The figure below shows two circles.

Find the value of x  if the difference of their areas is given by 20 cm²       (3 mks)

Use trigonometric identities to show that                                         (2 mks)

A school buys a lawn mower at Kshs. 48,000. The lawn mower depreciates in value at a rate of 15% per annum for the first year. Thereafter, the rate of depreciation annually is 10% for the subsequent years. Find the time it will take its value to be half the buying price.           (3 mks)

The mass (M ) of a cylinder varies jointly as the square of the radius (r ) and inversely as the square root of the height (h ). If the radius is reduced by 25% and the height increased by 21%, calculate the percentage change in the mass of the cylinder.     (3mks)

The table below represents a relationship between two variables Q and R , connected by the equation Q = kR +c where k  and c  are constants.

     (a) On the grid provided, draw the line of best fit for the data.                         (3 marks)

      (b) Use the graph in (a) above to find the value of c                                            (1 mark)

Make t  the subject of the formula                                               (3 marks)

The figure below shows a circle with segments cut off by a triangle whose longest side XY is the largest possible chord of the circle. XY = 14 cm and XZ = YZ

Calculate the area of the shaded part, correct to 2 decimal places. Use                    (3 marks)

Find the constant term in the expansion of the binomial                     (2 mks)

The position vectors of three points P, Q, and R are such that p = 2i +3j + 4k  , q = -i - 2j + k and r = 5i + 8j + 7k. Show that the points P , Q and R lie on a straight line.      (3 mks)

(a) Draw triangle PQR whose vertices are P (1, 1), Q (-3, 2) and R (0, 3) on the grid provided.   (1mk)

(b) Find and draw the image of PQR under the transformation whose matrix is  and label the image P¹Q¹R¹.     (3mks)

(c) P¹Q¹R¹ is then transformed into P¹¹Q¹¹R¹¹ by the transformation with the matrix   . Find the co-ordinates of P¹¹Q¹¹R¹¹ and draw P¹¹Q¹¹R¹¹.    (3mks)

(d) Describe fully the single transformation which maps PQR onto P¹¹Q¹¹R¹¹ Find the matrix of this transformation.   (3mks)