Give an expression for the n th term in the sequence 0 3 8 15 3 marks 9 SECTION

Give an expression for the n th term in the sequence

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16. Give an expression for the n th term in the sequence. 0, 3, 8, 15,………………………………………………… (3 marks) 9
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SECTION II, Attempt all the question in this section. (50 marks) 17. The population of a town in the 1989 census was shown as 60,000 people with a male to female ratio of 2 : 3. Another census had been taken in 1979 and another one is due in 1999. Statistics show that the growth rate of the town at the preceding census. Determine. a. The population of the town in 1979. (3 marks) b. The expected population in 1999. (3 marks) c. The expected number of males and females in the 1999 census. (4 marks) 10
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18. The table below shows how income tax was charged on income earned in a certain year. Taxable income per year (K£) Rate (sh per K£) 1 – 3630 2 3631 – 7260 3 7261 – 10890 4 10891 – 14520 5 Mordecai earns a salary of sh. 15, 200 per month. He is housed by the company with the result that 15% of his monthly salary is added as taxable income. Mordecai is a married man an is entitled to a family relief of Ksh 450 per month. Calculate how much income tax Mordecai pays per month. (10 marks) 11
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19. The figure shows two circles with centres P and Q and radii 6.6 cm and 8cm respectively centres P and Q are 10cm apart and PM : MQ = 2:3. Calculate (a) The size of angle RPS. (2 marks) (b) The size of angle RQS. (2 marks) (c) The area of the shaded region. (6 marks) (Take л = 3.142) 12
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20. In the figure below, ABCD is a parallelogram in which BC is produced to X such that BC=CX y is the mid-point of DC and AYX is a straight line. (a) Given that AB = a and BC = b express the following vectors in terms of a and b.(6 marks) (i) CX (ii) AC (iii) AX (iv) DX (b) Use vectors to prove that ACXD is a parallelogram. (4 marks) 13
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21. (a) Complete the following table for the equation. y – 1 = x 2 + 3x x -5 -4 -3 -2 -1 0 1 2 y 5 -1 11 (b) On graph paper provided, draw the graph of y – 1 = 3x + x 2 . (3 marks) (c) By drawing a suitable straight line, used your graph to solve the equation x 2 + 2x – 2 = 0. (5 marks) 14
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