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

Two boys and a girl shared some money. The elder got ⁴/₉ of it, the younger boy got ²/₅ of the remainder and the girl got the rest. Find the percentage share of the younger boy to the girls share.               (3mks)

Annette has some money in two denominations only. Fifty shillings notes and twenty shilling coins. She has three times as many fifty shilling notes as twenty shilling coins. If altogether she has sh. 3,400, find the number of fifty shilling notes and 20 shilling coin.   (3mks)

Solve the equation 2x² + 3x = 5 by completing the square method                    (3mks)

Simplify the expression                  (3mks)

Solve  the equation 8x² + 2x – 3 =0 hence solve the equation 8Cos²y + 2Cosy – 3 = 0 For the range 0⁰< y <180⁰                    (4mks)

 Show that the points P(3 , 4), Q(4 , 3) and R(1 , 6) are collinear.                    (3mks)

Solve the inequalities below , hence represent the solution on a number line.   (3mks)

The mean of five numbers is 20. The mean of the first three numbers is 16. The fifth number is greater than the fourth by 8. Find the fifth number.            (3mks)

 The volume of two similar solid spheres are 4752cm³ and 1408cm³. If  the surface area of the small sphere is 352cm², find the surface area of the larger sphere.         (3mks)

   Solve for x in the equation                              (3mks)

A famer has a piece of land measuring 840m by 396m. He divides it into square plots of equal sizes. Find the maximum area of one plot.        (4mks)

   (a) find the inverse of the matrix                                  (1mk)

   (b) Hence solve the simultaneous equation using the matrix method                      (2mks)

Each interior angle of a regular polygon is 120⁰ larger than the exterior angle. How many sides has the polygon?   (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)

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)

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)

A man spends ¹/₃ of his salary on rent and ²/₅ of the remainder on food. He saves the rest of his Income. If his savings amount to sh 4,200, find his income. (3 mks)

A bus service number 4 leaves a terminus every 20 minutes. Service bus 8 and 3 leaves ever 25 and 30 minutes respectively. If all the three services leave together at 6.00 a.m, at what other times during day time do they leave together?       (4mks)

The ratio of John’s earnings to Musa’s earnings is 5:3 if johns earning’s increase by 12%, his new figure becomes sh.56000.find the corresponding percentage change in Musa’s earnings if the sum of their new earnings is sh 9600. (3mks)

A number n is such that when divided by 3, 7, 11 or 13, the remainder is always one. Find the number n.    (3mks)

The sum of  ³/₈ ,  ²⁰/₃  and  x is  6⁵⁷/₁₂₀ . Find x.              (2mks)

Evaluate:                             (3mks)

A man is x years old now. In 10 years time, he will be twice as old as he was 5 years ago. How old will he be in 10 years time?     (3mks)

All prime numbers between 0 and 10 are arranged in a descending order to form a whole number

     (a)  Write down the number formed.  (1mk)

    (b) Test whether or not the number formed in (a) above is divisible by 11.  (2mks)

Express 0.872872872………….as a fraction         (3mks)

Evaluate                    (3mks)

-19 + (6-8) ÷ 2 x 5
     16 ÷ 4 x -3

A map is drawn to scale of 1:50,000. Find the area in cm² on the map of a field with an actual area of 60,000m². (3mks)

Using a ruler, a pair of compasses only and (proportional) a set square, construct on the upper side division of line BC is 6cm, a line BD such that DBC = 37.5⁰. Use the line BD to divide BC into 4 equal portions. (3marks)

Two men each working for 8 hours a day can cultivate an acre of land in 4 days. How long would 6 men, each working 4 hours a day take to cultivate 4 acres? (3marks).

The diagram below represents a prism whose cross section is a right angled triangle. Draw a labeled sketch of the net of the prism. (3mks)

Four schools: Lihanda, Kagito, Bar-Sari and Ndori are such that Lihanda is 6km from Kagilo on a bearing of 158°, Bar-Sauri is to the west of Kagilo and 20km away while Ndori is to the South of Bar-sauri on a bearing of 240° from Lihanda.

(a) Using a scale of 1:400,000 draw a scale diagram showing the relative positions of the four schools    (5mks)

(b) Using your diagram determine the distance and bearing of Ndori from Kagilo. (2 mks)

(c)  A mast is to be erected so that it is equidistant from Kagilo and Bar-sauri and 20km from Ndori. On the same diagram show the position of the mast and find its distance from Lihanda. (3mks)

A commemorative stone is sculptured in a shape of a frustum of a cone with the diameters of the top and bottom faces being 28cm and 49cm respectively. If the vertical distance between the faces is 45cm, find:

   (a) Find the cones vertical height. (2mks)

   (b) Find the volume of the stone. (3 mks)

   (c) Surface area of the stone. (5 mks)

In the diagram below, two circles centres A and C have radii 70cm and 102cm respectively, intersects at B and D . BD = 96cm

(a) Find the length AC (3 mks)

(b) Calculate

    i)  Angle BAD                                            (2 mks)

    ii)  Angle BCD                                                     (2 mks)

  iii)  The area of the shaded part.                                         (3 mks)