FUNCTIONAL SKILLS
MATHEMATICS
LEVEL 2
MARK SCHEME
Task 1
Question
Process Total Mark
For Evidence of Comment Criteria Ref R A I 1 (1) Converting the weight of apples
3 1 mark for correct method for conversion e.g. 16 ÷ 2.2
e.g. 50 x 2.2 e.g. 128 ÷ 2.2
R3
1 mark for correct solution
e.g. (16 ÷ 2.2 =) 7.2727r and (7.2727 x 8 =) 58.1818r(kg), e.g. (16 x 8 =) 128 and (128 ÷ 2.2 =) 58.1818r(kg)
Accept any correct value between 57.6 and 58.2 e.g. (50 x 2.2 =) 110 (lbs) and (8 x 16 =) 128(lbs), e.g. 50 x 2.2 (=110) ÷ 16 = 6.875 (buckets hold 50kg)
Accept rounding or truncation
A1
1 mark for correct conclusion
e.g. ‘Yes, Jenny has collected more than 50kg’ e.g. ‘Yes, 7 buckets is enough’
e.g. ‘Jenny has enough apples’
2a (2a) Calculating the number of packs of ingredients for mini apple
pies
4 1 mark for correct method to find any quantity e.g. flour 650 x 120 ÷ 8
e.g. butter 325 x 15 e.g. sugar 1000 ÷ 150
R2
1 mark for correct method to find number of packs of flour or packs of butter
e.g. (15 x 650 = ) 9750, 9 750 ÷ 1500 for flour e.g, (15 x 325 = ) 4875, 4875 ÷ 250 for butter
R2
1 mark for at least 3 correct solutions for number of packs e.g. flour 6.5, butter 19.5, sugar 2.25, eggs 5
Accept 3 correct rounded answers, from flour 7, butter 20, sugar 3, (eggs 5)
A1
1 mark for correct list of number of packs i.e. flour 7, butter 20, sugar 3 and eggs 5
I1 2b
(2b)
Check 1 1 mark for acceptable check
e.g. flour 7 x 1.5 = 10.5(kg) and 10.5 ÷ 15 = 0.7(kg) or 700(g) e.g. butter 20 x 250 = 5000(g),and 5000 ÷ 15 = 333.3r(g) e.g. sugar 3 x 1 = 3(kg) or 3000(g) which ÷ 15 = 200(g) e.g. eggs 5 x 6 = 30 and 30 ÷ 15 = 2
3 (3) Calculating the number of trays needed for Jenny’s mini apple pies
7 1 mark for valid approach
e.g. attempt to use diameter of pie and length or width of tray
R1 1 mark for correct conversion
e.g. 12 x 10 = 120(mm) e.g. 500 ÷ 10 = 50(cm)
A1
1 mark for correct method to find number of pies that fit along either side
e.g. 50 ÷ 12 or 500 ÷ 120
e.g. repeat addition of 12 until total is 50 or 70
R3
1 mark for correct solution for length or width e.g. (70 ÷ 12 =) 5.833r e.g. (500 ÷ 120 =) 4.166r e.g. (12 + 12 + 12 + 12) = 48(cm) Accept rounding or truncation but not 5.833r rounded to 6 A1
1 mark for correct interpretation of the remainders, e.g. only 5 circular pies can fit across the length and only 4 circular pies can fit across the width.
Allow correct interpretation of repeated addition.
Must be rounded down
I1
1 mark for correct answer to how many pies will fit into rectangular tray
e.g. (5 x 4 =) 20
e.g. (5 + 5 + 5 + 5 =) 20 e.g. (4 + 4 + 4 + 4 + 4 =) 20
A1
1 mark for valid explanation,
e.g. ‘5 trays are not enough to hold 120 pies as 5 trays x 20 pies = 100 pies’
e.g. ‘5 trays will not be enough, she needs 6 trays for 120 pies’
Working required. Allow follow through from their working, but not area method
I2
Task 2
Question
Process Total Mark
For Evidence of Comment Criteria Ref R A I 1a (4a) Converting currency and showing a check
3 1 mark for a correct method e.g. 18.00 x 71.1745 =
e.g. 1115 ÷ 71.1745 =
R3
1 mark for correct answer
e.g. (18.00 x 71.1745 =) 1281.141 (INR), e.g. (1115 ÷ 71.1745 =) (£)15.66572298
Allow rounding or truncation
A1
1 mark for correct interpretation of answer e.g. ‘It is cheaper to buy the ticket in India.’
I1 1b
(4b)
1 1 mark for valid check using a different method e.g. by reverse calculation 1115 ÷ 71.1745 or e.g. 18.00 x 71.1745 e.g. by estimation, 20 x 70 A2 2 (5) Interpreting a table and choosing the best type of insurance cover
4 1 mark for valid choice for comparison i.e. Super and Premium
I1 1 mark for correct method to find cost of Super or Premium,
e.g. 699 + 50 – 75 e.g. 799 – 100
R2
1 mark for correct costs
i.e. Super (£)674 and Premium (£)699
A1 1 mark for valid reason for their choice
e.g. ‘Super, because it is cheaper’
e.g. ‘Premium because it is slightly more expensive but covers more’
3
(6)
Calculating flight time
3 1 mark for correct method to find time difference e.g. 23:00 – 9:45,
e.g. 23:00 – (9:45 + 4:30) or 23:00 – 14:15
R1
1 mark for correct use of local time information e.g. 13:15 - 4:30
e.g. 23:00 – 4:30 e.g. 9:45 + 4:30
R3
1 mark for correct flight time i.e. 8 hours 45 minutes
i.e. 8¾ hours A1 4 (7) Interpreting a bar chart showing the age of the population in the UK and India in 2001
4 1 mark for at least 3 correct values from graph seen e.g. UK, 19, 12, India, 35, 18
I1 1 mark for correct method to find difference,
e.g. 35 + 18 – (19 + 12) (= 22) e.g. 53 – 31 (= 22)
May be implied by 22(%) seen
R2
1 mark for correct difference
e.g. ‘The proportion of under-25s in India is 22% higher than in the UK,’
e.g. ‘The difference is 22%.’
A1
1 mark for valid comment comparing populations
e.g. ‘The percentage of older people is higher in the UK than in India’
e.g. ‘The percentage of people in the 25 to 44 years age range in the UK and in India is about the same’
e.g. ‘4% of the UK population are over 80 years old but only 1 % of the population of India is over 80years old’
I2
Task 3
Question
Process Total Mark
For Evidence of Comment Criteria Ref R A I 1a
(8a)
Working out the total area
of the hall and living room floors
3 1 mark for at least 1 correct missing dimension for the living room seen
e.g. 2.1(m) e.g. 2.2(m)
R1
1 mark for correct method to find area of living room e.g. 5 x 3 + 2.2 x 2.9 =
e.g. 5.2 x 2.9 + 3 x 2.1 = e.g. 5.0 x 5.2 – 2.2 x 2.1 =
R3
1 mark for correct area of living room
i.e. 21.38(m2) A1
1b
(8b)
Check 1 1 mark for acceptable check e.g. 21.38 – (2.2 x 2.9) = 15 e.g. 21.38 – 6.38 = 15 e.g. (21.38 – 6.380 ÷ 5 = 3 e.g. (5 x 3) + (2 x 3) = 21 e.g. (5 x 3) + (3 x 2) = 21 e.g. (5 x 5) – (2 x 2) = 21 A2
2 (9) Working out which size of cleaning solution containers to buy
5 1 mark for correct substitution e.g. 55 x (30 + 7 x 3) ÷ 3
R1 1 mark for correct order of operations
e.g. 55 x (30 + 21) e.g. ‘x 51’
R2
1 mark for correct solution, i.e. 935 (ml)
A1 1 mark for correct choice of bottle,
e.g. 250 millilitres and 750 millilitres e.g. 1.5 litre Working required. Allow follow through from their working I1
1 mark for valid explanation,
e.g. ‘He should buy the 250 millilitres and the 750 millilitres because that will be just enough’
e.g. ‘Ryan should buy the 1.5 litre because he will have some left over in case of an accident’
e.g. ‘Ryan shoud buy the 1.5 litre because it will probably be cheaper than the 250 millilitres and the 750 millilitres’
Explanation and working must correspond
3
(10)
Hiring a carpet cleaner
5 1 mark for a valid day or valid overnight or valid half days e.g. Tue or Fri and Wed or Fri (half days)
e.g. Wed (overnight) e.g. Sat (day)
R1
1 mark for valid pick-up time, e.g. Tue and Wed 13:00 - 13:30 e.g. Tue and Fri 13:00 - 13:30 e.g. Wed and Fri 13:00 - 13:30 e.g. Wed 17:30
e.g. Sat 8:30
I1
1 mark for valid return time
e.g. Tue and Wed, 4 hours after pick-up e.g. Tue and Fri, 4 hours after pick-up e.g. Wed and Fri, 4 hours after pick-up e.g. Thu 8:30
e.g. Sat 17:30
I1
1 mark for correct cost e.g. (£)18 for 2 half days,
e.g. (£)16 for overnight on Wednesday e.g. (£)25 for Saturday
Allow follow through
R2
1 mark for valid explanation
e.g. ‘Overnight on Wednesday because hiring overnight is cheaper’ e.g. ‘Half days cost only £2.00 more than overnight and do not require Ryan to work late at night’
e.g. ‘Saturday because he can finish the job in one day and the weekend is more convenient than a weekday,’
Allow follow through
I2
Task 4
Question
Process Total Mark
For Evidence of Comment Criteria Ref R A I 1
(11)
Calculating the mean and
the range of Bed & Breakfast
bookings
6 1 mark for correct method to find mean e.g. 123 ÷ 12
e.g. 136 ÷ 12
R2
1 mark for correct means i.e. 10.25 and 11.3333r
Allow rounding or truncation
A1 1 mark for correct method to find range
e.g. 22 – 0 e.g. 20 - 6
R2
1 mark for correct ranges e.g. 22
e.g. 14
A1
1 mark for valid comment on the means
e.g. ‘The mean number of bookings increased a little from 2010 to 2011’
I2
1 mark for valid comment on range,
e.g. ‘There was more consistency in the number of bookings per month in 2011,’
e.g. ‘The range of bookings was lower in 2011 than 2010.’
I2
2a
(12a)
Calculating a percentage
2 1 mark for correct substitution, e.g. 100 x 136 ÷ 363
R2 1 mark for correct answer
i.e. 37.46556474(%)
Allow rounding or truncation
2b
(12b)
Check 1 1 mark for valid check
e.g. (37.5 x 363 ÷ 136) = 100.0919118 e.g. (100 x 140 ÷ 360) = 38.88r
Allow rounding or truncation
3 (13) Interpreting a bar chart and comparison of percentages
2 1 mark for correct reading from bar chart i.e. 64(%)
I1 1 mark for valid comment
e.g. ‘Tina’s percentage is not much more than half the local average percentage’
e.g. ‘Tina’s percentage was much lower, but more than half the local average percentage’
I2 4 (14) Calculating and comparing fractions
5 1 mark for correct values selected i.e. 28 + 44 (= 72)
Accept 72 R2 1 mark for correct total
i.e. 120
A1 1 mark for correct method to find useful value,
e.g. 72 ÷ 120 e.g. 3 ÷ 4 x 120
R3
1 mark for correct solution, e.g. 3/5
e.g. 90 e.g. 60%
A1
1 mark for valid comment,
e.g. ’No, only 3/5 of her guests gave a 4-stars or 5-stars rating’ e.g. No, she needed 18 more guests to give a 4-stars or 5-stars rating to meet her target’
e.g. ‘No, only 60% of her guests gave a 4-stars or 5-stars rating and her target was 75%’
Working required.
I2