- Make q the subject of the formula. (3 mks)

r=pq +^{1}/_{2}tq^{2} - Solve for x in

4cos^{2}x = 3sinx + 3 for 0 ≤ x^{o}≤ 180^{o}(3 mks) - The figure below shows two circles centre O
_{1}and O_{2}which are 7.5cm apart and of radii 4cm and 2.5cm respectively.

Calculate the value of KL to 2 decimal places. (3 mks) - Without using tables or calculators simplify (3mks)
- Express as a single logarithm. (3mks)
- The mass of some rabbits in a certain agriculture class were recorded as follows.

Calculate the quartile deviation of the data to 3 s.f (3 mks)Mass 1.0-1.9 2.0-2.9 3.0-3.9 4.0-4.9 5.0-5.9 6.0-6.9 No. of rabbit 7 16 14 8 13 2 - Given triangle AOB, O(0,0) A(2,0), B(0,4) and its image O'(
^{√3}/_{2},0) A'(√3,1), B'(-2,2√3). Find the matrix that maps OAB into O'A'B and describe the transformation represented by this matrix fully. (3mks) - Ketepa tea worth Ksh.40 per kg is mixed with Sasini tea worth Ksh. 60 per kg in the ration 3:1 in what ratio should this mixture be mixed with Kericho tea worth Ksh. 50 per kg to produce a mixture worth Ksh. 47 per kg. (3mks)
- Calculate the area enclosed by the curve y = (x-1)
^{2}+ 4 and the line y = -x + 7 (3 mks) - Expand in ascending process of x upto and including the term in x
^{3}(3 mks)

(3 - x - x^{2})^{4} - In the triangular based pyramid shown below, find the angle between planes VAC and VCB to 1 decimal place if the base is an equilateral triangle of side 10cm and edges VA = VB = VC = 16cm each. (4mks)
- Calculate the area bounded by the curve y=x
^{2}+ 5 and lines y = 0 and x-3 = 0. Using mid-ordinate rule with 6 strips giving your answer to 4 decimal place. (4 mks) - The matrix M is (
^{4}_{1}^{3}_{2}). Find the image of line y=2x + 1 under M. (3mks) - From a metal rod of length 2.00m, 15 students each cut a piece 5cm long. If all the students had an error of ± 0.2cm in their cuts, determine the minimum and maximum length of the rod that remained. (3 mks)
- Given that where k is a constant and t is increased by 44% and b reduced by 88%, find the ratio by which x is changed. (3mks)
- The numbers 2, x and y form a geometric sequence. The numbers x, 30 and y form an arithmetic sequence. Find the possible value of x and y. ( 3mks)

**SECTION B (50 MARKS)**

*Answer*

**any five**questions from this section