POLITICS. Candidates should answer four questions in Section A and two in Section B. A. 1. Compare the Referendum and a Second Chamber as means of checking possible arbitrary action by a House of Commons. 2. (a) Outline the essential features in the political structure of any two states of Continental Europe. (b) What are the chief advantages and disadvantages of the federal form of the state? 3. Write brief notes on the following: (a) The achievements of the Hague Conferences. (c) The Law of Neutrality. 4. Discuss briefly the validity of Acts of the Ontario legislature, (a) Establishing the metric system of weights and measures. (b) Making six per cent. the maximum interest rate. (c) Establishing an Upper House in Ontario. (d) Abolishing separate schools in the province. (e) Forbidding the manufacture of intoxicating liquors in the province. 5. (a) Account for the growing power of the Cabinet in the United Kingdom and in Canada. (b "The prestige of the Presidential office has declined. . . Its power has waned because the power of Congress has become predominant. . . Congress has virtually taken into its own hands all the substantial powers of government. The Executive has lost and Congress has gained weight. . Our latter day Presidents live by proxy; they are the executive in theory but the members of the cabinet are the executive in fact. In early days the Secretaries were only the President's advisers, 6. State what appears to you the most workable general principle of state action, and apply it to the following questions: the repression of heretical religious beliefs, the provision of free meals and free boots for school children, and compulsory vaccination. B. 7. Comment on the following: (a) "Aristotle differs from his master, Plato, much more in the form and method than in the substance of his political thought." (b) "The reader is struck, now by the purely Hellenic, now by the universal and permanent character of Aristotle's thought." (c) "While Plato and Aristotle had found the key to the good life in a scientifically organized state, Zeno and Epicurus found it in absolute indifference to political conditions." 8. (a) Compare Aristotle's and Machiavelli's theories of tyranny. (b) Describe and account for the striking difference in the spirit and in the form of Dante's and of Machiavelli's political writings. 9. State concisely the distinctive political theories of each of the following, noting their period and chief works: Maine, Polybius, Bodin, Spencer, Filmer, Montesquieu, Locke. JUNIOR MATHEMATICS., Note.-Candidates will answer three questions only from each section, and must obtain 25% of the marks in each section. A. 1. Find geometrically the relation between the sine and cosine of an angle; and show that cos10+3 cos20 sin30+2 sin10=1+sin30. 2. Show that in any triangle (a) a=b cos C+c cos B. (b) tan B= 3. A ship sailing due East at 12 nautical miles per hour sights a lighthouse in a direction 45° 35′ North of East; and 10 minutes later the direction is 52° 03′ North of East. Find (a) the distance of the lighthouse from the first position, and (b) the shortest distance at which the ship will pass it. 4. (a) Prove geometrically that cos (A+B)=cos 4 cos B--sin 4 sin B. (b) Express (sin 4x+sin 6r+sin 10.r) as a product of trigonometric functions. 1. (a) Find the difference between the sum of + 3 9 27 I + to 7 terms and to infinity. (b) If the sum of n terms of a series is 2n2+3n, find the 10th term. 2. (a) Find the dimensions of the largest possible rectangular field having a perimeter of 40 rods. (b) Graph 3x-x2-2, and show how to obtain from it the graph of 3x-x2-7. 3. (a) The pressure of the wind on a plane area varies jointly as the area and the square of the velocity of the wind. If the pressure on one square foot is one pound when the velocity of the wind is 16 miles per hour, what is the velocity of the wind when the pressure on 2 square yards is 50 pounds? (b) How many numbers of four digits can be formed by use of the figures 1, 2, 3, 4, 5, 6, if no digit is repeated in any number? In how many of these numbers does the digit 5 appear? 4. (a) Write down and simplify the 5th term in the expansion of (1—2x)-3. (b) If is one of the imaginary cube roots of unity, show that the other imaginary cube root is 2. C. 1. Give reasons for the statement— (a) The area of a crossed quadrilateral is the difference between the areas of the triangles that compose it. (b) The point at infinity is the external point of bisection of a line segment. Explain whether the external bisector of an angle contains the same idea as is found in statement (b). in geometry, and illustrate by deducing four other theorems from the theorem AB2=AC2+BC2-2BC.DC for the triangle. 3. State (a+b)2+(a—b) 2—2(a+b)(a—b)=4b2 as a theorem in geometry; and prove it by superposition of areas. Under what conditions may the equation itself be regarded as a proof of the theorem? 4. (a) D is a point in the base BC of the isosceles triangle ABC. Prove AB2-AD2-BD.DC. (b) D is a point in a fixed segment BC. Find the position of D in order that BD.DC and BD2+DC2 may have a maximum or minimum value. |