Functional Skills Mathematics Level 2 assessment www.cityandguilds.com September 2015 Version 1.0
Marking scheme PAPER-BASED V2
Level 2 Sample Paper 4 Mark
Represent
Analyse
Interpret
Open
Fixed
1A
3
3
0
0
3
0
1B
13
6
7
0
13
0
1C
5
0
0
5
5
0
1D
1
0
0
1
1
0
1E
3
0
0
3
3
0
2A
9
1
1
7
9
0
2B
2
1
1
0
2
0
2C
6
2
4
0
0
6
2D
3
2
1
0
3
0
2E
5
2
2
1
5
0
3A
5
1
3
1
5
0
3B
5
0
0
5
5
0
3C
3
1
2
0
0
3
3D
2
1
1
0
2
0
3E
2
0
0
2
2
0
3F
3
2
0
1
0
3
3G
4
1
1
2
3
1
3H
1
0
0
1
1
0
75
23
23
29
62
13
31%
31%
39%
83%
17%
Guidance notes for Sample Paper Mark Schemes Level 1 and Level 2 Notes: The mark scheme has been carefully constructed to avoid penalising candidates repeatedly for similar errors: 1) Principle of follow through applies throughout unless otherwise stated. This allows the candidates to gain credit for subsequent correct calculation based on a previous incorrect answer. 2) Units or numbers shown in brackets on the mark scheme are not required for the awarding of mark/s on the candidate’s paper. However, if a candidate states units they must be correct: eg 24(cm) means accept 24cm or 24 but not 24m eg (£)72.5(0) means accept £72.50 or £72.5 or 72.50 or 72.5 3) URT means unrounded, rounded or truncated; the underlining defines the acceptable limit of approximation: eg 860. 8652 URT (U is the unrounded version) the following are acceptable: 860 (T) or 861 (R) 860.8 (T) or 860.9 (R) or 860.86 (T) or 860.87 (R) or 860.865 (R) or 860.8652 (U) but not eg 900.
Total marks available: 75 Indicative pass mark: 45 (or above/below)
Functional Skills Mathematics Level Sample Assessment
NB incorrect money format given as an answer should only be penalised once on the whole paper and will lose 1 mark. Do not penalise any subsequent incorrect format. Task 1 Step Total Marks Marks awarded for marks Task 1 3 1 evidence of systematic/methodical plan indicated in sequence eg Step A sequential list or simple flow chart or spidergram/mindmap or ordered text or combination of suitable types. 2 content to include reference to at least THREE of: team - managers team - fitness team - same scores activities - swimming activities - fixed times, intro, lunch, prizes activities - to fit gaps activities - total times costs discount 1 reference to at least TWO of the above Task 1 13 Summary of expected solution for 1B Step B Team selection meeting criteria; activity choices to complete timetable gaps; costs of activities and discount. team selection – these marks may be awarded if answers seen in 1C 1 suitable teams of 5 employees including at least one manager 2 similar combined fitness level scores ie 16 and 17 matching team members’ individual scores individual scores do not have to be stated 1 combined level scores of 15 and 18 matching team members’ individual scores example Team A Team B Abbie (2) Alvin (3) Isaac (5) Lora (5) Ash (5) Shilen (4) Nita (2) Frank (2) Pete (2) Prita (3) Total fitness Total fitness 17 16 score score activity choice – these marks may be awarded if answers seen in 1C 4 3 additional activities chosen for the morning session AND 1 additional activity chosen for the afternoon session eg morning - fright wall, mud flume, power fan; afternoon - raft building 3 4 additional activities chosen that take 5 hours in total without morning and afternoon sessions identified 2 4 or 5 additional activities chosen that take 5 hours including activities not suitable for non-swimmers ie wipe out course and/or paddle boarding or 5 additional activities chosen taking 6 hours not including archery 1 additional activities chosen with one timing/calculation error eg incorrect time for one activity eg half hour or 15 minute gap left eg missing out lunch break eg incorrect totalling of times listed cost 2 correct total cost for their chosen activities AND archery eg £450.20 for 3xA, 1xB and 1xC 1 correct total cost for their chosen activities without archery Functional Skills Mathematics Level Sample Assessment
2 1
check 2 no marks for repeat calc
Task 1 Step C
5
1 1 1
Task 1 Step D
1
1 2 1 1
Task 1 Step E
3
3
2 1
or complete correct method, including archery, with one calculation error Note: correct method must include values in working shown correct value for their total costs with 15% discount eg £382.67 for £450.20 correct value for 15% of their total cost eg £67.53 for £450.20 or method for 85% eg x0.85 seen or x85÷100 eg their total cost – total cost x0.15 a complete correct check of any original calculation seen using a different method eg a reverse calculation OR a calculation using approximate values a correct check which is not finished team members listed clearly within a structure suitable for a notice timetable structure with rows and columns and appropriate delineation showing activities AND times with headings / labels for times and activities given data ie intro, lunch and prizes clearly shown with times all data entered for their activities AND times their data entered with one error or omission suitable reason based on results or data given eg ‘all activities are suitable for non-swimmers’ eg ‘my combination (of activities) fills the morning and afternoon up’ three comments relevant to one or more review prompts ie plan and methods or sensible answers or difficulties or other information or tackling a similar problem some acceptable comments some unacceptable comments eg My plan worked well. eg My plan worked in order so I (ie unqualified) picked activities and then I knew eg My methods worked well. how much they cost (ie unqualified) eg My answer is sensible because eg My answers seemed sensible. £382.67 is a reasonable amount for (ie unqualified) a training day eg I found it difficult to fit activities eg I found 1B difficult. (ie unqualified) into exact time slots on my eg There was not enough space in timetable 1D to write my answers. (inappropriate) eg I had all the information I eg It would be helpful to have the needed. (ie unqualified) actual prices in the table (instead of A, B and C) eg I would do nothing differently. eg Next time I wouldn’t do anything differently because I had (ie unqualified) two teams with equal fitness and 5 activities that fit exactly two comments one comment Total for Task 1 25 marks
Functional Skills Mathematics Level Sample Assessment
Step Task 2 Step A
Total Marks marks 9 1 1 3 2 1 1 2
Task 2 Step B
2
1 1 2
1
Task 2 Step C
6
Task 2 Step D
3
Task 2 Step E
5
5 4 3 2 1 1 3 2 1 3 2 1 2
1
Task 2 Marks awarded for suitable scale chosen eg 1:200 or 1cm=2m do not accept smaller than 1:500 (1cm=5m) scale indicated clearly, or arrow drawn on graph paper to indicate 2m or 10m do not accept dimensions drawn on diagram as substitute for a scale outline of food zone drawn to scale ± ½ small square any four sides drawn to scale ± ½ small square any two sides drawn to scale ± ½ small square width of access road drawn to scale ± ½ small square width of space for food vans drawn 4m in from edge of zone to scale ± ½ small square but not along or across road any one section access road and food van space and seating section labelled A complete correct check of one of the lines in 2A using their scale eg for scale 1:200 46m ÷ 200 = 23cm or 1 square = 2m so 5 squares = 10m 1cm = 2m AND 23cm = 46m A partial check eg for scale 1:200 1cm = 2m or 23cm = 46m or 1 square = 2m or 5 squares = 10m 8.74m accept 8.739014478m URT WITH UNITS 8.74(m) accept 8.739014478(m) URT 7.239014478(m) URT or complete correct method with one calculation error substitution into formula using their converted value for L 285(inches) from 8.74m their answer rounded up to the next whole metre eg 9(m) 4 for value for length of side divided by rounded length for pitch follow through 2B 4.33333333 (pitches) or 4.777777778 (pitches) URT 39(m) or 43(m) seen for longest length of seating section or complete correct method with one calculation error 440(m2) follow through 2A any area that forms part of the solution eg 5 x 10 = 50 or 39 x 10 = 390 or 20 x 5 = 100 or 34 x 10 = 340 or 39 x 20 = 780 or complete correct method with one calculation error a method for finding one of the smaller areas eg 5 x 10 correct decision and suitable explanation for their area with reference to comparative values eg ‘yes’ AND 440 > 375 (from 250 + 50% = 375) 190 > 125 (440 – 250 = 190 > 50% of 250) 76% > 50% (440 – 250 = 190 then 190 ÷ 250 = 0.76) 147 > 125 (440 ÷ 3 = 147) follow through 2A (may give a ‘no’ decision) correct explanation with wrong decision or 375m2 seen anywhere Total for Task 2 = 25 marks
Functional Skills Mathematics Level Sample Assessment
2A Scaled lengths for diagram
A 18m
Scaled length in centimetres Scale
F 34m B 46m E 10m
D 12m C 28m
Functional Skills Mathematics Level Sample Assessment
1:200
1:250
1:400
1:500
A
9
7.2
4.5
3.6
B
23
18.4
11.5
9.2
C
14
11.2
7
5.6
D
6
4.8
3
2.4
E
5
4
2.5
2
F
17
13.6
8.5
6.8
Road
1.5
1.2
0.75
0.6
Vans
2
1.6
1
0.8
Step Task 3 step A
Total marks 5
Task 3 Marks Marks awarded for 4
3
2 1
1
Task 3 Step B
Task 3 step C
5
no marks for line graph, pie chart, or table
3
1 1
1 2 1 3
2
1
one range correct max and min seen for one range ie 6 and 3 or 10 and 2 or 10 and 6 a complete correct check of any original calculation seen in 3C using a different method eg a reverse calculation OR a calculation using approximate values a correct check which is not finished
1
suitable comment using their average eg ‘(generally) they liked the fragrance’
1 Task 3 step D
Task 3 step E
2
no marks for repeat calc
2
3 correct averages corresponding to their choice Design of bottle Fragrance Hands clean Mean 4.5 7.5 8 Median 4 7 8.5 or 9 Mode 6 6 9 one correct average corresponding to their choice or 3 consistent correct averages if no choice indicated or incorrect choice if more than one type of average is attempted and there are some incorrect values allow 3 marks if one set of values is clear and correct eg all medians correct complete correct method and value for one average if no choice indicated or incorrect choice eg 81 ÷ 18 = 4.5 for median incorrectly stated method for one average mean, median or mode mean: ÷ 18 or 81 or 135 or 144 seen median: attempt to order data to find middle or (n+1) / 2th place seen eg 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6 (design) mode: attempt to tally seen eg 5 x 3, 5 x 4, 2 x 5, 6 x 6 (design) suitable explanation eg mean: includes all the test data eg median: because there is an outlier in fragrance (others median to enable one average to be used) eg mode: because it is the rating chosen by the most people bar chart with 3 bars only showing their averages suitable vertical axis label AND bar labels/ key note: allow references to average number of differences in title as alternative to vertical axis label continuous linear scale on vertical axis starting at (implied) zero and sufficient for their values all bar heights correct ± ½ small square one bar height correct ± ½ small square all three values for range correct Range Design of bottle 3 Fragrance 8 Hands clean 4
2
Functional Skills Mathematics Level Sample Assessment
Task 3 step F
3
1 2 1
Task 3 step G
4
2 1 1 1
straight line extension of both trend lines to Promotion 9 a value between 900 and 1200 for paper vouchers AND a value between 3900 and 4100 for online vouchers a value between 900 and 1200 for paper vouchers or a value between 3900 and 4100 for online vouchers or both values above in incorrect order 0.01 or 1% or 1/100 or 1 in 100 chance or 1 out of 100 do not allow 1:100 follow through 3F 1000/100000 end points clearly labelled ie 0 and 1 or 0% and 100% point marked clearly for their probability eg for 0.01 point marked clearly closer to 0 than 0.1
(0.1)
0.5
0 Task 3 step H
1
1
1
suitable explanation consistent with their decision and reference to (use of) paper vouchers eg ‘no’ and ‘(use of) paper vouchers decreasing’ eg ‘yes’ and ‘1000 vouchers expected to be used’ eg ‘their opinions varied a lot’ Total for Task 3 25 marks
Example charts for 3B
9 8 7 6 5 4 3 2 1 0
Median average rating scores Median rating score
Mean rating score
Mean average rating scores
Design of bottle
Fragrance
Hands feel clean afterwards
Functional Skills Mathematics Level Sample Assessment
9 8 7 6 5 4 3 2 1 0 Design of bottle
Fragrance
Hands feel clean afterwards
Mode average rating scores Hands feel clean afterwards Fragrance Design of bottle 0
1
2
3
4
5
6
Mode rating score
Functional Skills Mathematics Level Sample Assessment
7
8
9
10
Level 2 Sample Paper 4 Coverage and Range (Technical Skills)
Task 1
Task 2
Task 3
C2.1 Understand and use positive and negative numbers of any size in practical contexts
C2.2 carry out calculations with numbers of any size in practical contexts, to a given number of decimal places
C2.3 Understand, use and calculate ratio and proportion, including problems involving scale C2.4 Understand and use equivalences between fractions, decimals and percentages
C2.5 Understand and use simple formulae and equations involving one- or two-step operations
C2.7 find area, perimeter and volume of common shapes
C2.8 use, convert and calculate using metric and, where appropriate, imperial measures
C2.6 recognise and use 2D representations of 3D objects
C2.9 collect and represent discrete and continuous data, using ICT where appropriate C2.10 use and interpret statistical measures, tables and diagrams, for discrete and continuous data, using ICT where appropriate
C2.11 use statistical methods to investigate situations
C2.12 use probability to assess the likelihood of an outcome
Functional Skills Mathematics Level Sample Assessment
