Use squares square roots and reciprocal tables to evaluate              (3mks)

Makau, Wanjiru and Kemboi start a race at 9.03 a.m in the same direction to run round a circular course.  Makau makes the circuit in 252 seconds, Wanjiru in 308 seconds and Kemboi in 198 seconds.   If they start from the same point, at what time will they next be all at the starting point together?               (3marks)

Momanyi spent one eight of his February Salary on farming, half on school fees and two thirds of the remainder on food. Calculate his February salary and the amount he spend on school fees if he spent sh. 3200 on food.                     (3marks)

Evaluate without using tables or calculators              (3mks)

The figure below shows the area bound by the curve    and the line

(a) Find a , the value of x  at the point of intersection of the curve and the line.        (3 marks)

(b) Using the trapezium rule with 4 trapezia, estimate the area of the shaded region.    (4 marks)

(c) By integration, calculate the exact area of the shaded region       (3 marks)

The figure below represents a prism ABCDEFGH of length 6 cm. the section ADEH of the prism is a trapezium in which AD=11 cm, HE=8 cm, BG=5 cm and ÐADE=ÐDEH=90⁰

(a) Calculate correct to 1 decimal place;

 i) The angle between line DG and the plane ABCD.            (3 marks)

ii) The angle between planes ABGH and ABCD              (3 marks)

(b) Calculate the volume of the prism               (4 marks)

Awuor was paid an initial salary of Kshs. 180,000 per annum with a fixed annual increment. Wasonga was paid and initial salary of Kshs. 150,000 per annum with a 10% increment compounded annually.

(a) Given that Awuor’s annual salary in the 11th year was Kshs. 288,000, determine:

 i) Her annual increment                        (3 marks)

ii) The total amount of money Awuor earned during the 11 years             (3 marks)

(b) Determine Wasonga’s monthly earning, correct to the nearest 10 shillings during the 11th year.        (4 marks)

(a)       Complete the table below giving the values correct to 1 decimal place.      (2 marks)

(b)     On the grid provided and using the same axes, draw the graphs of

                 (4 marks)

(c) i) Using graphs in part (b),  find the values of x  for which:               (3 marks)

ii) determine the values of x  for which:              (1 mark)

A'(-6,0) , B'(-2,-3)  and C'(-2, 0)  are the vertices of the image of triangle ABC  under a transformation described by the matrix   

(a) Determine the coordinates of triangle ABC                    (3 marks)

(b)   i)  On the same grid, draw triangles ABC , A'B'C'                      (2 marks)

(ii)   Describe fully the transformation M                               (1 mark)

(c)Triangle A''B''C''  is the image of triangle A'B'C'  such that A''(0, 6) , B''(6, 2)  and C''(0, 2)

 i) Draw triangle A''B''C'' on the same axes                      (1 mark)

 ii) Find a single matrix of transformation that maps triangle ABC  onto triangle A''B''C''     (3 marks)

The figure below shows a hockey field of dimensions 60 metres by 48 m. The shaded area is an astroturf that is x metres wide.

(a) Form and simplify an expression in x for the:

i) Area of the field and the astroturf ;                         (1 mark)

ii) Area covered by the astroturf.                           (2 marks)

(b) Given that the shaded area is 220 m²,

i) find the value of x;                    (4 marks)

ii) calculate the perimeter of the field with the turf.      (3 marks)