BUSIA COUNTY FORM 4 JOINT EXAMINATION KENYA CERTIFICATE OF SECONDARY EDUCATION (K.C.S.E)

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1 NAME... INDEX NUMBER... SCHOOL... SIGNATURE /1 MATHEMATICS PAPER 1 TIME: 2½ HRS JULY/AUGUST 2015 DATE... BUSIA COUNTY FORM 4 JOINT EXAMINATION KENYA CERTIFICATE OF SECONDARY EDUCATION (K.C.S.E) Mathematics Paper 1 July/August 2015 Time: 2½ hours INSTRUCTIONS TO CANDIDATES a) Write your name, Index number, school, signature and date in the spaces provided above. b) This paper consists of two sections: Section I and section II c) Answer all the questions in Section I and only five questions from Section II. d) All answers and workings must be written on the question paper in the spaces provided below each question. e) Show all the steps in your calculations, giving your answers at each stage in the spaces provided below each question. f) Marks may be given for correct working even if the answer is wrong. g) Non programmable silent electronic calculators and K.N.E.C Mathematical tables may be used, except where stated otherwise. h) Answer ALL questions in English. SECTION I FOR EXAMINER'S USE ONLY QUESTION TOTAL MARKS SECTION II QUESTION TOTAL MARKS GRAND TOTAL BUSIA - TERM

2 BUSIA COUNTY MATHEMATICS PAPER 1 SECTION I (50 MARKS) Answer ALL the questions in this Section in the spaces provided 1. Evaluate without using tables or a calculator A line L is perpendicular to 3y - 4x = 7. Determine the acute angle between L and the x-axis. 3. Two trucks P and Q approach each other at 52km/h and 61km/h respectively. Truck P is 12.5m long and Q is 13m long. If they are 5m apart how many seconds elapses before the two completely pass each other. Give your answer to 2d.p (4 marks) 4. Find a scalar K such that (2 marks) K The ratio of Omondi and Kamau s earning was 4:3. Omondi s earning rose to sh 22,800 after an increase of 14%. Calculate the percentage increase in Kamau s earnings given that the sum of their earnings was ksh of each got an increment. (4 marks) 6. The interior angles of an irregular polygon are 70 and 110 and the rest are each 144. Determine the number of sides of the polygon. 7. Either by striding 48cm or 54cm, Joan takes an exact number of steps to cross the road. Find the least width of the road in metres. 8. Use logarithms to 4 d.p to evaluate: (4 marks) (0.58) The present ages of two children are 3 years and 5 years respectively. After how long will the sum of the squares of their ages be 130? 10. Pamba bought 4 mobile phones and 2 laptops for ksh, 108,000. Rebecca bought 3 mobile phones and 5 laptops from the same shop for ksh 228,000. How much will Juma pay for one mobile phone and 2 laptops. BUSIA - TERM

3 11. Using a pair of compasses construct a trapezium ABCD such that AB is parallel to DC. AB = 8.5cm BC = 5cm BAD = 90 and BCD =120. Measure the shortest distance from C to line AB. 12. The angle of elevation of the top of a flag post from a point A on the level ground is 12. The angle of elevation of the top of the flag post from another point B nearer to the flag post and 98m away from A is 34. B is in between A and the bottom of the flag post and the three points are collinear. Find the height of the flag post to the nearest metre. 13. Find a 2 x matrix m such that; m 2 1 ~ A car dealer buys a car for Ksh 1,500,000 and hires it for 24 weeks at a charge of ksh 3000 per day. Insurance costs Ksh 42,000 during the entire period. He sold the car through a dealer at sh 800,000. If the dealer was paid a commission of 2½% calculate the percentage profit made. 15. Given that 5x = 4y, evaluate 1 4 x 2 4xy y 4x 2 y x ( x 1)( x 2) 1 dx SECTION II (50 MARKS) Answer only FIVE questions from this section in the spaces provided 17. A ship sails from A to D through B and C. B is 500km on a bearing of N50 E from A. C is on a bearing of 340 from B and at a distance of 620km. The bearings of D from A and C are N20 W and 560 W respectively. a) Using the scale 1cm to rep 100km, show the relative positions of A, B, C and D. (4 marks) b) Find the distance of D from: i) A ii) C (2 marks) c) Find the bearing of D from B. (1 mark) d) If the ship was sailing at an average of 500km/h. Find how long the journey took. Give the answer to the nearest hour. BUSIA - TERM

4 18. a) Complete the table below for y = 8-10x - 3x 2. (2 marks) x y b) On the grid provided, draw the graph of y = 8-10x -3x 2 c) state the equation of the line of symmetry of y = 8-10x - 3x 2 (1 mark) d) Use your graph to solve: i) 3x x - 8 = 0 (1 mark) ii) 3x x + 6 = In the figure below AOD is a diameter of the circle centre O. BC is a chord parallel to AD and FE is a tangent to the circle at E. E F B M C A O D Given that OF bisects AOB and M is the intersection of BC and OE and EBC = BOE = 20. Giving reasons find the following angles. i) COE (2 marks) ii) BEC iii) BEF iv) OMB (2 marks) (2 marks) (2 marks) v) OFE (2 marks) BUSIA - TERM

5 20. The table below gives the marks scored by a group of students in an exam. Marks No. of students 3 4 x a) Given that the mean mark was , find x. (4 marks) b) State the modal class. (1 mark) c) Calculate the interquartile range. (5 marks) 21. The equation of a curve is given by y =x 3-5x 2 + 2x + 9 a) Find the gradient function of the curve and its value when x = -2. b) Determine i) the equation of the tangent to the curve at x = -2. ii) the equation of the normal to the curve at x = -2. (2 marks) c) The values of x at the turning points of the curve. (2 marks) 22. A glass is in the shape of a frustum of a cone. The bottom of the glass is a curve of radius 2cm. A father pours water into the glass to a height of 9cm, while the surface of the water is a circle of radius 6cm. a) Calculate the volume of the water in the glass. (4 marks) b) The son who is playing with marbles drops two spherical balls into the water. The water level in the glass rises by 1.5cm as a result. Calculate: i) the volume of one marble. (4 marks) ii) the radius of a marble. (2 marks) BUSIA - TERM

6 23. Two circles centres O and C have radii 7.2cm and 6.5cm respectively. The two circles intersect at P and Q and PQ =10cm. O 7.2 P 6.5 C Q a) Find (i) POQ (2 marks) (ii) PCQ (2 marks) b) The area of the shaded part. Give answer to 4s.f (4 marks) c) Express POQ in radians. (2 marks) 24. On a certain day Mwema bought plates worth Ksh 120. On another day Mrs Mwema spent the same amount of money but bought the plates at a discount of 20% per plate. a) If Mwema bought a plate at sh x write down a simplified expression for the total number of plates bought by the two people. b) If Mrs. Mwema bought 6 plates more than her husband find how much each spent on a plate. (5 marks) c) Find the total number of plates bought by the family. (2 marks) BUSIA - TERM

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