GCSE. Edexcel GCSE Mathematics A Summer Mark Scheme (Results)

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Transcription:

GCSE Edexcel GCSE Mathematics A 387 Summer 006 Mark Scheme (Results)

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 If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work.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

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.

Paper 555_06 P marked at top left and bottom B for both correct (B for one correct) ( B for each error if more than Ps) 36 9 part = 8 : : 6 A 8 B C 6 3 M for 36 ( + 3+) M (dep) or 3 or A cao 3 (a) Overlay (a) B for correct triangle with arcs (B for correct triangle, no arcs) (b) Overlay(b) M for pairs of correct intersecting arcs A for correct perpendicular bisector SC If no marks B for line within guidelines No because when n = 6 6n (= 35) is not prime B correctly showing when n = 6, 35 is obtained and identified oe or for correctly evaluating 6n when n is 0 or negative. (B for correctly evaluating 6n for at least 3 different whole number values of n or 35 oe with no working) M for 3% = 0.7 or 0.03x = 0.7.7 3 0.7 M for % = 0. oe or or 0.7 33.3 or 03 3 A for.7 SC B for seen (a)(i) x 9 B cao 5 3% = 0.7 % = 0. 00% = 03% =.7 6 (ii) p 5 B cao (iii) s 6 t 5 B cao (B for two of, s 6, t 5 in a product) (iv) q B cao (b) 6g 3 B cao (c) d + 6d B cao (B for d or 6d ) (d) x + 3x + x + 6 x + 5x + 6 B for x + 5x + 6 (B for 3 out of parts correct in working ) 3

Paper 555_06 7 8 9 0 + 6 M for + 6 or 6 + 36 or 5 6 + 36 = 5 7. 3 M for 6 + 36 or 5 5 A for 7.- 7. (a) 35 t < 0 B for correct interval (b) 8.5 3 7.5 7 3.5 7 37.5 5.5 390 0 3.75 M for fx consistently within interval including ends (allow error) M ( dep) consistently using midpoints. M (dep on st M ) for fx f A for 3.75 or 3.7 or 3.8 (a) 6.06.05 B for.05 (B for sight of.6(.) or.985 or.(.)).985 (b). B ft any answer to (a) correctly rounded to, 3 or Rotation 80º centre (0,0) a = 3 b = 3 3 significant figures B for rotation B for 80º or turn B for (0,0) Or B enlargement SF B centre (0,0) If no marks awarded SC B for correct reflections M for a complete method which leads to a single equation in a or b only (allow error) M (dep) substitute found value of a or b into one equation A cao SC B for one correct answer only if Ms not awarded, a =3 or b =

Paper 555_06 (a) 5 tan a = 6 5 M for tan(a =) 6 3 (b) Angle a = 39.8º sin 0º = 0 x 39.8 6.3 M for a = tan ( 6 5 ) or tan (0.83) to tan - ( 0.83) (Allow tan - 5 6) A for 39.8-39.8 SC 0.69 0.695 or.. seen gets MM A0 x M for sin 0 = 0 x = 0 sin 0º M for 0 sin 0 A for 6.7 6.3 (SC 7.5 or 5.87 seen gets MM A0) (a)(i) p + q B cao p + q (ii) q p B q p oe (b) (p + q) B (p + q) oe 8 50² 0 000cm² M for 50² seen A for 0 000cm² or m² 5 (a),, 0,, B for all correct (B for,0, if seen in list, B for,,, ) (b) p + p < 8 + 7 p < 3 p < 3 M for p + p < 8 + 7 A cao 6 P and C Q and D R and B S and A B for all correct (B for exactly or exactly 3 correct) 5

Paper 555_06 7 8 (a) (b) m = = c = 3 3 3 3 3 y = x + 3 M for clear attempt to find gradient of AB A for m = B for c = 3 in y = mx + c m does not have to be numerical A for y = x + 3 oe SC B for y = x + 3 seen B3 for x + 3 on its own B for x + 3 on its own B for correct on tennis 3 B for 3, 3, 3 correct on snooker M for 3 3 A for oe (c) 3 7 + 3 3 + 3 3 M for " " or " " " " 3 3 ' 3 M " " + " " " " 3 3 A for 7 oe (0.58 ) Or 3 M for + 3 ' A for 7 oe (0.58 ) 3 6

Paper 555_06 9 (a)(i) 6.75 B cao (ii) 6.65 B cao 0 (b)(i) 6.95 6. 65.0563 3 M for 6.95 6.65 where 6.9 < 6.95 6.95 and 6.65 6.65 < 6.7 A for.0563 (.) (ii) 6.85 6. 75 3.97778 If M not earned in (i), then M for 6.85 6.75 where 6.85 6.85 < 6.9 and 6.7 < 6.75 6.75 A for 3.9777 (..) (c)(i) B cao (ii) bounds agree to sf B for appropriate reason for (a) 6 6 7x y 7x y B for fully correct B for of 7, x 6, y correct in a 3 term product (b) 6x + 5x x 0 6x + x 0 B for fully correct (B for 3 out of terms correct in working including signs or (c) ( x + )( x + 3) x( x + ) 5 ± 5 8 x = 5± 57 5 ± 7.5983 = x = 6.79 or x =.79 x + 3 x 6.7 or.7 terms correct, incorrect signs) x + 3 B for x (B for x(x + ) or (x + )(x + 3) seen) 3 M for correct substitution into formula up to signs on b and c 5± 57 M for A 6.7 to 6.75 and.7 to.75 7

Paper 555_06 3 (a) 0 or 360 3 0 π 0. 360 (b) Area Sector = π = 0. = 6.836 Area segment = 66.3. ( 0.) 3 = 3. 688 Area Triangle ( )( ) o sin ADB sin 8 = 5 DB 5 sin 8 DB = sin 6 DB = 6.77 DC = 6.77 sin 5 0. sin0.7.8 3 66..7 5 0 B for or seen 360 3 0 M for π 0. 360 A for.7 -.8 M for π (0.) 0 3 or π (0.) oe 360 o M for ( 0.)( 0.) sin0 or any other valid method for area triangle OAC M (dep on at least of the previous Ms) for area of sector area of triangle OAC, providing the answer is positive. A 66.35 66.5 sin"6" sin 8 M for = 5 DB 5 sin 8 M for DB = sin"6" A for 6.7 6.8 M for DC =" 6.7" sin5 A for.65.7 Or o sin"6" sin"6 " M for = oe 5 AD o 5 sin"6 " M for AD = o sin 6 A for 6. 6. M for 6. sin 8 A for.65.7 8

Paper 555_06 Draw circle centre (0,0) radius Draw a line through (,) Show two intersections Fully correct explanation 3 M circle or semi-circle centre (0, 0) drawn or plotted with at least 8 points or stated A correct circle drawn or stated A straight line drawn through (, ) and cutting the (possibly freehand) circle at distinct points or for stating that any straight line through (,) will cut the circle in places as (,) is inside the circle 9