Functional Skills Mathematics Level 2 assessment

Transcription

1 Functional Skills Mathematics Level 2 assessment Marking scheme ONLINE April 2015 Version 1.0 V1 Level 2 Evolve Sample 2 Mark Represent Analyse Interpret Open Fixed S1 Q S1 Q S1 Q S1 Q S1 Q S2 Q S2 Q S2 Q S2 Q S2 Q S3 Q S3 Q S3 Q S3 Q S3 Q S3 Q S3 Q % 31% 39% 84% 16%

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 or 72.5 or or ) URT means unrounded, rounded or truncated; the underlining defines the acceptable limit of approximation: eg URT (U is the unrounded version) the following are acceptable: 860 (T) or 861 (R) (T) or (R) or (T) or (R) or (R) or (U) but not eg 900. Total marks available: 75 Notional pass mark: 50 (or above)

3 NB incorrect money format given as an answer should only be penalised once on the whole paper and will lose 1 mark, eg Section 1 Q2 ( ) (answer Optus 1 wash) loses one mark. Do not penalise any subsequent incorrect format. Maths Level 2: Section 1 Washing machine Section Total Marks Marks awarded for 1 marks Q1 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 Q2 13 Summary of expected solution for Q2 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 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) 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 3 value for the running cost + machine price scaled appropriately eg for Bubble ( ) for 5 years OR ( ) 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 or 780 or equivalent to find proportion of machine price for one wash

4 eg x 3 x 52 for number of washes in a year AND 5 for machine price for one year or 782 washes for 5 years or 156 washes for 1 year 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 ( ) Cost of electricity for 5 years ( ) Cost of water for 5 years ( ) Total cost for 5 years ( ) years: 780 washes and full price machine used for calc. Machine Bubble Optus Aqua Eco Swirl Cost to buy pro rata ( ) Cost of electricity for 1 wash ( ) Cost of water for 1 wash ( ) Total cost for 1 wash ( ) wash: machine price 780 and cost for 1 wash used for calc. Machine Bubble Optus Aqua Eco Swirl Cost to buy pro rata ( ) Cost of electricity for 1 year ( ) Cost of water for 1 year ( ) Total cost for 1 year ( ) year: machine price 5 and 156 washes used for calculation Machine Bubble Optus Aqua Eco Swirl Cost to buy pro rata ( ) Cost of electricity for 1 week ( ) Cost of water for 1 week ( ) Total cost for 1 week ( ) week: machine price 260 and 3 washes per week used for calc.

5 Q3 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 Q4 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 Q5 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. 2 two comments 1 one comment eg My plan worked well. (ie unqualified) eg My methods worked well. (ie unqualified) eg My answers seemed sensible. (ie unqualified) eg I found Q2 difficult. (ie unqualified) eg There was not enough space in Q4 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) Total for section 1 = 25 marks

6 Maths Level 2: Section 2 Football pitch Section Total Marks Marks awarded for 2 marks Q1 8 1 square drawn that encompasses the centre circle eg 10cm x 10cm on the diagram 2 square drawn 2cm x 2cm ± 1 small square AND containing centre spot 1 square 2cm x 2cm ± 1 small square drawn anywhere or two parallel sides drawn to scale ± 1 small square and containing centre spot 2 rectangle drawn 3cm x 4cm ± 1 small square AND containing centre line 1 rectangle 3cm x 4cm ± 1 small square drawn anywhere or two parallel sides drawn to scale ± 1 small square and containing centre line 2 rectangle drawn 5cm x 3.5cm ± 1 small square AND containing centre line 1 rectangle 5cm x 3.5cm ± 1 small square drawn anywhere or two parallel sides drawn to scale ± 1 small square and containing centre line 1 all pieces labelled clearly Q2 7 7 number of small squares for remaining turf eg 1064 for large 10m square follow through Q1 Some possible answers using different sizes large squares Length of side (m) Area (m 2 ) Area (m 2 ) * accept *for a square which fits the circle exactly there is wastage 6 complete correct method with one calculation error or rounding area eg 266(m 2 ) 0.25 = eg 266(m 2 ) x 4 = accept counting squares method 5 value for their incorrect area 0.25 or x 4 or value for correct area for their large square 134(m 2 ) eg 266(m 2 ) 4 method for area of their large square 134(m 2 ) eg 400(m 2 ) 134(m 2 ) or 0.25 or x 4 or x16 for counting method (1 large square /4m 2 is 16 pieces) 3 area of their large square AND 134(m 2 ) for area taken by businesses or area of their large square incorrect value for business pieces 2 area of their large square drawn in Q1 eg 400(m 2 ) or 134(m 2 ) 1 actual dimensions of their large square drawn in Q1 eg 20(m) or 16(m 2 ) or 48(m 2 ) or 70(m 2 ) for the area of one business piece

7 Q3 5 5 minimum price consistent with their large square eg 1.13 for 20m square follow through Q1 and Q2 4 unrounded minimum price consistent with their large square eg URT or complete correct method with one calculation error 3 remaining amount needed from small pieces eg ( ) cost for new turf eg ( )2 700 for 20m square 1 ( )1 500 for the total amount businesses pay Q4 3 2 suitable sensible value for price of small piece eg ( )1.20 or ( )1.50 or ( )2.00 or ( )2.50 or ( )3.00 or ( )4.00 or ( )5.00 or ( )10.00 or ( )20.00 AND corresponding justification eg It will cover the cost of the turf and raise money for charity eg I have charged higher in case we don t sell all the turf follow through Q3 1 suitable justification eg It pays for the turf and raises a bit for charity with unsuitable price chosen eg ( ) corresponding donation for charity Q5 2 2 complete correct check of one of the lines in Q1 or Q2 with reference to scale AND length of scaled line AND length of actual line eg 1:200, = 10 cm, OR 1 square = 2m therefore 3 squares x 2 = 7m 1 a partial check eg 1 square = 200cm or 8m = 4cm Total for section 2 = 25 marks Example for Q1

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9 Functional Maths Level 2: Sample 2: Section 3 Sea fishing competition Section Total Marks Marks awarded for 3 marks Q (kg) (kg) URT or or complete correct method with one calculation error (kg) URT Q2 2 2 no marks for a complete correct check of any original calculation seen in Q1 using a different method eg a reverse calculation OR a calculation using approximate values repeat calc 1 a correct check, which is not finished Q (kg) 1 maximum and minimum identified ie AND Q4 5 4 four correct averages for Island, Marine, Haven & Eastern follow through Q1 for Seaford Fishing club Number of team members Total weight of fish caught Average (mean) weight of fish caught per member Island kg (kg) URT Marine kg (kg) URT Haven kg 29.5(0) (kg) Eastern kg (kg) URT Seaford (kg) (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 Q5 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 Q6 7 Do not allow first 5 marks for table, pie chart or line graph 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 Q1 and Q4 1 one bar height correct 1 bars drawn in order OR order clearly indicated follow through Q1 and Q4 1 winning club clearly stated or indicated follow through Q1 and Q4 Q OR 25% OR ¼ OR 1 in 4 chance OR 1 out of 4 do not allow 1:4 1 4

10 2 probability scale showing either 0-1 or 0-100% or impossible / certain as end points AND showing/labelling their 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 Total for section 3 = 25 marks Example for Section 3 Q6

11 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