The figure below, two circles, centres E and G and radii 5 cm and 12 cm respectively intersect at F and H. EG = 13 cm.

(a) Show that ÐEFG=90⁰ .                                                     (3 marks)

(b) Calculate

(i) the size of obtuse ÐFEH                                                           (3 marks)

(ii) the area of the shaded part, correct to 2 decimal places. Use 3.142                    (4 marks)

In the figure below, PQRS is a trapezium. PQ is parallel to SR. The diagonals SQ and PR intersect at T and SR=2PQ. PQ=q , PS=s , PT=hPR  and ST=kSQ , where h  and k  are constants

(a) Find in terms of q  and s :

 i) QR ;                                                                       (2 marks)

 ii) PT ;                                                                            (2 marks)

 iii) ST .                                                                                (1 mark)

(b) Determine the values of h  and k                                                                                                                     (5 marks)

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, 2¹/₃  hours later on the same day and travelled towards A at average speed of 110km/hr.

(i) At what time of the day did the two vehicles meet?                 (4 marks)

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

(iii) A motorist started from her home at 10.30 a.m. on the same day as the matatu and travelled at an average speed of 100 km/h. She arrived at B at the same time as the minibus. Calculate the distance from A to her house.            (4 mks)

The displacement S  of a particle after t seconds is given by

Determine the:

(a) velocity of the particle when t=3                     (3 marks)

(b) value of t  when the particle is instantaneously at rest                    (3 marks)

(c) displacement when the particle is instantaneously at rest.                (2 marks)

(d) acceleration of the particle when t=2  seconds                          (2 marks)

The figure below shows a histogram drawn for marks scored by students in a mathematics contest

(a) State the modal class.                                       (1 mark)

(b) Draw a frequency distribution table from the histogram.                       (2 marks)

(c) Use the table in (b) above to calculate the mean mark                        (3 marks)

(d) On the histogram, draw a vertical line showing where the median mark lies             (4 marks)

A cylindrical milk urn has diameter 40 cm and height 1.4 metres.

(a) Calculate the capacity of milk in litres in the urn when it is full, to the nearest litre. Use  .            (2 marks)

(b) The milk is packed into tetrahedron packets of capacity 200 ml. Calculate the number of packets used.    (2 marks)

(c) The packets are packed into boxes that contain 24 packets each. How many complete boxes are used to package the milk?                                 (2 marks)

(d) Each box is sold at Kshs. 840, a profit of 12%. Calculate the buying price of each packet.            (4 marks)

Without using a calculator or mathematical table, solve for x  in             (2 mks)

The figure below shows an open cuboid ABCDEFGH. A particle traces a path from A to E through C as indicated by the arrows.

Draw the net of the solid and show the path on it.                    (3 marks)

A measuring cylinder has a diameter of 7 cm. Water fills the cylinder up to a height of 6 cm. A solid sphere is immersed into the cylinder and the height of water in the cylinder increases to 10 cm. calculate the radius of the sphere correct to 4 significant figures.                     (3 marks)

The cost of three toners and four cartridges is Kshs. 36,000. Oyoo bought one more toner and one less cartridge that are similar to the above and paid and paid Kshs. 1,500 more. Calculate the cost of one toner and one cartridge.                               (3 marks)