A photograph print measures 24 cm by 15 cm is enclosed in a frame. A uniform space of width x cm is left between the edges of the photograph and the frame. If the area of the space is 270 cm², find the value of x.        (4 mks)

Solve for x in the equation                                          (3 mks)

Three business partners, Bela Joan and Trinity contributed Kshs 112,000, Ksh,128,000 and ksh,210,000 respectively to start a business. They agreed to share their profit as follows:

30% to be shared equally

30% to be shared in the ratio of their contributions

40%  to be retained for running the business.

 If  at the end of the year, the business realized a profit of ksh 1.35 Million. Calculate:

(a) The amount of money retained for the running of the business at the end of the year.     (1mk)

(b) The difference between the amounts received by Trinity and Bela              (6mks)

(c) Express Joan’s share as a percentage of the total amount of money shared between the three partners.   (3mks)

   A Kenyan bank buys and sells foreign currency as shown below.
                                           Buying                       Selling
                                        Kenya shillings          Kenya shillings
1 Euro                                    84.15                       84.26
1 US Dollar                            80.12                       80.43
A tourist travelling from Britain arrives in Kenya with 5000 Euros. He converts all the Euros to Kenya Shillings at the bank. While in Kenya he spends a total of KSh. 289,850 and then converts the remaining Kenya shillings to US dollars at the bank. Calculate (to nearest dollar) the amount he receives?             (3mks)

Find all the integral values of x which satisfy the inequalities (3mks)
20-x>5+2x >x+5

Melisa ate ¹/₅ of her birthday cake and gave ²/₃  of the remainder to her friends. The rest was kept for her two sisters who were absent. If the two sisters shared their piece equally, what fraction of cake did each sister eat? (3 mks)

  Complete the table below for the function y = x³ + 6x² + 8x for   -5  x 1     (3mks)               

(a) Draw the graph of the function y = x³ + 6x² + 8x  for  -5  x 1           (3mks)

(use a scale of 1cm to represent 1 unit on the x-axis . 1cm to represent 5 units on the y-axis)

(b) Hence use your graph to estimate the roots of the equation  (4mks)

x3 + 5x²+ 4x = -x² – 3x -1                                                                                        

Mr. Kimanthi keeps Turkeys and chicken. The number of turkeys exceeds the number of chickens by 6. During the outbreak of a disease, ¼ of the chicken and ¹/₃  of the turkeys died. If he lost total of 30 birds, how many birds did he have altogether?    (4 mks)

Test whether  8260439 is divisible by 11.          (2 mks)

 Simplify the following expressions:-          (2mks)