Mark Scheme Sample Assessment Material

Transcription

1 Mark Scheme Sample Assessment Material GCSE GCSE in Mathematics Specification A Higher Tier Paper :(Non-Calculator) Edexcel Limited. Registered in England and Wales No Registered Office: One90 High Holborn, London WCV 7BH

2 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. 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. Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response. Mark schemes will indicate within the table where, and which strands of QWC, are being assessed. The strands are as follows: i) ensure that text is legible and that spelling, punctuation and grammar are accurate so that meaning is clear Comprehension and meaning is clear by using correct notation and labelling conventions. ii) select and use a form and style of writing appropriate to purpose and to complex subject matter Reasoning, explanation or argument is correct and appropriately structured to convey mathematical reasoning. iii) organise information clearly and coherently, using specialist vocabulary when appropriate. The mathematical methods and processes used are coherently and clearly organised and the appropriate mathematical vocabulary used. Guidance on the use of codes within this mark scheme M method mark A accuracy mark B working mark C communication mark QWC quality of written communication oe or equivalent cao correct answer only ft follow through sc - special case

3 Edexcel GCSE Sample Assessment Materials Edexcel Limited

4 MA0/H 3. FE No of tiles around room = lengths of room = 8,,, Total number of tiles = = Cost = Area of the room = 8 + = 5 Area of a tile = = 0.5 Number of tiles = = Cost = 89 M for doubling each length to show number of tiles for each side B for 8,, and M for a full method of finding the number of tiles ( + 8 ) A for at least one section correct M for M for full method for finding the area of the room A at least one area correct B for area of tile = 0.5m or 500 cm or tiles = m M for area of room area of a tile M for number of tiles. (a) 5p = 0 p = M add to both sides Total for Question: marks (b) 9 = 3q q = 3 M correct method to isolate ±3q (c) x 3 0 x = 3 M at least one expansion correct A 3 or a statement that the answer is indep of x depending on correct working Total for Question: marks 7 Edexcel GCSE Sample Assessment Materials Edexcel Limited 009

5 Edexcel GCSE Sample Assessment Materials Edexcel Limited

6 MA0/H 8. x x 5 x, x M x x 0 A x 0 A oe Chooses a suitable number of balls (say 0) 5 will be red The other 5 need to be shared out in the ratio :, Hence yellow and blue Total for Question: 3 marks 78 Edexcel GCSE Sample Assessment Materials Edexcel Limited 009

7 MA0/H 9. (a) (i) a 3 B cao (ii) x y 3 B x y 3 (B for out of 3 terms correct in a product) (b) x + 3x + 7x + x + 0x + M 3 or terms out of correct in a term expansion (c) 3p(q p) B cao (B p(3q p), p( q p), p(aq + bp) where a and b are numbers) (d)(i) (ii) 3 ( x ) ( x 3 ) 3 x x 0 x 0 = 3 x x 5 3 (3y )(y 3) ( 3 x 5)( x ) B cao (B (3y m)(y n) where mn = ±3 or m + n = ±0 M use of the factorised form with y replaced twice by 3x + B 3 x x 5 B cao Total for Question: marks Edexcel GCSE Sample Assessment Materials Edexcel Limited

8 MA0/H 0. Reds,, 8,, 30 3 B list of red and green multiples (both to at least 8) or explicitly Greens 9, 8, 7 0 states LCM B works out highest number (90 seen) 5 B (accept ) x 5 x =.5 Total for Question: 3 marks M a correct expression for x involving ratios of sides, e.g. x oe 5 x y 5 9 or y 9 x 5 y =.5 M x y 9 5 y 9 5 or y x 5 oe 9 Total for Question: marks 80 Edexcel GCSE Sample Assessment Materials Edexcel Limited 009

9 MA0/H. (a) M Attempts to list all outcome pairs A all found M (M, A oe or 3) (b) Prob Ali wins = 30 3 B Prob Ali wins = oe Number of wins = 80 M ' 80 A ft Total for Question: marks ' Edexcel GCSE Sample Assessment Materials Edexcel Limited 009 8

10 MA0/H 3. (a) B cao (b). 5 0 ( 00 0 ) 5. 0 M. 5 0 oe ( 00 0 ) Total for Question: 3 marks 8 Edexcel GCSE Sample Assessment Materials Edexcel Limited 009

11 MA0/H. Let AB = x, AD = y Area of rectangle = xy Area AXD = xy Area CYZ = 8 xy Shaded area = 5 xy 8 5 M a full method to find the unshaded area and subtracting from 8 B area of AXD = area of ABCD B area of CYZ = area of ABCD 8 Diagram M for dividing left into congruent triangles for dividing right into congruent triangles B left = A and A or shaded = of = = 8 B right = A and A and A or shaded = 3 of = 8 3 Substitution M for deciding upon suitable side lengths for AD and AB and calculating dimensions of internal shapes B for area of DZX B for area of ZXBY M for deciding upon suitable side lengths for AD and AB and calculating dimensions of internal shapes B for area ADX B for area ZCY Total for Question: marks Edexcel GCSE Sample Assessment Materials Edexcel Limited

12 MA0/H 5. (a) (i) BC = CO OB a b M BC = CO OB (ii) AQ = AO OB BQ 3b a M a + b + = a + b + (a b) (a b) (b) OX = b, AX = a + b = ( a + 3b) Correct reason, with correct working 3 B OX = b B AX = a + b C convincing explanation Total for Question: 7 marks 8 Edexcel GCSE Sample Assessment Materials Edexcel Limited 009

13 MA0/H = M for A for oe 70 ' 0 ' M 70 or ' 0' correct cases (M any correct cases) X 3 SC with replacement M M (3 (3 x x 5)( 5)(3 x x 7) 5) 3 x 7 3 B ( 3 x 5)( x 7 ) x 5 B ( 3 x 5)(3 x 5 ) x 7 B 3 x 5 Total for Question: marks Total for Question: 3 marks Edexcel GCSE Sample Assessment Materials Edexcel Limited

14 MA0/H 8. (a) B (b) ( + 3 ) ( 3 ) = M term expansion with 3, terms correct and sight of 3 or 9 9. (a) Smooth curve B correct plot of their values B smooth curve through their points Total for Question: 3 marks (b) x = 3 y = 0 3 M attempts to draw circle at origin M uses radius 3 cm (using graph scale correctly) B for substituting a value of x into y = x(x 3) and x y x y B for substituting y into x = 3 into x(x 3) and B cao Total for Question: 5 marks r r 8 Edexcel GCSE Sample Assessment Materials Edexcel Limited 009

15 MA0/H 0. QWC ii, iii = ( n ) ( n n = 8n ) n ( n n ) Fully algebraic argument, set out in a logical and coherent manner B the nth term for consecutive odd numbers is n oe (B n + k, k or n = n or x B use of n + and n oe M ( n ) ( n ) M n n ( n n ) C conclusion based on correct algebra QWC: Conclusion should be stated, with correct supporting algebra. ( n ) ( n ) = ( n ) ( n ) ( n n )) = n = 8n B use of n + and n oe M ( n ) ( n ) M ( n ) ( n ) ( n n )) C conclusion based on correct algebra QWC: Conclusion should be stated, with correct supporting algebra. Total for Question: marks Edexcel GCSE Sample Assessment Materials Edexcel Limited

16 MA0/H. L F FD CF > Histogram Cumulative Frequency polygon 8% B Scales labelled and also marked on the vertical axis with frequency density or with cumulative frequency M frequency densities calculated, at least one non-trivial one correct. A all correctly plotted (M cumulative frequencies correct) M Use 50 on the horizontal scale of CF diagram read off vertical axis (00-0) or Use 50 on the horizontal scale of a histogram and covert area to the left to a frequency M convert to a percentage A Total for Question: marks 88 Edexcel GCSE Sample Assessment Materials Edexcel Limited 009

17 . Jan Feb Mar. Fraction Decimal % kg % Not known 0.5.5% 5 kg %.5 kg 00 A X B A X B Y Y D Z C D Z C Edexcel GCSE Sample Assessment Materials Edexcel Limited

18 90 Edexcel GCSE Sample Assessment Materials Edexcel Limited 009

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