Functional Mathematics

Transcription

1 FUNCTONAL SKLLS CERTFCATE Functional Mathematics Level 1 Mark Scheme 4367 November 2016 Version/Stage: 1.0 Final

2 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 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. f, after the standardisation process, associates encounter unusual answers which have not been raised they are required to refer these to the Lead Assessment Writer. t 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 2016 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 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 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 CT, 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. nterpreting nterpreting and communicating the results of the analysis..1 Candidates interpret results and solutions..2 Candidates draw conclusions in light of situations..3 Candidates consider the appropriateness and accuracy of results and conclusions..4 Candidates choose appropriate language and fms of presentation to communicate results and solutions. 3

4 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 n particular, individual marks are mapped onto the following skills standards. Representing Making sense of the situations and representing them. A learner can: Ra Understand routine and non-routine problems in familiar and unfamiliar contexts and situations. dentify 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. nterpreting nterpreting and communicating the results of the analysis. A learner can: a b nterpret 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. t 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. eg, accept 0.5 as well as 2 1 4

5 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 Any 1 of patio a flower bed shown with crect size Ra Does not have to be in the crect position Does not have to be labelled Patio and both flower beds shown with crect sizes and in crect positions A1 Do not have to be labelled Allow patio to be 4 by by 4 Vegetable patch and lawn shown with Do not have to be in the crect positions equal areas Do not have to be rectangles 1(a) Vegetable patch and lawn with equal area and rectangular A1 Do not have to be labelled One single rectangle f each of lawn and veg patch. Must be the biggest they can fit in their remaining space All garden used and all 5 items included and labelled Additional Guidance Fully crect diagram with no labels A1A1B0 f the patio is put at the back of the garden then max 4 marks can still be awarded f the patio is 4 by 10 (4 at the front of the garden) then max 4 marks can still be awarded 5

6 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 Alternative method cm 1.25 m their their Seen implied Units must be compatible 1(b) 9 A1 Alternative method 2 SC2 8 SC2 he needs 5 me lights 1000 cm 1.25 m Shows multiples of their 1.25 to at least 8.75 repeated subtraction of their 1.25 from 10 to at least their 1.25 Seen implied Can be cm 9 A1 SC 2 8 SC 2 he needs 5 me lights Additional Guidance The SC2 f he needs 5 me lights may be based on 8 9 lights. Further clarification may lead to full marks Examples He needs five me lights as he already has 4 He needs 5 me lights as he needs 8 He needs 5 me lights as there are 3 gaps A1 A0 B0 M0 A0 6

7 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER (c) 40 gne units Reverse calculation 1(c) Check eg = 4 Alternative method eg Rectangle divided into 40 squares ft Ab 7

8 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 Alternative method 1 their (...) 9 5 = 45 5 their and Yes Alternative method 2 A2ft ft their 40 from (c) their 4.4(...) rounded up to nearest integer Only ft their 40 from (c) May be seen in a calculation eg 9 5 = 45 and 5 then used their 5 can be a decimal n 152 where n > 1 but not 750 Only ft their 40 from (c) A1ft 760 A1ft Crect conclusion f their value if 1st and 3rd method marks awarded 1(d) (...) 4 (packs can be bought) their and their 40 and Yes A2ft their 4.9(...) rounded down to nearest integer May be seen in a calculation Only ft their 40 from (c) A1ft 36 A1ft Crect conclusion f their value if 1st and 3rd method marks awarded Additional Guidance Alt 1 Building up to the first multiple after 40 implies the 2nd Use of 5 packs will usually gain M2 (unless from increct number rounded) A common increct answer is = No This gains M0A0A1ft Use of me decimal places eg 4.44 may also be seen Alt 2 wks out that 750 only buys enough full packs to cover 36m 2 8

9 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 Use of perimeter of 28 in (c) can gain full ft marks in d Alternative method dentifies the 3 exits, 1120, 1080 and 800 gnes the widest exit (1150) Allow must be adding 3 4 dos oe taking two dos from their 480 and checking the third do is big enough f the rest their can be used 2(a) 480 and 500 and Yes A2 A1 480 and 500 A1ft crect decision f their values Alternative method dentifies the 3 exits, 1120, 1080 and 800 gnes the widest exit (1150) their = 80 and 80 fits through smallest do = 50 and 50 fits though the smallest do May use 3 4 dos oe eg f 3 dos taking number of people f 2 of the dos away and checking remainder fits the third do 480 and valid accurate check of dos and Yes A2 A1 480 and valid check A1 ft crect decision f their values 9

10 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 Additional Guidance 2(a) f the 1150, 1120 and 1080 dos are chosen then the 3rd mark is f F the final A1 the decision must be based on both their values Examples 1) 3 exits 1120, 1080 and 800 give 500 people allowed so Yes M0A0A0 2) = 480 Yes me than 450 are allowed B0M0A0A0 3) = 480, dos allow = 600 so Yes she is crect B0M0A0A1ft ( 4 dos, one with the wrong size) Treat extra statements after Yes as further wking and igne. Example 480 and 500 Yes a maximum of 500 people are allowed A2 10

11 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 Alternative method Ra 750 their Their their 250 cannot be 1/3 Their 500 cannot be 750 2(b) ( )125 A1 Alternative method Ra Their ( )125 A1 11

12 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER Ra (0) (c) Their 2550 their 1510 their their their 2550 ( ) implies M3 their 2550 must be from an attempt to wk out total ticket sales their 1510 must be from an attempt to total at least 4 costs ( )1040 and Yes 1550 and 1510 and Yes 2550 and 2510 and Yes A2 A1( ) and and 2510 A1 ft crect decision f their values if 2 method marks sced 12

13 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 Alternative method hour 30 minutes 6.50 Their their 1 hour 15 minutes 8.00 their and No 1 hour 10 minutes and No A2 A hour 10 minutes A1ft crect decision f their value providing both time periods have been used Alternative method 2 2(d) hour 30 minutes 6.30 Their 6.30 their 1 hour 15 minutes 8.00 their 1 hour 15 minutes 6.45 Their hour 30 minutes 5.15 and No A2 A A1ft crect decision f their value providing both time periods have been used Alternative method their 1 hour 15 minutes hour 30 minutes and 6.50 and No She should leave at 5.15 A2 A and 6.50 A1ft crect decision f their values providing both time periods have been used 13

14 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 Alternative method 4 1 hour 30 minutes + their 1 hour 15 2 hours hours 40 2(d) cont d 2 hours 45 and 2 hour 40 and No A2 A1 2 hours 45 and 2 hour 40 Additional Guidance A1ft crect decision f their values providing both time periods have been used F No allow she will be (5 mins) late she should leave 5 mins earlier Their 1 hour 15 is an attempt to change one and a quarter hours to hours and minutes t cannot be just a quarter just 15 minutes To award the A1ft both time periods (1 h 30 and one and a quarter hours) must have been used Example = = 5.55 no she can leave at 5.55 A0A1ft Example 8 1 h 30 = 6.30 No M0A0A0 14

15 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER a 330 Alternative method Ra = 3 3b Their their 3 20 A1 SC (from 660 used) SC1 15 (from 1200 used) Check reverse alt method eg 20 3 = 60 Alternative method 2 Ab 3b Check Ra 300 their A1 calies per minute builds up to 300 in multiples of 15 SC (from 660 used) SC1 15 (from 1200 used) reverse alt method eg = 300 Ab Additional Guidance Alt 1 F the second their 1/3 cannot be ¼ wked out by halving and halving again 15

16 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 wks out crect calies f one machine uses each of the 3 machines at least once no me than 30 minutes on any machine total calies between 800 and 900 total time 60 minutes Full plan clearly communicated with crect calies f each machine shown time must not be one hour must have one minute on each crect total f their calies Must use at least 2 machines 3c Mark the table as their answer unless blank. Additional Guidance F the final igne total calies not within range total minutes not 60 as these are penalised earlier Example of crect plan Treadmill 10 minutes 150 calies Bike 30 minutes 330 calies Rower 15 minutes 300 calies Treadmill 5 minutes 75 calies total calies 855 The 3 machines listed with no other columns completed is zero f a machine is allocated as 0 minutes it is not being used 16

17 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER d their 60 + their their 60 their can be and Yes 18 and Yes A2 A A1ft crect conclusion f their values if 3 items added and 1st 2nd method mark awarded their Ra Ra Step 1 4(a) their Step 2 90 A1 Additional Guidance Step 1 and step 2 can be completed in reverse der. e multiply each value by 20 then find the mean Condone missing brackets when wking out the mean. Gives 40.5 as the mean 17

18 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 increased (by about their 12%) went up (me than 10%) reached 90 f the first time that year ft oe ft their (a) crect value of 90(%) seen Must be comparing May not clearly just the other 4 months Additional guidance 4(b) f there is a percentage in part a then ft this value f there is no percentage in part a but they have put a percentage in the box f May in b, ft the percentage in the box f part a has the answer 4.5 (f eg) then ft any percentage in the box in b but if the box is blank ft the value 4.5 (ie must say decreased) f part a is blank and there is no value put in the box in b then no mark can be awarded as there is no data to compare gne increct subtractions of their Must be comparing May not just Jan to April Eg the customer rating increased but then went down again in April B (c) their their Ra their 462 can be any number 84(%) A1 18

19 MARK SCHEME FUNCTONAL SKLLS MATHEMATCS LEVEL NOVEMBER 2016 Alternative method and Yes A1 Alternative method 2 4(d) and Yes Alternative method (01 ) 0.5(01 ) and Yes Alternative method Yes over half replied/440 is over half Yes 440 >438 Yes 440 is over half A1 A1 A1 19