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9. Locate one large manufacturing centre in each of the following countries, state the chief manufactures carried on, and give the names of the chief towns engaged in them :-Ireland, Scotland, France, or Germany. (30)
10. What countries or districts produce the following in large quantities?— petroleum, tin, wine, sulphur, logwood, palm oil, flax. Give two localities only for each. To what uses can the last four be applied? What kinds of climate do the last two require? (30) 11. What three quite different articles are manufactured in England in very large quantity? Where is each produced? Give the names of the towns engaged in, and the suitability of the district for, that particular manufacture. (30) 12. Make a list of the chief raw products (mineral, animal, and vegetable) of South America, mentioning the principal localities for each. State to what country each is chiefly exported and what is done with it, or, if used for manufacture in the country of its origin, state this.
COUNCIL OF HIGHER EDUCATION, NEWFOUNDLAND.
ARITHMETIC (Intermediate Grade).
Tuesday, June 20th, 1911. Morning, 9 to 11.
1. Reduce 30000 lb. to tons, cwt., qr., lb. [1 cwt. = 112 lb.]
2. Reduce and to decimals.
Express the difference between them as a percentage of the greater of them to two places of decimals.
3. A man having a draft for $2000 changes it into English money, and receives £410. 13s. 7d. Find, to the nearest cent, the rate of exchange for £1.
(10) 4. In one month's working of a mine, 50829 tons of rock are crushed and yield 9535.091 Troy ounces of fine gold, which are worth $194402-86. Find, to two places of decimals, the number of pennyweights of gold in 1 ton of rock, and find to the nearest cent the value of 1 ounce of fine gold. [1 oz. Troy = 20 pennyweights.]
5. Six houses are sold for $13000. They let for $180 each per annum. If 4 of them are occupied for the whole year, but 1 is empty for 6 months and another for 3 months, and the landlord has to spend $295 on repairs for the 6 houses, what percentage does he get on his capital? (14)
6. A cyclist starts at 12 miles an hour. After doing 30 miles, he rests for a quarter of an hour and then goes on at 11 miles an hour. A motor starts 1 hours later than the cyclist at 20 miles an hour. At the twenty-fifth mile it breaks down for 20 minutes, and then goes on at 15 miles an hour. Where will it overtake the cyclist?
7. What is the difference between the Simple and Compound Interest on $16680 for 3 years at 3 per cent. ? (Answer to the nearest cent.)
TOTS (to accompany Arithmetic paper).
Tuesday, June 20th, 1911.- Morning, 9 to 9.15.
Add these up, placing the totals in the spaces indicated:
Add these across, placing the totals in the spaces indicated :
2791623 +84 + 9 + 718+ 2059 + 315+ 79
N.B.-The totals are not to be copied into the Answer book.
ALGEBRA (Intermediate Grade).
Monday, June 19th, 1911.-Morning, 11.30 to 1.15.
Care should be taken to write out the work neatly and to omit no steps of the proofs.
Squared paper may be obtained from the presiding examiner.
2. Prove that 5x-1 is a factor of 15x3 — 38x2—23x+6, and find its
(iii) 2x2+3x= 10, correct to two decimal places.
4. Extract the square root of
5. What number must be added to 9x2-24x in order to form a perfect square?
If y = 9x2-24x+30, show that y always exceeds 14, whatever be the numerical value of x.
Find the values of x which make y equal to 39.
6. A man buys (a+b) tons of coal at (p-q) shillings per ton, and (a-b) tons at (p+q) shillings per ton. If he sells the whole at p shillings per ton, what profit does he make?
Verify your result when a 30, b = 11, p = 22, q = 3.
Either 7a. Taking inch as unit, draw the graph of (x+2) (x-3), from
x= -2 to x = 3.
Find, from your graph, the values of x which correspond to the following values of (x+2) (x-3):
(i) -2, (ii) -61.
Verify your results by algebraical solutions.
x4—6x3y+10x2y2 —xy3 — 6y4
Or 7B. Simplify
GEOMETRY (Intermediate Grade).
Wednesday, June 21st, 1911.-Morning, 9 to 11.
Figures must be drawn neatly.
Each candidate may take ONE paper ONLY, A or B or C.
Paper A.-Euclid, Books I and II, with Riders. [Any generally recognized symbols or abbreviations may be used, but the proofs must be geometrical.]
A 1. Show, with proof, how at a given point in a straight line to make an angle equal to a given angle. (6)
A 2. Prove that, if two triangles have two angles of the one equal to two angles of the other, each to each, and also have a side of one equal to a side of the other, these sides being adjacent to the equal angles, the triangles are equal in all respects.
A, B, C are three points on the bank of a river, P the point on the other bank directly opposite to A, and AB, BC are equal. On walking 100 feet from C, in a direction perpendicular to BC, I find myself in a line with P, B. What is the breadth of the river? Prove your statement. (16) A 3. Calculate the magnitude of the angle of a regular polygon of thirteen sides. (9)
A 4. Prove that equal triangles on equal bases, in the same straight line and on the same side of it, are between the same parallels. Two equal triangles stand on the same base and on opposite sides of it. Prove that the base bisects the straight line which joins their vertices.
A 5. The sides of a triangle are 24, 25, 7 feet long.
Prove that one angle
is a right angle, and calculate the length of the perpendicular drawn from this angle to the opposite side.
A 6. Prove that, if a straight line is divided into any two parts, the square on the whole line is equal to the sum of the squares on the two parts together with twice the rectangle contained by the two parts.