The cash price of a deep freezer is Kshs. 50,000. Mary bought the freezer on hire purchase terms by paying a deposit of Kshs. 25,000 followed by 24 equal monthly instalments of Kshs. 2,250 each. An annual interest, compounded quarterly was charged on the balance for a period of 2 years. Determine, correct to 1 decimal place, the interest rate per month.     (4 marks)

(a)  Expand  (1+2x)⁶  in ascending powers of x up to the term in x⁴                     (1 mark)

(b)  Use the expansion in (a) above to find the value of (0.98)⁶ correct to 5 decimal place.         (2 marks)

The cost C  of hiring a conference facility for one day consists of two parts, one which is fixed and the other varies as the number of participants n  attending a conference. If Kshs. 45,000 is charged for hiring the facility for 100 participants and Kshs. 40,000 for 60 participants, find the number of participants if Kshs. 63,000 is used to hire the facility.                 (4 marks)

In the figure below, PT is a tangent to the circle from an external point P. PT=24 cm and OP=25 cm.

Calculate the shaded area correct to 2 decimal places.                      (4 marks)

Find the value of p if the expression         is a perfect square, given that p is a constant.                     (2 marks)

Make x  the subject of the formula;                                        (3 marks)

An arithmetic progression is such that its first term and common difference are 3 and 2 respectively. The difference of the last and forty-first terms of this progression is 48. Find the number of terms in the progression. (3 marks)

A milk urn has a capacity of 18.48 litres. A cylindrical container of diameter 14 cm and height 10 cm is used to draw milk from the urn for sale. How many times will it be used to completely drain the milk from the urn?                (3 marks)

In the figure below, ABC is a tangent to the circle at B.

(a) Given that ÐABG=42⁰ , ÐEBD=27⁰  and ÐBGD=49⁰ , calculate the sizes of the following angles. Give reasons in each case

 (i) ÐDGE                                                             (2 marks)

 (ii) ÐGFE                                                              (3 marks)

 (iii) Ð DBC                                                            (2 marks)

(b) Given that BC=10  cm and CD=7  cm, calculate TS          (3 marks)

(a) Fill the table below for the function y=x²-4x+2  for -1≤x≤5                           (2 marks)

(b) (i) Draw the graph of the function y=x²-4x+2  for -1≤x≤5    (3 marks)

      (ii) On the same axes, draw line y = x – 1                                            (1 mark)

 (c) Determine the values of x at the points of intersection between the curve y=x²-4x+2  and line   y = x – 1      (2 marks)

 (d) Give the equation of the line of symmetry of the curve                 (2 marks)