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. 4001., with directions to pay J. Brown, 381. 2s. 6d., J. Smith 491. 5s. 9d., W. Eve 501., W. Robinson 991. 13s. 9d., each less 24 per cent.; and W. Walker 471. 16s. 8d., H. Biggs 531. 13s. 4d., and Charles Bunce 611. 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." ALGEBRA AND GEOMETRY. 1 Multiply together x+2 vxy +3 y, and x – 2 vxy + y; also a +b+c, - a+b+c, a-b+c, and a +b-c. 2 Simplify the expression 9c + х X 3 X x - y + 2xy +2 x y 2+ 3 Extract the square root of, 12bc ao 2% + 4 abx + 6 ac + 4.62 + 4 Solve the equations2 (3— 1) 4 + 15 12 6. 2 x a + x ✓ y y 11 x a a } + 5 Find three numbers such that the differences between each and the sum of the other two and their product are in the ratios 1:3:5 : 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) ? Write down the third term. 8 Prove the formula for the summation of arithmetical and geometric series; and sum the following :7 + 3 1 to n terms. 1 to infinity. 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 formulæ— cos (A + B) =cos A cos B + sin A sin B. cos 2 A + cos 4 A 2 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. 15 A triangular field, A B C, has two rectilinear sides, A B, A C, and one curvilinear, B C. Explain how to survey it; and if it be found that A B = 12:53 chains rectilinear distance, BC= 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 :- BC 0 846 64 6 0 0 85 400 5.0 2 0 0 0 000 R off B A B 1 2 5 3 4 8 6 5 2 5 C Begin at A and go west. 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 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. It is not so with him that all things knows, But most it is presumption in us, when Hail foreign wonder ! 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 (1) 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 ? 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 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 accu racy in its position is attained. |