(a) Express as single fraction in its simplest form         (2mks)

(b) When driven into a town a car travels x km on each litre of petrol.

i. Find in terms of x, the number of litres of petrol used when the car is driven 200km in town.     (1mk)

ii. When driven out of town the car travels (x +4) km on each litre of petrol. It uses 5 litres less petrol to cover 200km out of town to cover same distance in town. Use this information to write down an equation involving x, and show if simplified to    x² + 4x – 160 = 0              (3mks)

(c) Solve the equation      x² + 4x – 160 = 0             (3mks)

(d) Calculate the volume of petrol when the car is driven 40km in town (1mk)

The figure below shows triangle ABC inscribed in a circle. AB = 6 cm, BC = 9cm and AC = 10cm.

Calculate:

a) The radius of the circle              (6mks)

b) The area of the shaded parts              (4mks)

(a) Complete the table below by filling in the blank spaces for the function    y = -x + x² – 6.     (2mks)

(b) On the grid provided draw a graph of y = -x + x² - 6 with the domain     (3mks)

(c) From the graph find the values of x which satisfies the expressions

    i.      –x + x² – 6 = 0                              (2mks)

    ii.   – x + x² – 6 = 5                             (3mks)

(a) Using a ruler and a pair of compasses only, construct a triangle QRS in which angle QRS = 37¹ /₂ ⁰ , RS = 7cm and RQ = 6cm.     (4mks)

(b) Drop a perpendicular from Q to RS = to meet RS at T. measure QT,      (3mks)

(c) hence calculate the area of the triangle QRS.        (3mks)

The figure below shows triangle OAB in which M divides OA in the ratio 2:3 and N divides OB in the ratio 4:1, AN and BM intersect at X

a) Given that OA = a and OB = b, express in terms of a and b:

(i) AN                    (1mk)

(ii) BM                   (1mk)

b) If AX = sAN and BX = tBM, where s and t are constants, write an expression for OX in terms of a,b , s and t (2mrks)

c) Find the values of s        (4mks)

d) Hence write OX in terms of a and b       (2mks)

A trailer 30m long moving at an average speed of 60km/h started from station A towards station B at 4.00am ,a bus moving at an average speed of 90km/h and 20m long started also travelling from A towards B at 4.30am .

find:

a) The time the bus caught up with the trailer                 (4mks)

b) The time in seconds the bus took to pass the trailer completely          (3mks)

c) How far from A did the bus completely overtake the trailer            (3mks)

The table below shows income tax rates in Kenya in a certain year

Mr. King’ori earned a basic salary of ksh13, 120 and a house allowance of ksh3, 000 per month. He claimed a tax relief from a married person of ksh 455 per month

a) Calculate :

(i) The tax payable without relief                (4mks)

 (ii) The tax paid after relief                      (2mks)

b) A part from the income tax, the following month deductions are made; a service charge of ksh 100, a health Insurance fund of ksh and 2% of his basic salary as widow and children pension scheme. Calculate:

(i) The total monthly deductions made from King’ori’s income       (2mks)

(ii) Mr. King’ori’s net income from his employment                    (2mks)

In the diagram below ; PQ = 10cm and RS = 14cm. find the length of QR       (3mks)

The figure below shows a circle centre O, radius 8.4cm. The chord EF = 8.4cm. calculate the area of the unshaded region    (3mks)

Solve for x in the equation.                          (3mks)