11. An annual income of 200ol. is made up as follows250l. from a 6 per cent. stock, 350l. from an 8 per cent. stock, and the remainder from a 3 per cent. stock. How much of each stock is held? If 2000l. of the 3 per cent. stock is sold out at 94, what will be the cash realized? 12. Find the sum of money which with its simple interest at 3 per cent. per annum will in two years amount to 1290l. IV. [N. B. Two Propositions at least from the Second Book are required.] 1. Explain the terms-axiom, postulate, theorem, problem, hypothesis, corollary. 2. If a straight line fall on two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite angle on the same side; and also the two interior angles on the same side together equal to two right angles. 3. Describe a square that shall be equal to a given rectilineal figure. 4. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles on the other side of the base shall be equal to one another. 5. Construct a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third. 6. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. 7. From a given point draw a straight line equal to a given straight line. 8. In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle. 9. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts. 10. Describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. 11. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. V. Algebra. 1. Explain the terms-coefficient, index, factor, square root, simple equation, least common multiple. 2. (1) If a = 1, b = 2, c = −3, find the value of (2) If a = 7, b = −3, c = 5, find the value of 3. (1) Add together (a+b)3, (a-b)3, a3—b3. 4. Resolve into their simple factors (1) x2 + xy-6 y2; 5. Find the L. C. M. of (2) (62+c2-a2)2 —4b2 c2. (x+a)2, (x−a)2, x3-a3, x3+a3 ; and the G. C. M. of a3+6a2+11a+6 and a3+10a2 + 29a + 20. 7. Prove that a2 (b−c) — b2 (a—c) + c2 (a−b) is equal 9. Solve the equations: (1) 5(x+3) −2 (x − 4) = 5 x + 3 ; 10. A bag contains a certain number of red and white counters, of which the white are three times as many as the red in number. On taking out two-thirds of each sort, there are exactly forty counters remaining in the bag. Find the original number of each. A and B shoot 25 arrows apiece at a mark. B hits it twice as often as A, and A misses it three times as often Find the number of hits and misses of each. as B. A debtor pays his creditors five shillings in the pound. If his assets had been five times as great, and his debts one-third less, he would have had a balance in his favour of 1001l. Find his debts and assets. |