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

Transcription

1 GCSE Edexcel GCSE Mathematics A 7 Summer 006 Mark Scheme (Results)

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 If working is crossed out and still legible, then it should be given any appropriate marks, as long as it has not been replaced by alternative work.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

4 Paper _0 (a) x = 0 (b) 4 = M ( x = ) ( =6) or 6 seen 6 or 6 or both. Also accept 6 M for attempt at continual prime factorisation (at least correct steps); could be shown as a factor tree. A all correct prime factors and no others A or oe (a),, B all three correct (B one or two correct) (b) Bft points plotted correctly ± full square B smooth curve through their plotted points provided at least B awarded in (a). (c).6, 0.6 B for x=.4 to. and -0. to -0.4 otherwise ft ± full square depends on at least B in (b) (B for one value or line y= seen) 0..g M 0. 4 overlay 4 M quarter circle drawn centre A inside rectangle (ignore lines outside the rectangle) A radius 4 cm±mm B line drawn cm ±mm from DC. B ft (dep on two loci attempts drawn) region shaded 6 M ( 6 + 0) '60' or 6 seen or A oe M two of 400, 6, 0. = A or or or 00 6 or or A answer in range

5 Paper _0 7 (a) 6.g B cao (b) 7.g. B 7. or 7.49 or or How many pizzas have you eaten in the last week? Include a time period Proper response B include a time period B at least numeric response boxes 0 More than boxes 9 (a) B cao 0 (b) B cao (c).6 0 B cao (a) ( + )( x + 4) (b), 4 (a) SF =. 9 cm x M ( x ± )(x ± 4) B ft from (a) or, 4 M SF =,,., 0.6 oe (b) 4 0 cm (a) x =, y = (b) (4,), (,) (,), (,) M 4, 4 B cao oe B all correct and none incorrect B at least correct and not more than 4 points B line x= 6 drawn or one point correct 4

6 Paper _0 (a) He has taken it from this year instead of last year (b) B Reason or appropriate calculation 40 M oe. B cao 4 (a),, 69, 9, 00 (b) B ft for 4 or points plotted correctly ± full mm square at the end of interval dep on sensible table (condone one addition error) B dep for points joined by curve or line segments provided no gradient is negative. Ignore any point of graph outside range of their points. SC: B if 4 or points plotted not at end but consistent within each interval and joined. (c) 6-64 hours B 6-64 otherwise ft from cumulative freq graph B for hours (a) 90 90º 0 B 90 B angle in semi circle (= 90 o ) 0 0 B or (b) 70 º B angle at centre = twice angle at circumference OR B angle on a straight line with isosceles triangle

7 Paper _0 6 (a) T = km 600 k = T = M for T = km or 600 M for ( k =) T 0 (=.4) or = 400 oe ( T = ) (b) K T = P T = K T 60 M for T = or P 400 = oe 900 K M for ( K = ) or 60 = ( T = ) oe 900 or (K =) or 7 (a) (b) R = (6, 0), S = (,7) 6 = QS M subtraction of coordinates or position vectors 4 x or or, where x and y are integers y 4 SC: B for or B for 4 x B for or, where x and y are integers y 6

8 Paper _0 (a) x x + = x x x x = 4 9 M for A 4 9 oe 6 + x or x x + 6x + x x = x or = x x (b) (y ) = 4 9 y = ± y =, M (y-) 9 = " " or 4y y = 0 oe 4 oe 9 oe (a) Heights 4, B cao for bar from 7., height 4 mm squares B cao for bar from 7. 0, height mm square (b) Freqs 40, 0, B cao for all correct (B for any or correct) (c) Area up to. = 0x Area above = 6x 7 M for attempt to find area upto. and area above consistantly 6 x Frequency = 0 M for 0 or 0 or 6 oe 0x 0. 0 A 7 cao SC: If no marks earned B for mm = person oe 7

9 Paper _0 0 (a) B cao (b). B. oe (c) 4 6 (d) = = 64 " or ( ) " M ( =) 4 or A for 6 (accept m = 6) M or or or oe "6 " (a) BC = CE equal sides CF = CD equal sides BCF = DCE = 0 o BFC is congruent to ECD (SAS) (b) So BF=ED (congruent triangles) BF = EG ( opp sides of parallelogram) ( n + a) P = n + a np + ap = n + a a( P ) = n np n np a = P A for (accept p = ) B for either BC = CD or BC = CE CF = CE or CF = CD B for BCF = DCE = 0 o or correct reason B for proof of congruence B BF = EG or BF = ED B fully correct proof 4 M ( n + a) P = n + a M np + ap = n + a M a( P ) = n np or a( P ) = np n A for n np a = oe P

10 Paper _0 4 (a) ( )( x ) (b)(i) ( n a)( n + a ( n a)) or n a ( n an + a ) (b)(ii) x a ( n a) a and n a are integers n (n a) is even (a)(i) (0, ) B cao (ii) (,-) B cao (iii) (, ) B cao (b) y = f ( x) B cao B ( x a)( x b), where ab = 6 M for ( n a) ( n + a) seen or M for n an + a seen 4 M dep for identifying n a as an integer or multiplying by gives an even number or M dep for identifying an or a as an integer, or for the difference of two even numbers is an even number A correct proof B cao (c) Translation by + parallel to the y axis B for translation by 0 9