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Class D.—Algebra (Optional). Time allowed .- Three hours. 1. Explain the meaning of the expression v7^ +5Vp + 3r+l — [|^-; and'ftmdi'the value of fa; 2 — a?y + labx — Zy s, when a— 5, b=o, x—l, y—l. 2. Divide 2a 3 + 10 - 16a - 39a 2 + 15a 4 by 2 - 4a - 5a 2. 3. Eesolve into elementary factors x s + y"; a; 3 +%* — 132a:; x i — 2a:?/ 3 + 2a% 2 — xy'; (2a; + 3?/) 2 —(x — sy)". Eind the factors of x" -\- x— 2, and hence write [down the quotient obtained when this expression is divided into 2x (a: 3 —1)(«+2) 2. 4. Find the highest common factor of 2a: 3 - 10a; 3 + 42a; - 60, and 7a; 4 - 24a;" + 113a; 3 - 42a; - 15; and the lowest common multiple of xs + y 3, 3a; 2 + 2a;?/ — y", x% — x-y + xy~. 5. Simplify 2[a-3 (b - 2o) ] -(-B[a-26-2 ( - b + c) ]) ; , , r a-(b +c) . [ 3a-2b-c )~] . 1 , 26 . _ „. ~, tia x-a 2 . 6. Simplify - -^^- +I^, + x _ ¥a , and r + ?A(~^) - + zr-a--\y xj\ij i — x i) x'+xy xy—y* x _ „ , ~ .. 25~i' 16x+4i r, 23 7. Solve the equations ——r H — o ,° = 5 . —r; » x + l ix + 'J, x + 1 x 1 + a (2a —x) — ? =( x — ) + a 2. 8. A man has one kind of tea worth a pence per pound and another worth b pence per pound: how many pounds of each kind must he take to form a mixture of p pounds which he can sell for c pence per pound and gain 15 per cent. ? 9. Two pedestrians walk in opposite directions round a circle-a mile in circumference; they start from the same point, but the second starts ten minutes after the first. If the first walk at the rate of 3J miles an hour and the second at the rate of 3J miles an hour, where will they meet ? If they continue walking, where will they meet for the second time ?

Class D.—Euclid (Optional). Time alloived: Three hours. 1. Distinguish between a postulate and an axiom. Quote the axioms which are applicable exclusively to geometry. 2. The angles at the base of an isosceles triangle are equal to one another, and, if the equal sides be produced, the angles upon the other side of the base shall also be equal 3. To draw a straight line perpendicular to a given straight line, of an unlimited length, from a given point without it. Show how the construction might fail if the point, through which the circle is described, were taken in the given straight line, or on the side of it on which the given point is situated. 4. Parallelograms upon equal bases, and between the same parallels, are equal to one another. Show how a rhombus may be constructed equal in area to a given parallelogram. 5. In every right-angled triangle the square which is described upon the side subtending the right angle is equal to the squares described upon the sides which contain the right angle. 6. In obtuse-angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle by twice the rectangle contained by the side upon which, when produced, the perpendicular falls and the straight line intercepted between the perpendicular and the obtuse angle. 7. To describe a square that shall be equal to a given rectilineal figure. Show how to describe a rectangle that shall be equal to a given square and have one of its sides equal to a given straight line.

Class D.—Chemistry (Optional). Time alloived: Three hours. [Candidates arc not to answer more than nine questions.] 1. Five corked bottles are placed before you, each containing one of the following gases : Oxygen, hydrogen, nitrogen, chlorine, carbon dioxide (carbonic acid). How would you find out which gas each bottle contains ? 2. Write down an equation to show how chlorine gas may be got from common salt. 3. Arrange the following gases in the order of their specific gravity, all being at the same temperature and under the same pressure : C0 2 , NH 3 , CH 4 , H,S, H 2 O, CI, HCI, HI, PH 3 , NO, NO a , S0 2 . 4. What agencies are at work removing oxygen from the atmosphere ? 5. In what way do the breathing of animals and the growing of plants affect the composition of the atmosphere ?