Functional Skills Certificate Functional Mathematics

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

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.

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

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

1(a) 388 B1 circled indicated 3 52 156 4 65 260 their (156 + 260 + 388) 5 100 their 804 5 100 40.2(0) their 804 their 40.2(0) ( 4) Rc 416 804 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 804 763.(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 = 378 188.(575) 189 Yes 794 754.(3) Yes their 388 = 410 196.(175) Yes 826 784.(7) Yes their 388 = 508 219.(45) No 924 877.(8) No If 5% of their 804 is increct, the 3 rd can be awarded only if a method is seen. Fgetting their 388 98.8(0) sces M3A0 Misreads allow these misreads only 29 111 f 65 28 105 f 52 5 of 25

Crectly uses mile values f km values totaling 960 km e.g. 250 + 250 + 100 = 600 (miles) 150 4 = 600 (miles) Crectly uses km values f mile values totaling 600 miles eg 400 + 400 + 160 = 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) 240 4 = 960 (km) Crectly uses a conversion fact obtained from graph SC1 1.6 0.625 seen used with no evidence that the value has been obtained from the graph e.g. 960 80 50 = 600 (miles) 960 240 150 = 600 (miles) 250 + 250 + 100 is obtained from 400km + 400km + 160km 150 4 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 600 40 ( 5) 15 ( 5) ( )75 A1 960 [60, 70] ( 5) Check reverse alternative calculation B1ft Ab eg 75 5 40 = 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

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

Alternative Method 1 150 1.25 187.5(0) 80 3.6(0) 288 35 4.5(0) 157.5(0) cost from one me components their 187.5(0) + their 288 + their 157.5(0) 633 total cost from 3 components 150 1.8(0) 270 30 5.2(0) 156 20 6 120 income at nmal prices implied by 546 2(a) 6 0.6 6 0.4 6 2.4(0) reduced price of kettles (80 30) 5.2(0) 2 130 (35 20) their 2.4(0) 36 income at reduced prices 166 implies M2 184 implies their 270 + their 156 + their 120 + their 130 + their 36 their 546 + their 166 712 total income from 5 components their 712 their 633 their 633 + 75 708 Rc their 712 must be from at least 3 components 79 Yes 708 712 Yes A1 79 708 712 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

Alternative Method 2 2(a) 1.8(0) 1.25 0.55 their 0.55 150 82.5(0) 6 0.6 6 0.4 6 2.4(0) (80 30) 5.2(0) 2 130 (35 20) their 2.4(0) 36 80 3.6(0) 30 5.2(0) their 130 288 156 their 130 2 35 4.5(0) 20 6 their 36 157.5(0) 120 their 36 1.5(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 M2 2 1.5(0) M2 19.5(0) 97 Yes M6A1ft 2 1.5(0) M4 9 of 25

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) 18 + 8 26 (their 18 + their 8) 1500 39 000 their 39 000 60 60 650 60 10.8(3 ) 10 hours 50 minutes Rc A1 10 of 25

Alternative Method 2 (6 3) (2 4) 18 8 their 18 1500 27 000 their 8 1500 12 000 26 implies 3(a) their 27 000 60 60 450 60 7.5 their 12 000 60 60 200 60 3.3(3 ) 10 hours 50 minutes Rc A1 10.8(3 ) M3 7.5 & 3.3(3 ) M3 650 M2 11 of 25

Alternative Method 1 1500 11 16500 1500 0.11 165 3(b) (1500 their 1140) 0.9 their 360 0.9 324 (1500 their 1140) 50 their 360 50 18 000 (1500 their 1140) 0.9 their 360 0.9 324 (1500 their 1140) 0.5(0) their 360 0.5(0) 180 their 324 50 16 200 their 18 000 0.9 16 200 their 324 0.5(0) 162 their 180 0.9 162 16 500 16 200 No 165 162 No A1 16 500 16 200 165 162 A1ft crect decision f their values must sce all three M marks Alternative Method 2 1500 11 16500 1500 0.11 165 3(b) (1500 their 1140) 0.9 their 360 0.9 324 their 16 500 their 324 50.9 51 No 0.509 0.51 No their 165 their 324 A1 50.9 51 0.509 0.51 A1ft crect decision f their value must sce all three M marks 12 of 25

Alternative Method 3 1500 11 16500 1500 0.11 165 3(b) (1500 their 1140) 0.9 their 360 0.9 324 their 16 500 50 330 their 165 0.5(0) 330 324 330 No A1 324 330 A1ft crect decision f their values must sce all three M marks Alternative Method 4 1500 11 16 500 1500 0.11 165 3(b) (1500 their 1140) 50 18 000 their 16 500 their 18 000 ( 100) (1500 their 1140) 0.5(0) 180 their 165 their 180 ( 100) 91.6(6 ) 91.67 91.7 No A1 91.6(6 ) 91.67 91.7 No A1ft crect decision f their values must sce all three M marks 13 of 25

3(c) 12 4 + 13 8 + 14 16 + 15 12 + 16 7 + 17 2 + 18 1 = 720 48 + 104 + 224 + 180 + 112 + 34 +18 = 720 B2 B1 Allow up to three errs omissions Wking may be next to table Omitting = 720 is an omission Alternative Method 1 720 50 14.4 450 50 9 3(d) their 14.4 450 their 9 720 A1 6480 6480 Yes A1ft crect decision f their value must sce M2 decision should be yes if their 6480 = [6450, 6550] Alternative Method 2 720 50 14.4 3(d) 6500 their 14.4 A1 451 451.3 451.4 451 451.3 451.4 Yes A1ft crect decision f their values must sce M2 decision should be yes if their 451.3 = [447.9, 454.9] 14 of 25

Alternative Method 3 3(d) their 720 50 14.4 6500 450 14.44(4 ) 14.44(4 ) 14.4 Yes A1 14.44(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 4 450 50 9 6500 their 9 722.(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

Alternative Method 5 3(d) 450 50 9 6500 720 9.02(7 ) 9.028 9.03 9 9.02(7 ) 9.028 9.03 Yes A1 9 9.02(7 ) 9.028 9.03 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

530 10 5300 120 10 1200 530 + 120 650 530 11 5830 120 11 1320 4(a) 7100 their 650 their 650 10 = 6500 their 650 11 = 7150 Rc their 650 can be 410 their 650 cannot be 530 120 their 5300 + their 1200 6500 their 5830 + their 1320 7150 10.9 11 A1 SC1 17.3 4(a) Check reverse calculation 7100 10.9 = 650 650 120 = 530 7100 11 = 645. (45) (allow 650) And B1ft Ab 7150 11 = 650 6500 10 = 650 650 120 = 530 ft their values 645.(45) 530 = 125.(45) 650 530 = 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 650 11 = 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 650 530 = 120 (oe) 17 of 25

16 250 1000 = 4 (kw) 16 250 = 4000 watts = 4 kilowatts B1 250 1000 = 0.25 (kw) 4 0.25 = 16 16 0.25 = 4 (4 kw =) 4000 w 4000 250 =16 250 16 = 4000 4(b) 250 4 = 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 0.5 10.3 + 4.5 Step 1 5.15 + 4.5 9.65 4(c) their 9.65 4 0.35 13.51 Rc Step 2 31 their 13.51 Step 3 allow 30 their 13.51 405.3 418.(81) 419 Yes A1 418.(81) 419 A1ft Crect conclusion from their value Must sce at least two M marks 18 of 25

Alternative Method 1 F the arrangement of panels shown Can sce a maximum of M3 6.8 1.082 6.28 6 3.7 1.575 2.34 2 4.6 1.082 4.25 4 allow clear indication of crect integer values on diagram 4(d) 6.8 1.082 6.28 6 3.7 1.575 2.34 2 4.6 1.082 4.25 4 their 6 their 2 6 2 + 4 = 16 Yes Ia must use integers allow crect integer answer A1 6 2 + 4 = 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

Alternative Method 2 F the arrangement of panels shown Can sce a maximum of M3 6.8 1.575 4.31 4 3.7 1.082 3.41 3 4.6 1.082 4.25 4 allow clear indication of crect integer values on diagram 4(d) 6.8 1.575 4.31 4 3.7 1.082 3.41 3 4.6 1.082 4.25 4 their 4 their 3 4 3 + 4 = 16 Yes Ia must use integers allow crect integer answer A1 6 2 + 4 = 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

Alternative Method 3 F the arrangement of panels shown Can sce a maximum of M3 2.2 1.082 2.03 2 3.7 1.575 2.34 2 4.6 1.082 4.25 4 5 1.575 3.17 3 allow clear indication of crect integer values on diagram 4(d) 2.2 1.082 2.03 2 3.7 1.575 2.34 2 4.6 1.082 4.25 4 5 1.575 3.17 3 their 2 their 2 their 4 their 3 2 2 + 4 3 = 16 Yes Ia must use integers allow crect integer answer A1 2 2 + 4 3 = 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

Alternative Method 4 F the arrangement of panels shown Can sce a maximum of M3 6.8 1.082 6.28 6 5 1.575 3.27 3 2.2 1.082 2.03 2 allow clear indication of crect integer values on diagram 4(d) 6.8 1.082 6.28 6 5 1.575 3.27 3 2.2 1.082 2.03 2 their 6 their 3 6 3 2 = 16 Yes Ia must use integers allow crect integer answer A1 6 3 2 = 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

Alternative Method 5 F the arrangement of panels shown Can sce a maximum of M3A1 6.8 1.575 4.31 4 3.7 1.082 3.41 3 4.6 1.575 2.92 2 allow clear indication of crect integer values on diagram 4(d) 6.8 1.575 4.31 4 3.7 1.082 3.41 3 4.6 their 1.575 2.92 2 their 4 their 3 4 3 + 2 = 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

Alternative Method 6 F the arrangement of panels shown Can sce a maximum of M3A1 6.8 1.082 6.28 6 3.7 1.575 2.349 2 4.6 1.575 2.92 2 allow clear indication of crect integer values on diagram 4(d) 6.8 1.082 6.28 6 3.7 1.575 2.349 2 4.6 1.575 2.92 2 their 6 their 2 (+ their 2) 6 2 + 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

Alternative Method 1 (P =) 0.1768 (6502 3463) (P =) 0.1768 3039 537.29(52) 537.30 Alternative Method 2 A1 3039 can be 9965 must see symbol 4(e) (P =) 0.1768 6502 0.1768 their 3463 (P =) their 1149.55(36) their [612.25, 612,26] 537.29(52) 537.30 A1 I allow their 1149.55(36) + their [612.25, 612,26] must see symbol Need both symbol rounded to 537.30 f A1 Condone 537.30p 25 of 25