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)

The surface areas of two spheres are 36cm² and 49cm². If the volume of the smaller sphere is 20.2cm³, calculate the volume of the larger one.                                        (2 Marks)

Find the equation of the perpendicular bisector of line PQ where the co-ordinates of P and Q are P (-2, 8) and Q (4, 7).                                     (3 Marks)

Use logarithm tables correct to 4 significant figures to evaluate.                              (3 Marks)

In the diagram below, two circles, centres A and C and radii 7cm and 24cm respectively intersect at B and D. AC = 25cm.

(a) Show that angle ABC = 90⁰.                                                            (3 Marks)

(b) Calculate

(i) the size of obtuse angle BAD                                           (3 Marks)

(ii) the area of the shaded part                                             (4 Marks)

      The table shows marks obtained by 100 candidates at Goseta Secondary School in Biology examination.

(a) Determine the value of x                                                                                                        (2 Marks)

  (b) State the modal class                                                                                                              (1 Mark)

(c) Calculate the median mark                                                                                                     (2 Marks)

 (d) Calculate the mean mark                                                                                                        (5 Marks)

The following measurements were recorded in a field book of a farm in metres (xy = 400m)

(a) Using a scale of 1cm representing 4000cm, draw an accurate map of the farm.                   (3 Marks)

(b) If the farm is on sale at Kshs. 80,000.00 per hectare, find how much it costs.                   (7 Marks)