Functional Mathematics

Transcription

1 FUNCTIONAL SKILLS CERTIFICATE Functional Mathematics Level 2 Mark Scheme 4368 March 2017 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 2017 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 Examinations are marked to award positive achievement. Marks are awarded f demonstrating the following interrelated process skills. Representing Selecting the mathematics and infmation to model a situation. R.1 Candidates recognise that a situation has aspects that can be represented using mathematics. R.2 Candidates make an initial model of a situation using suitable fms of representation. R.3 Candidates decide on the methods, operations and tools, including ICT, to use in a situation. R.4 Candidates select the mathematical infmation to use. Analysing Processing and using mathematics. A.1 Candidates use appropriate mathematical procedures. A.2 Candidates examine patterns and relationships. A.3 Candidates change values and assumptions adjust relationships to see the effects on answers in models. A.4 Candidates find results and solutions. Interpreting Interpreting and communicating the results of the analysis. I.1 Candidates interpret results and solutions. I.2 Candidates draw conclusions in light of situations. I.3 Candidates consider the appropriateness and accuracy of results and conclusions. I.4 Candidates choose appropriate language and fms of presentation to communicate results and solutions. 3

4 In particular, individual marks are mapped onto the following skills standards. Representing Making sense of the situations and representing them. A learner can: Understand routine and non-routine problems in familiar and unfamiliar contexts and situations. Identify the situation problems and identify the mathematical methods needed to solve them. Choose from a range of mathematics to find solutions. Analysing Processing and using the mathematics. A learner can: Ab Apply a range of mathematics to find solutions. Use appropriate checking procedures and evaluate their effectiveness at each stage. Interpreting Interpreting and communicating the results of the analysis. A learner can: Ia Ib Interpret and communicate solutions to multistage practical problems in familiar and unfamiliar contexts and situations. Draw conclusions and 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

5 sce f frame 1 1(a) 27 A1 Mark holistically with 1(a) check Marks can be awarded from the scecard 1(a) check Reverse method eg = 10 Mark holistically with 1(a) ft must reverse to 7, 3, 10, 18, 8, 1, 9 0 Ab 5

6 Alternative method 1 (Frame 8) (Frame 9) their their 95 cannot be and Yes A2 Ib Ib A1 118 A1ft Crect conclusion f their value Alternative method (b) and 43 and Yes A2 Ib Ib A1 40 and 43 A1ft Crect conclusion f their values Marks can be awarded from the scecard Must sce at least f A1ft 118 may come from increct wking (Frame 8) = 85 (Frame 9) = = 118 M0 M0 A = 103 M0 M0 A0 6

7 Alternative method 1 1(c) Attempt to analyse at least one set of data eg (Jamil) 2 (wins) out of 6 (games) 4 (losses) out of 6 (games) (Tom) 3 (wins) out of 8 (games) 5 (losses) out of 8 (games) Converts data to comparable fm and makes conclusion eg 8 9 (Jamil) and (Tom) and Yes (Jamil) 33.(...%) and (Tom) 37(.5%) 38(%) and Yes (Jamil) 0.33(..) and (Tom) 0.37(5 ) 0.38 and Yes (Jamil) 1 : 2 and (Tom) 1 : 1.6(6 ) 1 : 1.7 and Yes A2 Ib Ib (Jamil) 6 2 (wins) 6 4 (losses) (Tom) 8 3 (wins) 8 5 (losses) (Jamil) 2 : 4 (Tom) 3 : A1 (Jamil) and (Tom) (Jamil) 33.(...%) and (Tom) 37(.5%) 38(%) (Jamil) 0.33(..) and (Tom) 0.37(5...) 0.38 (Jamil) 1 : 2 and (Tom) 1 : 1.6(6 ) 1 : 1.7 A1ft Crect conclusion f their comparable values Mark scheme f 1(c) continues on next page 7

8 Alternative method 2 Attempt to analyse at least one set of data (Jamil) 6 2 (wins) 6 4 (losses) eg (Jamil) 2 (wins) out of 6 (games) 4 (losses) out of 6 (games) (Tom) 3 (wins) out of 8 (games) 5 (losses) out of 8 (games) 3 5 (Tom) (wins) (losses) 8 8 (Jamil) 2 : 4 (Tom) 3 : 5 1(c) Converts data to comparable fm and makes conclusion eg (scaling and comparing number of wins) ( =) 2.6(6 ) 2.7 and 3 A2 A1 2.6(6 ) 2.7 and 3 2.2(5) 2.3 and 2 A1ft Crect conclusion f their values and Yes Ib Ib ( =) 2.2(5) 2.3 and 2 and Yes Must sce f A1ft Jamil plays 6 and wins 2 8

9 Alternative method 1 (means) (Jamil) (Tom) their 1056 their their 1384 their and 173 and Yes A2 Ib Ib A1 176 and 173 A1ft Crect conclusion f their means Alternative method 2 (medians) (Jamil) list may be in reverse der 1(d) ( ) ( ) (Tom) ( ) ( ) their 177 their must have attempted to der the data their 160 their and 171 and Yes A2 Ib Ib A1 178 and 171 A1ft Crect conclusion f their medians Mark scheme f 1(d) continues on next page 9

10 Alternative method 3 (scaling totals) (Jamil) (Tom) (d) their their and 1384 and Yes A and 1384 A and 1038 and Yes Ib Ib 1056 and 1038 A1ft Crect conclusion f their scalings Must sce M2 f A1ft 10

11 Alternative method their their their their their 6000 their must use (a) 3 with no increct wking A1 Ib Alternative method must use 1000 their their their their 20 their their 6000 their with no increct wking A1 Ib Mark scheme f 2(a) continues on next page 11

12 Alternative method must use 1000 their (3...) their 8.3(3...) (.3...) 500 their 208(.3...) with no increct wking A1 Ib Alternative method 4 2(a) must use their their their with no increct wking A1 Ib Allow mixed units f M marks eg Alt 1 F allow

13 (0...) (.6) 6 15 = = = 15 their 6 and their 2 and their 3 must be integers, rounded down when necessary 2(b) their 6 their 2 their 3 their values can be decimals Ib 36 with no increct wking A1 Only uses division of volumes (answer 45) Zero 2(c)

14 (Shop ) A D B C Shop and 8.8 (miles) (Shop ) C B D A Shop and 8.8 (miles) B2 (Shop ) A D B C and 8.8 (miles) (Shop ) C B D A and 8.8 (miles) B3 Ia Any valid route and crect distance f their route eg1 (Shop ) D C B A Shop and 9.8 (miles) eg2 (Shop ) A B D C Shop and 9.1 (miles) SC2 (Shop ) A D B C Shop with increct no distance (Shop ) C B D A Shop with increct no distance 2(d) SC1 (Shop ) A D B C with increct no distance (Shop ) C B D A with increct no distance SC1 ( =) 8.8 (miles) Condone a route shown unambiguously on the diagram (Shop ) D B C Shop A Shop and 8.9 (miles) (Shop ) C B D Shop A Shop and 8.9 (miles) (Shop ) A B C D Shop and 9.8 (miles) (Shop ) C D B A Shop and 9.1 (miles) (Shop ) D A B C Shop and 10.6 (miles) (Shop ) C B A D Shop and 10.6 (miles) 14

15 Exactly three squares with side 1 cm Exactly four circles with radius 1 cm Exactly three sinks at least 2 cm apart, against the same wall and exactly four chairs in a line, 2 cm from one wall (reception desk) rectangle 2 cm by 1 cm (display cabinet) rectangle 4 cm by 2 cm (waiting area) rectangle 4 cm by 3 cm Ia Ia three sinks four chairs three sinks and four chairs in crect positions do not have to be the crect shape size may be implied by labelling 3(a) (reception desk) rectangle 2 cm by 1 cm and (display cabinet) rectangle 4 cm by 2 cm and (waiting area) rectangle 4 cm by 3 cm All 10 items attempted and labelled and do can open fully Ia no item in the 8 squares in the top-left (2 squares hizontal by 4 squares vertical) Condone circles and rectangles drawn freehand if intention is clear All shapes must be drawn (apart from 3rd ) and on the grid Only mark 1st grid if 2nd grid blank Crect label on one sink can imply crect labels on other two sinks Crect label on one chair can imply crect labels on other three chairs 15

16 3(b) Erik wks exactly 8 shifts and Wendy wks exactly 4 afternoon shifts Jenny and Mia each wk exactly 8 different shifts and Craig and Fay each wk exactly 5 different shifts Craig does not wk on Saturday Each stylist has at least 1 full day off Ia Ia junis must be in the Juni columns no blanks in Juni columns stylists must be in the Stylist columns no blanks in Stylist columns Saturday row must be complete grid must be complete f Stylists Only mark 1st grid if 2nd grid blank Mark any shaded boxes that are completed 16

17 Alternative method income from cut and blow dries income from cut and colours their their total income from appointments (0) 10% of one cut and blow dry % of one cut and colour ( ) their 3.3(0) cut and blow dry payments to Craig, Fay 25 their 3.3(0) and Mia cut and colour payments to Craig, Fay 5 their 3.3(0) and 4 their 3.3(0) and Mia 3(c) and 16 their 3.3(0) 16.5(0) and 13.2(0) and 52.8(0) 82.5(0) ( ) their 6 9 their 6 total payments to Craig, Fay and Mia 2 their 6 and 3 their 6 and 4 their 6 12 and 18 and (0) their 2055 their 82.5(0) their 54 (total) income total costs ( ) A1 Mark scheme f 3(c) continues on next page 17

18 Alternative method income from cut and blow dries income from cut and colours their their total income from appointments (0) 10% of one cut and blow dry % of one cut and colour 5 their 3.3(0) 16.5(0) total payments to Craig and 2 their (0) total payments to Fay 3(c). 4 their 3.3(0) 13.2(0) and 3 their (0) total payments to Mia total payments to Craig, Fay and Mia 16 their 3.3(0) 52.8(0) and 4 their (0) 136.5(0) their 2055 their 28.5(0) their 31.2(0) their 76.8(0) (total) income total costs ( ) A1 Mark scheme f 3(c) continues on next page 18

19 Alternative method 3 3(c) their their ( ) and 4 33 and and 132 and ( ) and 3 60 and and 180 and their (0) their their (0) their 2055 their 82.5(0) their income from cut and blow dries income from cut and colours total income from appointments cut and blow dry payments f Craig, Fay and Mia cut and colour payments f Craig, Fay and Mia total payments f Craig, Fay and Mia 10% of cut and blow dry payment(s) 10% of cut and colour payment(s) 10% of total payments their 825 can be their 540 can be (total) income total costs their 2055 can be their 1365 ( ) A1 Mark scheme f 3(c) continues on next page 19

20 Alternative method 4 3(c) their their and and and their (0) their (0) their (0) their (0) their 2055 their 28.5(0) their 31.2(0) their 76.8(0) income from cut and blow dries income from cut and colours total income from appointments total payments f Craig total payments f Fay total payments f Mia total payments f Craig, Fay and Mia 10% of payment(s) f Craig Fay Mia 10% of total payments their 285 can be their 312 can be their 768 can be (total) income total costs their 2055 can be their 1365 ( ) A1 Mark scheme f 3(c) continues on next page 20

21 Alternative method 5 ( ) 33 + Jenny s income from cut and blow dries ( ) 60 and cut and colours ( ) cut and blow dry payments f Craig, Fay 5 33 and 4 33 and and Mia 165 and 132 and ( ) and 3 60 and 4 60 cut and colour payments f Craig, Fay and Mia total payments f Craig, Fay and Mia 120 and 180 and (c) their (0) their their (0) 90% of cut and blow dry payment(s) 90% of cut and colour payment(s) 90% of total payments their 825 can be their 540 can be their (0) + their 690 total income from appointments (0) their (0) cannot be 742.5(0) 486 their (0) (total) income total costs ( ) A1 Mark scheme f 3(c) continues on next page 21

22 Alternative method 6 3(c) ( ) 33 + ( ) and and and their (0) their (0) their (0) their (0) their (0) + their (0) their (0) Jenny s income from cut and blow dries and cut and colours total payments f Craig total payments f Fay total payments f Mia total payments f Craig, Fay and Mia 90% of payment(s) f Craig Fay Mia 90% of total payments their 285 can be their 312 can be their 768 can be total income from appointments their (0) cannot be 256.5(0) 280.8(0) 691.2(0) (total) income total costs ( ) A1 22

23 Alternative method 1 4(a) 2 6 ( 1) (1 ) ( 1) 12 and and (1 ) their 12 + their 30 + their 6 48 their ( )7.44 and Yes 744p and Yes 744 and 1000 and Yes A2 Ib Ib must add 3 components A1 ( ) (p) A1ft Crect conclusion f their value(s) Mark scheme f 4(a) continues on next page 23

24 Alternative method 2 4(a) 2 6 ( 1) (1 ) ( 1) 12 and and (1 ) their and their and their their their their 93 ( )7.44 and Yes 744p and Yes 744 and 1000 and Yes A2 Ib Ib must add 3 components A1 ( ) (p) A1ft Crect conclusion f their value(s) Must sce 1st, 3rd and 4th f A1ft Wking in watts can sce a maximum of M4 A0 24

25 p Allow p p 4(b) p A1 Ia Allow p p Must see p Mark holistically with 4(b) check 4(b) check Alternative method eg = 712 eg = 712 reverse calculation eg = 89 uses approximation to nearest 10p eg 8 90 = 720 ft Ab Must reverse to Mark holistically with 4(b) 25

26 Alternative method 1 (4 years) power of dinary bulbs in kw their units of electricity f dinary bulbs their 0.1 can be 100 their cost of electricity f dinary bulbs their 96 can be their 96 must be a time 4(c) their their their 7.12 from (b) total cost f dinary bulbs their cannot be their (6) 2.98 cost of electricity f low energy bulbs their cannot be their 2.97(6) (6) (6) and 22 and Yes A2ft Ib Ib total cost f low energy bulb ft their 7.12 from (b) A1ft 16.85(6) and 22 A1ft Crect conclusion f their values Mark scheme f 4(c) continues on next page 26

27 Alternative method 2 (4 years) power of dinary bulbs in kw their units of electricity f dinary bulbs their 0.1 can be 100 their cost of electricity f dinary bulbs their 96 can be their 96 must be a time 4(c) 0.2 their cost of electricity f low energy bulb 2.97(6) 2.98 their cannot be their their 2.97(6) difference in cost of electricity 11.90(4) their cannot be their their 7.12 from (b) difference in cost of bulbs 11.90(4) and 6.76 and Yes A2ft Ib Ib ft their 7.12 from (b) A1ft 11.90(4) and 6.76 A1ft Crect conclusion f their values Mark scheme f 4(c) continues on next page 27

28 Alternative method 3 (1 year) power of dinary bulbs in kw their units of electricity f dinary bulbs their 0.1 can be 100 their cost of electricity f dinary bulbs their 24 can be 240 their 24 must be a time 4(c) 1 their their their their 7.12 from (b) total cost f dinary bulbs their 3.72 cannot be their (4) cost of electricity f low energy bulbs their 3.72 cannot be their 0.74(4) their 0.74(4) (4) 4.21(4) and 5.50 and Yes A2ft Ib Ib total cost f low energy bulb ft their 7.12 from (b) A1ft 4.21(4) and 5.50 A1ft Crect conclusion f their values Mark scheme f 4(c) continues on next page 28

29 Alternative method 4 (1 year) power of dinary bulbs in kw their units of electricity f dinary bulbs their 0.1 can be 100 their cost of electricity f dinary bulbs their 24 can be 240 their 24 must be a time 0.2 their 3.72 cost of electricity f low energy bulb 0.74(4) their 3.72 cannot be (c) their 3.72 their 0.74(4) 2.97(6) difference in cost of electricity their 3.72 cannot be their their 7.12 from (b) difference in cost of bulbs 2.97(6) and 1.69 and Yes A2ft Ib Ib ft their 7.12 from (b) A1ft 2.97(6) and 1.69 A1ft Crect conclusion f their values Wking in minutes can sce a maximum of M6 A0 Must sce 2nd, 3rd, 4 th, 5th and 6th f A1ft 29