1. The area of a sector of a circle, radius 2.1cm, is 2.31cm².
The arc of the sector subtends an angle θ, at the centre of the circle.
Find the value of θ in radians correct to 2 decimal places.

2. The figure below shows a rectangular container of dimensions 40cm by 25cm by 90cm.
A cylindrical pipe of radius 7.5cm is fitted in the container as shown.

Water is poured into the container in the space outside the pipe such that the level is 80% the height of the container.
Calculate the amount of water, in litres, in the container correct to 3 significant figures.

3. A line L passes through points (-2,3) and (-1,6) and is perpendicular to a line P at (-1,6).

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Given that another line Q is parallel to L and passes through point (1,2), find the point of intersection of lines P and Q.

4. Muya had a  ha piece of land. He donated  ha to a school and  ha to a children's home.
The rest of the land was shared equally between his son and daughter. Find the size of land that each child got.

5. Without using mathematical tables or a calculator, evaluate sin 30°-sin60 °/tan60°

6. Twenty five machines working at a rate of 9 hours per day can complete a job in 16 days. A contractor intends to complete the job in 10 days using similar machines working at a rate of 12 hours per day. Find the number of machines the contractor requires to complete the job.

8. A cow is 4 years 8 months older than a heifer. The product of their ages is 8 years. Determine the age of the cow and that of the heifer.

9. The lengths, in cm, of pencils used by pupils in a standard one class on a certain day were recorded as follows:

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The percentage of pencils that were longer than 8cm but shorter than 15cm:

10. The lengths, in cm, of pencils used by pupils in a standard one class on a certain day were recorded as follows:

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Calculate the mean length of the pencils. Enter the mean length of the pencils: