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1、 This document consists of 12 printed pages. IB11 06_0580_21/7RP UCLES 2011 Turn over *2011* *9523289317* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education MATHEMATICS 0580/21 Paper 2 (Extended) May/June 2011 1 hour 30 minutes Candidates answ
2、er on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Mathematical tables (optional) Tracing paper (optional) READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You ma
3、y use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. If working is needed for any question it must be shown below that question. Electronic calculators should be used. If the degree of
4、accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For, use either your calculator value or 3.142. At the end of the examination, fasten all your work securely together. The number of
5、marks is given in brackets at the end of each question or part question. The total of the marks for this paper is 70. www.XtremeP 2 UCLES 2011 0580/21/M/J/11 For Examiners Use For Examiners Use 1 A concert hall has 1540 seats. Calculate the number of people in the hall when 55% of the seats are occu
6、pied. Answer 1 2 Shade the required region on each Venn diagram. ABAB A B(A B) 2 3 Calculate 810.25 42 . Answer 2 4 (a) Find m when 4m 42 = 412 . Answer(a) m = 1 (b) Find p when 6 p 6 5 = 6. Answer(b) p = 1 3 UCLES 2011 0580/21/M/J/11 Turn over For Examiners Use For Examiners Use 5 A hummingbird bea
7、ts its wings 24 times per second. (a) Calculate the number of times the hummingbird beats its wings in one hour. Answer(a) 1 (b) Write your answer to part (a) in standard form. Answer(b) 1 6 6 cm 2 cm NOT TO SCALE A company makes solid chocolate eggs and their shapes are mathematically similar. The
8、diagram shows eggs of height 2 cm and 6 cm. The mass of the small egg is 4 g. Calculate the mass of the large egg. Answer g 2 7 Find the length of the straight line from Q (8, 1) to R (4 , 6). Answer QR = 3 4 UCLES 2011 0580/21/M/J/11 For Examiners Use For Examiners Use 8 Calculate the radius of a s
9、phere with volume 1260 cm3 . The volume, V, of a sphere with radius r is V = 3 4 r3. Answer cm 3 9 AB CD 2x 5x x NOT TO SCALE AB is parallel to CD. Calculate the value of x. Answer x = 3 10 Solve the simultaneous equations. 3x + y = 30 2x 3y = 53 Answer x = y = 3 5 UCLES 2011 0580/21/M/J/11 Turn ove
10、r For Examiners Use For Examiners Use 11 A rectangular photograph measures 23.3 cm by 19.7 cm, each correct to 1 decimal place. Calculate the lower bound for (a) the perimeter, Answer(a) cm 2 (b) the area. Answer(b) cm2 1 12 A train leaves Barcelona at 21 28 and takes 10 hours and 33 minutes to reac
11、h Paris. (a) Calculate the time the next day when the train arrives in Paris. Answer(a) 1 (b) The distance from Barcelona to Paris is 827 km. Calculate the average speed of the train in kilometres per hour. Answer(b) km/h 3 6 UCLES 2011 0580/21/M/J/11 For Examiners Use For Examiners Use 13 The scale
12、 on a map is 1: 20 000. (a) Calculate the actual distance between two points which are 2.7 cm apart on the map. Give your answer in kilometres. Answer(a) km 2 (b) A field has an area of 64 400 m2 . Calculate the area of the field on the map in cm2 . Answer(b) cm22 14 Solve the equation 2x2 + 3x 6 =
13、0. Show all your working and give your answers correct to 2 decimal places. Answer x = or x = 4 7 UCLES 2011 0580/21/M/J/11 Turn over For Examiners Use For Examiners Use 15 A teacher asks 36 students which musical instruments they play. P = students who play the piano G = students who play the guita
14、r D = students who play the drums The Venn diagram shows the results. G D 5 x P 2 7 45 1 8 (a) Find the value of x. Answer(a) x = 1 (b) A student is chosen at random. Find the probability that this student (i) plays the drums but not the guitar, Answer(b)(i) 1 (ii) plays only 2 different instruments
15、. Answer(b)(ii) 1 (c) A student is chosen at random from those who play the guitar. Find the probability that this student plays no other instrument. Answer(c) 1 8 UCLES 2011 0580/21/M/J/11 For Examiners Use For Examiners Use 16 k cm The diagram shows a square of side k cm. The circle inside the squ
16、are touches all four sides of the square. (a) The shaded area is A cm2. Show that 4A = 4k2 k2. Answer (a) 2 (b) Make k the subject of the formula 4A = 4k2 k2. Answer(b) k = 3 9 UCLES 2011 0580/21/M/J/11 Turn over For Examiners Use For Examiners Use 17 C A B O T 24 NOT TO SCALE A, B and C are points on a circle, centre O. TA is a tangent to the
