Mark Scheme (Results) Summer Pearson Edexcel International GCSE In Mathematics A (4MA0) Paper 3HR

Transcription

1 Mark Scheme (Results) Summer 017 Pearson Edexcel International GCSE In Mathematics A (4MA0) Paper 3HR

2 Edexcel and BTEC Qualifications Edexcel and BTEC qualifications are awarded by Pearson, the UK s largest awarding body. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. For further information visit our qualifications websites at or Alternatively, you can get in touch with us using the details on our contact us page at Pearson: helping people progress, everywhere Pearson aspires to be the world s leading learning company. 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: Summer 017 Publications Code 4MA0_3HR_1706_MS All the material in this publication is copyright Pearson Education Ltd 017

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. When examiners are in doubt regarding the application of the mark scheme to a candidate s response, the team leader must be consulted. 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 Apart from questions, 7 and 18 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method Ques Working Answer Mark Notes or 6.84 or for 0.63 oe ( 5) 5 NB: Accept.3(6 ) in place of A1 for 0.63 or SC : B1 for an answer of 1.41(31 ) Total marks 5x x = 8 10 for correct rearrangement with x terms on one side and numbers on the other in a correct equation or the correct simplification of either x terms or numbers on one side in a correct equation eg. 4x 8 = 10 ; 5x = x 4x = or 4x = or 4x + = 0 or 4x = 0 NB: This mark implies the previous A1 oe e.g. dep on 4 3 Angle BCD = 14 o or Angle BCF = (=118 o ) or Angle ABC = (=38) for angle BCD = 14 o or angle BCF = (180 6) o or for a complete method to find x A1 Total 3 marks Total 3 marks

6 4 a A1 for b or 163(.461..) for = for (=.8 ) dep for for c 4 60 (=0.4) or.4 or (=144) 4 60 oe or A1 for oe or ( ) 60 oe (allow or answer of 684(.8 ) or 685) A1 for Total 8 marks 5a π.5 oe or π A b oe or 10 oe.5 50 or for digits A1 accept 19 if 18.8 seen Total 4 marks

7 6a b a b c a b 1 or 19 or 3 3 1(=63) or 19(=38) for a complete method 5 3 A (=18) or ft from (a) for a complete method to find age of 3 rd person (=18) 5 18 dep or for A1 ft from answer in (a) Total 6 marks 7 e.g. 7 1 or at least 3 divisions in a factor tree All 6 correct prime factors, no extras (,,,,3,7,(1)) A1 oe dep on, for the start of a correct method e.g. may be a factor tree or consecutive divisions condone 1 error e.g. from a factor tree, ignore 1s Total 3 marks 8a b Correct triangle ( 1, ) ( 1, 0) (, ) Correct trapezium (1, 1) (1, ) (3, 1) (3, ) B (B1 for a rotation of 90 o clockwise about a different centre i.e. a triangle in the same orientation as the correct triangle or rotation by 90 o anticlockwise about (0, )) 1 B1 Total 3 marks

8 9a 5 10e f B If not B then award B1 for 5 5, 10 or 10 a b ke f k e f or 10e f a, b 0 b (x 6)(x + 1) B If not B then award B1 for (x 1)(x + 6) or (x 3)(x ) or (x + 3)(x ) or (x 3)(x + ) Total 4 marks 10a (= 90.6) oe ( ) 100 "90.6" oe (dep) A1 for or or b M for a complete method oe 0 If not M then award for a correct first step (=66) or 0.x = 130 or 130 (=660) A1 Total 6 marks

9 11a Complete correct binary structure for selection of two counters OR At least one additional red 9 branch labelled and at least 0 b two blue branches labelled 11 0 Correct probability tree diagram A A for ' ' ' ' (ft diagram) for or or 4.75% 400 c ' ' ' ' or ' ' ' ' for one correct product ft from diagram 9 11 for ' ' ' ' oe 0 0 (ft from (a)) ' ' ' ' + ' ' ' ' for the complete method ft from diagram 9 11 for 1 ' ' ' 0 0 ' 0 3 A oe or or 50.5% 400 Total 7 marks

10 1a, 9, 18, 8, 39, 51, 63, 75, 86, 100 Correct table 1 B1 b (ft from sensible table i.e. clear attempt at addition) for at least 8 points plotted correctly at end of interval or for all 10 points plotted consistently within each interval in the freq table at the correct height Correct cf graph A1 accept curve or line segments accept graph that is not joined to (0,15) c E.g. for a mark drawn at 5 on their cumulative frequency diagram for intention to use 5 on cf axis ft from a cumulative frequency graph provided method is shown A ft from a cumulative frequency graph provided method is shown d E.g. reading of (%) or reading from graph at A = 5 or mark on cf axis from using A = 5 for a reading taken from 5 on age axis ft from a cumulative frequency graph provided method is shown "68" 100(000) 100 (dep) A1 for answer in the range Total 8marks 13 for either y = x + 1 or x + y = 10 drawn correctly for all lines drawn correctly Correct region 3 A1 for all 3 lines correct and the region identified Lines may be full lines or broken lines Total 3 marks

11 14 Scheme 1 (interior angle and angle ADC and an angle in triangle ADC) Let X be midpoint of DC (5 - ) 180 (Angle DEA =) = Angle EDA or EAD = ( ) = 36 Angle ADC or ACD = = 7 or Angle DAC = (=36) or 1 "16.18" "16.18" 10 Angle DAC = cos "16.18" "16.18" Angle DAX or CAX = (108 36) (=18) E.g. AX = 5 tan7 (=15.38 ) or AX = 5 tan18 (=15.38 ) or AX = 5 tanadc or AX = 5 tandax or AD = cos108 (=61.8) or AD = AD = cos108 10sin 7 sin 36 (=16.18) or (=16.18) E.g. Area = oe or sin7 or sin36 or sinadc or sindax or for 108 seen as an interior angle Angles may be seen on diagram 10 or for AD sin108 (=16.18 ) or sin AD sin 7 sin36 Allow 16 or 16. for AD throughout NB: Allow the value on the diagram for angle ADC or DAX if used in an otherwise correct trig statement dep on previous NB: Allow the value on the diagram for angle ADC or DAX if used in an otherwise correct area statement A1 for answer in the range SC: B4 for an answer in the range Total 6 marks

12 14 Scheme (only interior angle needed) Let X be midpoint of DC (Angle DEA =) (5 - ) = 108 or for 108 seen as an interior angle AD = cos108 (=61.8) or AD = cos108 (=16.18) AX = (= 36.8) or AX = (= 36.8) Allow 16 or 16. for AD throughout "36.8" (= ) A1 for answer in the range SC: B4 for an answer in the range Total 6 marks 15a 3 x 3 x 1 for one of 3 x (=6x ) or 3 x (=6x) or 1 6x 6x 1 A1 b substitute x = in (a) ft from answer to (a) (must be a quadratic expression) 0 A1 c 6x 6x 1 1 ft from answer to (a) (must be a quadratic expression) x = 1, 0 A1 for both correct solutions 1, 0 3 A1 for k = 1 and m = 0 Total 7 marks

13 16 cxy dy ax b both terms in original denominator multiplied by y e.g. cxy ax b dy or dy b = ax cxy for isolating terms in x and non x terms correctly ft from cxy + d = ax + b or cx + dy = ax + b x( cy a) b dy for taking out a factor of x correctly provided there are two terms in x b dy 4 A1 b dy dy b x for x oe e.g. x cy a cy a a cy Total 4 marks 17 1 (1+ 6) = 9 (9 + BC) oe or 1 (1+ 6) = 9 AC oe or AC = 4 1 (1 6) ( BC ) 9 oe or for a complete method 15 3 A1 Total 3 marks

14 18 y 4x 1 4x 6y 0 with subtraction or 10 x 4x 1or 3 1 y 3y 10 oe 4 for eliminating one variable multiplication of equation(s) to get same multiple of y with subtraction (condone one arithmetic error) or either rearrangement of one equation and then correct substitution into second equation (condone algebraic error in rearrangement) E.g. y 6y 8 or 4x 4x 8 = 0 E.g. (y )(y 4) (= 0) or 4(x )(x + 1) (=0) A1 A1 reduction to a correct 3 term quadratic; terms may not all be on the same side ft if first awarded and equation is quadratic for correct factorisation or correct substitution into formula for y =, y = 4 or x =, x = 1 correct x or y values implies previous 10 3 ( x ) or 10 ( y ) or ( 1) 3 x =, y = or x = 1, y = 4 (dep on the previous ) for correct substitution to find both values 6 A1 values for x and y must be correctly paired dep on awarded Total 6 marks

15 19 ( V c ) (=896π = 71930) 3 3 ( V H ) 36 (=31104π = 97716) 3 for volume of cone for volume of hemi-sphere NB : 54000π or implies first two method marks r r + (dep on at least ) " 36 53" oe " 36 " "54000 " r 3 = (dep previous ) 60 6 A1 for forming an equation with correct volume expression for cylinder Total 6 marks 0 p p p ( ) 1 or M for correct expansion p p p 1 or If not M then award for p p p 4 1 p p p 3 terms correct from ( ) 1 p1 p1 N ( 1) Shown A1 for correct factorised expression from correct working (dep on M) Total 3 marks Alternative method N ( k 1)( k 1) for correct factorisation ( p N 11)( 1 1) for correct factorisation and substitution (implies B1) p1 p1 N ( 1) Shown 3 A1 for correct factorised expression (dep on M)

16 1 (( BD) ) ( x ) ( x 3) ( x )( x 3)cos(10) ( x ) x x x 4 oe ( x 3) x 3x 3x 9 oe (independent) correct expansion of (x ) or (x 3) x 4x 4 x 6x 9 x 5x 6 (= 3x 15x 19) A1 correct quadratic for BD with all terms expanded may not be simplified Area = BD oe or Area = ( 3x 15x 19 ) (independent) 6x 30x 38 5 A1 Total 5 marks

17 8 a 8b y y T S x x

18 1 Cumulative percentage Age (years)

19 13 y R x

20 Pearson Education Limited. Registered company number 8788 with its registered office at 80 Strand, London, WCR 0RL, United Kingdom