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This document consists of 11 printed pages and 1 blank pages. IB09 06_0842_02/2RPMS © UCLES 2009 [Turn over *6542811678* UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge International Primary Achievement Test MATHEMATICS 0842/02 Paper 2 May/June 2009 MARK SCHEME Maximum Mark : 39 IMPORTANT NOTICE Mark Schemes have been issued on the basis of one copy per Assistant examiner and two copies per Team Leader.

2 © UCLES 2009 0842/02/M/J/09 Mathemati\bs mark s\bhem\–es – A\bhievement Test \– Guideline\b for marking\m te\bt paper\b These ma\bk schemes a\g\be designed to p\bovid\ge you with all the info\bma\gtion necessa\by to ma\g\bk the P\bima\by Mathematics A\gchievement Tests. \gAs fa\b as possi ble, the ma\bk scheme\gs give you full guid\gance \bega\bding acceptable a\gnd unacceptable alt\ge\bnativ e answe\bs and, whe\b\ge app\bop\biate, includ\ge examples of studen\gt wo\bk to illust\bate\g the ma\bking points. Howeve\b, \git is not always po\gssible to p\bedict all the alte\g\bnative answe\bs that\g may be p\b oduced by students \gand the\be could be \gplaces whe\be the ma\bke\b will\g have to use thei \b p\bofessional judgem\gent. In these cases\g it is essential tha\gt such judgement be ap\gplied consistently. \g The guidelines below\g should be followe\gd th\boughout ( unle\b\b the mark \bcheme \m\btate\b otherwi\be):  A co\b\bect answe\b shou\gld always be awa\bde\gd full m a\bks even if the wo\b\gking shown is w\bong. \g  Whe\be mo\be than one \gma\bk is available fo\g\b a que stion the ma\bk schem\ge explains whe\be ea\gch ma\bk should be awa\bd\ged. In some cases m\ga\bks a\be available fo\b demon\gst\bation of the co\b\be\gct method even if the \gfinal answe\b is inco\b\g\bect. The method ma\bks \gcan be awa\bded if th\ge co\b\bect method is used but \ga mistake has been \gmade in t he calculation, \besu\glting in a w\bong answ\ge\b. Method ma\bks can als\go be awa\bded if the\g calcu lation is set up an\gd pe\bfo\bmed co\b\bectly\g but inco\b\bect values have\g been used, e.g. du\ge to mi s\beading the question\g o\b a mistake ea\blie\b\g in a se\bies of calculation\gs.  If a question uses t\ghe answe\b to a p\bev\gious ques tion o\b pa\bt question\g that the student \g answe\bed inco\b\bectly,\g all available ma\bks\g can be aw a\bded fo\b the latte\g\b question if app\bop\bi\gate calculations a\be pe\bf\go\bmed co\b\bectly using \gt he value ca\b\bied fo\bw\ga\bd. Places whe\be s\guch conside\bation should\g be made a\be indicat\ged in the m a\bk schemes. In thes\ge cases, it is not possible to p\bovide \gall the alte\bnative\g acc eptable answe\bs and\g the ma\bke\b must fol\glow the student’s wo\bking to \gdete\bmine wh ethe\b c\bedit should \gbe given o\b not.  Half ma\bks should n\got be awa\bded and a\gt no poin t should an answe\b \gbe awa\bded mo\be tha\gn the maximum numbe\b \gof ma\bks available, \g\beg a\bdless of the quali\gty of the answe\b.  If the student has \ggiven mo\be than one \ganswe\b, the ma\bks can be aw\ga\bded if all the an\gswe\bs given a\be co\b\bect. Ho\gweve\b, if co\b\bect and\g inco\b\bect answe\bs a\be\g given togethe\b, ma\bk\gs should not be awa\bded (ma\bks\g fo\b co\b\bect wo\bking ou\gt can still be gaine\gd).  If the answe\b line is\g blank but the co\b\be\gct answe \b is given elsewhe\be,\g e.g. an annotation\g on a g\baph o\b at the end \gof the wo\bking out, \gthe ma\bk s can be awa\bded p\bo\gvided it is clea\b tha\gt the student has unde\bst\good the \bequi\bements \gof the question.  If the \besponse on t\ghe answe\b line is in\gco\b\bect but t he co\b\bect answe\b is \gshown elsewhe\be, fu\gll ma\bks can still be a\gwa\bded if the stude\gnt has made t he e\b\bo\b when copying\g the answe\b onto the answe\b line. If\g the inco\b\bect final \ganswe\b i s the \besult of \bed\gundant additional w\go\bking afte\b the co\b\bect ans\gwe\b had been \beached\g, the ma\bks can be awa\g\bded p\bovided the ex\gt\ba wo\bk does not cont\ba\gdict that al\beady do\gne.  Each question and pa\b\gt question should be\g consi de\bed independently\g and ma\bks fo\b one question should not \gbe disallowed if th\gey a\be cont\badicted by wo\bkin\gg o\b answe\bs in anot\ghe\b question o\b pa\bt ques\gtion.  Any legible c\bossed-o\gut wo\bk that has no\gt bee n \beplaced can be ma\g\bked; but, if wo\bk has\g been \beplaced, the c\bosse\gd-out pa\bt should b\ge igno\bed.

3 © UCLES 2009 0842/02/M/J/09 [Turn over  If the student’s \bes\gponse is nume\bically\g o\b alge b\baically equivalent \gto the answe\b in th\ge ma\bk scheme, the ma\bk sho\guld be given unless\g a pa\b ticula\b fo\bm of answ\ge\b was specified by \gthe question.  Diag\bams, symbols o\b \gwo\bds a\be acceptable\g fo\b explanations o\g\b \besponses.  Whe\be students a\be \be\gqui\bed to indicate the\g co\b\bect answe\b in a \gspecific way, e.g. by\g unde\blining, ma\bks sh\gould be awa\bded fo\b\g any unambi guous indication, e.g\g. ci\bcling o\b ticking.  Any method of sett\ging out wo\bking shoul\gd be accepted.  Standa\bd \bules fo\b ac\gceptable fo\bmats of\g answe\b s involving units, m\goney, du\bation and \gtime a\be given ove\bleaf. \g Each question on the \gtest pape\b has a bo\gx beside it fo\b t he teache\b to \beco\bd \gthe ma\bk obtained. \gIt is advisable to use th\gese boxes so that \gstudents, and othe\bs looking at th\ge test pape\bs, can \gclea\bly see whe\be the ma\bks have\g been awa\bded. It should also be n\goted that ma\bking in \g\bed ink and using the ma\bk boxe\gs is an essential \be\gqui\bement fo\b the Achievement \gtests. General rule\b for alte\mrnative an\bwer\b In most places on th\ge ma\bk schemes accept\gabl e and unacceptable \galte\bnative answe\bs a\be give\gn in detail, howeve\b som\ge gene\bal \bules a\be \ggiven ove \bleaf and a\be not n\gecessa\bily \bepeated \gin full fo\b each question that t\ghey apply. Number and Place valu\me The table shows va\g\bious gene\bal \bules i\g n te\bms of acceptabl\ge decimal answe\bs. Accept Accept omission of l\geading ze\bo if answe\b is clea\bly \gshown, e.g. .675 Accept tailing ze\bos, \gunless the question \gha s asked fo\b a specif\gic numbe\b of decimal \gplaces, e.g. 0.7000 Always accept app\bop\g\biate tailing ze\bos, e\g.g. 3.00m; 5.000kg Accept a comma as a \gdecimal point if tha\gt is that convention\g that you have tau\gght the students, e\g.g. 0,638

4 © UCLES 2009 0842/02/M/J/09 Unit\b Fo\b questions involvin\gg quantities, e.g. le\gngth, m ass, time o\b money,\g co\b\bect units must b\ge given in the answe\b. The ta\gble shows acceptabl\ge a nd unacceptable ve\bs\gions of the answe\b \g1.85m. Correct an\bwer Al\bo accept Do not accept Units a\be not given o\gn answe\b line and question do\ges not specify unit fo\b the\g answe\b. 1.85m Co\b\bect conve\bsions p\bovided that the unit is stated, e.g.\g 1m 85cm 185cm 1850mm 0.00185km 1.85 185m If the unit is given \gon the answe\b line, e.g. ……………………………m …..1.85…… m Co\b\bect conve\bsions, p\bovided the unit is\g stated unambiguously, e.g. …..185cm….. m …..185……m …..1850.… m etc. If the question stat\ges the unit that the answe\b sho\guld be given in a specified unit, \ge.g. “Give you\b answe\b in m\get\bes” 1.85m 1.85 1m 85cm 185; 1850 Any conve\bsions to othe\b units, e.g. 185cm Note: if the answe\b line \gis left blank but t\ghe co\b\be ct answe\b is given el\gsewhe\be on the page\g, it can be ma\bked co\b\bect if the \gunits match those o\gn the answe\b line o\g\b a\be unambiguously \gstated.

5 © UCLES 2009 0842/02/M/J/09 [Turn over Money Fo\b questions involvin\gg money, it is essen\gtial that app\bop\biat\ge units a\be given in \gthe answe\b. The table shows acc\geptable and unaccep\gtable ve\bsions. Accept Do not accept If the amount is in \g dolla\bs and cents, \gthe answe\b should be giv\gen to two decimal place\gs. $0.30 $9 o\b $9.00 If units a\be not give\gn on answe\b line Any unambiguous indi\gcation of the co\b\bect amount, \g e.g. 30 cents; 30 c $0.30; $0.30c; $0.30cents $0-30; $0=30; $0:30 30 o\b 0.30 without a un\git Inco\b\bect o\b ambiguous \ganswe\bs, e.g. $0.3; $30; $30cents; 0.30cent\gs If $ is shown on the\g answe\b line $....... 0.30……. $....... 0.30 cent\b…. Accept all unambiguo\gus indications, as show\gn above $....... 30……. $....... 30 cent\b…. (this cannot be accepted because it \gis ambiguous, but if the dolla\b s\gign is deleted it becomes acceptable) If cents is shown on\g the answe\b line ....... 30…….cents ....... $0.30 …….cents ....... 0.30 …….cents ....... $30…….cents

6 © UCLES 2009 0842/02/M/J/09 Duration Accept any unambiguo\gus method of showin\gg du\batio n and all \beasonabl\ge abb\beviations of h\gou\bs (h, h\b, h\bs), minutes (m,\g min, mins) and secon\gds (s, sec, secs). \g Accept Do not accept Any unambiguous indi\gcation using any \beasonable abb\beviat\gions of hou\bs (h, h\b,\g h\bs), minutes (m, min, mins\g) and seconds (s, se\gc, secs), e.g. 2 hou\bs 30 minutes; 2h \g30m; 02h 30m 5 min 24 sec; 00h 05m 24s Inco\b\bect o\b ambiguous \gfo\bmats, e.g. 2.30; 2.3; 2.30 hou\bs; 2.30 \gmin; 2h 3; 2.3h Any co\b\bect conve\bsion\g with app\bop\biate un\gits, e.g. 2.5 hou\bs; 150 mins 324 seconds 2.5; 150 324 Also accept unambigu\gous digital stopwatc\gh fo\bmat, e.g. 02:30:00 00:05:24; 05:24s Do not accept ambiguo\gus indications, e.g. \g 02:30 5.24

7 © UCLES 2009 0842/02/M/J/09 [Turn over Time The\be a\be many ways\g to w\bite times, in \gboth nu mbe\bs and wo\bds, an\gd ma\bks should be a\gwa\bded fo\b any unambiguous met\ghod. Accept time w\b\gitte n in numbe\bs o\b wo\bd\gs unless the\be is a\g specific inst\buction in the que\gstion. Some examples a\be given \gin the table. Accept Do not accept Any unambiguous indi\gcation of co\b\bect ans\gwe\b in numbe\bs, wo\bds o\b a \gcombination of the t\gwo, e.g. 07:30, 19:00 0730; 07 30; 07.30; 07,30; 07-30; \g7.30; 730 a.m.; 7.30am; 7.30 in the mo\bn\ging Half past seven (o’c\glock) in the mo\bning Thi\bty minutes past \gseven am Also accept: O-seven-t\ghi\bty 1900; 19 00; 19_00 etc. Nineteen hund\bed (hou\g\bs) Seven o’clock in the a\gfte\bnoon/evening Accept co\b\bect conve\bs\gion to 12-hou\b clock, e\g.g. 16:42 4:42 p.m. Sixteen fo\bty two Fou\b-fo\bty-two in the \gafte\bnoon/evening Fou\b fo\bty two p.m. \g Fo\bty two (minutes) pa\gst fou\b p.m. Eighteen (minutes) to \gfive in the evening \g Also accept a combin\gation of numbe\bs an\gd wo\bds, e.g. 18 minutes to 5 p.m. \g 42 minutes past 4 in t\ghe afte\bnoon Inco\b\bect o\b ambiguous \gfo\bmats, e.g. 07.3; 073; 07 3; 730; 73; 7.3; 7.\g3am; 7.30p.m 19; 190; 19 000; 19.00am; 7.00am \g 4.42am; 0442; 4.42 Fo\bty two (minutes) pa\gst sixteen Eighteen (minutes) to \gseventeen

8 © UCLES 2009 0842/02/M/J/09 Question Mark Answer 1 2Nn7 1 91, 79, 47, 43 Question Mark Answer 2 3Nn12 1 Any 2 chickens circled Question Mark Answer 3a 3Nc4 1 65 b 3Nc14 1 900 Question Mark Answer 4a 3P8 2 2 marks for correct answer ($)34.73 1 mark for evidence of: 35.27 + 30 and 100 – 65.27 (or pupil’s own answer) = wrong answer N.B. $5 x 6 is insufficient working for 1 mark b 4P6 2 No – with correct calculation e.g. 22.43 x 3 = 67.29 or 65 ÷ 22.43 = 2.8979 < 3 Also accept estimated calculations such as: 22 x 3 = 66 > 65 Allow 1 mark for No unsupported by correct calculation Question Mark Answer 5a 4Nn1 1 43 075 b 4Nn1 1 six thousand, four hundred and fifty-nine Accept any answer that is recognisable as the correct answer (misspelling is allowed) Question Mark Answer 6 4Nn10 1 765 and 567 should be circled

9 © UCLES 2009 0842/02/M/J/09 [Turn over Question Mark Answer 7 4Nc15 1 256 + 58 = 314 Question Mark Answer 8 4P5 1 6 (pencils) Do not accept 6 3 2 or 6 remainder 10 Question Mark Answer 9 4P4 1 Half of 60 is 30, half of 8 is 4, so 30 add 4 is 34 or equivalent correct explanation Sentences containing figures are acceptable. Question Mark Answer 10a 4D5 1 5 b 4D5 1 12 Question Mark Answer 11a 3Ss3 1 2 (lines of symmetry) b 4Ss1 1 accept rectangle or rhombus Accept a correct drawing showing a shape with two lines of symmetry Question Mark Answer 12a 4Sp8 1 90° b 4Sp7 1 4

10 © UCLES 2009 0842/02/M/J/09 Question Mark Answer 13a 5Sp1 1 (3, 1) b 5Sp1 1 Cross in the correct place (7,6) 0 012345678 1 2 3 4 5 6 7 8 x Question Mark Answer 14a 6Nn4 1 17, 19 They must be written in the correct order to get the mark. b 6Nn8 1 2 c 6Nn8 1 no Question Mark Answer 15 6Nc3 1 23178.8 Question Mark Answer 4 5 9 11 6 1 16 6P2 3 3 7 8 All four correct 3 marks Three correct 2 marks Two correct 1 mark One or none correct 0 mark

11 © UCLES 2009 0842/02/M/J/09 Question Mark Answer 17a 6D3 1 yes b 6D3 1 accept either: mean = 18 secs or: mode / median = 18.2 secs c 6D5 1 certain likely unlikely impossible Question Mark Answer 18 6Sm6 2 5.85 m² 2.5 x 1.8 = 4.5 m² 1.5 x 1.8 ÷ 2 = 1.35 m² 4.5 + 1.35 = 5.85 m² Units must be given. Allow 1 mark if correct working out shown but incorrect final answer. Question Mark Answer 19 6Nc9 1 3 1 Question Mark Answer 20 6Nn13 1 15 (red flowers) Question Mark Answer 21 6Sm2 1 2395 (kg) Question Mark Answer 22a 6Sm6 1 2 cm, 1 cm and 6 cm (working from the top down) b 6Sm6 1 26 cm

12 Permission to reproduce items where thir d-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to t race copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opport\ unity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a depa\ rtment of the University of Cambridge. 0842/02/M/J/09 BLANK PAGE