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 /2 MATHEMATICS PAPER 2 TIME: 2½ HRS JULY/AUGUST 2015 DATE... BUSIA COUNTY FORM 4 JOINT EXAMINATION KENYA CERTIFICATE OF SECONDARY EDUCATION (K.C.S.E) Mathematics Paper 2 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. FOR EXAMINER'S USE ONLY SECTION I QUESTION TOTAL MARKS SECTION II QUESTION TOTAL MARKS GRAND TOTAL BUSIA - TERM

2 BUSIA COUNTY MATHEMATICS PAPER 2 SECTION I (50 MARKS) Answer ALL the questions in this Section in the spaces provided 1. Evaluate without using tables or calculator. (3 marks) of Using a calculator, simplify; 1.32 x x x x a) Given that P and Q Find PQ. (1 mark) b) Hence, find the point of intersection of the lines 4x + y = 9 and 3y =2x -1 (3 marks) 4. Solve for x, (3 marks) 2 4 log x log 8 x 2 2 log 2 5. P and Q are the points on the ends of the diameter of the circle below. Q(9,8) O P(1,2) a) Write down in terms of x and y the equation of the circle in the form; ax 2 + by 2 + x + y + c = 0 b) Find the equation of the tangent at Q in the form ax + by + c = 0. BUSIA - TERM

3 6. Expand (1-1 / 2x ) 9 up to the fourth term, hence use your expansion to evaluate , correct to 4 decimal places. (4 marks) 7. Simplify the expression. (4 marks) 2 2x 3xy 2y 2 2 4x y 2 2x y 2x y 8. The cost per kg of two brand of tea x and y are sh 60 and sh 80. The two brands are mixed and sold at a profit of 20% above the cost. if 1kg mixture was sold at sh 78, determine the ratio in which the two brands were mixed. (3 marks) 9. Make P the subject of the formula. (3 marks) YP X Q P O 10. A farmer wishes to enclose a rectangular nursery against a long straight wall. He has 40m of fencing wire. What is the largest area he can fence using the wire. (3 marks) 11. In the figure below, not drawn to scale, AX = 3cm, XB =3cm and ÐCXB =90. Given that the circle has a radius of 4.5cm. Calculate the length CD. (23 marks) A C X B D 12. Given that OA = 3i + 2j - 4k and OB = 4i + 5j - 2k. P divides AB externally in the ratio 3: -2. Determine the position vector of P in terms of i, j and k. (3 marks) 13. Find the sum of the first six terms of the progression given; Log 2x + log 4x + log 8x + log 16x +... leaving your answer in the form a log bx 2 where a and b are integers. (3 marks) BUSIA - TERM

4 14. A varies as b and inversely as the square root of C. When B is increased by 26%, C is reduced by 19%. Find the percentage change in the value of A. (4 marks) 15. Solve the equation 4-4Cos 2 x = 4Sin x - 1 for the range 0 < x < 360. (3 marks) 16. Find the quartile deviation of the following set of scores. (3 marks) 138, 121, 111, 143, 101, 120, 107, 106, 137, 141, 140. SECTION II (50 MARKS) Answer only FIVE questions from this section in the spaces provided 17. The table below shows the rates of taxation in a certain year. Income in K p.a Rate of taxation in sh per K , ,701-15, ,601-19,500 7 Above 19,500 9 In that period, Mr. Omoit a teacher at Mundika Boys earning a basic salary of Ksh. 21,000 per month. In addition, he was entitled to a house allowance of Kshs 9,000 p.m and a personal relief of Kshs 1056 /per month. a) Calculate how much income tax Mr. Omoit paid per month. (5 marks) b) Mr. Omoit s.other deductions per month were co-operative society contributions sh 2,000 loan repayment, sh 2,500/- Calculate his net salary per month. c) Later in the same year, Mr. Omoit was transferred to Katira Secondary School where he earned hardship allowance equivalent to 30% of his basic salary. If on top of deductions in (b) above he also had deduction of sh 2,700 p.m to KCT. Calculate the percentage change in his net salary per month. (3 marks) 18. A dealer wishes to purchase cookers and refrigerators. he can buy at most 60 of both items. On average, a cooker and a refrigerator costs sh 24,000 respectively. He must spend at least sh 480,000. The number of refrigerators should be at most four times the number of cookers. He must buy more than 10 refrigerators. Taking the number of cookers to be x and the number of refrigerators to be y: a) Form all inequalities to represent the above information and graph them. (5 marks) BUSIA - TERM

5 b) If the dealer makes a profit of sh 1200 and sh 2000 per cooker and refrigerator respectively, find the maximum profit he will make. c) During a sales promotion week, the dealer declared a discount of 10% and 5% on the display prices of each other cooker and refrigerator respectively. Determine his new maximum profit.(3 marks) 19. The diagram below shows a right pyramid with a horizontal rectangular base PQRS and vertex V. The area of the base is 60cm 2 and the volume of the pyramid is 280cm 3. V S R P Q a) Calculate the height of the pyramid. b) Given the ratio of the sides PQ: QR is 3:5 find the lengths of i) PQ ii) QR c) Find the length of the slanting height. d) Calculate the angle between the planes VRQ and PQRS. BUSIA - TERM

6 20. Use ruler and a compasses only for all the constructions in this question. a) Construct a triangle ABC in which AB= 6cm, BC = 7cm and angle ABC = 75. Measure: i) the length of AC ii) the angle of ACB b) Locus of P is such that BP = PC. Construct P. (4 marks) c) Construct locus of Q such that Q is on one side of BC opposite A and angle BCQ = 30. d) i) the locus of P and locus of Q meet at X. Mark X. (1 mark) ii) Construct the locus of R in which angle BRC = 120. (1 mark) iii) Show the locus of S inside the triangle ABC such that XS > SR. (1 mark) 21. I own a motorcycle. Out of the 21 working days in a month, I only ride to work for 18 days. If I ride to work the probability that I am bitten by a rapid dog is 4 / 15, otherwise it is only 1 / 3 when I am bitten by the dog, the probability that I will get treatment is 4 / 5 and if I do not get treatment, the probability that I will get rabies is 5 / 7. a) Draw a tree diagram to show the events. (3 marks) b) Musing the tree diagram (a) above determine the probability that: i) I will not be bitten by a rapid dog. ii) I will get rabies iii) I will not get rabies (3 marks) 22. The diagram below shows two intersecting circles with centres X and Y. HG is a tangent to the circle centre X at C. GCE = 70 and CEF = 130. Given that CB = 5cm, BA = 4cm, AE = 12cm and radius DY = 6cm. H C G 70 B x A D 130 E F Y a) Determine: (i) Angle DXE BUSIA - TERM

7 (ii) Length DE b) Hence, calculate the area of the shaded region. (6 marks) 23. Two places P and Q are on the parallel of latitude 26 N. The two points lie on 10 W and 30 E longitudes respectively. a) Find the distance between P and Q along their parallel of latitude in i) km (Taking R = 6370km and = 3.142) ii) nm b) Find in km the distance between points P and Q along a great circle. c) Two planes X and Y left P for Q at an average speed of 1200 knots and 5000 knots respectively. If X flew along the great circle and Y along the parallel of latitude, which one arrived earlier and by how much time? (4 marks) 24. Triangle PQR is the image of triangle ABC under the transformation where A, B and C maps onto P, Q and R respectively. a) Given the points A(5, -1) B(6, -1) and C (4, -0.5). Draw the triangle ABC and its image triangle PQR on the grid provided below. (3 marks) b) Triangle PQR in part (a) above is to be enlarged by scale factor 2 with centre at (11, -6) to map onto P 1 Q 1 R 1. Construct and label triangle P 1 Q 1 R 1 on the grid above. 2 4 m c) By construction, find the co-ordinates of the centre and angle of rotation 0 2 which can be used to rotate triangle P 1 Q 1 R 1 onto P 11 Q 11 R 11 whose vertices P 11 (-3, -1) Q 11 (-7, -1) and R 11 (-3, -3) (3 marks) d) Find the co-ordinates of the vertices of the triangles LMN, the image of triangle P 1 Q 1 R 1 under a stretch scale factor 2, line y = 2, invariant L, M and N to map onto P 1 Q 1 and R 1 respectively. ( marks) BUSIA - TERM

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