The gradient of a curve at point (x,y) is 4x - 6. The curve has a minimum value at 5¹/₂ . Find the equation of the curve.                      (3mks)

Kapsabet Boys’ handball team scored the following goals in 6 matches; 10, 8, 14, 16, 6 and 18. Using assumed mean of 12, determine the standard deviation leaving your answer to 2 d.p.     (3mks)

If OA = , OB = . P divides AB externally in the ratio 2:1. Find the coordinates of P.        (3mks)

Using logarithms, evaluate                                      (4mks)

The equation of a circle is given as x² + y² + 4x -2y - 4 = 0. Determine the centre and the diameter of the circle.      (3mks)

Find the value of x given that log(x -1) + 2 = log(3x + 2) + log 25.            (3mks)

Two matrices P and Q are such that P = and Q = . Given that the determinant of QP is 44, find the value of k.   (3mks)

Without using a mathematical table or a calculator, evaluate leaving your answer in the form.  , where a, b and c are constants. (3mks)

The roots of the quadratic equation x² + px = q are x = -³/₇  and  x = 2. Find the values of p and q. (3mks)

Two variables x and y are related by the law y = -2 + bxⁿ where b and n are constants. The table below shows the variations between x and y

a) Write down the function y = -2 + bxⁿ in the linear form            (1 mark)

b) On the grid provided draw a suitable line graph to represent the relation y = -2 + bxⁿ .     (5 marks)

c) Find the values of b and n                    (3 marks)

d) Write a relationship connecting y and x (1 mark)