The distance between towns A and B is 360km. A minibus left town A at 8.15 a.m. and traveled towards town B at an average speed of 90km/hr. A matatu left town B two and a third hours later on the same day and travelled towards A at average speed of 110km/hr.

a) (i) At what time did the two vehicles meet?                                        (4 Marks)

(ii) How far from A did the two vehicles meet?                                        (2 Marks)

b) A motorist started from his home at 10.30 a.m. on the same day as the matatu and travelled at an average speed of 100km/h. He arrive at B at the same time as the minibus. Calculate the distance from A to his house.                               (4 Marks)

Oketch sells his car to Jane and makes a profit of 20%. Jane sells the same to Issa at Sh.180, 000, making a loss of 10%. Determine the price at which Oketch bought the car.                        (3 Marks)

Solve for x in  2^2x  -  18  x  2^x = 40                                                     (3 Marks)

Town X is 20km in a bearing of 060⁰ from Y, and Z is 30km in the direction 150⁰ from Y. Using the scale 1cm represents 5km, find by scale drawing:

(a) the bearing of Y from Z.                                        (2 Marks)

(b) the distance of X from Z.                                      (2 Marks )

Draw the net of the solid below and calculate the total surface area of its faces.                    (3 Marks)

In a book store, books packed in cartons are arranged in rows such that there are 50 cartons in the first row, 48 cartons in the next row, 46 in the next and so on.

(a) How many cartons will there be in the 8^th row?                                   (2 Marks)

(b) If there are 20 rows in total, find the total number of cartons in the book store.              (2 Marks)

Using a ruler and pair of compasses only, construct triangle ABC in which AB = 6cm, BC = 8cm and angle ABC = 45⁰. Drop a perpendicular from A to BC to meet line BC at M. Measure AM and AC.                                                        (4 Marks)

A measuring cylinder of base radius 5cm contains water whose level reads 6cm high. A spherical object is immersed in the water and the new level reads 10cm. Calculate the radius of the spherical object         (3 Marks)

In triangle ABC below, AC = BC, AB is parallel to DE, AB = 15cm, DE = 7.5cm and BE = 6cm.

Calculate

(a) Length CE                                                                     (2 Marks)

(b) Area of quadrilateral ABED.                                                     (2 Marks)

Give sin (90 – a) = ¹/₂ find without using trigonometric tables the value of cos a .           (2 Marks)