E.—lA

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7. What kinds of recreation and amusement are most suitable for teachers ? Why is physical exercise essential to health ? 8. What are the chief disadvantages of having one's house built on low ground? What are some of the best things to do in such a case. 9. Discuss generally the effect of the moderate and of the excessive use of alcohol and other stimulants on health. 10. What are the various substances used to cause puddings, &c, to be light and porous ? What are the modes of action of the several substances? State the special use of each. Algebra. — For Senior Civil Service. Time allowed: 3 hours. 1. Irad the value of —; : , when *= —%-a. Qj — CO X -j- Cb ** 2. Multiply ar 2 - 2* _1 +1 by x 2 +x -1. Test the result by making x=2. 8. Divide a i +a s (x —y)— a 2 (x +y)— z 2 by a 2 +ax —z. 4. Resolve (a¥-ft) s , (a a +6 a ) a — « 2 & 2 , # 2 4-7/ 2 — Ixy — x+y, into elementary factors; and reduce x m+nyn X i -Xy s X s -X 2 — 3*+ 2 , ~ . , , , 2-, „ / —, • —-— ±~, to their lowest terms. x m y m + n x'y+xy z +y* x*-3x+2 5. Simplify— (a) -J__|_l__7-J LVf. v ; x-1 las+l \x-2 x+2j) 6. Find the value of— α-x b-x , a 4-6 T+ax-l+bx< whenX = T^b7. Solve the equations— \i 3 1 \ a -> 4 X _IO 4x-9 te-14' th\ a 6 - 6 -- Ct =- -\ ' x+b x-a x—a+b' (c.) (α-ffl) (y-b)=xy=(x-2a) (y-2b). 8. A rectangular paddock contained 5 acres; but when a border, 8 yards wide, was taken off all round for planting, it contained less than 4 acres by 40 square yards. Find the length and breadth of the paddock. 9. In a municipal election there were two candidates. One of them polled half the constituency, obtaining a majority of a votes over his opponent. Supposing that -th part of the constituency refrained from voting, find the number of votes polled by each candidate. Algebra.—For Class D and Junior Civil Service. Time allowed: 3 hours. 1 If a= 1, b= 9, and c= 8, find the numerical value of and if x =o, y =3, 2=5, find the value of 2xy 3(x+y) 5z z ~ z y' 2. Write down the algebraical expression for the following: From the quotient obtained by dividing the number x by the number y is subtracted half the quotient obtained by dividing the number yby the number x ; the excess is multiplied by itself, and the result is divided by three times that number which when multiplied by itself gives the quotient obtained by dividing the number x by the number y. Explain the meaning of the following expression : [t +— )+ v "~ 6 . 3. Divide (i.) by f-z 3 -^+K s . (ii.) 4a 8 5 2 -4a5V-8a 2 6 3 -cV+l6a& 4 -aVby (2b + c)a. 4. Simplify 3 (a-2(6-3c)} + 4a-(s&+2c)- [3c-{a+2(6-c)}] ; 5 Eesolve into elementary factors — 21a 2 +29a&-106 2 ; (x 2 +fY-f(x+yY; 4 ft 2_9^_c 2 4-66 c. 6. Eeduce to its lowest terms f^+gs^rr^Tby ; and find the lowest common multiple of x-\-l, x' 2, — !, x+2, a; 3 -fB, x'-j-x —2. „. ~» 3xy-2y 2 . x(2x+y) , 7. bimpiity _ _ + 6x2y+7xyi - + 2yS , and find the value of when and y=^.