Find the area of a segment of a circle whose arc subtends an angle of 22½ on the circumference of a circle, radius 10cm. (3marks)

In a regular polygon, the exterior angle is ¹/₃ of its supplement. Find the number of sides of this polygon. (3marks)

Using the three quadratic identities only factorize and simplify: (4marks)
   (x-y)² -(x+y)²    
(x²+y²)² - (x²-y²)²

Solve for x in the equation      (3marks)
  x-3  -   x+3  =    x  
  4           6           3

A bag contains 5 red, 4 white and 3 blue beads . two beads are selected at random one after another.

(a) Draw a tree diagram and show the probability space.                (2mks)

(b) From the tree diagram, find the probability that;

 i. The last bead selected is red      (3mks)

ii. The beads selected were of the same colour                             (2mks)

iii. At least one of the selected beads is blue.                      (3mks)

The table below shows the distribution of mathematics marks of form 4 candindates in Mavoko Secondary school.

Use the above date to calculate:

(a) Mean  using assumed mean of 65            (3mks)

(b) Median                                      (3mks)

(c) Standard deviation                                      (4mks)

The table below shows how income tax was charged on income earned in a certain year.

Mr. Gideon is an employee of a certain  company and earns a salary of  ksh.15,200 per month. He is housed by the company and pays a nominal rent of Ksh. 1050 per month. He is married and is entitled to a family relief of ksh. 450 per month.

(a) Calculate his taxable income in K£ p.a                         (2mks)

(b) Calculate his gross tax per month.                          (4mks)

(c) Calculate his net tax per month                              (2mks)

(d) Calculate his net salary  per month                             (2mks)

       Evaluate             

                                                     (4mks)               

Use logarithm tables to evaluate.                                       (3 marks)

Coast bus left Nairobi at 8.00am and travelled towards Mombasa at an average speed of 80Km/hr. At 8.30am, Lamu bus left Mombasa towards Nairobi at an average speed of  120 km per hour. Given that the distance between Nairobi and Mombasa is 400Km.: determine:

(a) The time Lamu bus arrived in Nairobi.                     (2mks)

(b) The time the two buses met.                           (4mks)

(c) The distance from Nairobi to the point where the two buses met.             (2mks)

(d) How far coast bus is from Mombasa when Lamu bus arrives in Nairobi           (3mks)