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

Transcription

1 Mark Scheme (Results) January 015 Pearson Edexcel International GCSE Mathematics A (4MA0) Paper H Pearson Edexcel Level 1/Level Certificate Mathematics A (KMA0) Paper H

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 015 Publications Code UG04059 All the material in this publication is copyright Pearson Education Ltd 015 General Marking Guidance

3 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 o awrt answer which rounds to

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 6, 1, 18b and, where the mark scheme states otherwise, the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method or Allow or 60 or or A Note: SCB1 for 5000 or oe 1. or 41.6(66666) 10 oe with 41.6(66666) rounded or truncated to at least SF Total marks. (a) for A1 Accept 18 1 or 7/ but not unsimplified fractions (b) or Accept equivalent decimals (eg 18.50) for or or A1 Accept or Total 4 marks

6 . (a) 7(x 5) 1 B1 (b) 6c15 c 8 Any three terms correct. 4c 7 A1 (c) 6 16e B 6 B1 for 16 or e as part of a product or B1 for 4² e (d) a 10a a 5 Any three terms correct or a 9 a... or... 9a 5 a 9a 5 A1 Total 7 marks

7 eg ( (15 1) ( 110) ( 1 4) or M For a complete method or ( ) 1 ( 1 1 4) + (1 10 6) +( ) or 00 ( ) or 1 (15 1) 6 or 108 eg ( 1 4 1) and ( ) (4 and 0) or ( 1 4 1) and ( ) (4 and 60) or ( 1 4 6) and ( ) (1 and 0) or ( 1 4 6) and ( ) (1 and 60) or 1 (15 1) 6 or 108 or 1 ( ) 6 or 78 eg ( 1 4 6) or 1 or ( 1 4 1) or 4 or ( ) or 0 or ( ) or 60 or ( ) or or ( ) or 66 or ( ) or 45 or 15 6 or 90 or 15 1 or 180 or 5 6 or 150 or 5 1 or 00 or 10 6 or 60 or 10 1 or 10 or 11 6 or 66 or 11 1 or 1 or 4 1 or 48 or 4 6 or A1 If not M then M for different but non overlapping triangles or 1 trapezium If not M then for a correct area of a triangle or rectangle. Note: The lists of examples are not exhaustive. Total 4 marks

8 5. (a) (i) A1 oe e.g. accept /100 0./1 (a) (ii) or 1 ( ) or or (1 ("0." + 0.1)) ft if their answer to (a)(i) is 0 < (a)(i) < 1 oe eg accept 8/100 A1 0.8 ft for 0 < answer < 1 (b) A1 oe eg accept 1/50 (c) oe 1 A1 Accept 1 out of 60 Note: A0 for 1/60 Total 8 marks 6. 0y 4 18y 1 for 0y4 or 18y1 0y18y 1 4 or y = 5 For a correct equation with the y terms collected on one side of the equation and the non y terms on the other side. 1 A1 oe dep on at least 1 Total marks

9 7. (a) or (= 1.4) (= 1.4) 8 15 (= 0.4) dep "1.4" 1 (= 0.4) "1.4" 100 (= 1.4) (b) or 0.85 oe.4 A1 cao M 180 A1 for 15 or 1.8 or 85% = or 0.85x = 15 oe Total 6 marks 8. (a) or or 15 "15" or 5 5 dep on 11. A1 awrt 11. (b) 10 tan C or tan C tan 1.5 oe M for any complete and correct method M for any complete and correct method 8.7 A1 Accept 8.6( ) rounded or truncated to at least SF. Total 6 marks

10 9. (a) ( 7 4) 90 or (7 ) 180 For the sum of the interior angles 60 or an interior angle or 7180 or (7 ) Eg Allow for oe 7 or 18.( ) correctly rounded or truncated to at least SF. 900 A1 Mark the final answer (b) 1 ( (57148 ) ft For a complete and correct method ) or 0.5 (60/7) or A1 Accept Allow or oe Total 4 marks

11 10. (a) x 6 For a correct equation with y the y or y x subject or e.g. 4 diff of y values for any two correct 0 diff of x values points on the line. Allow 0.666( ) rounded or truncated to at least SF instead of A1 Allow A1 if follows an equation with an incorrect constant. Eg y = x + followed by an answer (b) 5 c or c 5 of A0 for x + or x Allow 0.666( ) rounded or truncated to at least SF instead of y x 11 A1 Allow ISW oe [e.g. y5 ( x ) ] Total 4 marks

12 11. (a) For identifying ², ³, and 5 or any product of integer powers of and and 5 where at least two powers are correct and the third is greater than 0 or A1 Accept 5 (b) For identifying ³, 4, 5 and 7 or any product of integer powers of and and 5 and 7, where at least three powers are correct and the fourth is greater than 0. Accept a product that includes, and 5 and 7 and multiplies to 680 (Eg ³ ² 5 7 9) or A1 4 Accept 5 7 Total 4 marks

13 1. Eg 9y6 or 9x 7 or 5(7 x) 4x = 8 or For a correct method to find an equation in x or y. 5y 4(7 y) = 8 Condone 1 arithmetic error. x, y 4 A Dep on A1 for each value Total marks 1. (a) Eg for two CF values obtained using IQ values of 85 and 115 (± 1 square) (b) CF = A1 Accept answer in range 69 7 unless clearly obtained by incorrect working for CF value of 75 or stated or marked on the graph A1 Accept answer in range unless clearly obtained by incorrect working Total 4 marks

14 14. ( ST ) 5 or 7 or (OT =) Accept ST or OT marked correctly on diagram PT 6 = (5+) or PT 6 "7" or "7" dep 6 1 oe A1 Total marks 15. h Accept 1.58( ) or or oe or or or 4 or or 0.69( ) rounded or truncated to at least SF 1 or 500 : 000 oe or 000 : 500 oe Eg ( h ) or 768 or 819 or oe for any correct expression for h. 0. A1 for awrt 0. Total marks

15 16. (a) (b) or oe " " or 1 or 1 oe Alternative: with replacement A1 oe, eg 1 7 Allow 0.16(666...) rounded or truncated to at least dp M for 4 5 or 5 4 or 0 oe Accept fractions evaluated , rounded or truncated to at least dp. A1 oe, eg 40 7 or 0 6 Allow 0.55( ) rounded or truncated to at least dp or oe M for 5 or 0 81 oe 4 or Accept fractions evaluated 0 = 0.4( ) = 0.49( ) 81 rounded or truncated to at least dp Total 5 marks

16 17. (a) P kq Allow kp q oe Do not allow P = q³ 70 for correct substitution in a correct 70 k(7.5) oe or k oe 7.5 equation. Implies first 16 A1 P q P 0.64q oe with P the subject 5 Award MA1 if P kq on answer line and k evaluated as 16 in part (a) or 5 part (b) (b) Eg q or 16 q q or q² = 1 Correct equation involving q² or p² ft k from an equation of the form Or P = 5 16 or 1 = 1 P kq if k 1 16 P² A1 5 1, 1.5 [ignore 0 or negative value.] 4 4 Total 5 marks

17 18. (a) For any two of x², 8x, or 4 x 8x 4 A1 Do not ISW (b) (x )( x ) ( 0) or M For correct factors or correct substitution into the quadratic ( 8) ( 8) 44 ( x ) formula. ft for a term quadratic if scored 4 in (a) Accept instead of. (c) If M not scored: for (a) = 0 if scored in (a) x A1 dep on M (, ) A1 dep on M For x < " " or x > " " ft positive values from (b) if scored in (b) A1 ft positive values from (b) if scored in (b). Accept or to x Do not penalise or Total 8 marks

18 19. (a) 1, 4, 5, 6, 7 1 B1 (b) 8 1 B1 (c) 1, 4, 7, 8, 9 1 B1 (d) 5, 6, 7 1 B1 Total 4 marks 0. (a) (x 1) For a correct expression Eg (x 1) 1 (x 1) A1 1 Accept or + x x x A0 for 4x²+ x² (b) y( x 1) x or yx y = x x(y 1) = y or xy x = y x( y ) y y(x ) = x x A1 x Allow x x Total 5 marks

19 r (r =) 0π or (r =) 0 For any correct expression for r or (r =) 64 15π 5 or (r =) 8 l 15 +"8" or l 17 dep on M 5 S = π "8" 15² + "8" or S 8 "17" ft for r and l if all M marks scored. Allow for π "8" 15² + "8" + π "8"² 47 A1 for awrt 47 Accept 16 Total 5 marks ( 7) (x 1) (x 1) (x 1)( x 1) cos 60. or cos60 = (x+1) + (x 1) ( 7)² (x+1)(x 1) Accept 5.9 ( ) in place of 7 rounded or truncated to at least SF Condone 7 8 4x 4x 1 4x 4x 1 (4x 1) or (e.g.) 8 4x 4x 1 4x 4x 1 4x 1 or 8 4x or 5 4x 1 Correct simplification as far as the first expression shown, or better. 1 A1 oe dep on at least Total marks

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