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(3.) He says he has no more money. (4.) Do you find what you are looking for ? (5.) I am sorry that you play instead of working. (6.) Will the concert take place this evening ? (7.) Your cousin (fern.) understands me when I speak German. (8.) It is a lovely day to-day, neither too hot nor too cold. (9.) Give me back my book and my letters. (10.) It is raining hard; lend me your umbrella until to-morrow morning.

Algebra. For Class D, and for Junior Civil Service,. Time allowed: 3 hours. 1. Express in algebraical symbols —"The quotient obtained by dividing the difference of the fourth powers of two numbers by the sum of the numbers is equal to the product obtained by multiplying the difference of the squares of the numbers by the difference of the numbers." Express in words + — (jfqrj) > and calculate its value when a=4,b=3, c = 2. 2. Prove the truth of the identities a— (b+c) =a-b —0, and a—(b — o)=a — b+c. 3. If s=i(a+b+c), prove that s 3 -1 (a 2 +62 + c 3) -ctbc = (s-a) (s-b) (s-c). Eind the continued product of a+b + c, a+b-c, a-b +c, -a + b+c, and show that if c 2 = a 3 + Z> 2 it reduces to 4a 2 b'\ 4. Eesolve into elementary factors 8a 3 (3x-2y + z)' 2 -(x- 3y - zf; 21?/ 2 + lly-2 ; 9« 2 + 6a6 + 2ic-c 2 . 5. Simplify 2 [x- [y + 2 (a>- z) + 3(?/ - 2x) ] - s (y - 2,5) ]-. 6 - Sim P llf y 6^-B^+s^-2' 2 3 ix l'+ffi" 2 x-1 „ ' A 1 1- x + x--7. Solve the equations, — 2 3 5 ~t~ — X- 5 ' x + 3a+b 3x + a-2b _ x-a + b "■" x+a-b 8 Two trains whose lengths are respectively a and b yards, and which are travelling at the rate of x and y miles an hour respectively, pass one another in p seconds when they are travelling in the same direction, and in q seconds when they are travelling in opposite directions : write down the equations which express these facts. 9 After I have given one-fifth of my money and lost two-thirds of the remainder, I find that one-quarter of what is still left is less by £10 than one-seventh of what would have remained from the original sum after I had paid away one-third of it. How much money had lat first ?

Euclid.—For Class D, and for Junior Civil Service. Time allowed: 3 hours. 1 Define the terms— surface, plana, hypothenuse, diameter, diagonal, polygon, perimeter. 2. Explain the distinction between a direct and an indirect demonstration, giving instances from the First Book of Euclid. ~-,., ■-, t ~ ,■ , 3. If the three sides of one triangle be respectively equal to the three sides of another tnangle, the two triangles shall be equal in every respect. __ X B, C, are three points in the circumference of a circle. If the straight lines joining A,B, and B C are equal show that they subtend equal angles at the centre of the circle. ' '4 If two'angles and a side in one triangle be respectively equal to two angles and the corresponding side in another triangle, the two triangles shall be equal in every respect. If this proposition were deferred till the three angles of a triangle had been proved to be together equal to two right angles, show that it would be reduced to one case, which might be proved by superposition. . 5. On a given straight line to describe a parallelogram which shall be equal to a given tnangle and have one of its angles equal to a , given angle _ 6 Draw a line DE parallel to the base BC of a triangle ABC, so that it shall be equal to the sum of the segments BD and CE, which it cuts off from the sides of the triangle. 7 If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part IMO 8. To divide a given straight line into two parts so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. .-,,:, If a straight line be divided in medial section, show that the rectangle contained by the whole line and the difference of its segments is equal to the rectangle contained by the two segments.