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NAME....................................................................................ADM NO................CLASS............TERM 3 END YEAR MATHEMATICAL EXAM 2010121/1MATHEMATICS P1NOV. 20102?HOURSINSTRUCTION T CANDIDATESThe paper consists of two sections; section I and Section II.Answer all questions in Section I and ONLY FIVE in section IIShow all working in the spaces provided.Show all steps in your working, giving your answers at each stage.FOR EXAMINER’S USE ONLYSECTION I12345678910111213141516SECTION II1718192021222324TOTALSECTION I (50 MKS)Without using mathematical table or calculators evaluate(3 mks)3 675 x 135 2025Simplify p2 + 2pq +q2(3 MKS)P3 – pq2 p2q – q3Solve for x without mathematical tables or calculators.(3 mks)36x – 1 + 62x – 222 = 0The terms of series are given as log 2x + log4x + log8x + ............................................................... Calculate the sum of the first six terms leaving answer in the form of a logb where a and b are constants.(3 mks)A car which travels at 120km/h is 300m from another car which travels at 72km/h and moving in the opposite direction. Find time taken by the two cars to meet, and the time they will meet if time now is 1.00 pm.(3 mks)A line with a gradient of -3 passes through the points (3, k) and (k, 8). Find the value of k and hence express the equation of the line in the form x + y = 1 where a and b are constants. (3 mks) a bA Kenyan bank buys and sell currencies as followsBuying in Ksh.Selling in Kshs.1 Hongkong dollar9.749.771 south African Rand12.0312.11A tourist arrived in Kenya with 105,000 Hongkong dollars and changed the whole amount to Kenya shillings. While in Kenya she spent sh.403,879 and changed the balance to South African Rand before leaving for South Africa. Calculate the amount in South African Rand that she received.(3 mks)The length of a rectangle is (3x + 1) cm and its width is 3 cm shorter than its length. Given that the area of the rectangle is 28cm2, find its length.(3 mks)Two points P and Q have co-ordinates (-2, 3) and (1, 3) respectively. A translation point P onto P1(10, 10) a) Find the co-ordinates of Q1 the image of Q under the same translation.(1 mk)b) The position of P and Q in (a) above are p and q respectively. Given that mp – nq = -12 Find the values of m and n. (3 mks) 9 Simplify completely(4 mks)4x2 + 2x – 12 + 1 2x2 – 8 x – 2Calculate the area of a regular polygon whose exterior angle is 180 and whose side is of length 10 cm.(3 mks)A boy at the top of a cliff 30m high observes two boats P and Q out in the sea. The boats and the foot of the cliff are on a straight line. The angles of depression from the boy of P and q are 420 and 270 respectively. Calculate the distance between the two boats.(4 mks)Express 3.5671 as a simplified fraction.(3 mks)Without using logarithms table or calculator, solve for x in : log 5 -2 + log(2x + 10) = log(x - 4)(3 mks)For a lifting machine, the effort E required to lift a load L is partly constant and partly varies as L. Given that L = 2 when E = 5.5 and L = 6 when E = 6.5. Write an equation connecting E and L.(3 mks)Atieno is now four times as old as her daughter and six times as old as her son. Twelve years from now, the sum of the ages of her daughter and son will differ from her age by 9 years. What is Atieno’s present age?(3 mks)SECTION II: ANSWER ANY FIVE QUESTIONSIn the year 2007, the price of a sofa set in the shop was shs.12,000/=a) Calculate the amount of money received from the sales of shs.240 sets that year.(2mks)b) i) In the year 2008 the price of each sofa increased by 20% while the number of sets sold decreased by 10%. Calculate the percentage increase in the amount received from the sales.(3 mks)ii) If at the end of year 2008 the price of each sofa set changed in the ratio 16:15, calculate the price of each set beginning of year 2009.(1 mk)c) The number of sofa sets sold in year 2009 was P% less than the number of sold in 2007. Calculate the value of P given that the amounts of money received from sales of the two years were equal.(4 mks)Using the figure above, which is not drawn to scale, calculate to four significant figures:a) Length of AE(1 mk)b) The length of AD(3 mks)c) Area of the piece of land ABCD above.(3 mks)d) The plot ABED is to be fenced round using five strands of barbed wire leaving an entrance of 2.5m wide. The barbed wire is sold in rolls of length 480m. Calculate the number of rolls that must be bought to complete the fencing.(3 mks)A bus left Mombasa and travelled towards Nairobi at an average speed of 60km/h. After 2? hours, a car left Mombasa and travelled along the same road at an average speed of 100km/h. If the distance between Mombasa and Nairobi is 500km, determine;a. i) The distance of bus from Nairobi when car took off.(2 mks) ii) The distance the car travelled to catch up with the bus.(4 mks)b) Immediately the car caught up with the bus, the car stopped for 25 minutes. Find the new average speed at which the car must travel in order to arrive in Nairobi at the same time as the bus.(4 mks) The table shows rate of taxation per annum.K? p. aRate of tax %1-5208105209 - 9744259745 - 142922014293 – 1889015Over 1884030a)Mr Rono pays sh.5400 as P.AY.E. He is entitled to house allowance of sh. 9,000 pm and tax relief of sh.1093 pm. Calculate his monthly basic salary.(7 mks)b) Mr. Rono’s other deductions per month were co-operative shares sh. 2000 Loan repayment sh.2500Calculate his net salary per month.(3 mks)A rhombus has its vertices as PQRS. The co-ordinates of the vertex P an Q of the rhombus are P(-1,3) and Q(2, 4). The diagonal QS and PR meet at a point M. Given that the equation of the line PR is y = x + 4, finda) Equation of diagonal QS.(2 mks)b) Co-ordinates of midpoint M.(2 mks)c) Co-ordinates of point R and S.(4 mks)d) Area of the Rhombus.(2 mks)In the figure above, O is the centre of the circle. Angle AEB = 500, angle EBC = 800 and angle ECD = 300. Giving reasons calculate;i) CDE(2 MKS)ii) DFE(2 mks)iii) Obtuse COE(2 MKS)IV) ADE(2 mks)v) If AF = 10cm and AE = 4cm while C = 9cm calculate the length of CD.(2 mks)Draw the graph of the equation on the grid provided y = x3 – 9x for -4 ≤ x ≤ 4.(5 mks)b) Use your graph to solve the equationsi) x3 = 9x(1 mk)ii) y – 5 = 0(2 mks)iii) x3 – 13x – 12 = 0(2 mks)Give the inequalities which define the region R.(6 mks)b) Under enlargement scale factor -3, the point P (3, 6) is mapped onto p1(7, 180). Find the centre of this enlargement and the image of point Q (1, 1) under the same enlargement. (4 MKS) ................
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