V. PURE MATHEMATICS (1).

2. Sides 7x+y = 11, 3x-y+ 1 = 0, x + 3y + 7 = 0 ; bisectors 99x +77y+71 = 0, 7x-9y = 37.

3. A straight line.

4. (i.) A circle; (ii.) an ellipse, parabola, or hyperbola according as the constant is >, =, or < the distance between the centres.

OS2

5. Two. 6. When the distance of the point from the origin >

BC

8. 8, 2√3.

9. A parabola.

VI. PURE MATHEMATICS (2).

1. (i.) 6, -7; (ii.) x = ±a, ±20°; y = ±b,

2a-b
3

5. 89.

6. sin(A+2B) is positive, cos(A+2B) is negative.

a-2b ±2 √3

8.

a sin y sin (a + β)

9. 9.65146, 20.5309.

VII. MECHANICS.

1. 5.632, 4.792.

3. Tension, W.

2. The c.g. is 3" 19 from A; 12 oz., 17 oz.

Pressures on the pegs, √5 w, 2N5w, 4w.

6

3

3

3

ANSWERS.

JUNE, 1892.

II. ALGEBRA.

1. a-a5b+9ab5.

2. x3+p2x2+pqx+q2.

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

11. 12th term, -4368a-6; middle term, 12870.

12. 18.

2.

V. PURE MATHEMATICS.

1-3x+3x2-3x4+3x-3x7+3x8 - .... 3. 8 and 4. 10. a2.

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

14. 7y2 + 24xy - 24ax - 6ay + 15a2 = 0. Centre,

3

(-a); directrix,

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. 8x3 – 8bx2 + 12abx-27a3, 8a3+4a2(bc) – 2abc + (bc).

8. a-b, a-b, 2-6, a, a+b; 10 terms. 9. 3360, 126.

I

10. 1-2x - 2x2 - 4x3 – 10x4.

11. 4.91956.

III. TRIGONOMETRY.

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

8.