*Answer all questions in this section in the spaces provided.*

- Ntutu had cows, sheep and goats in his farm. The number of cows was 32 and the number of sheep was 12 times the number of cows. The number of goats was 1344 more than the number of sheep. If he sold ¾ of the goats. Find the number of the goats that remained. (4mark)
- Use the prime factors of 1764 and 2744 to evaluate (3 marks)
- The mass of a solid cone of radius 14 cm and height 18 cm is 4.62 kg. Find its density in g/cm
^{3}. (3 marks) - The figure below represents a triangular prism ABCDEF. X is a point on BC.
- Draw a net on the prism (2 marks)
- Find the distance DX. (1 mark)

- A business man makes a profit of 20% when he sells a carpet for Ksh 36 000. In a trade fair he sold one such carpet for Ksh 33 600. Calculate the percentage profit made on the sale of the carpet during the trade fair. (3 marks)
- Simplify (3 marks)
- The area of a sector of a circle, radius 2.1 cm, is 2.31 cm
^{2}. The arc of the sector subtends an angle θ, at the centre of the circle. Find the value of in radians correct to 2 decimal places. (2 marks) - Expand and simplify (
*x*+ 2*y*)^{2}- (2*y*- 3)^{2}(2 marks) - A plane leaves airstrip L and flies o a bearing of 040
^{0}to airstrip M, 500 km away. The plane then flies on a bearing of 316^{0}to airstrip N. The bearing of N from L is 350^{0}. By scale drawing, determine the distance between airstrips M and N. (4 marks) - The sum of interior angles of a regular polygon is 1800
^{0}. Find the size of each exterior angle. (3 marks) - 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. (4 marks)
- Solve 4 ≤ 3
*x*- 2 < 9 +*x*hence list the integral numbers that satisfies the inequality.(3 marks) - The figure below shows a rectangular container of dimensions 40 cm by 25 cm by 90 cm. A cylindrical pipe of radius 7.5 cm was fitted in the container as shown.

Water is poured into the container in the space outside the pipe such that the water level is 80% the height of the container. Calculate the amount of water, in litres, in the container correct to 3 significant figures. (4 marks) - A minor arc of a circle substends an angle of 105
^{0}at the centre of the circle. if the radius of the circle is 8.4 cm, find the length of the major arc. ( Take π =^{22}/_{7}) (3 marks) - Twenty five machines working at the rate of 9 hours per day can complete a job in 16 days. A contractor intends to complete the job in 10 days using the similar machines working at the rate of 12 hours per day. Find the number of machines the contractor requires to complete the job. (3 marks)
- Points A (-2, 2) and B (-3, 7) are mapped onto A' (4, -10) and B' (0, 10) by an enlargement. Find the scale factor of the enlargement. (3 marks)

**SECTION II** (50 marks)*Answer any five questions in this section in the spaces provided.*