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)

A bus and a matatu left voi for Mombasa 240km away at 8:00 am travelled at 90km/h and 120km/h respectively. After 20 minutes the matatu had a puncture which took 30 minutes to mend. It then continued with the journey.

a.     How far from voi did the matatu catch up with the bus(6 mks)

b.     At what time did the matatu catch up with the bus?     (2mks)

c.      At what time did the bus reach Mombasa?  (2mks)

Two similar solids have surface areas of 48cm² and 108cm² respectively. Find the volume of the smaller solid if the bigger one has a volume of 162cm³. (3marks).

A Kenyan bank buys and sells foreign currency as shown below.

A tourist arrived in Kenya with £9600 which he converted into Kshs at a commission of 5%. He later used ¾ of the money before changing the balance of dollars at no commission calculate; to the nearest dollar, the amount he received. (3marks)

Solve the following inequality and show your solution on a number line. (3marks)
4x – 3 < ½ (x + 8) < x + 5

From a viewing tower 30metres above the ground, the angle of depression of an object on the ground is 30⁰and the angle of elevation of an aircraft vertically above the object is 42⁰.Calculate the height of the aircraft above the ground. (3marks)

Mr. Onyangos piece of land is in a form of triangle whose dimensions are 1200m, 1800m and 1500m respectively. Find the area of this land in ha.(give your answer to the nearest whole number) (3marks)