GCSE. Edexcel GCSE Mathematics A 1387 Paper 5525/05. Summer Edexcel GCSE. Mark Scheme (Results) Mathematics A 1387.
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1 GCSE Edexcel GCSE Mathematics A 87 Summer 005 Mark Scheme (Results) Edexcel GCSE Mathematics A 87
2 NOTES ON MARKING PRINCIPLES Types of mark M marks: method marks A marks: accuracy marks B marks: unconditional accuracy marks (independent of M marks) Abbreviations cao correct answer only ft follow through isw ignore subsequent working SC: special case oe or equivalent (and appropriate) dep dependent indep - independent 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. Send the response to review, and discuss each of these situations with your Team Leader. Any case of suspected misread loses A (and B) marks on that part, but can gain the M marks. Discuss each of these situations with your Team Leader. If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work.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. 5 Follow through marks Follow through marks which involve a single stage calculation can be awarded without working since you can check the answer yourself, but if ambiguous do not award. Follow through marks which involve more than one stage of calculation can only be awarded on sight of the relevant working, even if it appears obvious that there is only one way you could get the answer given.
3 6 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. 7 Probability Probability answers must be given a fractions, percentages or decimals. If a candidate gives a decimal equivalent to a probability, this should be written to at least decimal places (unless tenths). Incorrect notation should lose the accuracy marks, but be awarded any implied method marks. If a probability answer is given on the answer line using both incorrect and correct notation, award the marks. If a probability fraction is given then cancelled incorrectly, ignore the incorrectly cancelled answer. 8 Linear equations Full marks can be gained if the solution alone is given on the answer line, or otherwise unambiguously indicated in working (without contradiction elsewhere). Where the correct solution only is shown substituted, but not identified as the solution, the accuracy mark is lost but any method marks can be awarded. 9 Parts of questions Unless allowed by the mark scheme, the marks allocated to one part of the question CANNOT be awarded in anoth
4 (a) x x + 7x 8 x + x 8 M for terms correct ignoring signs (e.g x,x,7x,8 ) or terms with correct signs (e.g x, x,7x, 8 ) A cao y + y B cao B for y or y (c) p(p+6) B for p(p+6) or p (p+6) (B for p(ap+b) where a,b are numbers or p+6 seen on it s own, or part of an expression) (d) x(x y) B (B for (x xy) or x( 6x 9y) or x(...) ) question + response boxes oe st aspect: One question with time period (eg each night); ignore other questions. nd aspect: Response list (at least two), not overlapping.* rd aspect: Some mention of units (eg hours) in either question or responses Award B for all three aspects, or B for just two aspects. * 0-, -, -5 is OK, but 0-, -, - is not OK. reflection in y = x B cao accept the word reflected (B any statement including the word reflection ) (a) 5 x = x + B for x + seen OR.5.5x = x + 5 = x + x 5 M for correct rearrangement of terms A for 5 oe,,,0,, B (B for 5 correct and not more than one incorrect integers)
5 5 (a) 6 6 = M for or or 6 A accept M for attempt to convert to fractions with common ++ + denominator e.g two fractions, denominator of A correct conversion : 8 and 9, 0 or and seen (oe) A cao for 5 OR attempts to convert to decimals: must use at least dp M (or ) or etc A.,.7,.6 or 0., 0.7, 0.6 or 0.,. A.6 (recurring) 6 (a)(i) 6 5 B accept 565, 5 + (ii) 5 B accept 5, x + y = 0 and x y = x = 7 y = M for either x + y = 0 or x y = A for both values correct [(A for one value correct) If M0, award B for both values correct or B for one value correct, otherwise B0] SC B for x = or y = 7
6 7 6 8 or 8 M attempt to find the area of one face; or (8 9) or (6 9) or (0 9) or 7 or 5 or 90 or or cm or 8 M all five faces with an intention to add A cao numerical answer of 6 8 π ab d ( c + d) πbc B (indep) cm with or without numerical answer B (B for each one correct) Nb B for each of the th,5 th,6 th tick 9 (a) x x = M for x x = oe, or 0.5 A oe M A cao Accept 60 out of 00 (in words) 60 SC B for 00 0 (a) ( ) (0) 8 5 points plotted accurately points joined with smooth curve m= n=5 B for all correct [(B for each one correct) B ± full (mm) square ft table if at least B awarded (all 5 points plotted) B ft for any smooth curve if previous B gained NB: curve must pass within full square of the points B for B for 5 (B for 5 or 5) SC: award B only if m=, n=, for 8 5 seen 5
7 5 y = x + 5 M for clear attempt to find gradient eg fraction with = - -,5 in numerator,,- in denominator A for cao 6 B ft for y = " " x + 5 oe (eg y = x + 5) (B for y = mx + 5 or, -x+5 or y = " " x + c ) (a) on LH branch B cao & & on RH branches B + = (c) n = or 6 8 or : oe M for or from their tree diagram M for sum of two products 7 A for oe M for either tree diagram = or = 6 from their M for (=8) or A for cao SC: B for 6 seen in fraction or ratio 6
8 5 (a)(i) 50 B accept 50 or 0 (ii) B for angle at the centre is twice the angle at the circumference 0 B identifies angle between radius and tangent "50" or 80 "50" as 90 (may be in working or on diagram) o M "50" A ft from (a)(i) excluding a negative answer Or B for M for (80 90 " " ) A ft from (a)(i) excluding a negative answer Or B for 80 (a) SC: 80 0 can get B for 90 and/or B for cyclic quadrilateral (a) 0.77 B for.7 recurring or oe or 0.7 eg x = 0.99 so 00x = 9.99 M for 00x = x = 9 M dep for subtraction of both sides 9 so x = = 99 A for from correct proof Alternative method M for.000 M for remainders and A for 0.9 recurring 9 SC:B for 99 7
9 6 (a) d = kt 80 = k 7 (c) (a)(i) (ii) 5 = 5t d = 5t 5 (0, 9) (8, 5) M for d = kt or d t M sub d=80 and t= into their equation A for d = 5t oe (cao) B ft from (a) using k M ft from (a) for substituting d=5 into their equation A for cao (condone inclusion of ) B cao B for x = 8 cao B for y = 5 cao SC: B for (5, 8) 00 ( x 6x + 6) LHS = = 6 + 6x x RHS = 6 x + 8x x = LHS M for expansion of either set of brackets with at least of terms correct M for common denominator of or multiplying through by or reducing each numerator to a single term A for fully correct solution Alternative method ( x 8) ( x 8) M for (5 )(5 + ) 5 ( x 8) 5 + ( x 8) M for ( )( ) ( 8 x)( x + ) A for 8
10 8 9 (a) 80π 80π or 9 M for 90π 90π or 9 or or :9 oe 9 9 or 80π M for or 90π 9 or or or 9 : oe A cao SC:B for answer of π or 7 or 700 M for " " or 7 or ( 9 ) : ( 8 ) oe or 9 or 700 (a)(i) (ii) (iii) 6 = 6 or 6 = ( ) 8 6 A cao B cao B cao M for knowing negative power is a reciprocal or power of root is a cube root A cao for 6 7 = 9 or 7 = or 7 = / 5 oe M for 7 = 9 or 7 = / A for 5 oe (cao) Alternative method M for 9 7 = n A for 5 oe (cao) 9
11 0 (a)(i) (90, ) B cao could be indicated on diagram (ii) (i) (ii) (80, 0) (5, 0) (90, -) B cao could be indicated on diagram B cao could be indicated on diagram B cao could be indicated on diagram x M for substitution in correct formulae π x h = π (x) M (dep.) for correct unsimplified expression eg x h = 8x π (x) h = oe or h = 8x oe πx A for x cao (a) a b B ( ) ( MN = ) a b +a ( OX = ) a + b ( ) OM = a + b ( ON = ) a or 6 a (B for either OM or ON or a b + a SC: B for b a OY = b + a XY = a B for either OX or OY or (½ QR ) (½ QR =) a b or (½ RQ =) b a (hence parallel) B for XY = a or YX = a 0
12
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