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).

Use reciprocal tables to find the value of (0.325)^-1 hence evaluate and give your answer to 4 s.f. (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)

The graph in figure below represents the journey made by a matatu between two bus stops.

a.     What is the acceleration of the matatu? (2 marks)

b.     Calculate the deceleration of the matatu? (2 marks)

c.      What distance does the matatu cover while accelerating? (2 marks)

d.     Calculate the distance covered by matatu while decelerating (2marks) 

e.     Calculate the distance between the two bus stops. (2 marks)

An amount of money was shared among five boys Ali, Juma, Musa, Khalid and Mustafa. Ali got ³/₈ of the total amount while Juma got ²/₅ of the remainder. The remaining amount was shared equally among Musa, Khalid and Mustafa, each of which received Kshs 600.

a.     How much did Juma get?      (3 marks)

b.     How much was shared among the five boys. (2 marks)

c.      Ali, Juma and Mustafa invested their money and earned a profit of Kshs 1200. A third of the profit was left to maintain the business and the rest shared according to their investments. Calculate how much each got. (5 marks)

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)

A particle P moves in a straight line such that t seconds after passing a fixed point Q. its velocity is given by the equation  2t² -10t + 12   

find:

a.     The values of t when p is instantaneously at rest. (2 marks)

b.     An expression for the distance moved by P after t seconds. (2 marks)

c.      The total distance traveled by P in the first 3 seconds after passing point O. (3 marks)

d.     The maximum velocity attained by the body. (3 marks)

  On the graph paper provided plot the points P(2,2) Q(2,5) and R(4,4)

a.     Join them to form a triangle PQR   (1mk)

b.     Reflect the triangle PQR in the line x=0 and label the image s P₁Q₁R₁. (2mks)

c.      Triangle PQR is given translation by vector T (1,2) to P₁₁Q₁₁R₁₁.plot the triangle P₁Q₁R₁.       (3mks)

d.     Rotate triangle P₁₁Q₁₁R₁₁ about the origin through -90⁰.state the coordinates of P₁₁₁Q₁₁₁R₁₁₁.    (3mks)

e.     Identify two pairs of triangle that are direct congruence (1mk)