1 (a) The point P has coordinates (-3,2) and the point Q has coordinates (7,k). The line PQ has equation 3X+5y=2, find the value of k, hence find the coordinates of the midpoint of PQ;

(b) A line which passes through the point P is perpendicular to the PQ. Find an equation of the line, in the form px+qy+r=0, where p, q and r are constants;

2.The sides of rectangular floor are xm and (x+7)m. The diagonal is (x+8)m, calculate:

(i) the value of x

(ii) the area of the floor.

3.A rectangular box has length 10m, breadth 9m and 6m high. What is the longest length of the longest stick that will fit in to the box?

4.(a) Using ruler and a pair of compasses only,

construct the quadrilateral ABD such that |AB|=7cm, |BC|=5cm, angle ABC=120° and |AD|=|AC|=|DC|.

(b) construct the locus,

(I) L1 of points equidistant from B and C;

(ii) L2 Of points equidistant from B and A .

(C) (I) Locate, O, the point of intersection of L1 and L2.

(ii) With O as center, construct a circle to pass through A,B and C.

(d) Measure (i) angle BCD

(ii) the radius of the circle

5a.Factorise completely the expression

4x² -20xy + 25y² -m

5b.solve the equations

3x-y=4

x² -3xy+8=0

6a.The width of a rectangular room is 4m wider than its height and the length is 8m wider than the width . If the total area of the walls is 512m square .

Find the length of the room.

6b.The area of a rectangle is 6m². Find the dimensions of the rectangle.

7.S1 is the enlargement of S1 with scale factor 3/2 of a sphere. If the surface area of S1 is 240m square, find the radius of S2 correct to two significant figures. ( Take π 22/7)

8.A student was asked to prepare va rectangular model in the form of two joined right angled triangles with its shortest length being 15cm.

Find the length of the other two sides and the area of the rectangle if the sides are whole integers .

9.The sides of a right-angled triangle are (x-1)cm, (x+3)cm and (x+7)cm.

Find the value of x.

9b.An isosceles triangle has equal sides 6cm long and a base 4cm long . Find the altitude of the triangle; leave your answer in surd form.

10.Two passenger trains,A and B, 300km apart, start towards each other at the same time.They meet after 2hrs.If train B travels 8/7 as fast as train A,what is the speed of each train?

Q: The angle of depression of the top and bottom of a 40m building from the top of a tower are 40° and 60° respectively .The base of the building and the tower are on the same horizontal level .Find the height of the tower ,correct to the nearest meter.

A motorist drove from town A to town B, a distance of 40km in 30 minutes, stopped at B for 20 minutes and drove from town B to town C, 20km away,in 25 minutes. What is the average speed for the journey?

An aeroplane leaves Barcelona at 10:10pm and reaches Accra 4,415 km away at 5:50am the next morning. Find,correct to the nearest whole number,the average speed of the aeroplane in kmh/1