1. State the various proofs, celestial and terrestrial, of the earth's rotundity.

2. Mention the four largest rivers of Africa; and state what you know about the Congo.

3. Mention (i.) the position of each of the following places, (ii.) their historical, political, or commercial importance :-Dantzig, Valparaiso, Salonika, Granada, Toronto, Brisbane, Prague, Orleans, Sebastopol, Bucharest, Stettin, Leipsic.

4. Describe the position of the Black, Red, White, and Yellow Seas: what produce do we obtain from the shores of each?

5. Give an account of the chief industrial occupations of the United States.

6. Explain the cause of Earthquakes; and mention some parts of the globe which are very much exposed to them.

7. What possessions has Russia outside of Europe? Describe, as nearly as you can, the southern boundary of Asiatic Russia.

8. Give a geographical description of Japan, showing its position, dimensions, principal cities and ports, productions, manufactures, and government

1. Multiply eighteen millions four hundred and five thousand one hundred and ten by twenty-five thousand and one. Divide the product by one hundred and ninety.

2. What is the total cost of a city dinner at £4 13s. 9d. per head, the number of guests being 312?

3. 40 ac. 3 ro. 15 po. of land are cultivated at a net cost of 17s. 6d. a rood. The produce sells for £192 17s. 4d. What is gained ?

5. If of a sheep be worth £, and of a sheep be worth of an ox; how much must be given for 100 oxen ?

6. Multiply 2.083 by 059 and by 72300 successively; and divide 346.25 by 00505.

7. Determine the rent of an oblong field, the sides of which are respectively 1 fur. 23 po. 3 yds. and 30 po. 2 yds. long, at £2 5s. 4d. an acre.

8. A tradesman buys 500 yds. of cloth at 9s. 7 d. per yd., but has £44 Os. 2 d. thrown off the bill for cash; at what price per yd. can he afford to sell so as to gain 33 per cent.?

9. Divide £180 among A, B, and C, so that A may receive three times as much as B, and B and C together may receive half as much as A.

10. The General Rate being 4s. 2d. in the pound, what is the rateable value of a property that pays annually a rate of £726 13s. 4d.?

1. Prove that (a + b + c)2 + (a2 + b2 + c2) = (a + b)2 + (a + c)2 + (b + c)3.

Cxy

3. Find the G.C.M. of

+ 3xy + 3x1y2 + 11x3y3 + 4x2y1

and 5x1y -3x3y2+18x3y3 2xy4y5.

4. Extract the Square Root of

201 2 (a

and of 5 + 2 (x2 + 2/2)

5. Prove that

4

24

(ax + by)2 - (ay + bx)2 = (a2 — b2) (x2 — y2). 6. Reduce to their simplest forms :

(i.)

√ {(x2 + 4x3 — 8x + 4) (x2 — 2x − 2)2}. 7. Solve the equations:

x + 7 x + 2

=

=

+

= 1.

8. A certain number consisting of two digits when divided by the sum of its digits has a quotient 7: if the digit in the units' place be decreased by 2 and that in the tens' place by 1, and if the number thus formed be divided by the sum of its digits, the quotient is 10. Find the number.

Books I-IV., VI.

1. Define a circle, segment of a circle, angle of a segment, angle in a segment, sector of a circle; and prove that the angle in a semi-circle is a right angle.

2. If a parallelogram and a triangle be upon the same base and between the same parallels, the parallelogram shall be double of the triangle.

3. To describe a circle about a given square.

4. Prove that the two triangles formed by drawing straight lines from any point within a parallelogram to the extremities of two opposite sides, are together half of the parallelogram.

5. If two angles of a triangle be equal to one another, the sides also which subtend or are opposite to the equal angles shall be equal to one another.

6. Define similar triangles: and show that in a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

7. Describe a circle that shall have a given radius and shall touch a given circle and a given straight line.

-

GENERAL PAPER.

1. Give as many instances as you can from Genesis of cases in which the younger son was preferred to the elder.

2. What are the chief sins recorded of David and Solomon, and how were they punished?

3. Write a short account of the carrying of Israel into captivity: mentioning in what reign it occurred, and by whom the land was subsequently peopled.

4. Describe the position of the following places, and state anything of importance which is mentioned in connection with them:-Machpelah, Moriah, Beersheba, Padan Aram, Abel-Mizraim, Jericho, Gibeon, Ezion-geber, and Sheba.

5. With what nations did the Israelites contend, from their entrance into the Holy Land to the death of Samson? What length of time elapsed between the Exodus and the death of Samson?

6. State the relations of Egypt and Syria with the Jewish Monarchies.

7. What object does the author of the Chronicles appear to have had in writing these books? What special sources of information does he mention ?

8. In what connection do the following expressions occur, and what is their meaning ?

(i.) In the mount of the LORD it shall be seen. (ii) All the firstborn of my children I redeem. (iii.) Our life for yours, if ye utter not this our

business.

(iv.) Will GOD indeed dwell with men on the earth? (v.) As soon as thou art departed from me, a lion shall slay thee.

(vi.) If thou certainly return in peace, then hath not the LORD spoken by me.