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Wednesday, June 19th, 1912.-Afternoon, 3 to 6.
Not more than THREE questions may be attempted in each Section of the Paper. All questions carry equal marks.
1. Explain exactly how, and why, the wind system moves north and south with the sun, and illustrate the results of the movement on the east coast of the North Atlantic.
2. Explain, with rough diagrams, showing the winter and summer temperatures, the main differences between winter and summer in the British Isles.
3. Locate, and describe, the chief water-parting of Scotland, and show its relation to the railway system.
4. State, in the order of their importance, all the causes which led to the concentration of the cotton industry in Lancashire.
5. Name, locate, and account for the importance of the eight harbours which you consider the most important in the British Isles, naming them in the order of their importance.
6. Draw two rough maps of Europe, and mark off on them belts of temperature-one for winter and the other for summer. If possible, give the actual average temperature of each; and in any case label each with an appropriate badge-e.g., "very cold," "cold," "cool," warm, hot," or very hot."
7. Compare the Seine with the Elbe in physical character and economic importance.
8. Show the relation of the soil and climate to the typical vegetation of (a) Newfoundland and (b) Nova Scotia, and describe the distribution of the typical plants in each case.
9. Describe the exact position and the natural advantages of Algiers, Athens, Bordeaux, Florence, Grimsby, New York, Stettin, and Winnipeg.
10. What localities in the British Empire, outside the British Isles, are specially connected with barley-growing, cattle-rearing, coalmining, and salmon-fishing? In each case explain the causes to which the particular industry in due.
Elementary Mathematics.—Paper A.
ARITHMETIC AND ALGEBRA (Associateship).
Wednesday, June 19th, 1912.-Morning, 9 to 12.
1. Express 429 decametres as a fraction, in its lowest terms, of
6 kilometres 6 metres; and 1/2 of (\
correct to three places of decimals.
3 4 + + as a decimal, 13 19 25
2. Find the value of 2.72324801 of £2475. 158. 6d., correct to the
nearest sixpence; and that of
•782634 x 42.5682
correct to four (10)
3. Sixteen hundred dollars were divided as follows amongst A, B, C, and D. A, B, and C continued to go up in that order to D, beginning with A, and D gave them 4, 7, and 12 dollars respectively on each occasion, until there were not enough dollars left to pay the one of them whose turn it was to be paid, and that residue was D's share. How many dollars did each one of the four get? (8) 4. A merchant bought a ship's cargo and sold it at such a price that he obtained a profit at the rate of 10 per cent. If he had paid 5 per cent. less for the cargo than he did pay, and sold it for 5 per cent. more than he did sell it for, his profit would have been increased by £315. What sum did the merchant pay for the cargo? (10)
5. For what value of x is 2x4—3x3 — 27x2+53x-4 exactly divisible by x2+2x-7?
Find the numerical value of the quotient when x has that value.
ab (2a+b)(a+2b) — (a2 — b2)2 + (a2 —ab+b2)2 ; and find the factors of
(i) a2+2bc+b2-2a (b+c), (ii) 15x2+34x-72.
8. A spent 102 dollars in a certain number of days, and B spent 3 more dollars in 3 more days, 1 dollars more per day than B. expenditure?
and A spent on an average What was B's average daily (12)
9. Draw the graph of y = 44+8x-x2 for positive values of x not exceeding 10, and from it write down as accurately as you can, to one decimal place, the values of x when y = 55.
10. Obtain the expression for the sum of n terms of an Arithmetical Progression whose first term is a and common difference d. What is the greatest number of terms of the series 13, 17, 21, ... which may be taken without their sum exceeding 5500, and what will be the last term taken ?
11. Find the difference between the sum of the first 5 terms of the series
Elementary Mathematics.-Paper B.
Thursday, June 20th, 1912. Morning, 9 to 12.
Figures must be drawn neatly and accurately.
All construction lines must be clearly shown.
1. Construct a triangle ABC, with its sides AB, BC, and CA 23, 29, and 37 units long respectively. Bisect the angle BAC. In the line AF, which bisects the angle BAC, take F so that AF is 17 units long. Draw from Fa perpendicular to AC, and measure its length.
(10) 2. Make a square ABCD whose sides shall be 14 units long. In the diagonal AC produced through C, find a point X so that the area of the triangle ABX shall be 133 square units. Measure the length of BX. (10)
3. Describe an equilateral triangle about a circle whose radius is 19 units long. Measure the length of a side of the triangle.
Figures must be drawn neatly.
Recognized abbreviations may be used.
4. If two angles of a triangle are equal, prove that the sides which are opposite to them are equal.
ABCD is a quadrilateral of which the side AB is equal to the side AD, and the angle DBC is equal to the angle BDC. Show that AC bisects the angle BAD.
5. Prove that the sum of the angles of a triangle is equal to two right angles.
If the bisectors of the angles ADC, BCD of a quadrilateral ABCD meet at E, prove that the angle DEC is half the sum of the angles DAB and ABC.
6. If the square on one side of a triangle is equal to the sum of the squares on the other two sides, prove that the angle contained by those two sides is a right angle.
Show, without proof, how to divide a given straight line into two parts, so that the sum of the squares on the two parts may be to the square on the whole line as 9 is to 16. (12)
7. Prove that the rectangle contained by the sum and the difference of two straight lines is equal to the difference of the squares on the lines.
ABC is an isosceles triangle whose vertex is A, and a straight line XY parallel to BC meets AB in X and AC in Y. Show that the square on BY is equal to the square on CY together with the rectangle contained by BC and XY.
(12) 8. Prove that chords of a circle which are equal are equidistant from the centre.
If two equal chords intersect within a circle, prove that the segments of one chord are respectively equal to the segments of the other chord.
9. Prove that angles in the same segment of a circle are equal. ABCD is a parallelogram, and the angle BAD is an obtuse angle. The circle passing through the three points B, A, and D intersects BC and DC produced in E and F respectively. Prove that E and F are equidistant from A.
10. Prove that the angle in a semicircle is a right angle.
AB is the diameter of a semicircle, and C any point in the arc. In BC, or BC produced, a point D is taken so that BD is equal to AC. What is the locus of D?