4368 Mark scheme and Guidance

Transcription

1 AQA Qualifications Functional Mathematics Level Mark scheme Guidance 4368 June 2015 V1 Final Mark Scheme

2 Mark schemes are prepared by the Lead Assessment Writer considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the stardisation events which all associates participate in is the scheme which was used by them in this examination. The stardisation process ensures that the mark scheme covers the students responses to questions that every associate understs applies it in the same crect way. As preparation f stardisation each associate analyses a number of students scripts: alternative answers not already covered by the mark scheme are discussed legislated f. If, after the stardisation 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 exped 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 2014 AQA 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 MARK SCHEME FUNCTIONAL MATHEMATICS LEVEL JUNE 2014 Glossary f Mark Schemes Examinations are marked to award positive achievement. Marks are awarded f demonstrating the following interrelated process skills. Representing Selecting the mathematics infmation to model a situation. R.1 Cidates recognise that a situation has aspects that can be represented using mathematics. R.2 Cidates make an initial model of a situation using suitable fms of representation. R.3 Cidates decide on the methods, operations tools, including ICT, to use in a situation. R.4 Cidates select the mathematical infmation to use. Analysing Processing using mathematics. A.1 Cidates use appropriate mathematical procedures. A.2 Cidates examine patterns relationships. A.3 Cidates change values assumptions adjust relationships to see the effects on answers in models. A.4 Cidates find results solutions. Interpreting Interpreting communicating the results of the analysis. I.1 Cidates interpret results solutions. I.2 Cidates draw conclusions in light of situations. I.3 Cidates consider the appropriateness accuracy of results conclusions. I.4 Cidates choose appropriate language fms of presentation to communicate results solutions. 3 of 38

4 In particular, individual marks are mapped onto the following skills stards. Representing Rb Rc Making sense of the situations representing them. A learner can: Underst routine non-routine problems in familiar unfamiliar contexts situations. Identify the situation problems identify the mathematical methods needed to solve them. Choose from a range of mathematics to find solutions. Analysing Ab Processing using the mathematics. A learner can: Apply a range of mathematics to find solutions. Use appropriate checking procedures evaluate their effectiveness at each stage. Interpreting Interpreting communicating the results of the analysis. A learner can: Interpret communicate solutions to multistage practical problems in familiar unfamiliar contexts situations. Draw conclusions provide mathematical justifications. To facilitate marking, the following categies are used: M A B ft SC oe 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 following a mistake in an earlier step. Special case. Marks awarded within the scheme f a common misinterpretation which has some mathematical wth. Or equivalent. Accept answers that are equivalent. 1 eg, accept 0.5 as well as 2 4 of 38

5 F reflection of given shape in a vertical line seen in any grid B1 F reflection in a hizontal line of two shapes based on iginal shape 1(a) B1ft B1ft ft their four shapes based on iginal shape B3 if crect 5 of 38

6 Additional Guidance Award marks f designs based on the given shape only. Start by marking the bottom design award B3 if fully crect. If increct look f a crect reflection in a vertical line f the 1 st B1 a crect reflection of two shapes in a hizontal line f the 2 nd B1 B0B1ftB1ft 1(a) This sces the same mark if only the bottom design is shown. B1B1ftB0 This sces B3 only if the final grid is fully crect. B1B0B1ft The reflection in the vertical line the final translation can be seen in the bottom design, so award these marks whatever is shown on the other grids. 6 of 38

7 1(b) 100 cm 2 circled B1 Alternative Method 1 Allow ± 0.2 cm tolerance on all lengths ft f their areas 12 6 ( their 100) Total rug area 4 2 ( their 100) ( 4) Rb Area of white 1(c) their 7200 their (their 72 their 32) ( their 100) 40 Total rug area total white area F A2 must see colours cm 2 White 3200 cm 2 Black 4000 cm 2 A2ft A1 White 3200 Black 4000 F A1 must see colours ft their of 38

8 Alternative Method 2 Allow ± 0.2 cm tolerance on all lengths ft f their areas (c) their 120 their their 40 their 20 ( 4) Rb Must be scaled length scaled length total area white area their 7200 their total rug area total white area F A2 must see colours cm 2 White 3200 cm 2 A2 A1 White 3200 Black 4000 cm 2 Black 4000 F A1 must see colours 8 of 38

9 Alternative Method 3 Allow ± 0.2 cm tolerance on all lengths ft f their areas 1(c) 4 2 ( their 100) ( 4) ( their 100) ( 2) ( their 100) ( 2) ( their 100) ( 3) their their their (their 24 + their 4 + their 12) ( their 100) 40 White 3200 cm 2 Black 4000 cm 2 Rb A2ft White area Black area Total black area F A2 must see colours cm 2 A1 White 3200 Black 4000 F A1 must see colours ft their of 38

10 Alternative Method 4 Allow ± 0.2 cm tolerance on all lengths ft f their areas Rb (c) their 120 their 10 ( 2) their 40 their 5 ( 2) their 40 their 10 ( 3) Must be scaled length scaled length black area white area their 40 their 20 ( 4) their their their 1200 total black area F A2 must see colours cm 2 White 3200 cm 2 A2 A1 White 3200 Black 4000 cm 2 Black 4000 F A1 must see colours 10 of 38

11 Alternative Method 5 Allow ± 0.2 cm tolerance on all lengths ft f their areas 1(c) 4 2 ( their 100) ( 4) ( their 100) ( 2) ( their 100) ( 3) ( their 100) ( 8) their their their (their 6 + their 18 + their 16) ( their 100) 40 White 3200 cm 2 Black 4000 cm 2 Rb A2ft white area black area total black area F A2 must see colours cm 2 A1 White 3200 Black 4000 F A1 must see colours ft their of 38

12 Alternative Method 6 Allow ± 0.2 cm tolerance on all lengths ft f their areas Rb their 60 their 5 ( 2) Must be 1(c) their 60 their 10 ( 3 ) their 20 their 10 ( 8) scaled length scaled length black white their 40 their 20 ( 4) their their their 1600 total black area F A2 must see colours cm 2 White 3200 cm 2 A2 A1 White 3200 Black 4000 cm 2 Black 4000 F A1 must see colours 12 of 38

13 Additional Guidance Mark schemes when their (Alternative Methods 1, 3 5) their 100 = 1 their 100 = 10 their 100 = ( 10) 12 6 ( 1000) (c) 4 2 ( 4) ( 4) ( 10) ( 4) ( 1000) their 72 their 32 their 720 their 320 their their White 32 cm 2 A0 White 320 cm 2 A2 White cm 2 A2 Black 40 cm 2 Black 400 cm 2 Black cm 2 A1 f either (units not needed) 13 of 38

14 Alternative Method 1 their their [68, 69] their [146, 147] Allow any evidence of division by 150 [68, 69] No [146, 147] No A2ft A1 [68, 69] [146, 147] A1ft Crect conclusion f their values ft their 4000 from (c) Alternative Method 2 their (d) No A2ft A A1ft Crect conclusion f their values ft their 4000 from (c) Alternative Method their Award f using fmula crectly in reverse if their represents a number of strs e.g not [4101, 4102] 4100 No A2ft A1 [4101, 4102] 4100 A1ft Crect conclusion f their value ft their 4000 from (c) 14 of 38

15 Additional Guidance their 4000 Must be an area (not ). Follow through from (c) Allow 7200 ( digits 72) 3200 ( digits 32) even if their answer in (c) is different Any answer f the black area wked out in (d) takes precedence over their answer in (c) 1(d) Answer in (c) = = Yes Answer in (c) = = 5.46 No Answer in (c) = = 0.68 No Answer in (c) = No because only 1 pack is needed (implied division by 150) Answer in (c) = No A1ft Must sce M2 A1ft A2ft A2ft A2ft M0A0 15 of 38

16 Alternative Method oe e.g Allow (e) their their their Two costs added their can be 12.5(0) 25 Rc M2 their their their [41.32, 41.33] ( )[247, 248] Yes A2 their must be an amount of money A1 ( )[247, 248] A1ft Crect conclusion from their value 16 of 38

17 Alternative Method oe e.g Allow (e) their [37.57, 37.58] their their [37.57, 37.58] [225.45, ] (0) Rc M2 their their their their must be amounts of money their [225.45, ] + their 22.5(0) Both costs must have their VAT added ( )[247, 248] Yes A2 A1 ( )[247, 248] A1ft Crect conclusion from their value 17 of 38

18 Additional Guidance F A1ft Alternative Method 1: must sce a minimum of M0 Alternative Method 2: must sce a minimum of M0 2 m of rug canvas Alternative method [255, 256] No A2 2 m of rug canvas Alternative method (187.88) (25) 1(e) [37.57, 37.58] [225.45, ] their [225.45, ] + 30 [255, 256] No A2 Calculating VAT Adding on 20% with a clear but increct method f calculating 20% sces M0 Cidates might start by adding VAT to the unit costs (0) 15 Marks should be allocated as follows M2 wking out VAT total cost of packs of wool total cost of rug canvas total cost of wool canvas A marks as Alternative Methods of 38

19 Alternative Method 1 2(a) (0) (0) their their 212.5(0) Rb Ab (0) = ( )250 Yes A1 Must see full method f Alternative Method (0) Rb 2(a) 250 their 37.5(0) 212.5(0) their 212.5(0) 17 their 212.5(0) 12.5(0) Ab 212.5(0) 17 = ( )12.5(0) Yes 212.5(0) 12.5(0) = 17 Yes A1 Must see full method f 19 of 38

20 Alternative Method 3 2(a) (0) 212.5(0) 250 their 212.5(0) 37.5(0) their 37.5(0) (0) Rb Ab 37.5(0) = 15 Yes (0) = 37.5(0) = 37.5(0) Yes A1 Must see full method f 20 of 38

21 Alternative Method 4 2(a) their (0) their 212.5(0) 17 their 212.5(0) 12.5(0) (0) Rb Ab 212.5(0) 17 = 12.5(0) Yes 212.5(0) 12.5(0) = 17 Yes = 212.5(0) (0) = 212.5(0) Yes A1 Must see full method f 21 of 38

22 Additional Guidance Must see full method f M3A1 10% 25 5% % = = 250 Yes (full method shown) A1 2(a) 15% of 250 = = = 250 Yes (full method not shown) A = 16 M = = No A0 22 of 38

23 (free ) 3 (pay ) their their Rc any multiple of a single cost A1 Must see Additional Guidance 2(b) their 560 Misreads of 280 can sce M0A0 Misreads can be any other value in the table on the Data Sheet Do not allow combinations of student staff costs Can be any multiple of a single cost. E.g = 1400 M0M = 1050 A0 Using 3 f their = 840 M = 630 A = = 840 M = 630 A0 23 of 38

24 Alternative Method 1 (Comparing means) Total of at least 9 products shown attempted with at least 5 of the products crect their their [6.9, 6.93] Allow their their A2 A [6.9, 6.93] 2(c) 6.38 [6.9, 6.93] Maya A1ft Crect conclusion from their means Alternative Method 2 (Comparing medians) listing at least 26 values in ascending descending der listing at least 21 values in ascending descending der Selects 25 th 26 th highest values selects 20 th 21 st highest values 6 7 Maya A2 A1 6 7 A1ft Crect conclusion from their medians 24 of 38

25 Alternative Method 3 (Comparing modes) Mode f Harry 6 Mode f Maya 7 Maya B2 B1 Mode f Harry 6 Mode f Maya 7 Alternative Method 4 (Comparing modes ranges) 2(c) Mode f Harry 6 Mode f Maya 7 nge f Harry Maya 9 Mode 6 7 nge 9 f Harry Maya Maya A2 A1 Mode 6 7 nge 9 A1ft Crect conclusion from their modes ranges 25 of 38

26 Alternative Method 5 (Comparing proptions A) E.g. Sces of 7 me Harry = 24 Maya = 23 E.g. Sces of 9 10 Harry = 7 Maya = 10 Harry their 24 /50 Maya their 23 /40 Harry their 7 /50 Maya their 10 /40 2(c) Harry under half sce 7 me Maya over half sce 7 me Maya Harry 14% sce 9 10 Maya 25% sce 9 10 Maya Harry their 96 /200 Maya their 115 /200 Maya Harry 48% Maya 57.5% Maya A1 oe 26 of 38

27 Alternative Method 6 (Comparing proptions B) Total of at least 9 products shown attempted with at least 5 of the products crect 2(c) Harry their 319 /500 Maya their 277 /400 E.g. Harry their 1276 /2000 Maya their 1385 /2000 Maya Harry 63.8% Maya [69, 69.3]% Maya A2 A1 Harry their 1276 /2000 Maya their 1385 /2000 Harry 63.8% Maya [69, 69.3]% A1ft Crect conclusion from their comparable proptions 27 of 38

28 Additional Guidance 2(c) Comparing proptions A (Alternative Method 5) Two me (consecutive) sces combined their proptions compared can sce a maximum of 3 marks. Comparing proptions B (Alternative Method 6) All sces combined to give total sces f Harry Maya their proptions compared can sce 4 marks. Comparing modes (Alternative Method 3) Can sce a maximum of 2 marks F A1ft Alternative Methods 1 2 Must see a valid method f both means both medians Alternative Methods 4 6 Must sce M2 28 of 38

29 Alternative Method 1 3(a) (...) (...) their 8 their 4 their Rb 95 8 = = = 190 their 8 their 4 their 2 must be integers rounded up down 64 Yes A2 A1 64 A1ft Crect conclusion from their 64 obtained from the product of their three integers crectly rounded down 29 of 38

30 Alternative Method (...) (...) their 8 their their 2 30 Rb their 8 their 4 their 2 must be integers rounded up down e.g. 2 layers of 30 3(a) their 8 their their 4 15 their 4 their their Yes Yes Yes A2 A A1ft Crect conclusion from their values rounded down Additional Guidance F A1ft Must sce M2 30 of 38

31 80 (0.) ( )63.2(0) Rb (120 80) (0) 3(b) their 63.2(0) + their 19.8(0) Must add two costs f > 1 of each box Can be in pence ( )83 A1 SC2 ( ) SC1 ( ) (b) Check their = (0) + their 20 1 = 84 B1ft Ab ft their cost(s) Additional Guidance 40 double boxes Can sce SC2 M = M2A0 3(b) with no wking SC with no wking SC1 Checking mark f 40 double boxes = (0) (0) = 100 B1ft 31 of 38

32 80 5 ( 4) Rb 4.5(0) their Total income Allow 40 f their 20 Rc 2.5(0) their their (c) their 90 + their their ( )36 Must be 3 incomes Ingredient costs 4.8(0) their 36 (+ their 83) 173.8(0) Adding costs Allow their cost of boxes not included their 270 their 173.8(0) Profit 96.2(0) No 3.8(0) less No A2 ft their 83 from (b) A1 96.2(0) 3.8(0) A1ft Crect conclusion from their 96.2(0) 32 of 38

33 Additional Guidance Using 40 instead of 20 Can award M6A2 if 40 used in (b) Can award M6A1ft if 40 is not used in (b) Allow 4.5(0) nd their their rd 4.8(0) their 36 + their 100.8(0) 191.6(0) 5 th 96.2(0) 168.4(0) ( Yes) A2 A1ft 3(c) Boxes not included Can award M6A1ft if the cost of their boxes from (b) has been fgotten This affects 5 th onwards With 20 double boxes 4.8(0) their (0) 5 th their 270 their 90.8(0) 6 th 179.2(0) Yes A1ft With 40 double boxes 4.8(0) their (0) 5 th their 360 their 90.8(0) 6 th 269.2(0) Yes A1ft F A1ft Must sce 3 rd, 5 th 6 th 33 of 38

34 57 their [13.5, 13.6] B1 Rb their 57 must be a total length 4(a) 14 A1ft ft B0 SC1 Additional Guidance 2 m 1 (length) 5 m 2 (lengths) 7 m 2 (lengths) 10 m 3 (lengths) 11 m 3 (lengths) 12 m 3 (lengths) 2 nd Allow trial improvement. E.g = 50.4, = 54.6, Must see at least 3 trials = 58.8 A1ft Must round up If their 57 is a multiple of 4.2 (e.g ) can sce B0A0 only SC1 Look on diagram f number of lengths of individual sections 34 of 38

35 their attempt to complete all 5 days closing times All 5 closing times crect f their 58 B1 Rb A1ft 58 can be implied by h 36 min Do not need am pm ft B0 Must see am pm Additional Guidance 4(b) Latest closing time 10 pm Decimal times F A1 assume, e.g., a time of 7.6 pm means 6 minutes past 7 An attempt to complete the table with 80 their seen sces 58 can be implied from 6.6 Five times of 6.36 pm in table sces B1A1 Checking crect answer If all closing times are given in pm add up to 33 award B1A1 E.g. 7 pm, 7 pm, 5 pm, 7 pm 7 pm ( = 33) Implied can be implied from the times in the table. their 22 = 23 with neither 9 13 seen B (= 57) not seen but sum of pm times in table = 32 A1ft their 22 = 23 but 9 13 seen B (= 57) not seen but sum of pm times in table = 32 A0 35 of 38

36 Alternative Method 1 Attempt at total bottles Attempt at total cost of fridges Attempt at total bottles Attempt at total cost of fridges Attempt at total cost of display units Rc Must be f at least two fridges Must be total cost of all their fridges Must be f the same combination of fridges Must be total cost of all their fridges Must be f at least two display units Must be total cost of all their display units 4(c) Attempt at total cost of combination of at least 2 fridges at least 5 display units Clearly communicated combination of at least 2 fridges at least 5 display units with costs attempted Clearly communicated combination of at least 2 fridges with crect number of bottles given 400 Clearly communicated combination of at least 2 fridges at least 2 display units with crect total cost given between inclusive A1 A1 A1 Letters of fridges display units must be seen Fully crect examples 4(c) Fridge A 1 Fridge C bottles Unit X 1 Unit Y Fridge A 1 Fridge B bottles Unit Y Fridge B 2 Fridge C bottles Unit Y Fridge A 1 Fridge B bottles Unit X 1 Unit Y Fridge A bottles Unit Y of 38

37 Alternative Method 2 Attempt at total bottles attempt at total cost of fridges Attempt at total bottles Attempt at total cost of fridges Attempt at difference between total cost of fridges Rc Must be f at least two fridges Must be total cost of all their fridges Must be f the same combination of fridges Must be total cost of all their fridges Must be total cost of all their fridges 4(c) Attempt to make up the difference with at least five display units Clearly communicated combination of at least 2 fridges at least 5 display units with costs attempted Clearly communicated combination of at least 2 fridges with crect number of bottles given 400 Clearly communicated combination of at least 2 fridges at least 2 display units with crect total cost given between inclusive A1 A1 A1 Letters of fridges display units must be seen Fully crect examples 4(c) Fridge A 1 Fridge C bottles Unit X 1 Unit Y Fridge A 2 Fridge B bottles Unit X 1 Unit Y Fridge B 2 Fridge C bottles Unit Y Fridge A 1 Fridge B bottles Unit X 1 Unit Y Fridge A bottles Unit Y of 38

38 Additional Guidance 4(c) Start by checking their final answer with spread sheet. No letters of fridges display units Can sce M4 maximum Attempts do not need to give crect answers Use costs / numbers of bottles to identify the fridges display units used A marks Can only be awarded if fridges display units are identified by their letters Letters f fridges display units need not be listed together 38 of 38