Mark Scheme (Results) Summer 0 International GCSE Mathematics (4MA0) Paper 4HR
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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. 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 awrt answers which round to... 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 If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work.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.
Apart from Questions, (a), 0dii 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. Question Number Working Answer Mark Notes : 8 oe or 8: M.5 oe A translation B Also accept translated, translate etc Also accept B to the left and up Total marks These marks are independent but award no marks if the answer is not a single transformation Total marks (i) + 4 5 + 5 4 + 6 + or 6 + 0 + 0 + 4 + 0 or 80 4 M for sum of products condone one error 80 50 M (dep) for division by 50 5.6 A cao Also accept 6 if both method marks scored and 5 following 5.6 (ii) 5 B ft from their (i) Total 4 marks
4 (a) (, ) B B for B for (b) arc(s) centre P radius PA M Cross at (6, ) A Accept any clear indication. Condone omission of label if no ambiguity Total 4 marks 5 (a)(i) (ii) 5 M M for 80 or 4 0 85 80 80 4 M dep 0 8 A cao 4 0 or 4 0.5 5 M for 0 or 4 0.5 4 M for or.6 5 60 A cao (b) + or 5 M 5 may be denominator of a fraction or coefficient in an 0 or 0 5 or 64 or 5 oe M dep 5 equation such as 5x 0 448 A Also award for 8 : : 448 Total marks
6 (a)(i) ABC 68 or BCD 4 M May be stated or marked on diagram 68 A cao (ii) 60 (6 + + 68 + 4) M (b) (5 ) 80 or 80 or ( 5 4) 0 or 6 0 or 60 + 80 or (80 6) + (80 ) + (80 68 ) + (80 4) + (80 ) or + 68 + + 6 + 4 A ft from their (a)(i) Award marks if the answer to (ii) is answer to (i) M Condone incorrect interior angle 540 A Cao SC: Award B for answer of 8 Total 6 marks (i) < x < 4 B B for either < x or for x < as a final answer (ii) 0 B B for 4 correct and wrong or for correct and 0 wrong Total 4 marks 8 5. +.8 or.04 + 4.44 or 4.48 M for squaring and adding 5..8 M (dep) for square root 6.44 A for answer rounding to 6.44 Total marks
x 8 x 4 M for x 8 x 5x 55 or 5x 55 0 or M for correct rearrangement with x 5x 8 or terms on one side and numbers x x 55 on the other AND correct collection of terms on at least one side or for correct collection to terms M for correct rearrangement with y terms on one side and numbers on the other e.g x x 8 or correct collection and simplification of either numbers or x terms eg 5x 8 or 5x = a or bx = 55 A dependent on at least one M Total 4 marks
(a) 5 40 8 5 5 80 B cao (b) Points correct B + ½ sq (c) 5 or 5.5 indicated on cumulative frequency graph or stated Curve or line segments approx 4 from correct graph B ft from points if 4 or 5 correct or if points are plotted consistently within each interval at the correct heights Accept curve which is not joined to the origin M for 5 to 5.5 indicated on cumulative frequency graph or stated A If M scored, ft from cumulative frequency graph If M not scored, ft only from correct curve & if answer is correct (+ ½ sq tolerance) award M A Total 5 marks Product of positive integer powers of both and 5 only M Powers and/or products may be evaluated eg 5 5 or 45 A Also accept 5 Total marks OAP 0 or AOB 64 B OAB 58 or OBA 58 B May be implied by second B May be stated or marked on diagram B Award full marks for a correct answer Total marks
(a) x 6y 8 x 6y 5 5x y 5x y 6 5 4 M for coefficients of x or y the same or for correct rearrangement of one equation followed by substitution in the other eg 5x x 5 x = y = A eg 5 y M (dep on first M) for substituting for the other variable A cao dep Award full marks for correct values if at least first M scored (b) B ft from (a) Total 5 marks 4 80.04 or 50 or.04 or.086 4 M 50.04 M 5 A 55 A cao or M for 80.04 oe Total 4 marks 5 (a) 6 B cao (b)(i) B cao (ii) eg sum of opposite angles of a cyclic quadrilateral = 80 B Accept reasons which include opposite and cyclic, 80 o (or supplementary) and nothing incorrect Total marks
6 6. 5. 6. 5.cos M or 44.8 +.04 (.6 ).56 A for awrt 4. A for awrt. (.66 ) Total marks (a) y kx or (b) ky x M for y kx but not for 50 = 00k M for 50 = 00k Also award for 50 k y x oe 4 A for y x oe 4 Award marks if answer is y kx and k is evaluated as 4 oe in part (a) or part (b) 54 " " x M dep on at least first M in part 4 (a) 6 A ft from x 54 " " oe 4 Total 5 marks y x
8 (a) 6 M (b) (c) 6 6 6 5 oe A oe and no other terms M oe or for + 6 + oe oe or for + oe or for 0 A Sample space method award oe inc 0 marks for a correct answer; otherwise no marks SC M M M for 6 M for 6 + oe oe or 4 A Sample space method award oe inc 0 5 marks for a correct answer; otherwise no marks Total marks 6 + + oe π.4 8. or 56. 44 or. 4 M M π.4 or. 56 or 6. M π.4 or. or.6.. 86 A for awrt 86 Total 4 marks
0 (a) 4.5 6.5 B for both values correct (b) Points B Allow + ½ sq ft from their table Curve B ft from their points if at least 6 points plotted correctly (c) 0. to 0. and. B B for each correct value + ½ sq ft from their graph if at least mark scored in (b) tol (d)(i) B cao (ii) Draw y = x M from x = to at least x = approx. A ft from their graph if at least mark scored in (b) and dep on M Total 8 marks B 6 0 0 4 L S or B 6 4 L S M for complete, correct Venn Diagram (outline, labels and numbers) (accept blank instead of 0 M for correct outline and labels and at least non-zero numbers correct excluding,, (in L) A cao Total marks
4 5 B or 6 M sin 60 or.( Or 4 and. 6 or "." + "." 4 M Alternative methods M for.5 or sin 60 or 6.06 M (dep) for "6.06..." or. Or M for 4 and.5 M for "." and Or.5 "..." Other equivalent methods. dep on preceding marks summing all the areas to make up the hexagon A for answer rounding to Total 5 marks
(a) (b) x ( x ) (x )( x y x x ) M for factorising numerator and denominator A cao dep on method mark M Alternative method x y y xy x y or x ( y ) y M for isolating xy y x x terms (or y terms in alt method) or y ( x ) x x A dep on both method marks. x Accept x x Total 5 marks
ALTERNATIVES FOR QUESTION 6.06... sin60 4 6.65... =.5 6.06... 4 6.65... =.5 6.06....5 4 4 4 4.4... 84.8.....5... 4 4.4... 84.8.....5... sin60
6.65.. 6.65...... 60 o 5.5 sin60 6.65......
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