THREE HOURS allowed for this Paper and the one on School Management together.

The Tonic Sol-fa questions are printed in italic. Candidates must keep ENTIRELY to one set of questions or the other.

1. Place a note (semibreve) on each line and in each space of the annexed treble stave, and write against each note its name according to pitch.

1. What does "the modulator" represent, and what use is made of it in Tonic Sol-fa method?

2. In what kind of time is this passage of music written? Write it in three-crotchet time, prefixing the proper time signature, and mark each note that ought to be accented.

2. How do the strong and weak accents or "pulses" of the voice recur in two-pulse measure? in three-pulse measure? Show by examples, how these measures are represented in the Tonic Sol-fa notation.

3. Write the major scales of C (Do), F (Fa), and G (Sol), marking in each case the positions of the semitones.

3. Classify the tones of the scale as strong" and "leaning" tones, and state where the "little steps occur. 4. Transpose the adjoining passage of music half a tone higher, prefixing the proper key signature, and naming the key in each case.

4. Show the ordinary compass of children's voices in the Standard scale of α,

5. Write from memory any short tune which you have learnt, prefixing the proper key and time signa

tures.

5. Write, from memory, any short tune which you have learnt, stating the key.

ARITHMETIC.

Male Candidates.

The solution must in every instance be given at full length. A correct answer, if unaccompanied by the solution, or if not ob tained by an intelligible method, will be considered of no value. [This direction was repeated in the Arithmetic Paper for Female Candidates (p. 25), and in the Paper on Algebra (p. 27)].

SECTION I. 1. Add together four millions seventyeight thousand and ninety; fifty thousand six hundred and seventy-four; three hundred and five; ten millions four hundred and seven thousand and ninety-eight; seventy thousand six hundred and three. From the sum take away six hundred and six thousand seven hundred and seventy, and write out the answer in words.

2. Divide nine millions nine hundred and ninety-eight thousand five hundred and fifty by seven thousand eight hundred and forty-two, and write out the answer in words.

SECTION II. 1. How many inches in 3 miles 28 yards 2 feet ?

2. How many £ s. d. in 30,724,689 farthings?

SECTION III. 1. If a train can travel 54 miles in one hour, how long will it be travelling 278 miles 2 furlongs 12 yards ?

2. If a child attends for 4 years at school, paying at the rate of 2d. per week on an average of 36 weeks in a year; what is the whole amount?

SECTION IV. 1. What is the cost of 16 cwt. 3 qrs. 16 lbs. at £1 48. 8d. per cwt. P

2. A parcel of 5 lbs. 7 ozs. is carried 120 miles for 18. 8d., how much will it cost to carry 16 lbs. 5 ozs. a distance of 90 miles at the same rate ?

SECTION V. 1. Make out this bill of parcels, and

show how it should be receipted. How much change will there be out of a £10 note ?

16 cwt. at 13d. per cwt.; 4 ozs. at 3s. 2d. per oz.; 10 yards at 2s. 3d. per yard; 13 lbs. at 7d. per lb.; 3 dozen at 9d. per dozen.

2. If an engine and tender cost £4000 12s. 4d., and the engine cost one half more than twice as much as the tender, what was the separate cost of each ?

SECTION VI. 1. A man buys land at £42, and having built upon it, sells the land and houses so as to gain 20 per cent. on his whole outlay, and receives £9004 16s. How much did he spend in building?

2. Tea at 3s. 6d.`per lb. is mixed with tea at 2s. 4d. per lb. ; what is the proportion of the mixture when the mixed tea is worth 2s. 10d. per lb.

SECTION VII. 1. Simplify [} − ÷ + } − } + }] ÷ (3-1+1-7).

2. If a man travel 151 miles in 3 hours, how far can he go in 183 hours ?

SECTION VIII. 1. Multiply 70'048 by 3.23, and 2:07 by 3105; add the products together, and take away of 98 04717; what is the result?

2. Divide 4,900 by '07; multiply the quotient by '63 and divide by '049; what is the result?

SECTION IX. 1. Make notes for a first lesson on multiplication by two figures.

2. Explain the difference between the methods of long and short division.

3. Explain the method of practice, and show that in a decimal system there would be no need of this rule.

ARITHMETIC.

Female Candidates.

SECTION I. Add two millions seventy thousand and fifty nine; one hundred and twenty-seven; fifty thousand and sixteen; ninety thousand and thirty-two; four hundred and seven thousand one hundred and seven. Take away nine hundred and seven thousand nine hundred and five, and then say how much the remainder

differs from five hundred thousand, and write out the answer in words.

SECTION II. 1. Divide £270 among 23 persons.

2. If six articles are worth £15, what is the value of 5 of them ?

SECTION III. 1. Find by practice the value of 4,074 articles at 28. 91d. per dozen.

2. Make out the following bill of parcels in proper form, and show how it should be receipted :

11 lbs. at 3s. 2d. per lb.; 94 ozs. at 16d. per oz.; 9 yards at 33d. per yard; 6 lbs. at 74d. per lb.; 10 ozs. at 94d. per oz.; 3 dozen and a half at 6 for 7d.

SECTION IV. 1. If a man gets £3 3s. a week, and puts by £10 a quarter, how much does he spend weekly ?

2. What is the value of 1000 fourpenny pieces ?

SECTION V. 1. What is the value of 2 tons 14 cwt. 2 qrs. at £1 12s. 6d. per cwt. ?

2. A family of 14 persons has provisions for 30 days; after 21 days 4 more persons arrive; how long will the food last?

SECTION VI. 1. Find the greatest and least of the fractions, 9 23 13

20 489 28*

2. A man has £10 13s. 4d. a week in rents; his tenants cheat him of th, he pays 4d. in the £ for collection, and 94d. in the £ for rates; how much has he to spend ?

SECTION VII. 1. How many cubic inches will there be in a box 2 ft. 5 in. long, 1 ft. 10 in. broad, and 1 ft. 3 in. high? What weight of water will it contain if a cubie foot of water weighs 1000 oz.?

2. If I save £10 yearly and invest it in 3 per cents. and always put in the interest together with the saving for the 4 following years, what sum shall I have at the end of the time?

SECTION VIII. 1. Divide 3.5 by 007 and multiply the result by 0049 and then by 02.

2. Reduce 3 qrs. 21 lbs. to the decimal of a ton. SECTION IX. Explain, as for a class :

:

(1) How to subtract when the figure in the subtrahend

is greater than the figure in the minuend.

(2) How to multiply a fraction by a whole number; Or, (3) How to divide one fraction by another.

Euclid and Algebra.

EUCLID AND ALGEBRA.

Male Candidates.

EUCLID.

27

Capital letters, and not numbers, must be used in the diagrams. Not more than ten questions to be answered.

1. On the same straight line, and on the same side of it, there cannot be two triangles which have their sides terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.

2. Show how to bisect a given finite straight line. How would you practically do this?

3. 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 sides of the one 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.

4. Triangles upon equal bases and between the same parallels are equal to one another.

5. To a given straight line apply a parallelogram that shall be equal to a given rectilineal figure, and have an angle equal to a given rectilineal angle.

6. Construct a square equal to the sum of three given squares.

ALGEBRA.

1. Add together 8ax 7by + 3y2; ax2 + 2by - 7y2; 9ax+4y2 — 2; 7 + 3by — 2ya + 4ax; 6ax2 — y2.

2. From 4-7x+10a-126 take away 7a+2b -15x+20.

3. Multiply 8xy-3yx2-4xy by 7xy-8x+6y.

4. Divide

- qb2 by b— 1.

+ 3x2y2+ 2y by x2 + 2y and a +(q-x)b

5. Solve these equations:

(1)(x+3) + (2x-4)= x.

= x.

6. A goods train travels at the rate of 8 miles an