In a Science class ²/₃ of the class are boys and the rest are girls. 80% of the boys and 90% of the girls are right handed. The probability that the right handed student will break a test tube in any session is ¹/₁₀ and that for the left handed student is ³/₁₀ , regardless of whether boy or girl.

(a) Draw a tree diagram to represent this information.                                  (2 Marks)

(b) Using the tree diagram drawn, find the probability that:

(i) A student chosen at random from the class is left handed                    (2 Marks)

(ii) A test tube is broken by a left handed student.                                (2 Marks)

(iii) A test tube is broken by a right handed student.                              (2 Marks)

(iv) A test tube is not broken in any session                                      (3 Marks)

Find the centre and radius of a circle whose equation is x²+ y²+ 8x + y² – 2y – 1 = 0                  (3 Marks)

A coffee blender has two brands of coffee, Tamu and Chungu. A kilogram of Tamu costs Sh. 70 while a kilogram of Chungu costs Shs. 64. In what ratio should he mix the two brands to make a blend which costs Shs. 68 per kilogram?                                                    (2 Marks)

A pipe 3.0m long was cut into three pieces. The first piece and the second one were measured as 1.3m and 0.94m respectively. Find the limits within which the length of the third piece lies.                       (3 Marks)

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)