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)

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