GCSE. Edexcel GCSE Mathematics A Summer 2005 Mark scheme. Edexcel GCSE. Mark Scheme. Mathematics A 1387

Transcription

1 GCSE Edexcel GCSE Mathematics A 87 Summer 005 Mark scheme Mark Scheme Edexcel GCSE Mathematics A 87

2 Edexcel is one of the leading examining and awarding bodies in the UK and throughout the world. We provide a wide range of qualifications including academic, vocational, occupational and specific programmes for employers. Through a network of UK and overseas offices, Edexcel s centres receive the support they need to help them deliver their education and training programmes to learners. For further information please call our Customer Services on , or visit our website at Summer 005 Publications Code UG0670 All the material in this publication is copyright Edexcel Ltd UG0670

3 CONTENTS Notes on Marking Principles... Paper 55/0... Paper 55/0... Paper 55/ Paper 55/ Paper 555/ Paper 555/

4 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. 4 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 If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work.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. UG0670

5 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 another. UG0670

6 Paper 55/0 (a) (c) thousands, 000, 4000 B cao B cao B (a) grams, g B oe spelling centimetres, cm B oe spelling millilitres, ml, cm B oe spelling 5 B cao (a) (c) 06, 0 eg take away 4 46 B cao ignore extras B could be indicated on the diagram B cao UG0670

7 Paper 55/ = M for complete correct method (condone one computational error) (M for complete correct method with two computational errors) A cao x OR B inside of grid completed (condone missing zeros and one error) (B or errors) B cao (a) (i) (ii) (c) (d)(i) (ii) (iii) 8, 69 8 or 6 6 or 6 factor 8 or B B B B B cao B B cao 4 UG0670

8 Paper 55/0 6 (a) (c) (d) (e)(i) (ii) 7 (a) April & May Daffodil Feb Crocus 5 from 56 mm to 64 mm from 0 5 B for both B B B B for 5 oe B A single mark on the line, between 56 mm and 64 mm measured from end 0 B for B for or or or (c) (d) (e) B cao B cao B cao B cao 5 UG0670

9 Paper 55/0 8 (a)(i) (ii) 9 (a) (c) or.50 (, (0, ) (4, ) ) marked B cao B cao B Allow mm tolerance from (, ) B cao could be indicated on the diagram M for appropriate sum or product in or p or 00 seen eg , , , , , , 00 A cao M for or.50 or 5 or appropriate combination eg A cao 0 (a) hexagon B Condone spelling error (c) Sum of angles at a point is 60 B for 60 seen B for point, complete turn or a circle or similar unless accompanied by an incorrect angle SC If neither B scored, award B for a clear indication that the size of an angle, other than x, is 90 or a right angle (may be on diagram) M or attempt to sum 5 or 6 lengths A cao 6 UG0670

10 Paper 55/0 (a), 67, 76, 0, 0 5 B cao 7,,, 0, 5 B cao (c) 0.07, 0.07,0.7, 0.70, 0.7 B cao (d) 0.6,, 70%, 4 B (B for any in correct order) (a) 6 0 B Accept 4 0 pm Do not accept 4 0 (i).56 4 oe 8.9 M for.56 4 oe eg 56 4, division by twice (ii) 9 B ft from 8.9 unless whole number of pounds (a) 6 cm B for 6 cao for numerical answer (B for 5.5 Area 7 ) then B (indep) for cm with or without numerical answer See diagram Correct shape B (B for any sides correct or a correct enlargement scale factor or ) A cao 7 UG0670

11 Paper 55/0 4 (a) ( 4 ) 0 70 M for (4 + ) 0 A cao M for A cao (c) C 0( n ) B for C=0(n+) oe such as C ( n ) 0 (B for correct RHS or C n 0, C 0n oe B for C = some other linear expression in n or for n 0, 0n etc) Note: C = n scores no marks 5 B all correct 6 8 (B for correct) 8 UG0670

12 Paper 55/0 6 (a) p + 4q B for p + 4q (accept p etc) (B for p or 4q) y B accept y oe inc y y (c) c + 4d B for c + 4d (accept c etc) (B for c or 4d) (d) 8pq B accept in any order but must not include sign 7 (a)(i) 60 B cao (ii) eg top triangle is equilateral B for reason 80 "60" M for 90 A ft from (a)(i) if x < 90 SC B for if x < 90 0 M for 60 or 0 or 60 or 0 or 80 A cao 9 correct drawing B Condone hidden detail shown with solid lines and missing lines on front face (B for a correct sketch with other incorrect sketch(es) or for prism with correct cross section > cube wide or for attempt to draw prism with correct cross section or prism with correct plan and side elevation) 9 UG0670

13 Paper 55/ or M for rounding at least two of the numbers to sf or for sight of 640,. or 640, or 600, or 0 seen A for 0- Note: 0.5 scores M0 A0 (a) Points plotted B full ( mm) square positive B cao (c) Line of best fit B Must pass through (4.5,.45), (4.5,.55) AND (67.5,.75), (67.5,.85) (d) ~.65 B ft from single line segment with positive gradient + full ( mm) square (a) eg M for or 4 seen 500 eg A cao 750 M for or.5 seen or A cao 0 UG0670

14 Paper 55/0 (a) 4 0 M for 4 (=) or or attempt to divide diagram up into rectangles M or sum of areas of rectangles A cao M 680 or or 68 seen 00 M (dep) or M for (i) A cao (ii) or M For or 4.96 Accept 748 rounded up or down to next 50 followed by 50 A ft from (i) rounded up SC B for 680 (seen) leading to 4 UG0670

15 Paper 55/0 M for attempt to tally A for frequency correct or all tallies correct A for all frequencies correct (accept for /0) (a) Plain llll lll 8 Chicken lll Bovril llll 5 S & Vin llll 4 (c) 4 Plain or 8 B ft B ft (a)(i) (ii) (c) (a) (c) (d) 4 (i) (ii) 5 (a) (c) See diagram 0 (.5 +.0) = Correct lines Arrow at 48 Arrow at 6.7 Cylinder Cuboid B cao B cao B cao for both lines correct (B for one line correct) B cao (B for or ) B for 580 (± ) could be written on line B for could be written on line B allow half graduation B allow half graduation B ignore spelling B ignore spelling 4 M A for 4.45 M A cao M for or sight of digits 4 A for M ¼ of 0 (oe) A cao SC B for 90 UG0670

16 Paper 55/0 6 (a)(i) (ii) 7 (a)(i) (ii) (c) (d) 8 (a) (c) (d) See diagram See their diagram 4 0 Obtuse Accurate drawing 5 4, Jupiter - 0 B for 4 (± 0 ) B for obtuse (ignore spelling) B for accurate drawing ± mm B cao B cao B for explaining a suitable method B for a correct diagram B cao for both (B for one only ft from their 4) B accept 90 B accept 540 B accept 50 B cao UG0670

17 Paper 55/0 9 (a) = M A 8 8 M 8 or 8 0. or digits 796 seen A cao Or M for 40 (or digits seen) or 658 (or digits seen) A if correct M for or 796 seen A cao 45 = M 5 45 (or M 5 seen) A 58 (or M 5 45) A for 87 ft (c)(i) (ii) 80 5 B for 80 ( ± ) B 5 ( ± ) 4 UG0670

18 Paper 55/0 0 (a) Height of man = 4 4 = 4 (a) = 8 mean = 8 0 =.8 (a) 4 (a) x x ( ) B for height between.5m.0m inclusive B for height between m 6m inclusive (B for multiplying (a) by a number between and inclusive) (B for multiplying (a) by a number) 4 M for 9 or 4 seen A cao B M for attempt to add and 0 or.7 or.9 seen A for.8 SC B for.5 seen B cao Accept x, x, x, x x x B for x 9 cao M for 4.44 seen or 8.66( ) or 5.7 or 5.8 or better rounded or truncated A cao B ft M for 5 4 or or sight of digits 65 A cao M for digits or sight of digits 945 A cao 7 See diagram (y + y) y + y 8 60 o 8 (=0) Sector angles: G= 60; S= 80; B=0; Correct sectors labelled correctly Use angle measurer Angles drawn, labelled B for (y + y) B for y + y (Deduct B for each additional tick (>) to min 0) 4 B4 for fully correct and labelled pie chart (B for all angles correct or for a labelled pie chart with correct angles) (B for labelled pie chart with correct angle drawn) (B for 60 o 8 or 0 seen or implied) 5 UG0670

19 Paper 55/0 9 (a) (c) 0 (a) (c) (a) x+4+x+x+4+x 4 x + 8 = 54 4 x = 46 x =.5 Length = (a). 45 Correct plane Correct net Correct drawing 5 5 4x M for sum A for 0.45 o.e. SC B for 0.8 : 7.7 B for a correct plane defined by showing at least lines. (B for a line of symmetry on one face) B cao (B for equilateral triangles joined appropriately to at least one rectangle or for equilateral triangle joined appropriately to one of rectangles) B for two extra sides of length 6cm (± mm) B for construction arcs 6cm from each of the ends of the given line. B for 5 (± ) B for 5 (± 0.4) B horiz. line from (, 0) to (, 0) B line from (, 0) to (5,0) or horizontal translation of it SC B for any journey ending at (5,0) M for attempting to add x, x + 4, x, x + 4 may be implied by 4x + a (a > 0) A for 4x + 8 or 4(x + ) M for 4x + 8 = 54 A cao for.5 seen B ft for B cao M for π.45 (accept π as. or better) A for 7.59 to UG0670

20 Paper 55/ M for or A cao M for 5.40 or sight of.8 M dep for.80 7 A for.6 or equivalent x =. M for 7.60 x or. seen or 7.60 x.75 (oe) = x 8.9 (Award M for 0%, 5% and ½% correctly calculated) A for 8.9 or 89 M for 650 x 8.9 or digits 4745 seen A cao Accept Alternative M for (0) or 540 seen 7.5 M for " 540" or 94.5 seen or (oe) (Award M for 0%, 5% and ½% correctly calculated) M for (dep on both previous method marks) or digits 4745 seen A cao accept UG0670

21 Paper 55/0 Correct shape B B for any sides correct, or a correct enlargement scale factor or. (a) B all correct 6 8 (B for correct) sign B oe 80 (a) p+q B for p+q (accept p etc) (B for p or q or pq) y B accept y or y y 4 (a)(i) (ii) (c) c+4d B for c+4d (accept c etc) (B for c or 4d or c4d) (d) 8pq B accept in any order but must not include 60 eg top triangle is equilateral 50 B cao B for reason (80 "60") M 90 A ft from (a)(i) if x < 90 SC:B for answer from if x < 90 8 UG0670

22 Paper 55/0 5 (a) 4 0 M for 4 (=) or or attempt to divide diagram up into rectangles M A cao (i) M 680 or or 68 seen M (dep) (or M for ) A cao (ii) or M for or 4.96; accept 748 rounded up or down to next 50 followed by 50 A ft from (i) rounded up SC B for 680 (seen) leading to 4 6 (a) 5 5 = 0 5 = -5 M substitute e.g 5 and 5 - or 0 and -5 A cao M substitution e.g 5 4-7; do not accept 54-7 M or or 80 7 (NB 4 as 4 4) A cao 9 UG0670

23 Paper 55/ or or (a) Points plotted B full (mm) square positive B cao M for an attempt to multiply the units and tens, or correct partitioning M complete correct method (condone one arithmetic error) A for 90. cao OR M for putting the numbers in a grid M for multiplying out and addition (condone one error) A answer shown with point OR M for correct partitioning M and calculated oe (condone one error) A cao (c) Line of best fit B must pass through (4.5,.45), (4.5,.55) AND (67.5,.75), (67.5,.85) (d) approx.65 B ft from single line segment with positive gradient full (mm) square 0 UG0670

24 Paper 55/0 9 (a) M or 4 seen eg A cao M or.5 seen or eg A cao 0 C 0( n ) B for C 0( n ) oe such as C ( n ) 0 (B for correct RHS or C n 0, C 0n etc B for C = some other linear expression in n or n 0, 0n etc) NB: C=n scores no marks (a) 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) x 4x 7x 8 x x 8 M for 4 terms correct ignoring signs (e.g x,4x,7x, 8 ) or terms with correct signs (e.g x, 4x,7x, 8) A cao correct drawing B. Condone hidden detail shown with solid lines, or missing lines on front face. (B for : one sketch correct with other sketches incorrect cross-section correct with depth > cube, correct plan and side elevation) UG0670

25 Paper 55/0 600 or to M For rounding at least two of the numbers to sf, or for sight of 640,. or 640, or 600, or 0 seen A for 0 to NB: 0.5 scores M0 A0 4 (a) correct reflection B (B reflection in line other than x=) reflection in y x B cao Accept the word reflected (B any statement including the word reflection ) 5 (a)(i) 6 5 B accept 55, 5 4+ (ii) 5 B accept 5, x y 0 and x y 4 x = 7 y = M for either x + y = 0 or x y 4 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 = and y = 7 UG0670

26 Paper 55/0 6 (a) 5 x x B for x seen OR.5.5x x 5 x x 5 M for correct rearrangement of 4 terms A for 5 oe,,,0,, B (B for 5 correct and not more than one incorrect integers) 7 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-, -, 4-5 is OK, but 0-, -, - is not OK. UG0670

27 Paper 55/0 8 (a) 6 6 = M for or or 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) or or cm A cao for 5 4 OR attempts to convert to decimals: must use at least dp M (or ) or etc A 4.4, 4.47, 4.46 A 4.46 (recurring) 4 M attempt to find the area of one face; 6 8 or (8 9) or (6 9) or (0 9) or 7 or 54 or 90 or 4 M all five faces with an intention to add A cao numerical answer of 64 B (indep) cm with or without numerical answer 4 UG0670

28 Paper 55/0 0 ab B (B for each one correct) ( c d) bc Nb B for each of the 4 d th,5 th,6 th tick (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 (a) ( ) 4 (0)8 points plotted accurately points joined with smooth curve on LH branch B & & on RH branches 4 m= n=5 4 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 B for B for 5 (B for 5 or 5) SC: award B only if m=5, n= or for 8 5 seen 5 UG0670

29 Paper 55/0 5 5 y x 5 4 M for clear attempt to find gradient eg fraction with = - -,5 in numerator,,- in denominator A for 6 B ft for y " " x 5oe (eg y = x + 5) (B for y mx 5 or, -x+5 or y " " x c ) 6 (a)(i) 50 B accept 50 or 0 (ii) "50" B for angle at the centre is twice the angle at the circumference 0 B identifies angle between radius and tangent as 90 (may be in working or on diagram) 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) 6 UG0670

30 Paper 55/04 (a) (.) 6 M for 4.44 seen or 8.66( ) seen or 5.7 or 5.8 or better, rounded or truncated A cao B ft M for 5 4 or or sight of digits 65 A cao (a) M for digits or sight of digits 945 A cao M for 6 digits 0 A cao 4 See diagram (y + y) y + y B for (y + y) B for y + y 5 60 o 8 (=0) Sector angles: G= 60; S= 80; B=0; Correct sectors labelled correctly Use angle measurer 6 (a) (c) = 4 4 = 4 (Deduct B for each additional tick (>) to min 0) Angles drawn, labelled 4 B4 for fully correct and labelled pie chart (B for all angles correct or for a labelled pie chart with two angles correct) (B for labelled pie chart with one correct angle drawn) Correct plane Correct net Correct drawing (B for 60 8 or 0 seen or implied) B for a correct plane defined by showing at least lines. (B for a line of symmetry on one face) B cao (B for equilateral triangles joined appropriately to at least one rectangle or for equilateral triangle joined appropriately to one of the three rectangles) B for two extra sides of length 6 cm (± mm) B for construction arcs 6cm from each of the ends of the given line 4 M for 9 or 4 seen or x + 9 A cao 7 UG0670

31 Paper 55/04 5 B cao for 5( ) 5 B cao for 5( 0.4) 8 (a) (c) B horiz. line from (,0) to (,0) B line from (,0) to (5,0) or horiz. translation of it SC: B for any journey ending at (5,0) 9 (a) x+4+x+x+4+x 4x+8 M for attempting to add x 4, x, x 4, x may be implied by 4x+a, a>0 A for 4x+8 or 4(x + ) 4 x + 8 = 54 4 x = 46 x =.5 Length = (a) π M for 4x + 8 = 54 A cao for.5 seen B ft for M for sum A for 0.45 oe SC: B for 0.8 : 7.7 B cao M for π.45 (accept π as. or better) A for 7.59 to M for or A cao M for 5.40 or sight of.8 M (dep) for.80 7 A for.6 or equivalent 8 UG0670

32 Paper 55/ = M for or. seen or (oe) = (Award M for 0%, 5% and ½% correctly calculated) A for 8.9 or 89 M for or digits 4745 seen A cao Accept OR M for or 540 seen 7.5 M for 540 or 94.5 seen or 00 " 540".75 (oe) (Award M for 0%, 5%, and ½% correctly calculated) M for (dep on both previous M marks) or digits 4745 seen A cao accept UG0670

33 Paper 55/ /(60 60) = 79.6 M for or or for a correct method to obtain two comparable values e.g and (M for or 0.079(.) seen or or seen or for or seen or or 0.08 seen) A for 88 or 79.(.) or for two correctly calculated comparable values e.g and (a) 4x + = 6 4x = B for 4x + or x 4 M for a correct re-arrangement of their terms to isolate 4x or x A for. 5 oe v u = 5t v u 5 M for isolating 5t or t or for dividing through by 5 A oe 0 UG0670

34 Paper 55/ (9). 9.9(68)..7(7).4 5.7(04).5 8.8(75).4 5.7(04)..7(7).5 4.(9575) 8 (a) 6 (7++) 7. 4 B for trial between. and.4 inclusive (B for trial between and 4 inclusive) B for different trial between. and.4 exclusive B (dep on at least one previous B) for. NB trials should be evaluated to at least dp truncated or rounded M for 6 (7++) M (dep) for 7 or or A cao = = or 47. or M for or 4.7(75) seen M (dep) for (75) A for 47 or better B (indep) for rounding their answer correctly to the nearest whole number or or d.p OR M for M for 5.5 "0.95" or A for 47 or better B (indep) for rounding their answer correct to the nearest whole number or or d.p UG0670

35 Paper 55/04 9 (a) Angle in a semicircle B oe (c) + 6 = = 0 π M for + 6 M for A cao "0" M for π M (indep) for correct order of evaluation of r for any r A for 4 5 inclusive UG0670

36 Paper 55/04 0 (a) ( 0)+( 5)+(5 0)+(7 5)+ (9 5)+( 5) = = M for use of fx with x consistent within intervals (including end points) M (dep) for use of midpoints fx M (dep on st M) for use of f A 6.08 to (0),5,55,90,5, 0 B for all correct (c) graph B ft for 5 or 6 points plotted correctly full (mm) square at the end of interval dep on sensible table (condone addition error) B(dep) for points joined by curve or line segments provided no gradient is negative ignore any part of graph outside range of their points. (SC: B if 5 or 6 points plotted not at end but consistent within each interval and joined) UG0670

37 Paper 55/04 (d) 7 74 M (ft dep on graph being cf) for reading from graph at 7 A ft ± full ( mm) square Or B for 7 74 (a) (c) (d) a 7 5x y 4 x (x + )(x ) 4 a B accept B cao (B for two of 5, x, y 4 in a product) B cao B cao 80% = M for recognising that 80% is equivalent to 0 M for oe A cao 4 UG0670

38 Paper 55/04 x = y = 0.5 M for coefficients of x or y the same followed by correct operation, condone one arithmetical error M (dep) for substituting found value in one equation A cao SC: B for one correct answer only if M s not awarded B for or (B for or 4400,000,000 or 4000,000,000 or ) 5 (a). 9 tan x =..9 x = tan -. = M for tan x = M for tan -. A for or tan B (indep) ft for rounded to or 4 s.f 5 UG0670

39 Paper 55/04 6 SF= 9 9 M for or or. seen or 0.75 seen or 8 seen 9 6=8 9 or 9 6 or 6 9 or 0.66 or.5 or or oe seen A cao 6 UG0670

40 Paper 555/05 (a) x 4x 7x 8 x x 8 M for 4 terms correct ignoring signs (e.g x,4x,7x, 8 ) or terms with correct signs (e.g x, 4x,7x, 8 ) A cao 4 y y B cao 4 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-, -, 4-5 is OK, but 0-, -, - is not OK. reflection in y x B cao accept the word reflected (B any statement including the word reflection ) 4 (a) 5 x x B for x seen OR.5.5x x 5 x x 5 M for correct rearrangement of 4 terms A for 5 oe,,,0,, B (B for 5 correct and not more than one incorrect integers) 7 UG0670

41 Paper 555/05 5 (a) 6 6 = M for or or 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 4 OR attempts to convert to decimals: must use at least dp M (or ) or etc A 4.4, 4.47, 4.46 or 0.4, 0.47, 0.46 or 0.4, 4.4 A 4.46 (recurring) 6 (a)(i) 6 5 B accept 565, 5 4+ (ii) 5 B accept 5, x y 0 and x y 4 x = 7 y = M for either x + y = 0 or x y 4 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 8 UG0670

42 Paper 555/ or 48 4 M attempt to find the area of one face; or (8 9) or (6 9) or (0 9) or 7 or 54 or 90 or or or 48 cm M all five faces with an intention to add A cao numerical answer of 64 8 ab d ( c d) bc B (indep) cm with or without numerical answer B (B for each one correct) Nb B for each of the 4 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) ( ) 4 (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 9 UG0670

43 Paper 555/05 5 y x 5 4 M for clear attempt to find gradient eg fraction with = - -,5 in numerator,,- in denominator A for cao 6 B ft for y " " x 5oe (eg y = x + 5) (B for y mx 5 or, -x+5 or y " " x c ) (a) on LH branch B cao 4 & & on RH branches B 4 4 = (c) n 4 or 6 84 or : oe 4 4 M for or from their tree diagram 4 4 M for sum of two products 7 A for oe M for either 4 tree diagram or 4 M for 4 (=84) or 4 6 from their A for 4 cao SC: B for 6 seen in fraction or ratio 40 UG0670

44 Paper 555/05 4 (a)(i) 50 B accept 50 or 0 (ii) 5 (a) "50" or 80 "50" eg x = 0.99 so 00x = x = 9 9 so x 99 B for angle at the centre is twice the angle at the circumference 0 B identifies angle between radius and tangent as 90 (may be in working or on diagram) 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 0.77 B for.7 recurring or oe or 0.7 M for 00x 9. 9 M dep for subtraction of both sides A for from correct proof Alternative method M for.000 M for remainders and A for 0.9 recurring 9 SC:B for 99 4 UG0670

45 Paper 555/05 6 (a) (c) 7 (a)(i) (ii) d kt 80 k t 00 ( x 6x 64) LHS = 4 = 6 6x x 4 RHS = 6 x 8x x = LHS 4 d 5t 45 (0, 9) (8, 5) M for d kt or d t M sub d=80 and t=4 into their equation A for d 5t oe (cao) B ft from (a) using k M ft from (a) for substituting d=45 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) M for expansion of either set of brackets with at least of 4 terms correct M for common denominator of 4 or multiplying through by 4 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 4 4 UG0670

46 Paper 555/05 8 (a) or 9 M for or 9 or or :9 oe 9 9 or 80 M for or 90 9 or or or 9 : oe A cao SC:B for answer of 6 9 (a)(i) (ii) (iii) or 7 or or 64 (4 ) M for " " or 7 or 9 : ( 8) oe or 9 or 700 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) 4 UG0670

47 Paper 555/05 0 (a)(i) (ii) (i) (ii) (90, ) (80, 0) (45, 0) (90, -) B cao could be indicated on diagram B cao could be indicated on diagram B cao could be indicated on diagram B cao could be indicated on diagram 4 x M for substitution in correct formulae x h (x) M (dep.) for correct unsimplified expression eg 4 x h 4 8x (x) h oe or h 8x oe x A for x cao (a) a b B OM a + b ON MN a b +a OX a + b a or 6 a (B for either OM or ON or a b + a SC: B for b a OY b + 4a 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 44 UG0670

48 Paper 555/06 (a) v u = 5t v u x = 5x 5 = 4x (a) 6 (7++) M for isolating 5t or t or for dividing through by 5 A oe x M for x = 5( x 5) or x M for isolating terms in x correctly from A cao accept 5,, 5.5 M for 6 (7++) M (dep) for 7 or or A cao ax b cx d = = or 47. or M for or 4.7(75) seen M (dep) for (75) A for 47 or better B (indep) for rounding their answer correctly to the nearest whole number or or d.p OR M for M for 5.5 "0.95" or A for 47 or better B (indep) for rounding their answer correct to the nearest whole number or or d.p 45 UG0670

49 Paper 555/ (9). 9.9(68)..7(7).4 5.7(04).5 8.8(75).4 5.7(04)..7(7).5 4.(9575) 4 (a) Angle in a semicircle. 4 B for trial between. and.4 inclusive (B for trial between and 4 inclusive) B for different trial between. and.4 exclusive B (dep on at least one previous B) for. NB trials should be evaluated to at least dp truncated or rounded B oe + 6 = = 0 0 M for + 6 M for A cao (c) π 0 4 "0" M for π M (indep) for correct order of evaluation of r for any r A for 4 5 inclusive 46 UG0670

50 Paper 555/06 5 (a) ( 0)+( 5)+(5 0)+(7 5)+ (9 5)+( 5) = = M for use of fx with x consistent within intervals (including end points) M (dep) for use of midpoints fx M (dep on st M) for use of f A 6.08 to (0),5,55,90, 5,0 B for all correct (c) graph B ft for 5 or 6 points plotted correctly full (mm) square at the end of interval dep on sensible table (condone addition error) B(dep) for points joined by curve or line segments provided no gradient is negative ignore any part of graph outside range of their points. (SC: B if 5 or 6 points plotted not at end but consistent within each interval and joined) (d) 7 74 M (ft dep on graph being cf) for reading from graph at 7 A ft ± full ( mm) square Or B for UG0670

51 Paper 555/06 6 (a) a 7 B accept 5x y 4 B cao (B for two of 5, x, y 4 in a product) (c) x B cao (d) (a + b)(a - b) B for (a + b)(a - b) (B for (a b)(a b) 4 a 7 80% = M for recognising that 80% is equivalent to 0 M for oe A cao 8 x = y = B for or M for coefficients of x or y the same followed by correct operation, condone one arithmetical error M (dep) for substituting found value in one equation A cao SC: B for one correct answer only if Ms not awarded (B for or 4400,000,000 or 4000,000,000 or ) 48 UG0670

52 Paper 555/06 0 (a) tan x = M for tan x = 9. or tan M for tan - x = tan - = A for B (indep) ft for rounded to or 4 s.f (a) SF= 9 9 M for or or. seen or 0.75 seen or 8 seen 9 6=8 9 SF = 9, 9 7 = or 9 6 or 6 9 or 0.66 or.5 or or oe seen A cao M for A cao BE 9 = oe 7 49 UG0670

53 Paper 555/06 (a) 84 = a a +.4 = or a = M for substituting correctly, may be left M for correct rearrangement as far as a A for P = πr + r+a P a M subtracting a from each side P a = πr +r M for factorising to get ( ) r P a = (π + )r A for P a oe p a S.C oe is M M A0 5.4 Area ABC = ½ 4 8 sin06 (= 5.8) 5.8 M for ½ 4 8 sin06 4 (a) 4.5 M (dep) for (6..) or 07.6 A SC 07.6 is B B cao 500 x = M for A for (SC:B for no working) 50 UG0670

54 Paper 555/06 5 (a) 6x + x 0 + 6x 4 = 5 6x + 7x 9 = 0 M for an expression for the area involving either ( x )(x 5) (x ) or x(x ) (x )(7 x) or x(x 5) (7 x) or (x ) + (x ) + ( x )(7 x) where in each case at least one of or product terms must be correct M (indep) for one correct expansion involving x A for simplification to final answer 5 UG0670

55 Paper 555/06 5 (i) ( 9) x x or x + x = x , x A x =.5 or 4., or better 6 SC:M for answer.5 with no working or T & I (ii) 8 B cao length = 8 4 M for c ( 9) x up to signs in b & M for x A x. 5 or 4., or better OR M for ( x )(x ) (M for ( x a)(x b) with ab = ±9 A x =.5 or 4., or better OR 7 M for x 7 M x seen UG0670

56 Paper 555/06 6 (a) 8 8 P(win) = ( ) 5 M for or or for clearly identifying in P(R) P(R) + P(B) P(B) " " " " " " " " M for P(win) = (=) A for, oe 5 " " M for ( ) 50 or 0.5 A cao 5 UG0670

57 Paper 555/06 7 Lower bound of 00 is 50 Upper bound of 60 is B for 50 or 50 seen B for 65 or 55 seen M (Lower bound of load) (Upper bound of weight) Where 50 LB load < 00 and 60 < UB Weight 65 A for 7 requires fully correct working OR B for 50 or 50 seen B for 65 or 55 seen M (upper bound of load) (lower bound of weight) Where 00 UB load 50 and 55 LB weight < 60 A for requires fully correct working OR M A.8 A requires fully correct working OR M A 8.4(6) A 8 requires fully correct working 8 (a) x y 8 y 4 8 x B for 4 8 8x y (B for of 8, 4 x, 8 y ) x( x ) x B for x( x ) ( x 5)( x ) x 5 B for ( x 5)( x ) B cao 54 UG0670

58 Paper 555/06 9 (a) 6 = 5.66 M for 6 (= ) V 8.9 V A M sinx = oe 6 A x D M for DVA = sin - ( 6 ) A DVA = sin - ( ) 6 OR cos DVA cos DVA OR M for ( cosdva ) M for DVA cos 7 A UG0670

59 Paper 555/06 9 (c) AC = + - cos0 o AC = OR AN = sin 60 = OR VN = " " = cos AVC = cos AVC = 60 7 OR AVC = sin - 6, using AN OR AVC = cos - 6, using VN.6 4 M for any valid method for AC or AN or VN where N is the midpoint of AC A for AC = or AC = (=.46 ) or AN = (=.7 )or VN = (=5.74 ) M (indep) for correct method to find angle AVC A UG0670

60 Paper 555/06 0 (a) Graph translated unit to the right passing through the points (-,0), (,) and (,0) M for translation of or 0 0 A for right through the points, 4 sq Graph stretched units parallel to y-axis; passing through the points (-,0), (0,4) and (,0) M for graph stretched parallel to the y-axis by scale factor A through all points; 4 sq not on grid at x = 57 UG0670

61 Further copies of this publication are available from Edexcel Publications, Adamsway, Mansfield, Notts, NG8 4FN Telephone Fax Order Code UG0670 Summer 005 For more information on Edexcel qualifications, please visit Alternatively, you can contact Customer Services at or on Edexcel Limited. Registered in England and Wales no Registered Office: One90 High Holborn, London, WCV 7BH 58 UG0670