V. PURE MATHEMATICS.

2. 1-3x+3x2 − 3xa + 3x5 − 3x7 +3x8 — ....

10. a2.

11. (i.) x+2y=a, 2x-y=a; (ii.) 4x+3y=0, 3x-4y=0; a right angle.

3. 8 and 4.

9. Velocities, o, u; distance apart, a-ut. Taking point of projection as origin, and the axes horizontal and vertical, equation to C.G.

NOVEMBER, 1892.

II. ALGEBRA.

1.

8.x3 – 8bx2 + 12abx − 27a3, 8a3+4a2(bc)3 — 2abc + (bc)*.

2. 3a3-2a2b- §ab2+§b3.

8. a-b, a−b, 2a-1b, ja, a+b; 10 terms.

1. Cosine, tangent, cotangent, secant, cosecant 1.

ANSWERS.

JUNE, 1893.

II. ALGEBRA.

1. (2x-51)(3x-41), (x2-3xy+y2)(x2+3xy+y2),

7.

(x − 1)(x + 1)(x2 + x + 1)(x2 − x + 1). 3. x2--2x+5.

(i.) 7; (ii.) 7; (iii.) x = ±3, ±2; y=±2, ±3.

10.

O is the focus. If OT be the perpendicular from O on the tangent and OT be produced to 7' so that OT' = 207, a line through T' making angle a with the tangent is the directrix.

14.

Ax+By=0; Bx+Cy=0. If these lines coincide B2= AC, and the curve becomes two coincident parallel lines.

6.

S.W. wind, whose speed equals that of vessel. 10. 37 miles an hour; 65 min., 211⁄2 miles.