The length in centimeters of twelve rods are as follows: Find the mean value and standard deviation. 5.33, 5.31, 5.33, 5.22, 5.29, 5.34, 5.35, 5.31, 5.27, 5.28, 5.32, 5.25

1)a) Find an equation with integral co-efficients, whose roots are the squares
of the roots of the equation 2×2 + 5x – 6 = 0 (5 marks)

b) Find the greatest value of:

-10 + 14x – 2×2 and state the value of x at which it occurs. Sketch the curve
of y = -10 + 14z -2×2. Showing clearly the line of symmetry of the curve.(5 marks)

c) Solve by factorization the equation 2×2 – 5x + 3 = 0 (5 marks)

d) The sum to infinity of a geometrical progression with a positive common
ratio is 9 and the sum of the first two terms is 5. Find the first four terms
of the progression. (5 marks)

2)a) A committee of six is to be formed from nine women and three men. In how
many ways can the members be chosen so as to include at atleast one man?(6 marks)

b) i) Find the middle term in the expansion of (6x + (4 marks)

ii) What is the value of the constant term in the expansion of:

(4 marks)

c) Express 24 sin x + 7cosx in the form R sin (x + and hence solve the
equation 24 sin x + 7 cos x + 15 = 0 (7 marks)

 

 

 

 

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