2. Reduce of a guinea to the fraction of a pound; and 20 feet 7 inches to the fraction of a mile.

3. If 1·6 of a sum of money be equal to 375 of 8 shillings, what is the sum?

4. If I pay £169 198. as wages to 29 men for 108 days' work, what amount must I pay for 12 days' work to 660 men?

5. What is the meaning of the words abstract and concrete as applied to numbers? Prove that 7 multiplied by 3=3 multiplied by 7.

ENGLISH HISTORY.

1. Name the first and last sovereigns of each English dynasty, with dates.

2. What parts of our coast were first visited by the Romans, Saxons, Danes, and Normans, respectively? From whence did these people come?

3. Describe the events which led (1) to the accession of Canute, and (2) to that of William the Conqueror.

PUPIL TEACHERS-FIRST YEAR.

Wednesday, November 27, forenoon.

(Time allowed, 24 hours.)

ALGEBRA.

1. Find the value of x3-2xy2+y-1 when x=2, y = 3.

1. What do you understand by a definition in Euclid? Give a definition of parallel straight lines.

Write out the 12th axiom.

2. To bisect a given rectilineal angle. Write out this proposition and explain why in your construction you describe the equilateral triangle "on the side remote from" the vertical angle.

3. Demonstrate prob. XXIV.

4. What do you mean by a corollary? Write out the corollaries to the theorem :

If two straight lines cut one another the vertical angles shall be equal.

5. If two straight lines bisect each other at right angles, any point in either of them is equidistant from the extremities of the other.

PUPIL TEACHERS-FIRST YEAR.

Tuesday, November 26, afternoon.

(Time allowed, 24 hours.)

GRAMMAR.

1. Give the meaning of the Latin prepositions sub, inter, de, trans, post, ob. Show what is the force of each in the following English words: Depart, postpone, subtract, translate, object, interrupt, detract, subdue, transatlantic.

2. Explain how the possessive case is written in English. Give any exceptions to the general rules.

3. Write a good definition of a verb. Explain why the definition is imperfect when the verb is simply stated to be a word which expresses action.

4. Write out the principal rules of punctuation.

5. Parse fully:

And now there came both mist and snow,

And it grew wondrous cold;

And ice, mast-high, came floating by,

As green as emerald.

MUSIC.

1. Make a table showing the relative values of all kinds of notes with their corresponding rests.

2. Explain fully the construction of the major diatonic scale.

3. Write out three bars of music in †, 4, 4, and times; respectively.

4. Define diatonic, major, scale, key, clef, bar, and semitone.

5. What do you understand by the following: Allegro, rall., dim., ff., da capo, adagio.

HER MAJESTY'S TRAINING SHIPS.

PUPIL TEACHERS-THIRD YEAR.

Wednesday, November 27, afternoon.

(Time allowed, 24 hours.)

RELIGIOUS KNOWLEDGE.

1. Mention events in the period from Joshua to Samuel, connected with the following places: Shiloh, Kirjath-jearim, Mount Ephraim, Jabesh-Gilead, Dan, Gaza.

2. Give a history of the last days of Joshua.

3. State briefly who the following were: Hannah, Naomi, Manoa, Jephthah, Nun, Achan.

4. Write out all that you know of Barnabas.

5. Give an account of Paul's speech in the presence of Agrippa.

6. Describe the arrangement of the order of morning prayer up to the Apostles Creed. Write out the different responses in the litany.

PUPIL TEACHERS-THIRD YEAR.

Tuesday, November 26, afternoon.

(Time allowed, 3 hours.)

[N. B.-The solution must in every instance be given at full length. A correct answer, if unaccom panied by the solution, or if not obtained by an intelligible method, will be considered of no value.]

ARITHMETIC.

1. Explain, as to a class, the rules for multiplication and division of decimals.

2. If .875 lb. cost .93 shillings, what will be the cost of 21 cwt.?

3. By selling tea at 48. 8d. a pound, a grocer clears one-seventh of his outlay: what

profit per cent. will he clear by selling the same tea at 58. a pound?

4. What is the interest on 30,029 rupees 4 annas 6 pice at 4 per cent.?

Give the result in English money when a rupee is worth 18. 10d.; the rupee containing 16 annas, and the anna 12 pice.

5. A man has £5,000 stock in the 3 per cents, which he sells, and invests the proceeds in the 34 per cents at 874. If the increase in his income be £5, what is the price of the 3 per cents?

ALGEBRA.

1. Take out of brackets, a — (x— a) — [ x − (a — x)]. Give the value of this when a=3 and x = —

3.

5. A bankrupt owes A twice as much as he owes B, and C as much as he owes A and B together; out of £300, which is to be divided among them, what must each receive? 6. There is a certain number of which the cube root is one-fifth of the square root; find it.

PUPIL TEACHERS-THIRd Year.

Monday, November 25, afternoon.

(Time allowed, 3 hours.)

EUCLID AND MENSURATION.

1. If two circles touch one another internally, they shall not have the same center. 2. A segment of a circle being given, to describe the circle of which it is a segment. 3. If two straight lines cut one another within a circle, the rectangle contained by the segments of one of them shall be equal to the rectangle contained by the segments

of the other.

4. The circles described on the equal sides of an isosceles triangle as diameters will intersect at the middle point of the base.

5. The three sides of a triangle are 20, 30, and 40 feet; find its area.

6. What is the circumference of a circle whose diameter is 5.75 yards?

7. Investigate an expression for the area of a regular polygon in terms of its sides.

8. A piece of land ABCD, of which the sides are straight, measures from A to C 1.260 feet, and the shortest lines to AC from B and D respectively measure 580 and 460: find the area.

PUPIL TEACHERS-THIRD YEAR.

Monday, November 25, forenoon.

(Time allowed, 24 hours.)

GEOGRAPHY.

1. Define the term Oceania. Name the islands belonging to Great Britain, Spain, and Holland, respectively, in Oceania.

2. What races principally people Oceania? Describe the peculiarities of these races. 3. Write what you know of the physical character of the islands of the Pacific and of the Asiatic Archipelago, and mention their chief productions.

4. Name and give the locality of the chief mountain chains and rivers of Africa. Describe their direction. Mention the principal towns on banks of latter.

5. Describe the position of, and state what gives importance to, the following places: Brisbane, Honolulu, Easter I., Hobart Town, Ascension.

6. Draw a map of Africa, putting in the leading physical features; also the chief towns in the British, French, and Turkish possessions.

S. Ex. 52—————7

PUPIL TEACHERS-THIRD YEAR.

Tuesday, November 26, forenoon.

(Time allowed, 24 hours.)

HISTORY.

1. Describe the events in English history connected with the names of Francis I of France, Philip II of Spain, and Mary Queen of Scots.

2. Give your opinions on the characters of James I and Charles II, illustrating what you say by acts of their reigns.

3. What were the principal features of the rule of Oliver Cromwell? Explain how his policy influenced public opinion abroad.

4. Write a history of the reign of Queen Anne.

MUSIC.

1. Write out the following scales: B (Si) minor, A (La) major, F (Fa) minor, and G (Sol) minor, both ascending and descending.

2. Make a table of compound times, and give specimens of each.

3. Show in what respects the scale B↳ (Si flat) minor differs from the scale of B major.

4. Write the following in the bass clef, retaining the same pitch:

5. What do you understand by the following terms used in music: Scale, key, clef, diatonic, tone, interval, mode, stave, and signature?

SENIOR PUPIL TEACHERS-FIFTH AND SIXTH YEARS.

Monday, December 2, forenoon.

(Time allowed, 20 minutes.)

MENTAL ARITHMETIC.

N. B.-This paper is not to be opened till the examiner in charge gives the word. The answers are to be entered on the page opposite to the question. No erasures or alterations are permitted. They will be marked as errors.

(Write your name in full on this page.)

1. Multiply 786 by 55.

2. Divide 450 by .375.

3. Find the value of +1+3.

Questions.

4. Reduce 1 week 3 days to the decimal of 7 weeks 1 day.

5. Find the value of 842.

6. Find a mean proportional between 49 and 81.

7. Find the value of 280 articles, at 198. 6d. each.

8. Find the value of 970 articles, at 104d. each.

9. Find the value of 104 dozen articles, at 18. 6d. each.

10. Find the annual value of 8 acres 3 roods 10 poles, at £3 58. the acre. 11. What is the value of 7 ounces, at 38. 4d. per pound avoirdupois

12. What is the value of 2 pounds, at £2 188. 4d. per cwt.?

13. Find the simple interest on £825 for 2 years, at 5 per cent. per annum

14. The buying price of goods was £6 68. 8d.; lost 5 per cent; what was the selling price?

15. What is the true discount on £525 for 1 year at 4 per cent.?

Illustrate how this is a useful formula in solving many equations.

3. A certaiu number is formed by the product of three consecutive numbers, and if it be divided by each of them in turn, the sum of the quotients is 47. Find the number. 4. Expand by the Binomial Theorem (2x-3y)5.

5. On how many days can five persons be placed in different positions about a table at dinner?

6. From the investigation of the extraction of the square root of an algebraical expression, prove the rule for the extraction of the square root of a number.

7. Find the continued product of x ·a, xa, x2. ax + a2, and x2 + ax + a2.

8. Given the log 2.301030, and log 7 = .845098, write down the legarithms of 5, 4916, .0007, 3.5, and 200,000.

SENIOR PUPIL TEACHERS-SIXTH YEAR.

EUCLID.

(Time allowed, 3 hours.)

1. The straight lines which join the extremities of two equal and parallel straight lines towards the same parts are also themselves equal and parallel.

2. To divide a given straight line into two parts so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.

3. The opposite angles of any quadrilateral figure inscribed in a circle are together equal to two right angles.

4. To describe a circle about a given square.

5. If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another; and if the segments of the base have the same ratio which the other sides of the triangle have to one another, the straight line drawn from the vertex to the point of section shall bisect the vertical angle.