Expand  upto the term in . Use your expansion to estimate the value of to 3 decimal places.                                                                                                                                       (4 Marks)

A quantity y varies partly as another quantity x and partly as the square of x. When x = 20, y = 45 and when x = 24, y = 60.

(a) Express y in terms of x                                                             (3 Marks)

(b) Find x when y = 75                                                                    (1 Mark)

Simplify      leaving your answer in the form , where a, b and c are rational numbers.     (3 Marks)

In the figure below, BT is a tangent to the circle at B. AXCT and BXD are straight lines. AX = 6cm, CT = 8cm, BX = 4.8cm and XD = 5cm. (Figure not drawn to scale)

Find the length of

(a) XC                                                                        (2 Marks)

(b) BT                                                                         (2 Marks)

Make x the subject of the formula in the equation below , Hence find the value of x when a = 2 and b = 6.                   (4 Marks)

Given that a = 3i – 2j + 3k and b = 2i - 4j – 3k where i, j and k are unit vectors,find |2a + 3b|    (3 Marks)

Solve for x in the equation                                                   (3 Marks )

      Log (5x + 75) – 2 Log 3 = Log (2x – 9)

The radius of a cone increases in the ratio 4:3 while it’s height decreases in the ratio 3:4. Determine the percentage change in the volume of the cone.                                           (3 Marks)

In the grid provided below, show the region R that is satisfied by the three inequalities given below.           (4mks)

The marked price of a shirt is Sh. 800. A customer buys the shirt after being given a discount of 13%. The seller then realizes that he made a profit of 20% on this sale. Find how much the seller had bought the shirt.               (2 Marks)