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4 On which side of a cash book must the balance always fall? 5 On which side of a cash book should an amount paid away be entered?

6 A transmits to B. 4007., with directions to pay J. Brown, 381. 2s. 6d., J. Smith 497. 5s. 9d., W. Eve 50l., W. Robinson 997. 13s. 9d., each less 2 per cent.; and W. Walker 477. 16s. 8d., H. Biggs 537. 13s. 4d., and Charles Bunce 617. 8s., each less 5 per cent.; and to retain the balance, if any, till further instructions. Supposing that B has done all this, make out such an account as it would be necessary for him to send to A, to show exactly what has taken place.

7 Give the entries of the same transactions, as A would enter them in his cash book on receiving the above account. 8 State in few words what "book-keeping by double entry" is, and in what it is preferable to book-keeping by single entry."

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ALGEBRA AND GEOMETRY.

1 Multiply together x+2xy +3 y, and x-2xy + y; also a+b+c,- a+b+c, a−b+c, and a+b-c. 2 Simplify the expression

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5 Find three numbers such that the differences between each and the sum of the other two and their product are in the ratios 13:5:192.

6 Prove that

(1) The difference of the squares of any two odd numbers is divisible by 8.

(2) Every square is the sum of as many consecutive odd

numbers as there are units in the root.

7 How many terms are there in the expansion of (3 x - 8y)6? Write down the third term.

8 Prove the formulæ for the summation of arithmetical and geometric series; and sum the following:

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9 Find the least positive integer solution of 13 x

9y= 3. 10 Determine the number of permutations of n letters taken r together, noticing the case in which n = =r, and certain letters recur. Ex.: Sebastopol.

11 Prove the formula

cos (A+B) cos A cos B + sin A sin B.

cos 2 A+ cos 4 A2 cos 3 A cos A.

12 Given two sides and the included angle of a triangle: find the other angles and the third side.

13 Determine the exponential expressions for sin A and cos A. 14 Describe Hadley's sextant.

Explain how to survey 12.53 chains rectilinear

15 A triangular field, A B C, has two rectilinear sides, A B, A C, and one curvilinear, B C. it; and if it be found that A B distance, B C 8.46 chains, and perpendicular from C on A B 5.25 chains, determine the approximate area, assuming any curvature you please; or determine the area and draw the figure from the following notes :

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16 Define a straight line, a plane angle, a circle, a segment of a circle, a parallelogram, proportion, reciprocal proportion. 17 The angles which one straight line makes with another upon one side of it are either two right angles, or are together equal to two right angles.

18 Divide a straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part.

19 If two circles cut each other, the straight lines joining their centres will bisect their common chord at right angles. 20 Draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. 21 Inscribe a circle in a given triangle.

22 If the sides of two triangles about each of their angles be proportionals, the triangles shall be equiangular, and have their equal angles opposite to the homologous sides.

ENGLISH GRAMMAR.

Write the following passages in ordinary prose, and explain any peculiarities in the construction:

This gentle and unforc'd accord of Hamlet
Sits smiling to my heart, in grace whereof
No jocund health that Denmark drinks to day
But the great cannon to the clouds shall tell,
And the king's rouse the heaven shall bruit again
Re-speaking earthly thunder.

King. I must not hear thee; fare thee well, kind maid,
Thy pains not us'd must by thyself be paid;
Proffers not took reap thanks for their reward.

Helena. Inspired merit so by breath is barred;
It is not so with him that all things knows,
As 'tis with us that square our guess by shows

But most it is presumption in us, when
The help of heaven we count the act of men.
Dear sir, to my endeavours give consent,
Of heaven not me make an experiment.
I am not an impostor that proclaim
Myself against the level of mine aim;

But know I think and think I know most sure,
My art is not past power nor you past cure.

Hail foreign wonder!

Whom certain these rough shades did never breed,
Unless the goddess that in rural shrine
Dwell'st here with Pan or Sylvan.

HISTORY.

In questions 1 and 6, only (1) or (2) are to be answered. 1 State fully the benefits which you consider to have resulted— To Europe from the Crusades.

(2) To England from the Norman Conquest.

2 What were the claims

(1) Of Edward III. to the throne of France ?

(2) Of Henry VII., and of James I., to the crown of England?

3 At what periods of English History did the principle of elective monarchy prevail over that of hereditary suc

cession?

4 What were the Petition of Right, Instrument of Government, Act of Uniformity, Act of Settlement, and Act of Navigation?

5 Explain fully the allusions contained in the following pas

sage:

"After half a century, during which England had been of scarcely more weight in European politics than Venice or Saxony, she at once became the most formidable power in the world; dictated terms of peace to the United Provinces; avenged the common injuries of Christendom on the pirates of Barbary; vanquished the

Spaniards by land and sea; seized one of the finest West India Islands; and acquired on the Flemish coast a fortress which consoled the national pride for the loss of Calais."

6 What important constitutional questions were raised— (1) By the illness of George III.?

(2) By the protracted trial of Warren Hastings?

7 State very briefly the occasions on which six of the following battles were fought, and discuss more fully their political results:

(1) Agincourt, Bannockburn, Culloden, Dettingen, Hastings, Naseby.

(2) Barnet, Jena, Nancy, Pavia, Pultowa, Tewkesbury. N.B.-Three battles are to be selected from each class. 8 What wars were ended by the following peaces :—

Versailles, Bretigni, Westphalia, Utrecht? Give the dates and principal articles of agreement.

9 When did England gain possession of the following places:Canada, the Cape of Good Hope, Corfu, Ceylon, and New York? From whom respectively were they

taken?

10 Who was the first King of Prussia? Give his former title, and the circumstances which led to its being changed.

11 On what pretext did Charles VIII. of France invade Italy? 12 When was the Spanish power at its height, and what led to its decline?

NATURAL SCIENCE.

1 State the three laws of motion. Are they to be deduced from experiment or from à priori principles ?

2 Define centre of gravity, and find the centre of gravity of any triangle.

3 Explain some of the methods by which the sphericity of the

earth is demonstrated.

4 Describe the transit instrument, and the mode in which accuracy in its position is attained.

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