B.—la

26

and (v) find a value of x which shall make the expression— a: 2 - 4a; + 6 a?" -2x + 3 2a; 2 + 9 a; — 4 "•" a; — 2 x equal to 0 12. A rectangular field contains 30 acres, and if it were 44 yards longer and 30 yards narrower its area would be the same : find its length and breadth.

Algebra. — For Civil Service Senior (Old Regulations). Time alloived : 3 hours. 1. Divide \* x* -y * 4 -tI * 8 +V**- i x + A b Y t&~f x + i 2. Simplify— 9a 3 + 6a 2 6 - 12a& 2 - 8/) 3 V-> 18a" + 9a*b - 5ab 2 - 2b* ... . ll(a; + 2) 11a; + 12 11a; - 30 ("•) 6a; 2 + 7.r -3 + 12a; 2 - l&r + 3 + 8.r 2 + 6,r - 9 3. If a + b + c = 0, prove a s + b" + c" =3a6c Find the factors of — (i.) 4a 2 6 2 - (a 2 +b2 - c 2) 2 (ii.) a 4 + 4 (iii.) X s - 8x 2 -x + 8 (iv.) a; 8 — 4a; 2 +x + 6 (v.) (y +z - 2a;) 3 +(z+ x - 2?/) 8 +(x+ y - 2z)' 4. Solve the equations— . x— 5 a; —6 a; — 1 x— 2 .. W ~ x~-'l ~ x -2 + x- 3 = U (ii.) 4ate 2 + 2x(a -bf-(a- bf =0 (iii.) (a; 2 - sa; + 2) 2 = a; 2 - sa; +22 ( 14a; 2 - sxy - 13;/ 2 + 22 = 0 V lV ') \ 3a; 2 + sxy - iy 2 + 12 = 0 5. If a and /3 are the roots of the equation x 2 — px + q = 0, and a and y are the roots of the equation x 2 — P.r + Q = 0, find a, /3, y. 6. Describe the method of proof called " Mathematical Induction." Employ it to prove— !'+»+»+. .. . +w . = {«i!L|i)( a 7. Simplify — (i 1 123% 2 - 4a 6 ;/ 3 - gSa: 5 ;/ 4 + 9x*y 5 - 9a: 3 ;/ 6 I■' ~~ 8x 6 y s - Ha; 8 ?/ 5 - 9xjf ( ii.) C_£.Y + C_IL.V _■ V— \x -yj \g +y/ x x-y a+j \* - 2// V* + 2// \ x -y) * a ~ 2/ 2 V* + ?// 8. Solve the equations — fit («-!)' , (»-2)' -. (as - 9)(* -8) .... a; + to a; — m ra 4 v ' a; 2 +mx+ m 2 a; 2 -mx+ m 2 x(a: 4 + x 2 m 2 + m 4) a; = 2j/ n ( m ) 4a; + 7« ( iv.) ) p 2 »■ r i(a - a) + m(j/ - o) + »(* — c) = lJ (v.) v"a; +V9+a; = 9 9. A can do a piece of work in a hours, B in b hours, and C in c hours : how long will they ake all working together ? 10. Two bodies move in the same direction round a circle 999 ft. in circumference, and are together every 37 seconds : if the velocity of one is four times that of the other, what are their velocities ?

Algebra. — For Class D, and for Civil Service Junior. Time alloived . 3 hours. 1. Find the value of— t\y xl \y 2 y xl J x+ y when x = \, y = \. 2. Find the sum of — 3 (a + b) - 4 (a + b) 2 + 5 (a + b)"; (a + b) 2 - 2 (« + b) s - (a + bf + Z(a + b) 2 - (a + b) in its simplest form.