Functional Skills Mathematics Level 2 sample assessment · Functional Skills Mathematics Level 2 mark scheme – Sample Paper 2 Maths Level 2: Task 2 – Orienteering Step Total marks

Functional Skills Mathematics Level 2 mark scheme – Sample Paper 2

Functional Skills Mathematics Level 2 sample assessment Marking scheme PAPER-BASED

www.cityandguilds.com

May 2015 Version 1

Level 2 Sample Paper 2

Mark Represent Analyse Interpret Open Fixed 1A 3 3 0 0 3 0 1B 13 6 7 0 13 0 1C 4 0 0 4 4 0 1D 2 0 0 2 2 0 1E 3 0 0 3 3 0 2A 3 2 0 1 3 0 2B 2 0 0 2 2 0 2C 12 5 7 0 12 0 2D 2 1 1 0 2 0 2E 6 0 0 6 6 0 3A 3 1 2 0 0 3 3B 2 1 1 0 2 0 3C 2 1 1 0 0 2 3D 5 1 3 1 0 5 3E 2 0 0 2 2 0 3F 7 1 0 6 7 0 3G 4 1 1 2 2 2

75 23 23 29 63 12 31% 31% 39% 84% 16%

V1

These materials relate to the assessments that will be in use from September 2015


Functional Skills Mathematics

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 Notional pass mark: 50 (or above)


NB incorrect money format given as an answer should only be penalised once on the whole paper and will lose 1 mark, eg 1C (£)0.324 (answer Bubble electricity 1 week) loses one mark. Do not penalise any subsequent incorrect format.

Maths Level 2: Task 1 – Washing machine

Step Total

marks Marks Marks awarded for

Task 1 Step A

3 1 evidence of systematic/methodical plan indicated in sequence eg 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:

suitable washing machine (based on criteria) number of washes over a period of time eg 5 years cost of electricity cost of water prices of the washing machines (total) costs

1 reference to at least TWO of the above

Task 1 Step B

13

Summary of expected solution for 1B correct comparison for any two machines including machine prices, electricity costs and water costs using a consistent time period/number of washes eg for 5 years or for 1 year or 1 week (3 washes) or 1 wash, for which a table of results is provided. Other consistent periods of time are acceptable and can be worked out by the marker washing machine costs

3 Correct prices for Bubble and Optus ie £399 for Bubble and £329 for Optus

2 Correct price for two machines including either Bubble or Optus eg £399 for Bubble and £299 for Aqua

1 Correct price for ANY two machines including either Bubble or Optus or only Bubble and Optus chosen (without prices)

water and electricity costs 5 total cost for water and electricity for a defined number of

washes/period of time for ANY two machines 4 total cost for water and electricity for a defined number of washes/period of

time for any one machine 3 values for units of electricity used x cost of unit and units of water used x cost

of unit eg (£)0.12 x 1.2 = (£)0.144 and (£)0.003 x 45 = (£)0.135 for Bubble for one wash eg (£)0.12 x 1.2 x 3 = (£)0.432 and (£)0.003 x 45 x 3 = (£)0.405 for Bubble for one week See table below for alternatives

2 values for units of electricity used x cost of unit or units of water used x cost of unit eg (£)0.13 x 1.2 = (£)0.156 or (£)0.003 x 50 = (£)0.15 for Optus for one wash eg (£)0.13 x 1.2 x 3 = (£)0.468 or (£)0.003 x 50 x 3 = (£)0.45 for Optus for one week See table below for alternatives

1 units of electricity or litres of water used for each wash by their machine eg 1.2 or 45 for Bubble or 1.3 or 50 for Optus

running costs and machine price (scaled costs) 3 value for the running cost + machine price scaled appropriately

eg for Bubble (£)616.62 for 5 years OR (£)123.32 for 52 weeks OR (£)2.37 for 3 washes OR (£)0.79 for one wash


See table below for alternatives 2 running cost + machine price related by scaling

eg x 3 x 52 x 5 or x 780 or equivalent to find the number of washes in 5 years eg ÷ 3 ÷ 52 ÷ 5 or ÷ 780 or equivalent to find proportion of machine price for one wash eg x 3 x 52 for number of washes in a year AND ÷ 5 for machine price for one year

1 780 or 782 washes for 5 years or 156 washes for 1 year check

2 no

marks for

repeat calc

a complete correct check of any original calculation seen using a different method eg a reverse calculation OR a calculation using approximate values

1 a correct check, which is not finished Example costs for different time periods/number of washes

Machine Bubble Optus Aqua Eco Swirl Cost to buy (£) £399.00 £329.00 £299.00 £259.00 £329.00Cost of electricity for 5 years (£) £112.32 £121.68 £84.24 £84.24 £102.96

Cost of water for 5 years (£) £105.30 £117.00 £98.28 £102.96 £114.66

Total cost for 5 years (£) £616.62 £567.68 £481.52 £446.20 £546.62

5 years: 780 washes and full price machine used for calc.

Machine Bubble Optus Aqua Eco Swirl

Cost to buy pro rata (£) £0.51 £0.42 £0.38 £0.33 £0.42Cost of electricity for 1 wash (£) £0.14 £0.16 £0.11 £0.11 £0.13Cost of water for 1 wash (£) £0.14 £0.15 £0.13 £0.13 £0.15Total cost for 1 wash (£) £0.79 £0.73 £0.62 £0.57 £0.701 wash: machine price ÷ 780 and cost for 1 wash used for calc.

Machine Bubble Optus Aqua Eco Swirl Cost to buy pro rata (£) £79.80 £65.80 £59.80 £51.80 £65.80Cost of electricity for 1 year (£) £22.46 £24.34 £16.85 £16.85 £20.59Cost of water for 1 year (£) £21.06 £23.40 £19.66 £20.59 £22.93Total cost for 1 year (£) £123.32 £113.54 £96.30 £89.24 £109.321 year: machine price ÷ 5 and 156 washes used for calculation

Machine Bubble Optus Aqua Eco Swirl Cost to buy pro rata (£) £1.53 £1.27 £1.15 £1.00 £1.27Cost of electricity for 1 week (£) £0.43 £0.47 £0.32 £0.32 £0.40Cost of water for 1 week (£) £0.41 £0.45 £0.38 £0.40 £0.44


Total cost for 1 week (£) £2.37 £2.18 £1.85 £1.72 £2.101 week: machine price ÷ 260 and 3 washes per week used for calculation.

Task 1 Step C

4 1 table structure showing at least two washing machines with rows and columns and appropriate delineation

1 headings / labels for at least three of (washing) machine price, electricity costs, water costs, total running costs, total cost, period of time, number of washes

1 their data entered for running costs (electricity, water and machine price) for both machines

1 their total costs for both machines in the table with units indicated Task 1 Step D

2 2 two valid reasons corresponding to the choice of washing machine eg ‘Optus/Bubble meets the criteria of wash cycle and spin speed’ eg ‘Bubble is cheaper over the 5 years’ Do not accept ‘meets criteria’ without qualification

1 one valid reason Task 1 Step E

3 3 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 helped me structure my work to find the best machine. eg I made sure I worked out electricity and water for 5 years because the machine price was 5 years. eg Results are sensible because the more water and electricity used, resulted in higher costs. eg I found it difficult that the information for the electricity was for one wash and I needed to find it for 5 years. eg It would be useful to know how long the machine would actually last. eg I would work it out for 5 years instead of 1 year. eg I would check all the electricity and water costs.

eg My plan worked well. (ie unqualified) eg My methods worked well. (ie unqualified) eg My answers seemed sensible. (ie unqualified) eg I found 1B difficult. (ie unqualified) eg There was not enough space in 1D to write my answers. (inappropriate) eg I had all the information I needed. (ie unqualified) eg I would choose a different washing machine. (ie unqualified) eg I would check all my answers. (ie unqualified)

2 two comments 1 one comment

Total for Task 1 = 25 marks


Maths Level 2: Task 2 – Orienteering

Step Total marks

Marks Marks awarded for

Task 2 Step A

3 No

marks available if route goes

through lake

3 suitable line joining all 7 checkpoints in any order ie not through lake AND visiting each check point only once

2 line joining 6 checkpoints in any order but not through lake or line visiting a checkpoint more than once but not through lake

1 line joining checkpoints in any order omitting start and finish

Task 2 Step B

2 2 two reasons for route eg it is the shortest route eg it passes through each checkpoint eg it starts at the furthest point (for A) eg it passes through each checkpoint only once

1 one reason for route

Task 2 Step C

12 12 times taken for all 6 stages corresponding to route marked on map AND total time taken from either correct addition of their stage times or correct calculation from total distance See table below for times calculated from straight line routes drawn on map. Accept correct times for other routes drawn by candidate

Stage Minutes

Start to A 20 ± 1

Start to B 16 ± 1

Start to C 12 ± 1

Start to D 13 ± 1

A to B 10 ±1

A to C 10 ± 1

B to C 12 ± 1

B to D 26 ± 1

C to D 16 ± 1

D to E 12 ± 1

D to finish 8 ± 1

E to finish 16 ± 1

total time eg start, B, A, C, D, E, finish = 80 minutes eg start, C, A, B, D, E, finish = 86 minutes


if 12 marks not achieved apply the following 3-part mark scheme

Table of answers for straight line route measurements. Accept correct distances for other routes drawn by candidate

Stage Measurement (cm) ± 0.2cm

Distance (km) Time (minutes)

Start to A 10 2 20

Start to B 8 1.6 16

Start to C 6 1.2 12

Start to D 7 accept 6.7 1.4 14

A to B 5 1 10

A to C 5 1 10

A to D 13 2.6 26

B to C 6 1.2 12

B to D 13 2.6 26

C to D 8 1.6 16

D to E 6 1.2 12

D to finish 4 0.8 8

E to finish 8 1.6 16

Part 1 – measurement of distances on map (see table above)

3 all 6 stage measurements ± 0.2cm

2 4 stage measurements correct ± 0.2cm

1 2 stage measurements correct ± 0.2cm

1 total distance consistent with their stages eg start, B, A, C, D, E, finish = 40cm eg start, C, A, B, D, E, finish = 43cm

Part 2 – calculation of distances (see table above)

4 correct conversions of all their stage measurements in km

3 correct conversion of four of their stages measurement in km

2 correct conversion of one of their stages measurement in km

1 correct method for conversion seen eg x 20 000(scale) ÷ 100(cm) ÷ 1000(m) or x 200 ÷ 1000 or x 0.2

Part 3 – calculation of times (see table above)

3 correct time for all their stage distances

2 correct time for one of their stage distances

1 correct method for calculating time needed eg ÷ 6(hours) or ÷ 6 x 60(minutes) or equivalent or 1km takes 10 minutes seen

1 correct total time for their stages from the total distance or from addition of the stage times

Task 2 Step D

2 2 a correct explanation of one of the distances in 2C with reference to the scale, measured distance and actual distance eg scale is 1:20 000 and 6(cm) x 20 000(cm) = 120 000(cm) (= 1.2km)

1 a partial check


eg 1:20 000 seen (for scale) or 5cm (their measurement)= 1km (actual distance)

Task 2 Step E

6 no

marks available for table, bar chart or graph

1 clearly structured flowchart showing stages, distances and times

1 suitable connectors (eg arrows) linking components

1 units for distance and time indicated

2 all their results entered correctly

1 all their results entered with one error or omission eg one stage is one error

1 total time seen



Maths Level 2: Task 3 – Sea fishing competition

Step Total

marks Marks Marks awarded for

Task 3 Step A

3 3 24.38(kg)

2 24.3825(kg) URT or 195.06 ÷ 8 or complete correct method with one calculation error

1 195.06(kg) URT

Task 3 Step B

2 2 no

marks for

repeat calc

a complete correct check of any original calculation seen in 3A using a different method eg a reverse calculation OR a calculation using approximate values

1 a correct check, which is not finished Task 3 Step C

2 2 12.28(kg) 1 maximum and minimum identified ie 31.23 AND 18.95

Task 3 Step D

5 4 four correct averages for Island, Marine, Haven & Eastern follow through 1A for Seaford

Fishing club

Number of team members

Total weight of fish caught

Average (mean) weight of fish caught per member

Island 11 321.45kg 29.22272727(kg) URT

Marine 9 275.95kg 30.66111111(kg) URT

Haven 7 206.50kg 29.5(0) (kg)

Eastern 7 227.90kg 32.55714286(kg) URT

Seaford 8 195.06(kg) 24.3825(kg) URT

3 three correct averages (from Island, Marine, Haven & Eastern)

2 one correct average (from Island, Marine, Haven & Eastern)

1 correct method for calculating any one average (from Island, Marine, Haven & Eastern)

1 all values filled in correctly, in the correct places in the table follow through for all clubs

Task 3 Step E

2 1 suitable comment comparing Seaford mean to other clubs eg Seaford mean is lowest so they came last do not accept lowest mean without explanation

1 suitable comment comparing Seaford range to other clubs with reference to variation or consistency eg Seaford range is the highest so there is more variation in weight

Task 3 Step F

7 Do not

allow first 5 marks

1 suitable bar chart with 5 bars showing average weights

1 suitable vertical axis label with units and bar labels/key

1 continuous scale on weight axis starting at (implied) zero

2 all bars correct heights ± ½ small square follow through 3A and 3D


eg 3F

0

5

10

15

20

25

30

35

Seaford Island Haven Marine Eastern

Mean weight (kg)

Fishing club

Fishing competition results

for table,

pie chart or line graph

1 one bar height correct

1 bars drawn in order (low to high or high to low) OR order clearly indicated eg first, second etc follow through 3A and 3D

1 winning club clearly stated or indicated follow through 3A and 3D

Task 3 Step G

4

2 0.25 OR 25% OR ¼ OR 1 in 4 chance OR 1 out of 4 do not allow 1:4

1 4

2 probability scale showing either 0-1 or 0-100% or ‘impossible’ / ‘certain’ as end points AND showing/labelling their calculated probability eg 0.25

Example of a probability scale

1 probability scale showing either 0-1 or 0-100% or ‘impossible’ / ‘certain’ as end points or line drawn without extremes indicated eg without 0 and 1 but with their probability shown approximately to scale along the line


Probability of Seaford organising (0.25)

WINNER: Eastern


Level 2 SAMPLE PAPER 2

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

C2.6 recognise and use 2D representations of 3D objects

C2.7 find area, perimeter and volume of common shapes

C2.8 use, convert and calculate using metric and, where appropriate, imperial measures

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

Documents

Functional Skills Mathematics Level 2 sample assessment · Functional Skills Mathematics Level 2 mark scheme – Sample Paper 2 Maths Level 2: Task 2 – Orienteering Step Total marks