MATHEMATICS.

Morning Paper.

I. TODHUNTER, ESQ., M.A.

OBLIGATORY PORTION.

1. Divide 36291. 1s. 03d. by 243.

2. Reduce 7 tons 15 cwt. 2 qrs. 16 lbs. to ounces; and 3 roods 27 poles 26 yards to square inches.

3. Find the value of 83 quarters 5 bushels 3 pecks of corn at 11. 7s. 6d. per quarter.

4. If 11 horses eat 191 bushels of oats in 7 days, how long will 113 bushels last 35 horses? 5. Reduce the following expression to its simplest form :

a sovereign of of
crown; also of
crown; also of of a ton

⚫00016

of a guinea + of of of 2 of a

a shilling

of a cwt. + of a lb.

8. Find the value of £4.66875; of 655 of a day; and of 953125 of a mile.

9. What is the interest of 256l. 10s., for 3 years and 73 days, at 33 per cent. per annum?

10. Find the discount on 2967. 15s. due 16 months hence, at 4 per cent. per annum.

11. How many planks 12 feet 6 inches long by 9 inches wide will be required to floor a room which measures 50 feet by 16 feet?

12. Extract to five places of decimals the square roots of 5 and of 2.

MATHEMATICS.

Afternoon Paper:

I. TODHUNTER, ESQ., M.A.

VOLUNTARY PORTION.

1. One English pound is equivalent to 25.4 francs; 3.75 francs are equivalent to 105 kreutzers; 60 kreutzers are equivalent to 1 florin. Find in English money the value of 1143 florins.

2. A person buys shares in a railway when they are at 197. 10s. each, 157. having been paid on each; he sells them at 321. 9s. when 251. has been paid on each; how much does he gain?

3. Under what circumstances will the Dr. side of a cash book be the greatest?

4. A has a balance of cash in hand on January 1st of 401. On January 10th B remits to him 8167., with directions to purchase certain goods on his [B's] account. Accordingly A buys of C goods worth 721., of D goods worth 4921., of E goods worth 431. 4s.; all on January 11th. On January 15th, January 17th and January 20th respectively A pays for these goods. A is to be allowed by B

5 per cent. on his purchases. Give a copy of A's cash book, of A's ledger acct. for B, of A's ledger acct. cash,' and of the account which A should render to B. In each case rule paper for yourself. 5. Calculate by logarithms the value of

7. A person buys some tea at 6s, per lb. and also some at 4s. per lb. ; in what proportion must he mix them so that by selling his tea at 5s. 3d. per lb. he may gain 20 per cent. on each pound sold?

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

9. Equal straight lines in a circle are equally distant from the centre, and those which are equally distant from the centre are equal to one another.

10. Describe a circle about a given triangle.

11. The sides about the equal angles of equiangular triangles are proportionals; and those which are opposite to the equal angles are homologous.

12. If two straight lines be at right angles to the same plane, they shall be parallel to each other.

13. Define the Trigonometrical Functions of an angle, and find their values for an angle of 60°. 14. Investigate an expression for the area of a triangle, the length of the sides being known; and apply it to the case in which the lengths are 42, 56, and 70.

15. Two sides of a triangle are 45 feet and 35 feet, and the included angle is 64° 12′; find its other angles.

16. What is the diameter of a circle to contain an acre?

17. The diameter of a well is 3 feet 9 inches, and its depth 45 feet; what did the excavation cost at 7s. 3d. per cubic yard?

18. Prove the parallelogram of forces as far as regards the direction of the resultant force.

If a heavy triangle is suspended from a fixed point by strings attached to the angles, the tension of each string is proportional to its length.

19. An inclined plane makes an angle of 30° with the horizon; what force must be exerted parallel to the plane to keep at rest a body weighing 3 cwt., the coefficient of friction being ?

COMMERCIAL GEOGRAPHY.

G. W. DASENT, D.C.L.

1. On the accompanying map of Europe insert the names of the seas, bays, islands, and chief headlands; trace the course of the Volga, Oder, Elbe, Rhine, and Ebro; mark the chief mountain

ranges by name, as well as the positions of Archangel, Hamburgh, Constantinople, Odessa, Oporto, Copenhagen, Corinth, Leipzig, Trieste, Marseilles, and Smyrna.

2. Mention the principal articles of export and import at each of the places mentioned in the previous question.

3. What districts in Europe are most productive(1) of corn, (2) of wine, (3) of coal, and (4) of iron?

4. Descending the Danube from its source to its mouth, mention the States through which it flows, and the chief places of interest on its banks.

5. Explain fully the meaning of the terms plateau, isthmus, archipelago, delta, sound, watershed, basin, Gulf Stream, monsoon, and tradewind.

6. Draw a map-(1) of the Baltic, (2) of the Black Sea and the Sea of Azoff, (3) of the Persian Gulf.

N.B.-One of these maps only to be chosen.

7. Enumerate the several States which form the Confederation of the United States of America, distinguishing Free from Slave States, and mentioning what articles Great Britain imports from the Slave and what from the Free States.

8. Write a letter describing the overland route to Calcutta vid Marseilles, and containing information on the natural productions of the States through which the writer is supposed to pass, and on their commercial relations with other nations.

gress of

9. Give a short sketch of the origin and proany British Colony, describing its physical geography, form of government, natural productions, commerce, and population.