In the figure below, O is the centre of the circle.  PQ and PR are tangents to the circle at Q and R respectively.  <PQS  =  40⁰ and   <PRS  =  30⁰.  RTU is a straight line.

Calculate by giving reasons

(a)      <QRS                                                                                                  (2mks)

(b)      <RTQ                                                                                                    (2mks)

(c)      <RPQ                                                                                                     (2mks)

(d)      Reflex < QOR                                                                                                   (2mks)

(e)      <TRO given that TR  = TQ                                                                       (2mks)

 The table below shows income tax rate

An employee earns a monthly basic salary of sh. 30,000 and is also entitled to taxable allowances amounting to Ksh. 10,480.

(a) Calculate the gross income tax                                                                           (4mks)

(b) The employee is entitled to a personal tax relief of Ksh. 800 per month. Determine the net tax. (2mks)

(c) If the employee received a 50%  increase in his total income, calculate the parentage increase on the income tax.                       (4mks)

Obtain the values of x for which the matrix is singular                                            (3mks)

Solve for y in the following equation below:                                                  (4mks)

A quantity P varies partly as the cube of Q and partly varies inversely as the square of Q. when Q = 2, P = 108 and when Q = 3, P = 259. Find the value of P when Q = 6.              (3mks)

A two digit number is such that the difference between the ones digit and the tens digit is 2.  If the two digits are interchanged, the sum of the new and the original number is 132.  Find the original number                                                                               (3mks)

Using a ruler and a pair of compasses only construct triangle ABC such that BC=6cm, <ABC=75⁰ and BCA=45⁰. Drop a perpendicular to BC from A to meet BC at O hence find the area of triangle ABC                                                (3mks)

Use reciprocals, squares and square root tables only to evaluate                            (3mks)

A straight line L₁ has its X intercept a = -3 and its y-intercept b = 5. Find the equation of another line L₂ which passes through (1, -2) and is perpendicular to L₁          (3mks)

(a) Find the inverse of the matrix                                                    (1 mark)

(b) Hence solve the simultaneous equation using the matrix method           (2 marks)

4x +3y = 6

3x + 5y = 5