If line p = 5x + 3 is parallel to line p = wx + 5. Find the value of w.

• A. 7
• B. 3
• C. 6
• D. 5

The angle subtended at the centre by a chord of a circle radius 6cm is 120°. Find the length of the chord.

• A. 3cm
• B. 6cm
• C. \(4\sqrt{2}\) cm
• D. \(6\sqrt{3}\) cm

Four vectors \(r = \alpha i + \beta j\), where \(\alpha \text{ and } \beta\) are constants, \(s = 2i -j, m = 3i + 2j\) and \(n = i + j\) are such that the magnitude of r is three times as s and is parallel to the vactor (m - n).

(a) Find the values of \(\alpha\) and \(\beta\).

(b) Calculate the magnitude and direction of (r - s).

Find the nth term of the linear sequence (A.P) (5y + 1), ( 2y + 1), (1- y),...

• A. (8 + 3n)y + 1
• B. 8y + 3n + 1
• C. (8 - 3n)y + 1
• D. 8y - 3n + 1

(a) Using a ruler and a pair of compasses only, (i) construct \(\Delta\) XYZ such that |XY| = 8 cm and < YXZ = < ZYX = 45°. (ii) locate a point P inside the triangle equidistant from XY and XZ and also equidistance from YX and YZ. (iii) construct a circle touching the three sides of the triangle (iv) measure the radius of the circle.

(b) The length of the sides of a hexagon are x - 5, 2x, 2x, 2x + 7, 2x and 2x - 1. If the perimeter is 144 cm, find the value of x.

Find the value of a if the line 2y - ax + 4 = 0 is perpendicular to the line y + (x/4) - 7 = 0

• A. -4
• B. 4
• C. 8
• D. -8

If (x + 3) is a factor of the polynomial \(x^{3} + 3x^{2} + nx - 12\), where n is a constant, find the value of n.

• A. -1
• B. -2
• C. -3
• D. -4

If b³ = a^-2 and c^{\(\frac{1}{3}\)} = a^{\(\frac{1}{2}\)}b, express c in terms of a

• A. a^{-\(\frac{1}{2}\)}
• B. a^{\(\frac{1}{3}\)}
• C. a^{\(\frac{3}{2}\)}
• D. a^{\(\frac{2}{3}\)}

lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y.

• A. 9/16
• B. 3/4
• C. 1
• D. 4/3

The sides of a triangle are in the ratio of 3:5:7 and its perimeter is 30cm. The length of the greatest side of the triangle in cm is

• (a) 6
• (b) 10
• (c) 14
• (d) 16