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)

Use table of square roots and reciprocals only to evaluate.                   (3mks)

Use the matrix method to solve the simultaneous equations:          (3mks)

Make g the subject of the formular:                                           (3mks)

 In June 2009, a cleaner salary was Ksh 15,300. Given that the company increases the cleaner’s money by ksh 800 every month of May since. What was the cleaner’s salary in May 2014?       (3mks)