Functional Skills Certificate Functional Mathematics

Transcription

1 Functional Skills Certificate Functional Mathematics Level 2 Mark scheme 4368 June 2016 Version: 1.0 Final

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 2016 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 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 25

4 In particular, individual marks are mapped onto the following skills stards. Representing Making sense of the situations representing them. A learner can: Rc 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 Processing using the mathematics. A learner can: Ab Apply a range of mathematics to find solutions. Use appropriate checking procedures evaluate their effectiveness at each stage. Interpreting Ia 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 Method marks are awarded f a crect method which could lead to a crect answer. A B ft SC oe 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 25

5 1(a) 388 B1 circled indicated their ( ) their (0) their 804 their 40.2(0) ( 4) Rc seen implies 0.95 seen ft their 388 from (a) their 804 must be an amount of money 0.95 their 804 sces M2 allow if their 804 is not an amount of money 1(b) 190.(95) Yes 191 Yes (80) 764 Yes A1ft ft their 388 from (a) their 804 can be their 156 their 260 their 416 their 388 These answers sce M3 A1ft their 388 = (575) 189 Yes (3) Yes their 388 = (175) Yes (7) Yes their 388 = (45) No (8) No If 5% of their 804 is increct, the 3 rd can be awarded only if a method is seen. Fgetting their (0) sces M3A0 Misreads allow these misreads only f f 52 5 of 25

6 Crectly uses mile values f km values totaling 960 km e.g = 600 (miles) = 600 (miles) Crectly uses km values f mile values totaling 600 miles eg = 960 (km) B2 B1 Attempts to use incomplete use of mile values f km values totaling 960 km values f mile values totaling 600 any conversion fact obtained from graph F B1 allow all values ± ½ small square 1(c) = 960 (km) Crectly uses a conversion fact obtained from graph SC seen used with no evidence that the value has been obtained from the graph e.g = 600 (miles) = 600 (miles) is obtained from 400km + 400km + 160km is obtained from 240km These values are the easiest to read accurately but any combination can be used. Award B1 f Crect method with inaccurate readings ± ½ square e.g. uses [395, 405] instead of 400 Crect method but the final = 600 = 960 is not given is wked out increctly 1(d) their ( 5) 15 ( 5) ( )75 A1 960 [60, 70] ( 5) Check reverse alternative calculation B1ft Ab eg = 600 Holistic marking Award marks f 1(d) if wking seen in space f check Award marks f check if seen in space f 1(d) Treat contradicty wk in both spaces as choice 6 of 25

7 1(e) stays at 3 4 different campsites including Point St Gilles distances crect less than 5 hours (less than 375 km) return to Caen included fully crect clearly communicated plan including 3 4 different campsites named including Point St Gilles all distances crect < 375 km journey from Caen both at start (can be implied by crect distance to 1 st campsite) end (must be named) total number of nights at campsites given equal to 14 B1 B1 B1 B2 Ia not Caen allow if at least three different distances are given with a maximum of one increct can be > 375 km B1 clearly communicated plan including F B1 3 4 different campsites named all distances attempted number of nights at each campsite attempted distances number of nights can be increct campsites need not include Point St Gilles Igne increct times if distances are given Crect times imply crect distances can sce B4 if distances are not given If La Croix Paris is the 1 st campsite chosen a direct journey to a subsequent campsite is > 375km so maximum possible sce is B1B0B1B1 Visiting the same campsite me than once Counts only as one different campsite If the journey to from this campsite is the same F final B2 the distance need be given only once F 2 nd B1 only counts as one distance 7 of 25

8 Alternative Method (0) (0) (0) 157.5(0) cost from one me components their 187.5(0) + their their 157.5(0) 633 total cost from 3 components (0) (0) income at nmal prices implied by 546 2(a) (0) reduced price of kettles (80 30) 5.2(0) (35 20) their 2.4(0) 36 income at reduced prices 166 implies M2 184 implies their their their their their 36 their their total income from 5 components their 712 their 633 their Rc their 712 must be from at least 3 components 79 Yes Yes A A1ft crect decision based on their value must sce 2 nd, 6 th 7 th 633 M2 712 M4 730 M3 97 Yes M6A1ft 8 of 25

9 Alternative Method 2 2(a) 1.8(0) their (0) (0) (80 30) 5.2(0) (35 20) their 2.4(0) (0) (0) their their (0) 20 6 their (0) 120 their (0) their 82.5(0) their 2 their 1.5(0) 79 Yes Rc profit per mug profit on mugs reduced price of kettles income at reduced prices loss on saucepans loss on kettles total profit A1 79 A1ft crect decision based on their value must sce 2 nd, 6 th 7 th 82.5 M (0) M2 19.5(0) 97 Yes M6A1ft 2 1.5(0) M4 9 of 25

10 Tom wks f between 1 4 hours inclusive befe 1 pm B1 do not award if Tom appears on same row me than once Ali wks f exactly 3 hours B1 do not award if Ali Wes appear on same row me than once Wes wks f exactly 4 hours 2(b) all 5 wk with nobody doing 5 me consecutive hours all 5 wk 3 different people at each hour B1 Ia B1 Ia do not award if rota is incomplete do not award if rota is incomplete Tom in me than once in the same row can sce a maximum of B0B1B1B0 only Ali Wes in me than once in the same row can sce a maximum of B1B0B1B0 only Tom Ali Wes in me than once in the same row can sce a maximum of B0B0B1B0 only Alternative Method 1 3(a) (6 3) + (2 4) (their 18 + their 8) their (3 ) 10 hours 50 minutes Rc A1 10 of 25

11 Alternative Method 2 (6 3) (2 4) 18 8 their their implies 3(a) their their (3 ) 10 hours 50 minutes Rc A1 10.8(3 ) M3 7.5 & 3.3(3 ) M3 650 M2 11 of 25

12 Alternative Method (b) (1500 their 1140) 0.9 their (1500 their 1140) 50 their (1500 their 1140) 0.9 their (1500 their 1140) 0.5(0) their (0) 180 their their their (0) 162 their No No A A1ft crect decision f their values must sce all three M marks Alternative Method (b) (1500 their 1140) 0.9 their their their No No their 165 their 324 A A1ft crect decision f their value must sce all three M marks 12 of 25

13 Alternative Method (b) (1500 their 1140) 0.9 their their their (0) No A A1ft crect decision f their values must sce all three M marks Alternative Method (b) (1500 their 1140) their their ( 100) (1500 their 1140) 0.5(0) 180 their 165 their 180 ( 100) 91.6(6 ) No A1 91.6(6 ) No A1ft crect decision f their values must sce all three M marks 13 of 25

14 3(c) = = 720 B2 B1 Allow up to three errs omissions Wking may be next to table Omitting = 720 is an omission Alternative Method (d) their their A Yes A1ft crect decision f their value must sce M2 decision should be yes if their 6480 = [6450, 6550] Alternative Method (d) 6500 their 14.4 A Yes A1ft crect decision f their values must sce M2 decision should be yes if their = [447.9, 454.9] 14 of 25

15 Alternative Method 3 3(d) their (4 ) 14.44(4 ) 14.4 Yes A (4 ) 14.4 A1ft crect decision f their values must sce M2 decision should be yes if their 14.44(4 ) = [14.3, 14.6] 3(d) Alternative Method their (2 ) Yes A1 722.(2 ) A1ft crect decision f their values must sce M2 decision should be yes if their 722.(2 ) = [716.6, 727.7] 15 of 25

16 Alternative Method 5 3(d) (7 ) (7 ) Yes A (7 ) A1ft crect decision f their values must sce M2 decision should be yes if their 9.02(7 ) = [8.958, 9.097] 16 of 25

17 (a) 7100 their 650 their = 6500 their = 7150 Rc their 650 can be 410 their 650 cannot be their their their their A1 SC (a) Check reverse calculation = = = 645. (45) (allow 650) And B1ft Ab = = = 530 ft their values 645.(45) 530 = 125.(45) = 120 alternative method Holistic marking 4(a) Award marks f 4(a) if wking seen in space f check Award marks f check if seen in space f 4(a) Treat contradicty wk in both spaces as choice Note that = 7150 (oe) on its own is only a valid check if it is an alternative method. To sce as a reverse method it also needs = 120 (oe) 17 of 25

18 = 4 (kw) = 4000 watts = 4 kilowatts B = 0.25 (kw) = = 4 (4 kw =) 4000 w = = (b) = 1 kw 4 4 = 16 Award only if a clear connection between watts kilowatts is seen This could either be through crect use of 1000 crect use of units Step (c) their Rc Step 2 31 their Step 3 allow 30 their (81) 419 Yes A1 418.(81) 419 A1ft Crect conclusion from their value Must sce at least two M marks 18 of 25

19 Alternative Method 1 F the arrangement of panels shown Can sce a maximum of M allow clear indication of crect integer values on diagram 4(d) their 6 their = 16 Yes Ia must use integers allow crect integer answer A = 16 A1ft crect conclusion from their values must sce M3 See extra sheet f possible arrangements that do not give 16 panels Crect bottom section only M0A0 Contradiction between the diagram wking lines mark wking lines 19 of 25

20 Alternative Method 2 F the arrangement of panels shown Can sce a maximum of M allow clear indication of crect integer values on diagram 4(d) their 4 their = 16 Yes Ia must use integers allow crect integer answer A = 16 A1ft crect conclusion from their values must sce M3 See extra sheet f possible arrangements that do not give 16 panels Crect bottom section only M0A0 Contradiction between the diagram wking lines mark wking lines 20 of 25

21 Alternative Method 3 F the arrangement of panels shown Can sce a maximum of M allow clear indication of crect integer values on diagram 4(d) their 2 their 2 their 4 their = 16 Yes Ia must use integers allow crect integer answer A = 16 A1ft crect conclusion from their values must sce M3 See extra sheet f possible arrangements that do not give 16 panels Any one crect section only M0A0 Contradiction between the diagram wking lines mark wking lines 21 of 25

22 Alternative Method 4 F the arrangement of panels shown Can sce a maximum of M allow clear indication of crect integer values on diagram 4(d) their 6 their = 16 Yes Ia must use integers allow crect integer answer A = 16 A1ft crect conclusion from their values must sce M3 See extra sheet f possible arrangements that do not give 16 panels Crect large rectangle only M0A0 Contradiction between the diagram wking lines mark wking lines 22 of 25

23 Alternative Method 5 F the arrangement of panels shown Can sce a maximum of M3A allow clear indication of crect integer values on diagram 4(d) their their 4 their = 14 No A1 Ia must use integers allow crect integer answer See extra sheet f other possible arrangements that can sce A1 max Crect bottom section only M0A0 Contradiction between the diagram wking lines mark wking lines 23 of 25

24 Alternative Method 6 F the arrangement of panels shown Can sce a maximum of M3A allow clear indication of crect integer values on diagram 4(d) their 6 their 2 (+ their 2) = 14 No Ia must be integers allow crect integer answer See extra sheet f other possible arrangements that can sce A1 max Crect bottom section only M0A0 Contradiction between the diagram wking lines mark wking lines 24 of 25

25 Alternative Method 1 (P =) ( ) (P =) (52) Alternative Method 2 A can be 9965 must see symbol 4(e) (P =) their 3463 (P =) their (36) their [612.25, 612,26] (52) A1 I allow their (36) + their [612.25, 612,26] must see symbol Need both symbol rounded to f A1 Condone p 25 of 25