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

Transcription

1 Mark Scheme (Results) Summer 2017 Pearson Edexcel International GCSE In Mathematics A (4MA0) Paper 3H

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 f employers. F further infmation visit our qualifications websites at 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 wld s leading learning company. Our aim is to help everyone progress in their lives through education. We believe in every kind of learning, f all kinds of people, wherever they are in the wld. We ve been involved in education f over 150 years, and by wking across 70 countries, in 100 languages, we have built an international reputation f our commitment to high standards and raising achievement through innovation in education. Find out me about how we can help you and your students at: Summer 2017 Publications Code 4MA0_3H_1706_MS All the material in this publication is copyright Pearson Education Ltd 2017

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 f what they have shown they can do rather than penalised f omissions. Examiners should mark accding to the mark scheme not accding 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 wthy of credit accding 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 wk 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 crect answer only o ft follow through o isw igne subsequent wking o SC - special case o oe equivalent (and appropriate) o dep dependent o indep independent o eeoo each err omission

4 No wking If no wking is shown then crect answers nmally sce full marks If no wking is shown then increct (even though nearly crect) answers sce no marks. With wking If there is a wrong answer indicated on the answer line always check the wking 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 wking that the crect answer has been obtained from increct wking, award 0 marks. Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. If wking is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative wk. 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 wking f an obvious answer. Igning subsequent wk It is appropriate to igne subsequent wk when the additional wk does not change the answer in a way that is inappropriate f the question: eg. Increct cancelling of a fraction that would otherwise be crect. It is not appropriate to igne subsequent wk when the additional wk essentially makes the answer increct eg algebra. Transcription errs occur when candidates present a crect answer in wking, and write it increctly on the answer line; mark the crect 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 International GCSE Maths: Apart from Question 9, 10, 14b, 19b and 22, where the mark scheme states otherwise, the crect answer, unless clearly obtained by an increct method, should be taken to imply a crect method. Q Wking Answer Mark Notes 1 (a) 5(2a + 5) 1 B1 (b) w(7w 4) 1 B1 (c) f p³ ( )5p² p³ 5p² 2 A1 (d) x² + 7x 3x 21 f 3 crect terms 4 crect terms igning signs x² + 4x + c x 21 x² + 4x 21 2 A1 (e) 2³ ³ A1 Total 8 marks

6 2 (a) Vertices at (5, 3) (5, 9) B2 If not B2 then award (3, 9) (3, 5) (1, 5) (1, 3) 2 B1 f shape of crect size and ientation in increct position 4 out of 6 vertices crect (b) Vertices at (7, 1) (7, 3) B2 If not B2 then award (4, 3) (4,2) (6, 2) (6,1 ) 2 B1 f crect ientation but increct position B1 f rotation 90 clockwise about (7, 3) Total 4 marks 3 (a) (b) E.g f a crect scale fact a crect first step E.g (=75) A1 E.g f a crect scale fact a crect first step E.g A1 Total 4 marks

7 4 (a) 3 < L 4 (b) Eg B1 Accept 3 4 M2 f d f at least 4 products with crect midinterval values and intention to add. If not M2 then award f d used consistently f at least 4 products within interval (including end points) and intention to add f at least 4 crect products with crect mid-interval values with no intention to add ( ) dep on (ft their products) NB: accept their 40 if addition of frequencies is shown A1 Allow 2.82, Total 5 marks 5 (a) A1 f truncated rounded to at least 1 dp (b) B1 ft from (a) provided answer to (a) has me than 3 sig figs Total 3 marks

8 6 (3, 2) (2, 0) (1, 2) (0, 4) (1, 6) (2, 8) (3, 10) Crect line between x = 3 and x = 3 3 B3 f a crect line between x = 3 and x = 3 (inclusive) If not B3 then award B2 f a crect line through at least 3 of (3, 2) (2, 0) (1, 2) (0, 4) (1, 6) (2, 8) (3, 10) f all above points plotted crectly but not joined If not B2 then award B1 f any 2 crect points stated (could be in a table) plotted may be seen in wking e.g = 6 f a line with a positive gradient through (0, 4) f a line with gradient 2 Total 3 marks

9 7 cos22 = 14.9 AC 14.9 sin(90 22) AC AC 14.9 oe sin 90 sin(90 22) f BC = 14.9 tan22 oe (= ) AND (AC 2 = ) (AC = ) 14.9 cos22 AC 14.9 ( sin 90) sin 68 f (AC ) = A1 Accept Total 3 marks

10 8 (a) "28.8" 640 ( 100) dep M2 f ( 100) (b) oe oe A1 M A1 f a complete method If not M2 then award f (=7.04) x = oe Total 6 marks 9 Arc centre Q cutting QP and QR at A and B with AQ = BQ and arcs with same radius centre A and B intersecting in guidelines Crect angle bisect 2 A1 dep on f a relevant pair of intersecting arcs within guidelines SC: B1 f line within guidelines Total 2 marks

11 10 Eg 10x + 35y = x 6y = 32 6x + 21y = x 21y = 112 f coefficient of x y the same and crect operation to eliminate selected variable (condone any one arithmetic err in multiplication) f crect rearrangement of one equation followed by crect substitution in the other. A1 cao (dep on ) (dep on 1st ) f substituting their found value into one of the equations crect method of elimination to find the second variable (as f first ) x = 5, y = 3 4 A1 cao Award 4 marks f crect values if at least first sced Total 4 marks

12 11 (a) oe 2 A1 f (b) 4, 32, 62, 78, 86, 90 1 B1 cao 14 oe E.g., 0.31(1 ), 31(.1 )% 45 (c) (30, 4) (40, 32) (50, 62) (60, 78) (70, 86) (80, 90) (ft from sensible table i.e. clear attempt at addition) f at least 4 points plotted crectly at end of interval f all 6 points plotted consistently within each interval in the freq table at the crect height (e.g. used values of 25, 35, 45 etc on age axis) crect cf graph 2 A1 accept curve line segments accept curve that is not joined to (20,0) (d) E.g. reading from graph at t = 65 reading of mark on cf axis from using t = 65 f evidence of using graph at t = 65 ft from a cumulative frequency graph provided method is shown A1 dep on a cf graph in part (c) ft from a cumulative frequency graph provided method is shown Total 7 marks

13 12 (a) B1 cao (b) f oe (e.g ) oe n where n is an integer A1 Total 3 marks

14 13 (a) E.g. 8 ( ) (=1.5) 8 9 ( 0.75) ( ) 9 d 8 oe 9 12 f a crect scale fact a crect equation (may be in ratio fm e.g. 12 : 8 = 9 : d) accept rounded truncated to 2 me decimal places 6 2 A1 (b) oe V 12 f a crect scale fact ( 3.375) 8 (c) w A1 3 q p oe 2 A f f q p 3 ( ) q p 3 oe w p q 3 3 p q q q 2 p oe e.g. w p Total 6 marks 3

15 14 (a) x 4 1 B1 (b) 6 + 4y = 3(5 2y) f removing fraction 6 + 4y = 15 6y f crect expansion of bracket in a crect equation 4y + 6y = y = 9 f a crect equation with y terms isolated on one side ft their equation if first awarded 9 10 oe 4 A1 dep on at least M2 SC: B2 f an answer of y = 1.5 oe with wking shown y = 0.1oe with wking shown Alternative scheme 6 4y f dividing both terms on LHS by 3 5 2y 3 3 allow 1.3(3 ) 4y 6 f a crect equation with y terms 2y isolated on one side allow 1.3(3 ) 10 y 3 f y terms collated 3 allow 3.3(3 ) 9 10 oe 4 A1 dep on at least M2

16 14 (c) g gh = 3h h = gh g f a crect equation with terms in g isolated on one side of the equation g(1 h) = 3h h = g(h 1) f taking g out as a common fact (must be two terms in g but terms may not be crect (terms in g may not be isolated)) 3h 1 g oe (1 h) 3 A1 f 3h 1 g oe e.g. (1 h) 13h g ( h 1) Total 8 marks 15 3 P kr Allow mp = r³ Do not allow P = r³ m 343 = oe m = oe 3 k oe k = 8 f crect substitution into a crect equation. Implies first P = 8r³ 3 A1 f P = 8r³ oe (P must be the subject) (Award M2A0 f crect equation with r as subject given as final answer) Award M2A1 if P = kr³ on the answer line and k evaluated as 8 Award M2A0 if P 8r 3 is given as final answer Total 3 marks

17 16 E.g e 2 3e 2 e² e 2 e² f rational terms crect ( e² ) irrational terms crect (5e 2 3e 2 ) NB: may be fully partially simplified e² = 6 oe rational terms crect and e = 6 dep on 5 2 e 3 2 e = 2 f oe 5e 3e = f oe e = 6 f = 12 3 A1 Total 3 marks

18 17 (a)(i) a + b oe 1 B1 (a)(ii) a + 0.5b 1 B1 f a + 0.5b oe ft from (i) (a)(iii) 0.5a + 0.5b 1 B1 f 0.5a + 0.5b oe (may not be simplified) ft from (i) (b) 4 6 PX 1.5 (7, 3) seen as codinates f R 2 3 PV = (X) = ( , ) (3 + 6, 1 + 3) (9, 9 4) OX 4 OV = V ("9"5, "4" + 4) dep (4, 8) 3 A1 SC: If M0 then award B1 f (4, y) (x, 8) Total 6 marks 18 (a) 1, 4, 5, 40 2 B2 f all four crect (B1 f 2 3 crect) (b)(i) 1 1 B1 ft from their Venn diagram (b)(ii) 45 1 B1 ft from their Venn diagram Total 4 marks

19 19 (a) 4 x y 3 x(y 3) = 4 4 y x 3 y(x 3) = 4 f x(y 3) = 4 y(x 3) = 4 xy = 4 + 3x 4 y 3 x xy = 4 + 3y 4 x 3 y 4 3x x oe 3 A1 (implies the first ) f 4 3x x oe e.g. 4 3 x

20 19 (b) E.g. fg( a) 4a ( 1) a23a E.g. 4a = a 23a 7a = a = a 2 3 a a 2 3 a 1 a oe 3 f a crect expression f fg(a) f a crect equation where the fraction has been removed. 3 A1 dep on Accept 0.333(333...) rounded truncated to at least 3SF (b) Condone the use of x rather than a Alternative scheme E.g. g(a) = f -1 (1) g(a) = f use of f -1 fg(a) = f -1 (1) oe a 2 a 2 NB. ft f f -1 = 7 = 1 a a E.g. 7a = a 2 f a crect equation where the fraction has been removed. NB. ft f f A1 dep on a oe 3 Accept 0.333(333...) rounded truncated to at least 3SF Total 6 marks

21 = oe = and oe oe oe f a complete method A1 f oe e.g accept 0.218( ) 21.8(18 )% rounded truncated to at least 3SF SC : with replacement (maximum 2 marks) f oe oe e.g and oe A1 f oe e.g. 2 9 Total 3 marks

22 21 B1 f identifying the crect angle on the diagram (may be implied by a crect trig statement) (MC=) ( ) f a crect method to find MC VC Accept 18.6( ) rounded truncated to at least 3sf. (VC=) Accept 19.9(4993..) rounded truncated to at 19.9(499..) least 3 sf 1 7 VCM tan 349 VCM sin 398 VCM cos dep f a complete method to find angle VCM (could be use of sine cosine rule) e.g tan A1 accept Total 4 marks

23 22 E.g. 3 x15 3 x15 2( x 6) ( x 8)( x 6) 2x 12 ( x 8)( x 6) 3( x8) 2( x15) E.g. 2( x8)( x6) 3( x8) 2( x15) 2( x 8)( x 6) 2( x 8)( x 6) 3x 24 2x 30 2( x8)( x6) x 6 2( x8)( x6) x² 2x 48 crectly factised NB : May be seen at a later stage f a crect common denominat with numerats crect This may be a single fraction two fractions; denominats may be expanded if so, must be crect. f a crect single fraction with brackets in numerat removed crectly; denominats may be expanded if so, must be crect. f a crect single fraction with the numerat simplified; denominats may expanded if so, must be crect. 1 2( x 8) 5 A1 dep on at least M2 1 1 f 2( x 8) 2x x 2(8 x) Total 5 marks

24 Alternative scheme 22 E.g. 3 x15 3 x15 2( x 6) ( x 8)( x 6) 2x 12 ( x 8)( x 6) x² 2x 48 crectly factised NB : May be seen at a later stage 2 3( x 2x 48) (2x 12)( x 15) f a crect common denominat with 2 (2x 12)( x 2x 48) numerats crect This may be a single fraction two fractions; denominats may be expanded if so, must be crect. E.g x 6x 144 2x 30x 12x (2x 12)( x 2x 48) 2 x 12x 36 2 (2x 12)( x 2x 48) 2 ( x 6) E.g. 2 (2x 12)( x 2x 48) x 6 2( x8)( x6) f a crect single fraction with brackets in numerat removed crectly; denominats may be expanded if so, must be crect (2x 3 + 8x 2 120x 576 ) f a crect single fraction with the numerat factised; denominats may expanded if so, must be crect. 1 2( x 8) 5 A1 dep on at least M2 1 1 f 2( x 8) 2x x 2(8 x) Total 5 marks

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