# Simplify the expression 48 5 3 leaving the answer in

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11. Simplify the expression √48 √5 +√3 leaving the answer in the form ?√? + ? where a, b and c are integers (3 mks) 12. A point P moves inside a sector of a circle, centre O, and chord AB such that 2cm < OP ≤ 3cm and angle APB = 65 0 Draw the locus of P (4 mks) 13. The table below shows income tax rates in a certain year Monthly income in Kenya shillings Tax rate in each shilling Up to 9 680 From 9 681-18 800 From 18 801 to 27 920 From 27 921 to 37 040 Over 37 040 10% 15% 20% 25% 30% In that year, a monthly personal tax relief of kshs 1056 was allowed .calculate the monthly income tax paid by an employee who earned salary of Ksh 32 500. (4 mks) 14. Solve the equation
118 Pyramid Consultants P.O Box 67593 00200 Nairobi 0722614502 / 0733494581 6 cos 2 x +7 sin x 8 = 0 for 0 0 x ≤ 90 0 (4 mks) 15. The position of two towns are (2 0 S,30 0 E) and 2 0 S, 37.4 0 E) calculate , to the nearest km, the shortest distance between the two towns.(take the radius of the earth to be 6370 km) (2 mks) 16. The vertices of triangle T are A(1, 2), B(4, 2) and C(3, 4). The vertices of triangle Tʹ, the image of T are Aʹ( 1 / 2 ,1) , Bʹ(2,1) and Cʹ( 3 / 2 . 2). Determine the transformation matrix 𝑀 = ( ? ? ? ? ) that maps T onto Tʹ. (3 mks) SECTION 11(50 MKS) Answer only five questions from section 17. The hire purchase (H.P) price of a public address system was Kshs 276000. A deposit of Kshs 60000 was paid followed by 18 equal monthly installments. The cash price of the public address system was 10% less than the H.P price. (a) Calculate (i) The monthly installments (2 mks) (ii) The cash price (2 mks) (b) A customer decided to buy the system in cash and was allowed a 5% discount on the cash price. He took a bank loan to buy the system in cash. The bank charged compound interest on the loan at the rate of 20% p.a. The loan was repaid in 2 years. Calculate the amount repaid to the bank by the end of the second year (3 mks) (c) Express as a percentage of the Hire Purchase price, the difference between the amount repaid to the bank and the Hire Purchase price (3 mks)
119 Pyramid Consultants P.O Box 67593 00200 Nairobi 0722614502 / 0733494581 18. In the figure below, PR is a diameter of the circle center O. Points P, Q, R and S are on the circumference of the circle. Angle PRQ = 72 0 , QS = QP and line USV is tangent to the circle at S. Giving reasons, Calculate the size of (a) ˂ QPR (2 mks) (b) ˂ PQS (2 mks) (c) ˂ OQS (2 mks) (d) ˂ RTS (2 mks) (e) ˂ RSV (2 mks) 19. (a) Complete the table below for y = x 3 +4 x 2 -5 x -5 (2 mks) x -5 - 4 -3 -2 -1 0 1 2 y= x 3 +4 x 2 -5 x -5 19 -5 (b) On the grid provided, draw the graphs of y = x 3 +4 x 2 -5 x -5 for - 5 ≤ x ≤ 2 (3 mks) (c) (i) Use the graph to solve the equation x 3 +4 x 2 5 x 5 = 0 (2 mks) (ii) By drawing a suitable straight line on the graph, solve the equation x 3 + 4 x 2 5 x -5 = - 4 x 1 (3 mks)
120 Pyramid Consultants P.O Box 67593 00200 Nairobi 0722614502 / 0733494581