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456/1 MATHEMATICS Paper 1 September 2012 2 1 hours 2 POST MOCK EXAMINATION Uganda Certificate of Education MATHEMATICS PAPER ONE DURATION: 2hrs. 30mins. Instructions: i) ii) iii) Attempt all questions in section A and not more than 5 in section B. All necessary working must be shown on the same sheet of paper as the rest of the answer. Simple, silent non-programmable calculators may be used. SECTION A 40 MARKS 1 2 b 2a , evaluate 7 * 5 * 2 . 3 3x 5 y 9 1. Given that a * b 2. Use matrix method to solve the equations: 3. A solid cone has a base radius of 5cm and height 12cm . Calculate the total surface area. (4 marks) 4. Solve the equation: log 10 10 x 50 log 10 x 4 2 5. A function is defined by g x i) ii) 6. 2 y 5 x 16 (4 marks) (4 marks) (4 marks) x2 4 . Find: x 2 5x 6 values of x for which g x 0 values of x for which g x is not defined. (4 marks) P varies as Q and inversely proportional to the square of R , given that P 3 when R 2 and Q 6 , find the value of Q when P 2 and R 3 . 7. Given that A1, 3 and B13, 12 , the point X divides AB in the ratio 1 : 2 , find the length of AX . (4 marks) © MATHEMATICS DEPT @ RGSS Page 1 8. Edward wanted to exchange Kenyan shillings Ksh 540,000 to Tanzanian shillings (TZsh ) . It is given that 1 Ug sh 1.8 TZsh and 1 Ksh 25 Ugsh . Calculate how much (TZsh ) Edward got. (4 marks) 9. In the figure above, angle OQP 40 o , find the length OQ and OP .(4 marks) 10. The line through the points A1, 3 and B 3, 5 is perpendicular to the line through Q1, 4 . Determine the equation of the line through Q . SECTION B (60 Marks) Attempt only (FIVE) questions in this section 11. a) b) c) d) 12 The marks below were obtained by some students in a Math test. 5.1 5.6 6.7 3.0 2.1 4.2 3.4 3.8 8.3 3.8 7.5 4.5 3.4 3.8 5.8 5.0 5.6 7.6 9.1 8.7 2.5 5.6 2.7 6.4 6.1 9.2 9.0 6.4 4.0 4.9 7.7 5.4 5.8 4.6 7.5 5.2 6.0 6.6 2.2 9.4 4.4 5.2 3.4 6.4 7.2 8.0 5.2 4.4 Draw a frequency distribution table of equal class intervals of 10 beginning with 2.0 Using a Working mean of 5.45, calculate the average mark. Draw a histogram and use it to estimate the mode. Calculate the median. A triangle ABC with vertices A2, 5 , B2, 1 and C5, 1 is rotated through a half turn by a matrix M to form the image A' B' C ' . a) Determine the matrix M and the coordinates of A' B' C ' . b) A' B' C ' is then reflected along the line x 0 by a matrix of transformation N to form triangle A' ' B' ' C ' ' . Determine matrix N and the coordinates of A' ' B' ' C ' ' . c) Plot triangle ABC and its images on the same axes and describe fully the transformation that maps A' ' B' ' C ' ' back to ABC . © MATHEMATICS DEPT @ RGSS Page 2 13a) b) c) 14. i) ii) iii) iv) 15. a) b) c) d) Using a ruler and pair of compasses only, construct a quadrilateral ABCD in which AB 5cm , BC 6cm , , CD 9cm angle ABC 60 o and BCD 135 o . Drop a perpendicular from D to meet BC at M. Construct the circumference of triangle CDM and determine: i) the length of AD ii) the radius of the circle. Mrs Opio bought 3kg of sugar, 2 loaves of bread and 3litres of milk. Mrs Musoke bought 4kg of sugar, 3 loaves of bread and 3litres of milk. Mrs Dubai bought 2kg of sugar, 4 loaves of bread and 5litres of milk. The prices at the local shop for 1 kg sugar, 1 loaf of bread and 1 litre of milk are shs 2000, shs 1400 and shs 800 respectively, while at the super market the corresponding prices are shs1700, shs1000 and shs 700 respectively. The return journey for each lady is shs 1400. Write down a 3 X 3 matrix for the commodities bought. Write down a 3 X 3 matrix for the prices of the commodities. Determine by matrix multiplication the total expenditure for each person from each of the shops. Calculate the percentage savings Mrs Musoke makes by buying the commodities at the super market. A tailor makes two types of dresses: Casual wear and Party wear. Two materials A and B are used. Material A is limited to 20 metres and material B is limited to 15 metres. The table below shows the size for each material takes for a dress and the profit made. Dress Material A Material B Profit Casual 2m. 3m. $12 Party 4m. 1m. $10 Write down all the inequalities that satisfy this information. Represent these inequalities on a graph. Find the maximum profit. Find how many dresses of each type should be made to maximize the profit. © MATHEMATICS DEPT @ RGSS Page 3 16a) If hx nx m , and h4 19 and h5 22 , find n and m , and hence h 6 . b) Given that f 1 x 3x , find f x and hence f 5 and f 5 . 4x 5 17a) A balanced die and a balanced tetrahedron are tossed together. The faces of the die are marked 1 to 6 while those of the tetrahedron are marked 1 to 4. i) Make a table to show the possible outcomes of the experiment. ii) Find the probability that the numbers appearing on top are the same or the sum of the numbers appearing on top is greater than 7. b) i) ii) Gabriella picks two balls in succession from a basket containing 4 white balls and 5 Yellow balls without replacement. Find the probability that the two balls picked are: of the same colour. of different colours. SUCCESS END © MATHEMATICS DEPT @ RGSS Page 4