GCSE Mathematics. Higher Tier Unit 1 Statistics and Number Mark scheme H November Version 1.0 Final.

Transcription

1 GCSE Mathematics Higher Tier Unit 1 Statistics and Number Mark scheme 43601H November 2015 Version 1.0 Final.

2 Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the standardisation events which all associates participate in and is the scheme which was used by them in this examination. The standardisation process ensures that the mark scheme covers the students responses to questions and that every associate understands and applies it in the same crect way. As preparation f standardisation each associate analyses a number of students scripts. Alternative answers not already covered by the mark scheme are discussed and legislated f. If, after the standardisation process, associates encounter unusual answers which have not been raised they are required to refer these to the Lead Assessment Writer. It must be stressed that a mark scheme is a wking document, in many cases further developed and expanded on the basis of students reactions to a particular paper. Assumptions about future mark schemes on the basis of one year s document should be avoided; whilst the guiding principles of assessment remain constant, details will change, depending on the content of a particular examination paper. Further copies of this mark scheme are available from aqa.g.uk Copyright 2015 AQA and its licenss. All rights reserved. AQA retains the copyright on all its publications. However, registered schools/colleges f AQA are permitted to copy material from this booklet f their own internal use, with the following imptant exception: AQA cannot give permission to schools/colleges to photocopy any material that is acknowledged to a third party even f internal use within the centre.

3 Glossary f Mark Schemes GCSE examinations are marked in such a way as to award positive achievement wherever possible. Thus, f GCSE Mathematics papers, marks are awarded under various categies. If a student uses a method which is not explicitly covered by the mark scheme the same principles of marking should be applied. Credit should be given to any valid methods. Examiners should seek advice from their seni examiner if in any doubt. M A B ft SC M dep B dep Method marks are awarded f a crect method which could lead to a crect answer. Accuracy marks are awarded when following on from a crect method. It is not necessary to always see the method. This can be implied. Marks awarded independent of method. Follow through marks. Marks awarded f crect wking following a mistake in an earlier step. Special case. Marks awarded within the scheme f a common misinterpretation which has some mathematical wth. A method mark dependent on a previous method mark being awarded. A mark that can only be awarded if a previous independent mark has been awarded. Or equivalent. Accept answers that are equivalent. 1 eg, accept 0.5 as well as 2 [a, b] Accept values between a and b inclusive Accept answers which begin 3.14 eg 3.14, 3.142, Use of brackets It is not necessary to see the bracketed wk to award the marks. 3 of 15

4 Examiners should consistently apply the following principles Diagrams Diagrams that have wking on them should be treated like nmal responses. If a diagram has been written on but the crect response is within the answer space, the wk within the answer space should be marked. Wking on diagrams that contradicts wk within the answer space is not to be considered as choice but as wking, and is not, therefe, penalised. Responses which appear to come from increct methods Whenever there is doubt as to whether a candidate has used an increct method to obtain an answer, as a general principle, the benefit of doubt must be given to the candidate. In cases where there is no doubt that the answer has come from increct wking then the candidate should be penalised. Questions which ask candidates to show wking Instructions on marking will be given but usually marks are not awarded to candidates who show no wking. Questions which do not ask candidates to show wking As a general principle, a crect response is awarded full marks. Misread miscopy Candidates often copy values from a question increctly. If the examiner thinks that the candidate has made a genuine misread, then only the accuracy marks (A B marks), up to a maximum of 2 marks are penalised. The method marks can still be awarded. Further wk Once the crect answer has been seen, further wking may be igned unless it gs on to contradict the crect answer. Choice When a choice of answers and/ methods is given, mark each attempt. If both methods are valid then M marks can be awarded but any increct answer method would result in marks being lost. Wk not replaced Erased crossed out wk that is still legible should be marked. Wk replaced Erased crossed out wk that has been replaced is not awarded marks. Premature approximation Rounding off too early can lead to inaccuracy in the final answer. This should be penalised by 1 mark unless instructed otherwise. 4 of 15

5 1(a) Negative Accept eg strong negative, weak negative One straight line through both gates (20, 75 90) and (80, 30 40) 1(b) Igne outside gates Line must cross at least 5 large squares Joining points only B0 If the points are joined and a line of best fit is also drawn then mark the line of best fit 1(c) 66 ft 1 ft their line of best fit ± small square 2 Accept any value in the range [62, 70] if B0 awarded in (b) 2(a) 1 ( 6 420) seen 70 A1 Accept 70 out of 420 2(b) and 0.46 and 46% B2 circles one two crect values and no me than one increct value 5 of 15

6 9 brown-eyed girls and 23 girls 9 brown-eyed boys and 17 boys (their 23 their 9 2) ((their 17 their 9 3) + 2) 15 their ( 100) their 15 must be their total blue 37.5 A1ft ft their 9 and their 23 their 9 and their 17 if B0 M2 sced Condone an answer of 38 if full method 37.5 seen 3 If build up is used f the percentage, the answer must be crect a fully crect method seen The 2 nd M may be implied by a crect ft percentage f their total blue The table ds not need to be completed and only the relevant parts need be crect (ie 9, 12, 23 and 15 9, 17, 5, 7 and 15) but the crect table f reference is Boys Girls Total Brown Blue Green Total States a valid reason about increasing sample size interviewing a variety of people eg ask me people ask boys and girls ask adults too 6 of 15

7 seen May be implied by A1 Accept % ( better) Decimal answer is Alternative method 1 Crect conversion of one value to another fm 5 12 fraction 2 : 3 ratio 41.(...)% 42% 40% Accept in wds eg 5 out of 12 Accept missing percentage signs 0.41(...) Box A and crect comparable fms eg and and : 21 and 14 : (...)% 42% and 40% 0.41(...) 0.42 and 0.4 Q1 Strand (ii) Logical argument with steps shown Alternative method Box A and 4.8 (and 5) Box A and (and 2) Q1 Strand (ii) Logical argument with steps shown 7 of 15

8 (their 16 + their 91 + their 88 + their 80 + their 22) 31 Attempt at fx using one crect midpoint Condone missing brackets eg 275.7(...) implies A (...) 9.6 A1 Accept 10 if crect method shown SC (lower class bounds used) (upper class bounds used) Igne rounding/ truncation once 9.6 better seen A1 ( ) 31, answer 10 A1 Igne increct/ no use of brackets if crect answer given A implies M0 A seen rounded to = 10 A0 297 in table then = 10 (no rounding shown) M0 A0 A crect product in the table 297 seen ds not imply if there is a choice of methods 8(a) 20 8 of 15

9 Vertical line drawn at 34 (f median) Vertical lines drawn at 30 and 38 (f lower and upper quartiles) 1 ± small square 2 1 ± small square 2 8(b) Whiskers drawn to 5 and 70 and complete, crect plot Mark intention throughout Accept unconventional plots eg Q1ft ft B0 B0 if fully crect structure and 4 out of 5 measures crectly plotted 1 ± small square 2 Strand (ii) Crect structure line through middle of box arrows/ dots/ longer vertical lines/ no endings on whiskers any depth of box Median at 35 is in tolerance so give benefit of the doubt (even if median = 35 stated) 3 6 (total = ) 18 Implied by three integers with a sum of 18 1, 1, 16 A1 May be implied by an answer of A1ft ft crect calculation of the range of a group of three integers with a sum of 18 9 The three integers must be clearly in a group of three If me than one group of three integers is given but all have a sum of 18 A0 0, 0, 18 with no increct range given A0 A0 0, 0, 18 with answer = 18 A0 A1ft 1, 3, 15 with answer = 14 M0 A0 A0 1, 2, 15 with answer = 14 A0 A1ft 1, 1, 16 with answer = 14 A1 A0 9 of 15

10 Men and modal class (women) = Condone mode = [164, 166] 10(a) Women chosen Igne reference to range if mode also seen in (a) and Men chosen Igne reference to median mean if mode also seen in (a) and Men chosen Range median mean only B0 B (range =) (range =) (range =) 50 Condone [194, 196] [154, 156] Men and minimum range (women) is 30 A1 Condone Men and range (women) is 40 result of [194, 196] [154, 156] 10(b) Crect wking value f any of the three ranges, even if seen in part (a) sces the M mark but must be referring to range in (b) to sce the A mark Any suggestion of using the mode f the decision in this part NB The frequency f (ie at 175) is 30 The range of frequencies = 35 1 = 34 Use of men s range as A0 M0 M0 A (%) seen (0) A1 SC Misread as increase SC2 10 of 15

11 Mean One value not representative Accept any indication that one of the values is non-typical, that the mean would be non-typical 12 Mark the reason independently of the given average Igne non-contradicty statements alongside a crect reason Accept any indication that 3420 is significantly different compared to all others Accept outlier, anomaly, extreme value etc Accept an indication that it would skew the mean Do not accept inaccurate to mean unrepresentative if this is the only reason given Just stating that 3420 is very large with no comparison B0 B B fraction 13(a) If eg seen but then further wk can sce max (but not if choice) 625 seen with answer Condone an attempt to change fm eg crect fraction to percentage crect decimal to fraction f max eg = eg = of 15

12 (b) A1 SC1 f an increct answer (< 1) crectly converted to standard fm = 0.03 Answer SC Answer SC1 Answer only of SC B3 B2 at least five cells crect three four cells crect seen (...) seen F B2 accept any of these values: of 15

13 Alternative method 1 Counts the squares in one rectangle their their 3 + their 4 + their their their 75 + their their dep eg (squares) respectively respectively If crect, the areas will be in the ratio 36 : 15 : 20 : 10 At least two must be in the crect ratio their 7.2 their their 180 their 405 ( 81) 81 their 16.2 ( 81) 81 their 405 dep 5 small squares 1 tree 1 small square 0.2 tree 36 A1 SC1 frequency density scale 1 cm 5 Alternative method 2 15(a) Labels vertical axis 1x, 2x, 3x, 4x, 5x 2.4 3x x + 1 4x + 2 x ( = 81) dep Allow one err omission 16.2x = 81 x = 5 dep 36 A1 SC1 frequency density scale 1 cm 5 NB If the student only labels the widths of the rectangles: 2.4 (often 2.5), 0.6 (often 0.5), 1 and 2 then this 2 is a width and not an area F the 1 st any other method must be clear and must include at least two areas in the crect ratio If the frequency density scale is linear but increct eg 1 cm 20, then at least two areas crect f that scale implies the first M mark Dividing the rectangles into squares is not enough f the first mark, the number of squares needs to be stated Answer of 36 implies 4 marks (unless clearly from wrong wking) M0 M0 dep dep A1 13 of 15

14 (b) A1 fraction Crect use of their areas from part (a) Alternative method seen Condone [6995, 7000) (48, 48.5] 144 A1 Must be using 6995 and 48.5 Alternative method seen = 6984 and = Condone (48, 48.5] n = a and (48, 48.5] (n + 1) = b where a < 6995 and b > A1 Must be using (6995 and) 48.5 Additional Guidance Answer only of 144 B0 M0 A = , answer 144 A = 144 M0 A is equivalent to 48.5 so can have full marks, however eg will not gain the A mark 14 of 15

15 a b n n n n dep dep (...)% A1 SC2 SC of 15