The towns X and Y are on the same latitude south of the equator. The longitude of X is 120⁰W and the longitude of Y is 143⁰E. the shortest distance between X and Y measured along the parallel of latitude is 5068 nautical miles. Find the latitude on which X and Y lie. (4 marks)

If  P =    and Q =    Given that PQ is a singular matrix. Find the value of x. (4 marks)

The figure below shows an equilateral triangle of radius 8 cm. calculate the length of the side of the triangle.               (2 marks)

The sum of four consecutive even integers is greater than 248. Determine the first four such integers.                      (3 marks)

The ratio of the interior angle to that of the exterior angle of a regular polygon is 7:2. Find the number of sides of the polygon.                 (3 marks)

Cheluget gets a commission of 2.4% on sales up to sh. 200,000. He gets an additional commission of 1.2% on sales above this. Calculate the commission he gets on sales worth sh. 380,000.                          (3 marks)

Simplify                                                                        (2marks)

In Boresha Bank customers may withdraw cash through one of the three tellers at the counter. On average, one teller takes 3 minutes, the others take 5 minutes and 6 minutes respectively to serve a customer. If the three tellers start to serve the customers at the same time, find the shortest time it takes to serve 210 customers.              (4 marks)

Evaluate without using a calculator                           (3 marks)

(a) Complete the table below for y = x³ + 4x² – 5x - 5                                                          (2 Marks)

(b) On the grid provided, draw the graph of y = x³ + 4x² – 5x – 5 for                   (3 Marks)

(c)  i) Use the graph to solve the equation  x³ + 4x² – 5x – 5 = 0                                               (2 Marks)

ii) By drawing a suitable straight line on the graph, solve the equation                               (3 Marks)

      x³ + 4x² – 5x – 5 = -4x - 1