITION.

1 Accent each of the following words in two ways, and construct sentences which shall contain these words :-refuse, desert, protest, compound.

2 Correct, if necessary, the spelling of the following words, and give the reasons for your corrections :—moveable, truely, skillful, blisful, lodgement.

3 Correct, if necessary, the following, and give the reasons for your corrections :—

Divide this among the two.

The man has come, him who you saw.
These books are their's, those are your's.
The captain with his men, were taken.

We laid our money upon camels, concealed in
bales of cheap goods, and travelled to the shores
of the Red Sea.

4 Distinguish between the following words and modes of expression-acquittal and acquittance, attendance and attention, beside and besides, in course and of course. 5 Put the following sentence into plainer and more modern language: "Alcidamas, the sorcerer, hath many notable arguments to prove that voluntary and extemporal far excelleth premeditated speech."

6 What historical events have influenced the composition of the English language? Name the chief writers of the reigns of Anne and George I.