Mark Scheme (Results) January Pearson Edexcel International GCSE Mathematics A (4MB0) Paper 01R

Transcription

1 Mark Scheme (Results) January 018 Pearson Edexcel International GCSE Mathematics A (4MB0) Paper 01R

2 Edexcel and BTEC Qualifications Edexcel and BTEC qualifications come from Pearson, the world s leading learning company. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. For further information, please visit our website at Our website subject pages hold useful resources, support material and live feeds from our subject advisors giving you access to a portal of information. If you have any subject specific questions about this specification that require the help of a subject specialist, you may find our Ask The Expert service helpful. Pearson: helping people progress, everywhere Our aim is to help everyone progress in their lives through education. We believe in every kind of learning, for all kinds of people, wherever they are in the world. We ve been involved in education for over 150 years, and by working across 70 countries, in 100 languages, we have built an international reputation for our commitment to high standards and raising achievement through innovation in education. Find out more about how we can help you and your students at: January 018 Publications Code 4MB0_01R_1801_MS All the material in this publication is copyright Pearson Education Ltd 018

3 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

4 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.

5 1 x x 3z z x 3 z OR x x z 3z x z x zx 3z OR Factor tree (prime factors of 16 or 61) HCF = km 4.55 litres 91 litres (oe) 48 (km per gallon) 4 (a) 0 1 B1 (b) 1 B (m) (oe) for either of the other two lengths of the triangle 6 Shaded area = (oe, can be implied) awrt 3.43 (cm ) OR (Accept ) OR (oe)

6 9 BC (oe) BC = 6 (cm) 10 (1,5), (5,1), (, 4), (4,), (3, 3) OR a 6 x 6 table with 5 possible double rolls identified OR at least 3 correct probability products added All 5 correct probability products added, , awrt 0.139, 13.9% OY 6 4 OY "3" " 4" Second M mark for the modulus of their OY but not for OX or YX NB: Accept working for YO 5 (obtained from correct working) A0 max if OY 3 4 used 1 BCD 45 or DBC 45 and ACE=60 OR Join AB ABC 60 (Alt. Seg Thm) RBA=75 3 B1 B1 B1 ACB 75 o s on straight line an d Tangents to a circle have the same length. OR s on straight line and Isosceles s OR (From 1 st B1: Alternate Segment Thm twice)) NB: Accept angles on diagram

7 13 4x 45 9x Condone lack of brackets for only 45 = 5x (oe) x = 3 Accept x or 3 (Pythagoras) (3) NB: No working shown scores M0 M0 A0 even if correct answer given. 15 (a) 3, 6, 9, 1, 15 only 1 B1 (b) C = {6, 1, 18,, 48} First B mark in (b) can be implied by A B C {3, 9, 15} (so C ={3, 9,, 45}) 3 B1 B1 B1 A B C {3, 9, 15} NB: ft on (a) n A B C 3(cao) 16 (a) (b) B (-1eeoo) B (-1eeoo)

8 17 x1.05 New R or (oe) y = or 1.4 or R (oe) 7 " " 1R 5 increase = 100 (oe) R 3 rd M mark for correct method to convert to required % , , etc. e.g. 40% w 5y x x 3y 5y x 18 (removing denominators correctly) 5yw xw x 6y 10y 4x (expanding) (OR w5y x 8y x (removing denominators) 5yw xw 16y x (expanding) ) 5yw 16y x xw (collecting terms in y) x w 1, xw y x (oe) 5w16 5w16 19 (a) (oe, no errors) 4 ( ) ( ) (b) 55 85, NB: No working seen scores M0 A NB: ft on 4 figure accuracy of their (a) giving their 3 sf answer 1 B1 ft (c) (or better) 1 B1 ft

9 0 (a) 4 1 (one term correct) t 4 "1 " 0 (equating their t f(t) to 0) t = + (cao) 4 4 "" 8 (oe) "" (metres) 1 (a) x + y = B1 (b) x y (oe) 1 B1 (c) x x " 1" " " (oe but complete method to solve SEs for x and y with no errors) NB: c s SEs in (a) and (b) must be linear SEs in x and y with (a) having unit coefs. x = 5 y = 35 (a) 1 4 x OR 3x 6 (oe) 3 x x NB: 3 x scores A (b) B1 ft B1 ft Open circle at x=3 and closed circle at x= One single line joining the two circles

10 3 (a) One term correct 9x 30x (b) " 9x 30 x" 5 4 9x 30x 5 0 3x 5 (Attempt to factorise c s quadratic) x 4 (a) 6 10 sin ABC sin 50 5 OR 1 OR oe 1 6 sin 50 ABC sin 10 (b) ABC = awrt AB 10 sin " ABC" sin50 10sin " ABC " AB sin50 () ( ) (OR AB cos " ABC " cos " ABC " ) AB AB = (cm) awrt

11 5 (a) of the tank filled in 1 hour, x so (oe) seen x 3x 48x seen) or 1 1 (isw after correct answer 16 4x (b) ) The 3 taps fill x 3x " " 15 OR 48x So to fill in tank we must have 3x 15 " " 1 (tank) x 4 tanks of water in 15 hours 4 45x30 48x (removing denominators) (OR 16 4x 15 () 4x = 40 ()) x = 10

12 6 (a) B (1 each incorrect pair) Probability pairs (0.3, 0.7), (0.9, 0.1), (0.4, 0.6) (b) , 3% (c) "0.30.9" OR " " , , 55%

13 7 (a) ABC 90 o AC AC= awrt 33.5 (km) (b) Point X is st BX is perpendicular to CX (see diagram) o BCX 0 15 tan BCA BCA Bearing of A from C = 70 " BCA" 0 o 4 () () () (OR 30 tan BAC BAC o bearing of C from A is 00 "63.435" bearing of A from C is " " (oe) ) o awrt 317