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Data collected form an experiment involving two variables X and Y was recorded as shown in the table below.The variables are known to satisfy a relation of the form y = ax^{3}+ b where a and b are constants
Two variables P and L are such that P varies partly as L and partly as the square root of L. Determine the relationship between P and L when L = 16, P = 500 and when L = 25, P = 800.5 marks A tailor makes two types of garments A and B. Garment A requires 3 metres of material while garment B requires 2 Â½ metres of material. The tailor uses not more than 600 metres of material daily in making both garments. He must make not more than 100 garments of type A and not less than 80 of type B each day.(a). Write down all the inequalities from this information. (3mks)b) Graph the inequalities in (a) above (3mks)c) If the business makes a profit of shs. 80 on garment A and a profit of shs. 60 on garment B, how many garments of each type must it make in order to maximize the total profit? (4mks)Fill in the table below to 2 decimal places for the graph of y = sin x and y = 2sin (x30) for the range – 180 £ x £180 (2mks)The curve of the equation y = x+ 2x^{2}, has x = ½ and x = 0 as xintercepts. The area bounded by the xaxis, x = ½ and x = 3 is shown by the sketch below.The table below shows income tax rates

Marks 
1019 
2029 
3039 
4049 
5059 
6069 
7079 
8089 
9099 
Frequency 
2 
6 
10 
16 
24 
20 
12 
8 
2 
Using an assumed mean of 54.5, calculate the
a) Mean mark (4mks)
b) Variance (4mks)
c) Standard deviation (2mks)
(a) A and B are two points on earthâ€™s surface and on latitude 40^{0} N. The two points are on the longitude 50^{0}W and 130^{0}E respectively. Calculate the distance from A to B along a parallel of latitude in kilometers. (2mks)
(b) The shortest distance from A to B along a great circle in kilometres (Take p = ^{22}/_{7} and radius of the earth = 6370km) (2mks)
Seven people can build five huts in 30 days. Find the number of people, working at the same rate that will build 9 similar huts in 27days. (3mks)
A quantity P varies partly as Q and partly as the square root of Q, given that P=30 when Q=9, and P=14 when Q=16. Find P when Q=36. (3mks)
A carpenter wishes to make, a ladder with 18 crosspieces. The cross pieces are to diminish uniformly in lengths from 65cm at the bottom to 31cm at the top. Calculate the length in cm, of the eighth crosspiece from the bottom. (3mks)
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