Mark Scheme (Results) January 08 Pearson Edexcel International GCSE Mathematics B (4MB0) Paper 0R
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General Marking Guidance All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last. Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions. Examiners should mark according to the mark scheme not according to their perception of where the grade boundaries may lie. There is no ceiling on achievement. All marks on the mark scheme should be used appropriately. All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, i.e. if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate s response is not worthy of credit according to the mark scheme. Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited. Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response. Types of mark o M marks: method marks o A marks: accuracy marks o B marks: unconditional accuracy marks (independent of M marks) Abbreviations o cao correct answer only o ft follow through o isw ignore subsequent working o SC - special case o oe or equivalent (and appropriate) o dep dependent o indep independent o eeoo each error or omission
No working If no working is shown then correct answers normally score full marks If no working is shown then incorrect (even though nearly correct) answers score no marks. With working If there is a wrong answer indicated on the answer line always check the working in the body of the script (and on any diagrams), and award any marks appropriate from the mark scheme. If it is clear from the working that the correct answer has been obtained from incorrect working, award 0 marks. Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work. If there is a choice of methods shown, then no marks should be awarded, unless the answer on the answer line makes clear the method that has been used. If there is no answer on the answer line then check the working for an obvious answer. Ignoring subsequent work It is appropriate to ignore subsequent work when the additional work does not change the answer in a way that is inappropriate for the question: eg. Incorrect cancelling of a fraction that would otherwise be correct. It is not appropriate to ignore subsequent work when the additional work essentially makes the answer incorrect eg algebra. Transcription errors occur when candidates present a correct answer in working, and write it incorrectly on the answer line; mark the correct answer. Parts of questions Unless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in another.
(a) 00 348 oe 60 ($) 580 (b) 75 "$580" $348 OR 00 0.40 0.5 "580" OR 0.75 0.60 "580" ($)87 x 4 y 0 4 Rearranging st coef of x or y is the same in both eqns OR isolating x or y Substituting expression (or value correctly obtained) for x or y to obtain y or x NB: Allow a total of slip in both M marks.
3 (a) 576 3 7 α = 7 f 3 r 3 (b) f = 5 + t "7" = 3 (= 9) (oe) t = 4
4 One of (ie st column) (,) : 7 x (,) : 4x 37 (3,) : 35 6x x 6 One of (ie nd column) x y y (,) : + " " y (,) : 3 4 " x" 3 (3,) : 5 6 " x" 5 y One of (ie 3 rd column) (,3) : " x" z " y" 4 (,3) : 3" x" z 4" y" (3,3) : 5" x" z 6" y" 4 z 3
5 (a) 4 B 5 correctly positioned B 5, 0 and 5 correctly positioned B 45 and 0 correctly positioned B 4x correctly positioned in T and x correctly positioned in H (b) 50 = 5 + 45 + 5 + x + 0 + 0 + 5 + 4x (oe) B ft (ie 50 = their 8 values) (c) (eg 50 = 0 + 5x (oe)) (cao) x = 6 Collecting their two x terms and equating them to their 7 constant values (d) "0" "0" "45" "5" "0" "0" "30" (oe), "0.375", "37.5"% "80" B Ft NB: ft on their diagram
6 (a) 3, 0.6 5 (b) 3 OR.5 OR not 3/ B B (c) yx3 6 (oe) OR 6 3x 3 x h - : x x, x y3 6 (oe) x, 3 3 x, 6 3x h (oe) x (d) 8x xx 3 3x 3 (removing denominators, oe, allow minor slip) x 5x 9( 0) (oe) 5 5 4 9 x NB: on their trinomial quadratic. 0.558 8.06 (INDEP)
7 (a) 65 t 70 fd = 4 (8 x cm squares) units 70 t 80 freq = 50 runners 80 t 95 fd=4units 95 t 5 fd = 4.5 units 5 t 40 freq = 75 and fd = 3 units 5 B B B B B ft (b) 95 t 5 B Ft NB: ft on 50 for 70 t 80 (c) Using a correct mid-pt At least 3 correct products 06.5 067.5 "50" 75 6087.5 9005 "75" 7.5 305 65 350 "3750" 550 9450 956.5 9987.5 305 305 98 (minutes) 4 (cao)
8 (a) (i) AB 8b4a B (ii) PO a B (b) (c) (d) 8 b a a b PQ " 8 4 " PO OQ m PR PA AR 3 a " 8b 4 a " n 4 8 PR 3 n a n b, 4 8 3a a b, 3n a 4 a 8 b n n n PR parallel to OB means comp of a in PR above is zero (OR since triangles AOB and ARB are similar, AP 3 PR, AO 4 OB 8 Comp of b in (c) means that PR 6b b n ()) 4 m 4 4 n 3 3 NB: Cand. must use vectors as required by question. NB: So a and b terms separated (e) Triangles OAB and OPQ are similar (oe) OAB 4 OPQ APQB = 50 = Triangle OAB 50 4 OPQ OPQ (oe) OPQ 0 cm OPQ 3
9 (a) Triangle S drawn and labelled B (b) (c) 3 3 Triangle T drawn and labelled T 4 4 6 Either point (-,) indicated OR At least two construction lines through (-,) 6 7 7 Triangle U U 0 0 NB: Award A if (-,) not indicated and no construction lines but U drawn correctly Award A0 if U drawn correctly except for one Vertice. B (-ee) 3 A (-ee) (d) Triangle V drawn and labelled V 3 B) ft (-ee NB: ft on triangle U (e) 3 " " 3 A (-ee) 5 3 Triangle W drawn and labelled W 3 5 (f) -4 B (g) : 4 B
0 (a) 0 sin 5 AB (b) 47.34047.3 (cm) FC cos 0 5 4.09544. (cm) (c) AC " AB" 5 " AB" 5 cos95 " " 5 " " 5 cos95 AC AB AB 3 (d) Method : ABCD ABC ACD 50.9 (cm) 6 Scheme: ABC: (angle for area formula), (area formula) ACD: (angle or side for area formula), (area formula) ABCD: (adding areas) ABC 5 80 90 0 95 NB: ABC must be evaluated to 95 ABC 5 " AB " sin" ABC " 353.6 using 4sf 353.4 using 3sf )
( Point X is st AD is perpendicular to CX AX 0 " FC" ) " AX " cos CAD CAD o 47.94 using 3sf answers o " AC" 47.9 using 4sf answers () ( ACD 40 " AC " sin" CAD " 755. using 4sf 755.8 using 3sf [OR CX " AC " " AX " ACD 40 " CX " ] NB: (OR ABC 5 80 90 0 95 ABC must be evaluated to 95 ) ( ( ( ) ) ) 5 sin 95 BAC sin 7.07 "50.9" ABC "47.34" "50.9" sin" BAC "
CAD 65 "7.07" 47.93 ) ACD 40 "50.9" sin" 65 7.07 " Finally: ABCD " ABC " " ACD " 08.8 using 4sf 09. using 3sf ABCD = 0 (cm ) Method : ABCD = ( ABE BCF ) + CFED Scheme: ABE + BCF: (full method for area) CFED: (side or angle need to find CX), (full method for CX), (area formula for CFED) ABCD: (adding areas), ABCD = ( ABE BCF ) + CFED ( ABE BCF ) = " AB" 0sin 65 " FC" 5sin 0
464.85 using 3sf 465.06 using 4sf Point X is st AD is perpendicular to CX AX 0 " FC" CX " AC " " AX " 37.79 using 3sf 37.76 using 4sf (OR 0 tan 5 (BE = 4.89) () BE FE = CX = " BE" 5sin 0 ()) CFED " CX " " FC " 0 644.3 using 3sf 643.7 using 4sf ABCD = ( BCF ABE ) + CFED 08.8 using 4sf 09. using 3sf ABCD = 0 (cm ) Method 3: ABC ACX CXD Scheme: ABC: (angle for area formula), (area formula) 6
ACX: (full method for area formula) CXD: (full method for area formula) ABCD: (Adding areas) ABCD = ABC ACX CXD ABC 5 80 90 0 95 NB: ABC must be evaluated to 95 ABC 5 " AB " sin" ABC " 353.6 using 4sf 353.4 using 3sf ( Point X is st AD is perpendicular to CX AX 0 " FC" ) BE 0 tan 65 4.89 and BF 5sin 0 5.30 FE 37.7598 ACX "34.095" "37.76" 643.78 DX 0 "4.095" 5.905 CXD 37.76 5.905.479
ABCD = 353.4 + 643.78 +.479 (=.479) ABCD = 08.6 0 Method 4: ABE BED BCD Scheme: ABE + BED : (area formula for ABE), ( ABE = BED) BCD: (full method for DBC), (area formula) ABCD: (Adding areas), ABE BED BCD (BE = 0tan65 = 4.89) 6 ABE 0 "4.89" (= 48.9) and ABE BED (Congruence) DBE 5 DBC 70 5 45 BCD 5 "47.34" sin"45" 50.97 ABCD = 48.9 + 48.9 + 50.97 ABCD = 08.770
(a) 4 3 3x x 6x 9x 6 ( Expanding, allow slip) (OR 4 3 3 a 6 9 6 0 3 3 3 3 ()) cc (b) dy 3x 6x (differentiating, one term correct) dx "3x 6 x" 0 3x x (solving term quadratic) (0, 3) and (, Working must be seen 4 (c) 3 (3), [Accept 8 Accept Accept 7 8 64 ] NB : () Do not award respective for (b) in (c). () dp answers required, penalise ONCE 3 B3 eeoo)
(d) Curve - mark for straight line segments each point missed each missed segment each point not plotted each point incorrectly plotted tramlines very poor curve NB: () Accuracy for both plotting and drawing is ss = ±0.05 () Deduct errors starting with the last epen mark box 3 B3 eeoo) (e) to Accept 3 ) ie.3 to.38) ieto.56) 4 B B B B