AQA Qualifications Functional Mathematics Level Mark scheme November Version/Stage: Final V1.0

Transcription

1 AA ualifications Functional Mathematics Level Mark scheme 4368 November 2014 Version/Stage: Final V1.0

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 AA its licenss. All rights reserved. AA retains the copyright on all its publications. However, registered schools/colleges f AA are permitted to copy material from this booklet f their own internal use, with the following imptant exception: AA 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 17

4 In particular, individual marks are mapped onto the following skills stards. Representing Rb 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 17

5 Alternative Method 1 any 2 from (0) (0) Rb their 85 + their their (0) their 147.9(0) + their 32 their 32 can be 12, (a) 179.9(0) Yes A (0) ft crect ft decision f their 179.9(0) Alternative Method (0) Rb their 8.7(0) (0) 175 their (0) 27.1(0) their 32 can be 12, (0) Yes 27.1(0) 32 Yes A (0) (0) 32 ft crect ft decision f their values 5 of 17

6 The first two marks may follow either scheme 1(a) The last three marks may follow either scheme Wk may be seen in table Must sce M3 to award ft All gifts different must have at least 8 items At least two from each group implied by costs 1(b) Checks total by adding all of their item costs Ab must be adding at least one item from each group oe eg subtracts all items of their item costs from Obtains crect total f their items between Items clearly communicated must have at least 8 items names must be included 1(b) Condone errs in item prices f but not (c) their oe 225 1(c) Only award the 2 nd if there is a method shown f their 45 6 of 17

7 their number of 3.6 m boards f widest part their 1.8(0) can be (a) ( 2) number of 1.2 m lengths 2.4 lengths f both narrower parts A2 must see decking lengths 12 of 3.6 m 8 of 2.4 m Yes ft crect ft decision f their values 16 of 3.6 m 2 of 2.4 m Yes SC4 4 of 3.6 m 20 of 2.4 m SC2 20 of 3.6 m 2(a) Must sce M3 to award ft Use of 0.6 to award marks answers must be multiplied by 4 to convert to division by of 17

8 Any combination that can be used f three me of the 8 sides e.g implied by costs e.g must be at least two lengths Any combination with total length 15.6 m 16.2 m e.g (= 15.6 m) (= 15.6 m) (= 15.6 m) (= 15.6 m) (= 15.6 m) (= 16.2 m) (= 16.2 m) (= 16.2 m) (= 16.2 m) (= 16.2 m) 2(b) Wks out total cost of their arrangement e.g Rb implied by costs e.g e.g = (= 112) (= 104) (= 108) (= 104) Crect total cost f their arrangement e.g. ( =) 116 ft (= 124) (= 108) (= 112) (= 108) 9 12 (= 108) ft any arrangement f only must be an arrangement with total length 15.6 m 16.2 m f ft 5 of 2.4 m 2 of 1.8 m of 2.4 m 6 of 1.8 m 104 must see edging lengths 2(c) 14 B2 shows 4 posts needed f 3.6 m side 3.0 m side shows 8 cners 8 of 17

9 3(a) (0) (0) (50 6) (0) 1.5(0) (0) 2 2.4(0) their 12.5(0) their 1.50 their 2.4(0) Rb quiz prize / fee total bus fare could be combined within other calculations crectly combines their total income their total expenditure could be implied by intermediate calculations e.g. their 21 their 4.79 their 11 + their (0) allow their 2.4(0) = 1.2(0) must see symbol SC2 ( )17.41 ( ) (a) their 2.4(0) = 1.2(0) sces M0A0 All method marks can be sced f wking in pence with units shown not shown. symbol is not needed f M marks Magic numbers 21 f M2 f f M2 f of 17

10 3(b) Table completed with each of A, B, C D playing exactly 3 games Table completed with A, B, C D each playing no me than once in each round B0 all players play all games in each round Table completed with A, B, C D with no games repeated Check 3(b) Crect recd of their number of games played by A, B, C D ft Ab must ft from their complete table allow a tally chart, a list of opponents, the rounds played in number of games played B0 all players play all games in each round Check 3(b) Mark as a strict follow through from their list ie a crect answer will not necessarily sce e.g. 3, 3, 3, 3 only sces if their complete table is crect Accept totals, tallies, the rounds played in opponents listed If opponents rounds are listed they must be crect The check may be elsewhere on the page 10 of 17

11 Attempt to analyse at least one set of data. F example Number of wins number of losses f Fiona / Grant Number of wins number of games f Fiona / Grant Number of losses number of games f Fiona / Grant e.g. Fiona 3 wins () 7 losses 3 wins () 10 games 7 losses () 10 games Grant 2 wins () 6 losses 2 wins () 8 games 6 losses () 8 games 3(c) Proptions f Fiona Grant given in the same fm. F example in wds as a fraction as a ratio e.g. 3 out of 10 2 out of 8 3 in 10 2 in 8 3 / 10 2 / 8 3 : 10 2 : 8 7 : 10 6 : 8 Yes their crect proptional representations given in crect comparable fm. F example in wds with the same number of wins, losses games as a decimal as a percentage as a fraction with a common denominat as an equivalent ratio with the same number of wins, losses games Examples of crect comparable fm Fiona 12 wins out of 40 6 wins to 14 losses Grant 10 wins out of 40 6 wins to 18 losses % 25% : : 40 3(c) Crect proptions assigned to wrong players can sce up to M2 Crect comparable proptions with no conclusion sces M2A0 Igne wking f (d) Allow wking f this question in (d) if it clearly refers to (c) Assume any relevant wking next to the table is f (c) unless clearly only used in (d) 11 of 17

12 3(d) ( ) ( ) ( ) ( ) Allow one err omission their their their their Yes Yes (d) Igne wking f (c) Allow wking f this question in (c) if it clearly refers to (d) Assume any relevant wking next to the table is f this part unless clearly only used in (c) An attempt at the total can be implied by a total at the bottom of the column of numbers 4(a) of 17

13 975 (metres) gives crect distance of Station to Dungeon (10:00 +) their :13 13 min Rb gives Dungeon arrival time allow 10:15 if crect calculation seen their 10: hours 12:43 gives Dungeon leaving time Castle Museum 525 (m) 7 min Minster 825 (m) 11 min gives a 2 nd attraction gives the crect distance time to get there from the Dungeon implied by crect arrival time at 2 nd attraction Jvik 225 (m) 3 min 4(b) Castle Museum their 12:50 their 15:20 Minster their 12:54 their 15:24 Jvik their 12:46 their 15:16 gives a 3 rd attraction to visit gives the distance crect walking time from their 2 nd attraction ft ft gives arrival leaving times f their 2 nd attraction ft their time from leaving the Dungeon their walking time allow times rounded to nearest 5 min if calculation of walking time seen ft their 2 nd attraction allow times rounded to nearest 5 min if calculation of walking time seen gives arrival leaving time well communicated plan with all times distances crect must include 3 attractions visited Dungeon visited distances to each attraction arrival leaving times at each attraction 2½h spent at each attraction complete route starting finishing at the station time of arrival back at the station (befe 6.30 pm) A2 well communicated plan with up to two errs in times distances well communicated plan with all times distances crect but with one of the following omissions one attraction not visited all distance not given all arrival times not given (including arrival time back at station) 13 of 17

14 4(b) Distances (1 st 4 th marks) There are up to 2 marks (, ) awarded f crect distances in a crect plan. If neither can be awarded, give 1 mark () f any crect distance seen. Time calculation (2 nd mark) One M mark is awarded f crectly wking out the time to walk from the Station to the Dungeon. If this mark is not awarded, give f any crect calculation of walking time seen including total walking time. Adding 2.5 hours (3 rd mark) One mark () is awarded f crectly wking out the time to leave the Dungeon after a 2.5 h stay. If this mark is not awarded, give an extra if their leaving time is wked out crectly at the 2 nd 3 rd attraction. Walking times This table shows the walking times in minutes between attractions. Station Castle Museum Minster Dungeon Jvik Centre Station Castle Museum Minster Dungeon of 17

15 [81, 81.1] 5(a) [81, 81.1] Condone if plotted crectly on graph wking seen their (8, [81, 81.1]) plotted ft ± ½ small square 5(b) uses a valid numerical graphical method to show the trend in the values of F f both Sam Dave trend lines on graphs must cross between weeks 8 13 uses the trend to predict that Sam s F > Dave s F between weeks 8 13 states implies that Sam s statement is crect B2 uses a valid numerical graphical method to show the trend in the values of F f both Sam Dave trend lines on graphs must cross between weeks 8 13 crectly describes the trends f both Sam Dave with no numerical graphical justification predicts that Sam s F > Dave s F between weeks of 17

16 F B2 must show both trends use them to make a prediction appropriate conclusion. A conclusion of No possibly is acceptable if the trends predictions are crect but must be qualified by a statement relating to the possibility that the trends might not continue. Example 1 (Numerical justification of trend) Sces B2; description of trend only Description of trend (Values of F at weeks 4 8) Dave F increases by 4 in 5 weeks Sam F increases by 15 in 5 weeks Prediction At week 13 Dave s F = 85 At week 13 Sam s F = 91 Conclusion Sam will become fitter than Dave between weeks 8 13 (about week 10) Example 2 (Numerical justification of trend) Sces B2; description of trend only Description of trend (Difference in values of F between weeks 4 8) 5(b) Dave 4 16, 5 12, 6 6, 7 8, 8 5 Prediction 9 3, 10 1, 11 1, 12 3, 12 5 Conclusion Decreasing by about 2 each week Sam will become fitter than Dave between weeks Example 3 (Graphical justification of trend) Sces B2; description of trend only Description of trend Draws trend lines f both Dave Sam extending to week 13 Trend lines cross between week 8 13 Prediction conclusion The lines cross so Sam will become fitter than Dave between weeks 8 13 Example 4 (No graphical numerical justification of trend valid prediction) Sces only Sam s F is increasing faster than Dave s. He should become fitter than Dave about week 10. Example 5 (Unjustified numerical description of trend valid prediction) Sces only Sam s F is increasing twice as fast as Dave s. He will be fitter than Dave after week of 17

17 5(c) their their their their 684 can be 68.4 their 684 can be 6.25 their 145 can be 5 [2208.9, 2209] 2210 ft Yes Yes = (d) = 840 Yes = = = = 2800 Yes = 70(%) Yes = of 17