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© WJEC CBAC Ltd.
GCSE MARKING SCHEME
APPLICATIONS OF MATHEMATICS (LINKED PAIR PILOT) SUMMER 2015
EAS Practice Papers SET2 Mathematics – Numeracy Unit 1 – Foundation Tier
SET 2 – Numeracy U1 FT Mark Comments
1. Indicates the five correct dates.
8th, 14th, 15th, 24th and 25th. (April 2014)
Strategy of looking at 12 out of 20 or equivalent.
Strategy of looking at 5 out of 8 or equivalent
Statement that both are correct.
B4
S1
S1
B1
7
For all five with no extras.
B3 for four, B2 for three, B1 for two.
Penalise ‘extras’ as follows,
-1 for 1 or 2, -2 for 3 or 4, -3 for 5 or 6 and
-4 for more than 6 (only from marks gained).
Correct numbers must be compared for award of S1
marks.
S0,S0,B1 for an unsupported correct statement.
2. 1st Diagram Circle : 4
Square : 5
2nd Diagram Right Hand Circle : 7
Square : -15
Bottom Circle : -18
B1
B1
B1
B1
B1
5
FT from a negative answer in the square
All parts (a) – (b) marked at the same time
To be viewed with diagram
3.(a) Missing inside segment = 2
Perimeter = 9+9+8×3+2×2
= 46 (cm)
To be viewed with diagram (b) Area = 8×3+4×3×3OR 8×9 – 2×3×2
(= 24 + 36) (= 72 – 12)
= 60
cm2
S1
M1
A1
M1
A1
U1
6
You must also check the diagram for any working.
Must be seen in part (a). Attempt to add all sides of the shape.
Use 42+2x for M1 where x stands for ‘their 2’
S1, M1 for methods that imply the '2', e.g.
9×2+8×2+4×3 C.A.O.
Attempt to add all areas of the shape OR difference of
areas
C.A.O.
Independent of all other marks.
4. a) Multiples of 7
b) 28 and 35 placed correctly
B1
B2
3
B1 for either
5. Any correct strategy for finding the need for
paying for 9 bottles from Len’s store AND 8
bottles from Deb’s store
9 × 90(p) or 8 × (£)1.00
810(p) or (£)8.10 or (£)8
810(p) or (£)8.10 AND (£)8 AND Deb’s store
Organisation and communication Accuracy of writing
S1
M1
A1
A1
OC1
W1
6
Or equivalent
Or equivalent
Or equivalent
6. Use overlay
2 rectangles 6cm by 3cm
1 rectangle 6cm by 4cm
2 rectangles 4cm by 3cm
Makes a correct net
B1
B1
B1
B1
4
Use overlay (± 2mm)
To gain each B1, each pair of rectangles must not
be disjointed
Penalise – 1 only, if height of 1 cm used.
7. (2 x adult one-day tickets 2 x £21.50 = £) 43
AND (2 x child one-day tickets 2x £17.50 = £) 35
(2 x 6 adult individual rides 2 x 6 x £2.50 = £) 30
(2 x 8 child individual rides 2 x 8 x £2.50 = £) 40
(Tickets are )2 child one-day tickets and 12 (adult)
individual ride tickets
(Cost = £30 + 35 = £) 65
B1
B1
B1
B1
B1
5
Accept a sight of 78
Accept sight of 70 for 2nd and 3rd B1s.
May be implied by answer of 65.
FT their prices for the cheapest option.
SC1 B0 if sight of (£)78 and (£)70 AND conclusion
to buy individual ride tickets
8. (a)An attempt to find values that can be directly
compared.
Finding
(Zac) 60/100(oe) (Josh) 62/100 (oe) (Lowri) 58/100
(oe)
OR
OR
OR
Most: Josh AND least: Lowri
(b) (48 ÷ 6 =) 8
(8 + 9 =) 17
M1
A1
A1
B1
B1
5
All %, OR all fractions with common
denominator, OR all decimals, OR a valid
combination e.g. Zac 3/5 = 60% = 0.6
All fractions must have the same denominator
If only one error made, then FT.
SC1 if most: Josh, AND least: Lowri with no
supporting work.
Alternative:
FT their 8 6n – 54 = 48
6n = 102 B1
n = 17 B1 FT ‘their
102’
9. Ribbon marking for 12(a) and (b)
(a) 0.15 × (£)480 or equivalent
OR an attempt to calculate 24 × (£)22
(Total cost = ) 0.15 × (£)480 + 24 × (£)22 or
equivalent
(£72 + £528 =) (£)600
(b) (Difference in price =) (£)600 – (£)480
OR (£)120
(Percentage increase =) 120/480 × 100% or equivalent
25%
M1
M1
A1
B1
M1
A1
6
Valid method for finding either 15% of (£)480 OR
24 × (£)22 (implied by sight of (£)72 or (£) 528
respectively)
A complete correct method
CAO
Attempt to find difference in price.
FT ‘their (a)’
A complete correct method
OR 600/480 × 100(%) (= 125%) B1
600/480 × 100(%) – 100(%) M1
25(%) A1
To be viewed with diagram 10. Volume = 20 × 15 × 10 (× ½)
= 1500 (cm3)
= 1500/1000
= 1·5 litres
M1
A1
M1
A1
4
No need for the ½ for the M1.
CAO
FT 'their 1500'/1000
‘litres’ not required but A0 for incorrect units.
To be viewed with table
11. (a) (£) 8.40 and 10:35 (a.m.)
(b) Taxi fare is (£)17 - (£)27
Tube tickets cost (£)20
Compares (£)17 with (£)20
Compares (£)27 with (£)20
B2
B1
B1
B1
B1
6
F.T. their
figures
Per person solutions
Taxi fare is (£)17 - (£)27
B1
Divides any taxi fare by 5
B1
Compares (£)3.40 with (£)4
B1
Compares (£)5.40 with (£)4
B1
2 taxis (Maximum 3 marks
available)
Taxi fare is (£)34 - (£)54
B1
Tube tickets cost (£)20
B1
Taxi (always) more than tube
B1
12.(a) All points plotted correctly
(b)TRUE
FALSE
FALSE
FALSE
TRUE
B2
B2
4
Intention: closer to the correct intersection than to any
others
B1 for indication of at least 3 correct points
Penalise joining point to point -1
B1 for any 4 correct
To be viewed with diagram
13. Area trapezium = ½ × 5 × (6 + 10)
= 40 (cm2)
Triangle: ½ × 10 × x = 40
(x = ) 8 (cm)
M1
A1
M1
A1
4
For equating ‘their 40’ (any value) with ½ × 10 × x
FT correct evaluation from ‘their 40’ (their value)
SC2 for an answer 8(cm) from area of trapezium =
5 × (6 + 10) = 80 followed by area of triangle =10 ×
x = 80,
or
SC1 for a 2 stage method equating 10 × x with
5 × (6 + 10) with error in calculating x
A full one stage method 10 × x = 5 × (6 + 10) or
equivalent is correct for 3 marks.
EAS Practice Papers SET2 Mathematics – Numeracy Unit 1 – Intermediate Tier
SET 2 – Numeracy U1 IT Mark Comments
All parts (a) – (b) marked at the same time
To be viewed with diagram 1.(a) Missing inside segment = 2
Perimeter = 9+9+8×3+2×2
= 46 (cm)
To be viewed with diagram (b) Area = 8×3+4×3×3OR 8×9 – 2×3×2
(= 24 + 36) (= 72 – 12)
= 60
cm2
S1
M1
A1
M1
A1
U1
6
You must also check the diagram for any working.
Must be seen in part (a).
Attempt to add all sides of the shape.
Use 42+2x for M1 where x stands for ‘their 2’
S1, M1 for methods that imply the '2', e.g.
9×2+8×2+4×3 C.A.O.
Attempt to add all areas of the shape OR difference of
areas
C.A.O.
Independent of all other marks.
To be viewed with table
2. (a) (£) 8.40 and 10:35 (a.m.)
(b) Taxi fare is (£)17 - (£)27
Tube tickets cost (£)20
Compares (£)17 with (£)20
Compares (£)27 with (£)20
B2
B1
B1
B1
B1
6
F.T. their
figures
Per person solutions
Taxi fare is (£)17 - (£)27
B1
Divides any taxi fare by 5
B1
Compares (£)3.40 with (£)4
B1
Compares (£)5.40 with (£)4
B1
2 taxis (Maximum 3 marks
available)
Taxi fare is (£)34 - (£)54
B1
Tube tickets cost (£)20
B1
Taxi (always) more than tube
B1
3.
(a)Travel dates = 15th – 22rd (November)
(b) (month before =) Sight of 15th October
(three weeks before =) 24th September
(c) (Eastplane based in the) UK with valid reason
(d) (AF112)
= 06:25(+1) – 22:40 (= 7hrs 45 min)
(Flight time =) 7h 45m – 4h
= 3h 45m
(e) Explanation referring to the flight time being exactly 4 hours
OR need to take into account time difference of 4 hours
B1
B1
B1
E1
M1
M1
A1
E1
8
Look at calendar for indication for this part of the
question
Award B1 for any indication e.g. start holiday on 15th
November.
FT for subtracting a month from ‘their 15th Nov’
15th October could be implied
FT for subtracting 3 weeks from ‘their 15th Oct’
If no marks gained SC1 for subtracting 3 weeks then
subtracting a month (25th October; 25th September)
OR for subtracting 4 weeks rather than a calendar
month (25th October; 27th September)
Reason could include reference to: 40 minute
turnaround at Moscow; outward flight code EP401
followed with return flight code EP402; first flight of
the day, etc
Be generous with this mark.
Condone reference to ‘Outward’ and ‘Inward’ above
timetables.
‘-4hrs’ might be implied by both times given as
London or Moscow times (gains second M1).
(look for 02:25(+1), 02:40(+1) )
FT ‘their 7hrs 45 min’
Could refer to needing to add 4 hours to the difference
(0 hours). Ignore further extraneous explanation.
4.(a) All points plotted correctly
(b) Line of best fit with points above and below
(c)TRUE
FALSE
FALSE
FALSE
TRUE
B2
B1
B2
4
Intention: closer to the correct intersection than to
any others
B1 for indication of at least 3 correct points
Penalise joining point to point -1
The line must be fit for purpose, it should not pass
through the intersection of the axes
Ignore also joining point to point
B1 for any 4 correct
5.
No, Yes, No
Far Flung: No and most expensive or most often late
Statement that implies Celtic Flights is more reliable than Roly
Air
B1
E1
E1
3
Accept percentages used within comparison
Do not accept percentages quoted without
interpretation. Accept statements such as ‘only
74%’ as a comparison
No with statement of 1 of the 2 reasons
Unambiguous and not contradicted. In either
reason box for Celtic Flights or Roly Air
6. Ribbon-marking for parts (a) and (b)
(a) 0•15 × (£)480 or equivalent OR an attempt to calculate 24
× (£)22
(Total cost = ) 0•15 × (£)480 + 24 × (£)22 or equivalent
(£72 + £528 =) (£)600
Organisation and communication Accuracy of writing
(b) (Difference in price =) (£)600 – (£)480 OR (£)120
(Percentage increase =) 120/480 × 100(%) or equivalent
25(%)
M1
M1
A1
OC1
W1
B1
M1
A1
8
Valid method for finding either 15% of (£)480 OR
24 × (£)22
(implied by sight of (£)72 or (£) 528 respectively)
A complete correct method
CAO
Attempt to find difference in price. FT ‘their (a)’
A complete correct method
OR 600/480 × 100(%) (= 125%) B1
600/480 × 100(%) – 100(%) M1
25(%) A1
7. (a) Neither school can be accommodated in the Red block
(b) A correct allocation of rooms
Red block - females
Teachers
School S
Number
2
Room A
(4)
School
__ Number
4
Room B
(6)
School
__ Number
6
Teachers
School L
Number
2
Corridor
Room C
(8)
School
__ Number
8
Room D
(4)
School
__ Number
4
Room
E(6)
School
__ Number
6
Room F
(8)
School
__ Number
8
Green block - males
Teachers
School S
Number
2
Room A
(6)
School
__ Number
__
Room B
(8)
School
__ Number
__
Teachers
School L
Number
2
Corridor
Room C
(10)
School
__ Number
__
Room D
(6)
School
__ Number
__
Room
E(8)
School
__ Number
__
Room F
(10)
School
__ Number
__
E1
B3
4
OR equivalent statement
If incomplete or incorrect award
B1 for a correct allocation of rooms for girls
S = 8,8 and L = 4,4,6,6 OR S = 4,6,6 and L = 4,8,8
OR S = 4,4,8 and L = 6,6,8
(no need to fill number in room as all beds used)
B1 for correct possible allocation of rooms for boys
e.g. S= 6,6,8,8 and L = 10,10 (many combinations)
B1 for correct possible allocation of beds for boys
e.g. S = 6,6,7,7 and L = 10,8 (many combinations)
Be aware that there are multiple correct answers for
allocation of rooms.
Need to check no. of beds used for boys as not at full
capacity.
8. A comment that states that it may appear that
reported crime has decreased because the
axes are not perpendicular.
B2
2
Accept any wording that suggests this.
B1 if only refers to the misunderstanding.
B1 if only refers to the reason.
9.
Method 1 (total profit = total selling price – total cost price)
(Money taken for full-price fruit cakes =) ¾ x 20 x (£)6 (=
(£)90)
(Money taken for reduced-price fruit cakes =) 5 x 0.7 x (£)6 (=
(£)21)
(Total money taken for chocolate cakes =) 13 x (£) 2 + 2 x
(£)1 (= (£)28)
(Total cost =) 20 x (£)3 + 15 x (£)1 ( =(£)75)
(Profit =) (£) [90 + 21+ 28] - (£)75
= (£) 64
OR
Method 2 (total profit = fruit cake profit + chocolate cake profit
(Full-price fruit cake profit =) ¾ x 20 x (£)6 - ¾ x 20 x (£)3
OR ¾ x 20 x (£)(6 - 3) (= (£)45)
(Reduced-price fruit cake profit =) 5 x 0.7 x (£)6 - 5 x (£)3
OR 5 x (0.7 x (£)6 - (£)3) (=(£)6)
(Full-price chocolate cake profit =) 13 x (£)2 - 13 x (£)1
OR 13 x (£)(2 – 1) (=(£)13)
(Reduced-price chocolate cake profit = 0)
(Total profit =) (£) [45 + 6 + 13 (+0)]
= (£) 64
B1
B1
B1
B1
M1
A1
OR
B1
B2
B1
M1
A1
6
Or equivalent e.g. (£) 0.60 x 5 x 7
FT from ‘their ¾ x 20’
Consideration of ‘+ 2 x (£)1’ can be implicit
FT provided at least B2 awarded
C.A.O.
B1 for sight of 5 x 0.7 x (£)6 or (£)1.20
FT from ‘their ¾ x 20’
FT provided at least B2 awarded
C.A.O.
10. (a) All 9 numbers placed correctly
(b) Venn diagram 2 AND full reason, e.g. ‘multiples of
4 are a subset of multiples of 2 and there is a multiple
of 2 which is a multiple of 5’, or ‘set B is a subset of
set A, and set A intersects with set C’, or ‘A & B share
some of the numbers, but C only shares numbers with
A’, or ‘C & B have nothing in common, and B shares
everything with A’
B3
E2
5
B2 for any 7 or 8 numbers placed correctly, the
other numbers omitted or incorrectly placed, OR
B1 for any 5 or 6 numbers placed correctly, the
other numbers omitted or incorrectly placed.
Any ambiguous duplicates are marked as an
incorrect placement for that number
OR selects Venn diagram 2 and explains why the
other 2 Venn diagrams are not selected
E1 for choice of Venn diagram 2 AND a partial
reason, i.e. only mentions 1 aspect or attempts an
explanation e.g. ‘4 times table is within 2 times
table’, or ‘shows which of A are within 4 times
table’, or ‘22 is in A but not in C’, or ‘no multiples
of 4 in C’ OR
E1 for selection of Venn diagram 2 and explains
why 1 of the other 2 Venn diagrams are not
selected
Accept informal words such as ‘within’ for
‘subset’, ‘overlap’ for ‘intersection’
11. Straight lines parallel to all verticals and horizontals,
with lines of radius distance away from the steps
(+2mm)
All inner steps, locus turn at 90° vertex
All outer steps, arcs with wheel radius (+2mm)
B2
B1
B2
5
B1 for straight lines, or series of points (>6),
parallel to 2 verticals/horizontals, radius distance
away (+2mm), OR straight lines parallel to all 6
verticals and horizontals but not radius distance
away
Do not accept curves with free hand sketches
B1 for arcs with wheel radius (+2mm) at 2 outer
steps, OR intention of arcs at all outer steps but not
necessarily at wheel radius
If B5 penalise extra lines drawn -1
12. (a) Reason, e.g. outside the bookshop
(b) Two boxes if you are 30
(c) Suitable question with at least 3 boxes, no overlaps
or gaps and prices from a low value upwards (to maybe
£20) considered or a number of boxes given but
concentrated at lower prices
E1
E1
B2
4
Accept reference to people not buying, but
checking out ready for downloading, ‘showcasing’,
or that ‘older people are more likely these days to
buy from shops than younger people’
Do not accept reference to groups under 20 and
over 40.
Or refers to widths groups for younger or older
people, or unequal groups.
Allow ‘overlap(s)’. Ignore incorrect response if
correct response is given.
Do not accept ‘doesn’t give options for under 20s
or over 40s’, or ‘2 options for 20 year olds’
B1 Suitable question with at least 3 boxes, with
either consistent overlaps or gaps OR a suitable
range of prices is not considered,
OR
B1 for suitable choice of groups with no gaps or
overlaps but without a suitable question being
asked
Examples of consistent overlaps or gaps:
‘£0 - £5, £5 - £10, £10 - …’
‘under £5, £6 - £10, £11 - £15, £16 - …’
‘over £5, over £10, over £20’*
*however possible B2 if asked to tick only one box
13. 5 970 000
2.4 x 1010
A1
A1
14. Class A has 12 girls
Class B has 18 girls
There are twice as many girls as boys in class B,
or ⅓ of class B boys, or ⅔ of class B girls
Class B has 9 boys
B1
B1
B1
B1
4
FT 1½ × ‘their 12’ correctly evaluated (but NOT 1½ ×
4)
Sight of 18 implies first B1, B1
OR Class B: Angle girls 240°±2° and angle boys
120°±2°
This may be implied from their numbers of girls and
boys
in class B
Note: ⅓ of 18 does not imply ⅓ of class B
boys, hence B0 ‘18 is ⅔’, implies B1
CAO
15. (a) (Millet) 3 × 850/10
255(g)
(b)Attempt to find unit cost e.g. for 1kg
(For the 250g bag, 1kg costs) £1.96
(For the 300g bag, 1kg costs) £1.80
(For the 4kg bag, 1kg costs) £1.90
Considering buying 10 or more 300g bags
Working with or choice of 15 of the 300g bags, or
5000÷300 with an answer of 16(.666…), 17 or 16, or
trials including 15 or 16 or 17 of the 300g bags
(Cheapest way to buy 5kg is
15 (300g bags) at 54(p) + 2 (250g bag) at 49(p)
= (£)8(.)10 + 98(p) )
= (£)9(.)08
M1
A1
B1
S1
M1
A1
6
CAO
OR for one correct costing for 5kg
e.g. (£)7(.)60 + 4×49(p) = (£)9(.)56
OR At least 2 combinations of bags to a total of 5kg
OR any 2 correct costings for buying 5kg
OR stating any 3 possible combinations of bags to 5kg
250g 300g 4kg Cost £
4 0 1 1.96 +7.60 = 9.56
20 0 0 9.80
14 5 0 6.86 + 2.70 = 9.56
8 10 0 3.92 + 5.40 = 9.32
2 15 0 0.98 + 8.10 = 9.08
OR equivalent, e.g. repeated additions or multiples,
16(a)(i) 2950 (miles)
3050 (miles)
79.5(hours) or 79 ½ (hours) or 79 h 30 min
80.5(hours) or 80½(hours) or 80 h 30 min (b)(ii) 3050 ÷ 79.5
B2
B1
3
All 4 correct entries
B1 for any 2 correct entries
Do not accept 79.3 or 80.3 as 2 correct entries, allow
this as equivalent to counting 1 correct entry
FT their greatest distance divided by their least time,
provided distance >3000 and time < 80
Accept sight of 3050
79.5
17. Volume scale factor ×27
Length scale factor ×3
Number of larger pebbles needed (15/3 = ) 5
B1
B1
B1
3
Allow for sight of 54/2 or 27 provided not connected
to
irrelevant working
Accept 3√27. Allow for sight of 3 provided not
connected to irrelevant working
Award of the 2nd B1 implies also the 1st B1
SC2 only for an answer of 5 without relevant working
EAS Practice Papers SET2 Mathematics – Numeracy Unit 1 – Higher Tier
SET 2 – Numeracy U1 HT Mark Comments
1.
(a)Travel dates = 15th – 22rd (November)
(b) (month before =) Sight of 15th October
(three weeks before =) 24th September
(c) (Eastplane based in the) UK with valid reason
(d) (AF112)
= 06:25(+1) – 22:40 (= 7hrs 45 min)
(Flight time =) 7h 45m – 4h
= 3h 45m
(e) Explanation referring to the flight time being exactly 4 hours
OR need to take into account time difference of 4 hours
B1
B1
B1
E1
M1
M1
A1
E1
8
Look at calendar for indication for this part of the
question
Award B1 for any indication e.g. start holiday on 15th
November.
FT for subtracting a month from ‘their 15th Nov’
15th October could be implied
FT for subtracting 3 weeks from ‘their 15th Oct’
If no marks gained SC1 for subtracting 3 weeks then
subtracting a month (25th October; 25th September)
OR for subtracting 4 weeks rather than a calendar
month (25th October; 27th September)
Reason could include reference to: 40 minute
turnaround at Moscow; outward flight code EP401
followed with return flight code EP402; first flight of
the day, etc
Be generous with this mark.
Condone reference to ‘Outward’ and ‘Inward’ above
timetables.
‘-4hrs’ might be implied by both times given as
London or Moscow times (gains second M1).
(look for 02:25(+1), 02:40(+1) )
FT ‘their 7hrs 45 min’
Could refer to needing to add 4 hours to the difference
(0 hours). Ignore further extraneous explanation.
2.(a) All points plotted correctly
(b) Line of best fit with points above and below
(c)TRUE
FALSE
FALSE
FALSE
TRUE
B2
B1
B2
4
Intention: closer to the correct intersection than to any
others
B1 for indication of at least 3 correct points
Penalise joining point to point -1
The line must be fit for purpose, it should not pass
through the intersection of the axes
Ignore also joining point to point
B1 for any 4 correct
3.
No, Yes, No
Far Flung: No and most expensive or most often late
Statement that implies Celtic Flights is more reliable than Roly
Air
B1
E1
E1
3
Accept percentages used within comparison
Do not accept percentages quoted without
interpretation. Accept statements such as ‘only
74%’ as a comparison
No with statement of 1 of the 2 reasons
Unambiguous and not contradicted. In either
reason box for Celtic Flights or Roly Air
4. Ribbon-marking for parts (a) and (b)
(a) 0•15 × (£)480 or equivalent OR an attempt to calculate 24
× (£)22
(Total cost = ) 0•15 × (£)480 + 24 × (£)22 or equivalent
(£72 + £528 =) (£)600
Organisation and communication Accuracy of writing
(b) (Difference in price =) (£)600 – (£)480 OR (£)120
(Percentage increase =) 120/480 × 100(%) or equivalent
25(%)
M1
M1
A1
OC1
W1
B1
M1
A1
8
Valid method for finding either 15% of (£)480 OR
24 × (£)22
(implied by sight of (£)72 or (£) 528 respectively)
A complete correct method
CAO
Attempt to find difference in price. FT ‘their (a)’
A complete correct method
OR 600/480 × 100(%) (= 125%) B1
600/480 × 100(%) – 100(%) M1
25(%) A1
5. (a) Neither school can be accommodated in the Red block
(b) A correct allocation of rooms
Red block - females
Teachers
School S
Number
2
Room A
(4)
School
__ Number
4
Room B
(6)
School
__ Number
6
Teachers
School L
Number
2
Corridor
Room C
(8)
School
__ Number
8
Room D
(4)
School
__ Number
4
Room
E(6)
School
__ Number
6
Room F
(8)
School
__ Number
8
Green block - males
Teachers
School S
Number
2
Room A
(6)
School
__ Number
__
Room B
(8)
School
__ Number
__
Teachers
School L
Number
2
Corridor
Room C
(10)
School
__ Number
__
Room D
(6)
School
__ Number
__
Room
E(8)
School
__ Number
__
Room F
(10)
School
__ Number
__
E1
B3
4
OR equivalent statement
If incomplete or incorrect award
B1 for a correct allocation of rooms for girls
S = 8,8 and L = 4,4,6,6 OR S = 4,6,6 and L =
4,8,8 OR S = 4,4,8 and L = 6,6,8
(no need to fill number in room as all beds used)
B1 for correct possible allocation of rooms for boys
e.g. S= 6,6,8,8 and L = 10,10 (many combinations)
B1 for correct possible allocation of beds for boys
e.g. S = 6,6,7,7 and L = 10,8 (many combinations)
Be aware that there are multiple correct answers
for allocation of rooms.
Need to check no. of beds used for boys as not at
full capacity.
6. A comment that states that it may appear that
reported crime has decreased because the
axes are not perpendicular.
B2
2
Accept any wording that suggests this.
B1 if only refers to the misunderstanding.
B1 if only refers to the reason.
7.
Method 1 (total profit = total selling price – total cost price)
(Money taken for full-price fruit cakes =) ¾ x 20 x (£)6 (=
(£)90)
(Money taken for reduced-price fruit cakes =) 5 x 0.7 x (£)6 (=
(£)21)
(Total money taken for chocolate cakes =) 13 x (£) 2 + 2 x
(£)1 (= (£)28)
(Total cost =) 20 x (£)3 + 15 x (£)1 ( =(£)75)
(Profit =) (£) [90 + 21+ 28] - (£)75
= (£) 64
OR
Method 2 (total profit = fruit cake profit + chocolate cake profit
(Full-price fruit cake profit =) ¾ x 20 x (£)6 - ¾ x 20 x (£)3
OR ¾ x 20 x (£)(6 - 3) (= (£)45)
(Reduced-price fruit cake profit =) 5 x 0.7 x (£)6 - 5 x (£)3
OR 5 x (0.7 x (£)6 - (£)3) (=(£)6)
(Full-price chocolate cake profit =) 13 x (£)2 - 13 x (£)1
OR 13 x (£)(2 – 1) (=(£)13)
(Reduced-price chocolate cake profit = 0)
(Total profit =) (£) [45 + 6 + 13 (+0)]
= (£) 64
B1
B1
B1
B1
M1
A1
OR
B1
B2
B1
M1
A1
6
Or equivalent e.g. (£) 0.60 x 5 x 7
FT from ‘their ¾ x 20’
Consideration of ‘+ 2 x (£)1’ can be implicit
FT provided at least B2 awarded
C.A.O.
B1 for sight of 5 x 0.7 x (£)6 or (£)1.20
FT from ‘their ¾ x 20’
FT provided at least B2 awarded
C.A.O.
8. (a) All 9 numbers placed correctly
(b) Venn diagram 2 AND full reason, e.g. ‘multiples of
4 are a subset of multiples of 2 and there is a multiple
of 2 which is a multiple of 5’, or ‘set B is a subset of
set A, and set A intersects with set C’, or ‘A & B share
some of the numbers, but C only shares numbers with
A’, or ‘C & B have nothing in common, and B shares
everything with A’
B3
E2
5
B2 for any 7 or 8 numbers placed correctly, the
other numbers omitted or incorrectly placed, OR
B1 for any 5 or 6 numbers placed correctly, the
other numbers omitted or incorrectly placed.
Any ambiguous duplicates are marked as an
incorrect placement for that number
OR selects Venn diagram 2 and explains why the
other 2 Venn diagrams are not selected
E1 for choice of Venn diagram 2 AND a partial
reason, i.e. only mentions 1 aspect or attempts an
explanation e.g. ‘4 times table is within 2 times
table’, or ‘shows which of A are within 4 times
table’, or ‘22 is in A but not in C’, or ‘no multiples
of 4 in C’ OR
E1 for selection of Venn diagram 2 and explains
why 1 of the other 2 Venn diagrams are not
selected
Accept informal words such as ‘within’ for
‘subset’, ‘overlap’ for ‘intersection’
9. Straight lines parallel to all verticals and horizontals,
with lines of radius distance away from the steps
(+2mm)
All inner steps, locus turn at 90° vertex
All outer steps, arcs with wheel radius (+2mm)
B2
B1
B2
5
B1 for straight lines, or series of points (>6),
parallel to 2 verticals/horizontals, radius distance
away (+2mm), OR straight lines parallel to all 6
verticals and horizontals but not radius distance
away
Do not accept curves with free hand sketches
B1 for arcs with wheel radius (+2mm) at 2 outer
steps, OR intention of arcs at all outer steps but not
necessarily at wheel radius
If B5 penalise extra lines drawn -1
10. (a) Reason, e.g. outside the bookshop
(b) Two boxes if you are 30
(c) Suitable question with at least 3 boxes, no overlaps
or gaps and prices from a low value upwards (to maybe
£20) considered or a number of boxes given but
concentrated at lower prices
E1
E1
B2
4
Accept reference to people not buying, but
checking out ready for downloading, ‘showcasing’,
or that ‘older people are more likely these days to
buy from shops than younger people’
Do not accept reference to groups under 20 and
over 40.
Or refers to widths groups for younger or older
people, or unequal groups.
Allow ‘overlap(s)’. Ignore incorrect response if
correct response is given.
Do not accept ‘doesn’t give options for under 20s
or over 40s’, or ‘2 options for 20 year olds’
B1 Suitable question with at least 3 boxes, with
either consistent overlaps or gaps OR a suitable
range of prices is not considered,
OR
B1 for suitable choice of groups with no gaps or
overlaps but without a suitable question being
asked
Examples of consistent overlaps or gaps:
‘£0 - £5, £5 - £10, £10 - …’
‘under £5, £6 - £10, £11 - £15, £16 - …’
‘over £5, over £10, over £20’*
*however possible B2 if asked to tick only one box
11. 5 970 000
2.4 x 1010
A1
A1
2
12. Class A has 12 girls
Class B has 18 girls
There are twice as many girls as boys in class B,
or ⅓ of class B boys, or ⅔ of class B girls
Class B has 9 boys
B1
B1
B1
B1
4
FT 1½ × ‘their 12’ correctly evaluated (but NOT 1½
× 4)
Sight of 18 implies first B1, B1
OR Class B: Angle girls 240°±2° and angle boys
120°±2°
This may be implied from their numbers of girls and
boys
in class B
Note: ⅓ of 18 does not imply ⅓ of class B
boys, hence B0 ‘18 is ⅔’, implies B1
CAO
13. (a) (Millet) 3 × 850/10
255(g)
(b)Attempt to find unit cost e.g. for 1kg
(For the 250g bag, 1kg costs) £1.96
(For the 300g bag, 1kg costs) £1.80
(For the 4kg bag, 1kg costs) £1.90
Considering buying 10 or more 300g bags
Working with or choice of 15 of the 300g bags, or
5000÷300 with an answer of 16(.666…), 17 or 16, or
trials including 15 or 16 or 17 of the 300g bags
(Cheapest way to buy 5kg is
15 (300g bags) at 54(p) + 2 (250g bag) at 49(p)
= (£)8(.)10 + 98(p) )
= (£)9(.)08
M1
A1
B1
S1
M1
A1
6
CAO
OR for one correct costing for 5kg
e.g. (£)7(.)60 + 4×49(p) = (£)9(.)56
OR At least 2 combinations of bags to a total of 5kg
OR any 2 correct costings for buying 5kg
OR stating any 3 possible combinations of bags to
5kg
250g 300g 4kg Cost £
4 0 1 1.96 +7.60 = 9.56
20 0 0 9.80
14 5 0 6.86 + 2.70 = 9.56
8 10 0 3.92 + 5.40 = 9.32
2 15 0 0.98 + 8.10 = 9.08
OR equivalent, e.g. repeated additions or multiples,
14(a)(i) 2950 (miles)
3050 (miles)
79.5(hours) or 79 ½ (hours) or 79 h 30 min
80.5(hours) or 80½(hours) or 80 h 30 min (b)(ii) 3050 ÷ 79.5
B2
B1
3
All 4 correct entries
B1 for any 2 correct entries
Do not accept 79.3 or 80.3 as 2 correct entries,
allow this as equivalent to counting 1 correct entry
FT their greatest distance divided by their least
time,
provided distance >3000 and time < 80
Accept sight of 3050
79.5
15. Volume scale factor ×27
Length scale factor ×3
Number of larger pebbles needed (15/3 = ) 5
B1
B1
B1
3
Allow for sight of 54/2 or 27 provided not
connected to
irrelevant working
Accept 3√27. Allow for sight of 3 provided not
connected to irrelevant working
Award of the 2nd B1 implies also the 1st B1
SC2 only for an answer of 5 without relevant
working
16(a) Axis labelled frequency density with a uniform scale
from 0 to 5(minimum)
Frequency densities 1.8, 2.2, 5, 0.6, 0.2
Correct histogram
(b) Explanation:
• Median is in the group 40<t≤60
• Estimate so we don’t know, or
• (Estimate of the) median is 44, or
• It (may be) is nearer 40 than 60
B1
M2
A1
E1
E1
6
Do not accept a scale using less than half the paper or
for
scales to ≥100
FT for their uniform scale
M1 for any 3 correct frequency densities
Each E mark is independent.
Accept ‘median is in same group’
Accept ‘median could be towards the lower end of the
median group’.
17.(a) x = 0·36666.... 10x = 3·6666.... with an attempt to
subtract
33/90 (=11/30) or 363/990 or equivalent
(b) 2/3
(c) 5√3 + 3 – 5√3 + 2×3
= 9
M1
A1
B2
B1
B1
6
Or 10x and 100x, or equivalent. Or an alternative
method.
CAO (3·3/9 gets M1 A0)
B1 for (3/2)-1 or 1/(3/2) or 1/1·5 or (8/27)1/3
or (3√8 /3√27) or 3√(8 /27)
B0 for 8/271/3 or 81/3/27
FT from one incorrect term
EAS Practice Papers SET2 Mathematics-Numeracy Unit 2 – Foundation Tier
SET 2 – Numeracy U2 FT Mark Comments
To be viewed with diagram
Parts (a) & (b) marked at the same time 1 (a) Pointer showing 320g
1. (b) Reading 620 (g)
One cube weighs (620–320)/5
= 60 (g)
B2
B1
M1
A1
B1 if calculation shown and F.T. their pointer.
OR B1 for sight of 320 in the working but nothing
on their diagram OR 260 shown on their diagram.
Pointer drawn takes precedence over written value(s)
Pointer nearer correct mark than the ones each side
of it
Complete method, subtraction and division
FT 'their 620 and 320’
Allow B1, SC1 for 620/5 = 124 (g)
Unsupported 124 (g) gets M0,A0
2.
Person
Should have
flu
vaccination?
Yes or No
Reason
Denise Ye Is a diabetic
Jack Yes Is over 65 and/or has a
chest condition
David No
Does not meet any
requirements or
equivalent, OR gives at
least 2 reasons for not having the flu jab.
Alys Yes Is pregnant
B4
4
Award B1 for each correct response and valid
reason.
Award SC2 for ALL CORRECT reasons with
ALL INCORRECT Yes/No.
If no marks awarded, award SC1 for Yes, Yes, No,
Yes
3. (a)(i) Church (2, 5)
Castle (-4, -3)
(ii) Skating park (S) plotted at (3, 0)
(b) (i) 45 (minutes)
(ii) ¾ (hours) + 20 (mins) + 1.5 (hours)
Changing all to hours OR all to mins correctly
155 mins or 2 hrs 35 mins or 2.58(3....)hours ISW
B1
B1
B1
B1
M1
B1
A1
7
Reverse coordinates B0 throughout (c)
Accept any indication of (3, 0)
For adding the 3 times given. FT ‘their 45 minutes’
Either 45 + 20 + 90 OR ¾ + 1/3 + 1.5 or equivalent
Do not accept 0.3 for 1/3 for A1 but allow for B1
If units used they must be correct. Do not accept
2.35 but allow 2:35
4. (a) Working towards 13 & 12 boxes or Engaging
with buy 1 get 1 half price
13 x (£)27.6(0) or 12 x (£)13.8(0)
(£)358.8(0)
(£)165.6(0)
(£)524.4(0)
(b) A, B & D circled
S1
M1
A1
A1
A1
B2
7
FT ‘their (£)358.8(0)’ + ‘their (£)165.6(0)’
If M0 awarded allow SC1 for sight of (£)13.8(0).
Possible S1 can still be awarded.
Alternative method:
Cost of 2 boxes = 1.5 x £27.60 B1
.: cost of 24 boxes
= 12 x 1.5 x £27.60 = 496.80 M1A1
Total cost including 25th Box
= 27.60 + 524.40 M1 A1
Award B1 for any 2 correct nets circled and C not
circled
5.
(Annual cost of units) 15000×4.028(p)
60420(p) or (£)604.2(0)
(Fixed charge per year £6.98 × 12 =) (£)83.76
(cost of units + fixed charge per year – 48) ÷12
(£639.96÷12 or 63996÷12)
(Monthly payment=) (£)53.33 or 5333(p)
M1
A1
B1
M1
A1
5
Alternative mark scheme- Monthly cost
(Monthly cost of units=)15000÷12×4.028(p)
(£)50.35 or 5035(p)
(Monthly discount=)(48÷12=)(£)4
(£)604.2(0) ÷12 + 6·98 – 4 .
(=£50·35+6·98 – 4)
(Monthly payment=)(£)53.33 or 5333(p)
To be viewed with diagram
Parts (a) to (e) marked at the same time 6. (a) (Day) 2
(b) 3 (days)
(c) 2 (days)
(d) 17.5 (mm) OR 17½ (mm)
(e)(i) 50 × 1.40 (=70) or 2.5 × 1.40 (=3.5) or
90÷1.40 (=64.2857…) or 4.5÷1.40 (=3.2142…) or
equivalent
‘Not correct’ stated or implied with correct
interpretation of their appropriate calculation
(ii) Notices that the pictogram is number of cases not
prices/costs
B1
B1
B1
B1
B1
E1
E1
7
Allow 'on day 1, day 2 and day 4'
Allow 'on day 1 and day’ 4
Depends on B1
Alternative:
Sunday = 90 and Wednesday = 50 leading to
either 90/50 or 40/50 B1
which indicates 80% more sold on Sunday rather
than 40% E1
Do not accept
100 × 50/90 = 55.55..% is incorrect, hence B0
‘Wednesday sales 55.5…% of Friday sales’, is
incorrect, hence E0
Accept ‘no’ as implied within a suitable
explanation
7. (a) (Number of necklaces is) 918 ÷ 34
= 27 (necklaces)
(Number of yellow beads is 27×10 =) 270
(Number of black beads is 27×6 =) 162
(b) Deciding to make two bracelets
8 bags of purple beads
3 bags of green beads
B1
M1
A1
M1
M1
A1
Note: Sight of 270 (yellow) or 162 (black) implies
M1, A1
FT their consistent ‘derived 27’ × 10 correctly
evaluated
FT their consistent ‘derived 27’ × 6 correctly
evaluated
OR sight of needing 48 purple or 18 green
Reversed answer: ‘3 purple bags and 8 green bags’
following correct working award B1, SC1. Note
intention to match 72s is incorrect working.
If no marks, allow SC2 for 4 bracelets with 16
bags of purple beads and 6 bags of green beads,
OR
SC1 for other possible number of bracelets with
the number of whole bags of purple and green
correctly evaluated in the correct ratio
8. Parts (a) & (b) marked at the same time
(a) 11·8 (cm)
11·8 × 10
= 118 (km)
To be viewed with diagram
(b) Use Overlay
Bearing 097º from A
Bearing 342º from B
Point (X)
B2
M1
A1
U1
Allow 11·6 – 12·0 inclusive (Ignore km here)
FT ‘their 11·8’×10
km not required but A0 for incorrect units
Unsupported answers within 116120 inc get
B1,M1,A1.
Unsupported answers outside 116120 inclusive get
0.
Allow ±2°
Allow ±2°
F.T. if at least M1 awarded.
Unambiguous dots within the boundaries of the
overlay can get the M1s. One unambiguous dot
within the ‘box’ gets all 3 marks. Watch out for line
segments.
An unambiguous point of intersection does not
require X.
9. (Time driving = 2hrs 15min + 1hr 45min)
= 4 (hours) or 240(min)
(Av. Speed =) 200
4
= 50
m.p.h.
B2
M1
A1
U1
B1 for sight of either 2(hrs) 15(min) or 135(min)
OR 1(hr) 45(min) or 105(min)
Alternative method
4hours 25min - 25min
= 4(hours) B2
B1 for sight of 4(hrs) 25(min) or 265(min).
F.T. their time. Do not penalise if they incorrectly
note
‘their F.T. time’ (e.g. use 3·3 for 3hrs 30 min).
A0 if they have incorrectly used ‘their F.T. time’.
Independent of other marks. Allow any unambiguous
correct notation.
200 / 240 = 0·83(33..). m.p.min gains M1,A1,U1.
200 / 240 = 0·83(33..). m.p.h gains M1,A1,U0.
200 / 240 = 0·83(33...) gains M1,A1,U0.
10. (a) A correct combination with cost.
A different combination with cost.
Organisation and communication Accuracy of writing
B2
B2
OC1 W1 6
B1 for a correct possible choice with no cost or an
incorrect cost.
B1 for an incorrect combination of at least four
containers with a correct cost.
B1 for a different correct possible choice with no
cost or
an incorrect cost.
B1 for a different incorrect combination of at least
four
containers with a correct cost.
Small Medium Large Cost
0 4 1 (£)44
1 5 0 (£)46
4 0 2 (£)48
5 1 1 (£)50
6 2 0 (£)52
11. 24 (seconds)
M1
A1
B1
M1
A1
5
Award B1 for other multiples of 24 eg 48
(seconds) OR for listing multiples of 8 AND
multiples of 6.
Parts (a) & (b) marked at the same time
12. (a) 23 (years)
(b) FALSE
TRUE
FALES
TRUE
FALSE
B1
B2
3
Comes from 47 - 24
B1 for any 4 correct
13. (cost of room) (5 x 24 = ) (£)120
(total cost of meals) 27 x 154
(£)4158
(total money spent) 120 + 4158 + 356 + 165
(£)4799
(total money collected from tickets) 154 x 35
(£)5390
(Money given to charity) (£)591
B1
M1
A1
M1
A1
M1
A1
B1
8
FT ‘their 120’ and ‘their 4158’ but not 24 and 27.
FT ‘their correct total collected’ – ‘their total
money spent’
Unsupported correct answer implies all previous
marks.
Alternative method
(cost of room) (5 x 24 = ) (£)120 B1
(Difference in meal and ticket price) 35 – 27 M1
= (£)8 A1
(Total money from this difference) 8 x 154 M1
= (£)1232 A1
(total money spent) 120 + 356 + 165 M1
(£)641 A1
(Money given to charity) (£)591 B1
EAS Practice Papers SET2 Mathematics – Numeracy Unit 2 – Intermediate Tier
SET 2 – Numeracy U2 IT Mark Comments
Parts (a) & (b) marked at the same time 1. (a) (i) 23 (years)
(b) FALSE
TRUE
FALES
TRUE
FALSE
B1
B2
Comes from 47 - 24
B1 for any 4 correct
2. 24 (seconds)
M1
A1
B1
M1
A1
5
Award B1 for other multiples of 24 eg 48
(seconds) OR for listing multiples of 8 AND
multiples of 6.
3. (Time driving = 2hrs 15min + 1hr 45min)
= 4 (hours) or 240(min)
(Av. Speed =) 200
4
= 50
m.p.h.
B2
M1
A1
U1
B1 for sight of either 2(hrs) 15(min) or 135(min)
OR 1(hr) 45(min) or 105(min)
Alternative method
4hours 25min - 25min
= 4(hours) B2
B1 for sight of 4(hrs) 25(min) or 265(min).
F.T. their time. Do not penalise if they incorrectly
note
‘their F.T. time’ (e.g. use 3·3 for 3hrs 30 min).
A0 if they have incorrectly used ‘their F.T. time’.
Independent of other marks. Allow any unambiguous
correct notation.
200 / 240 = 0·83(33..). m.p.min gains M1,A1,U1.
200 / 240 = 0·83(33..). m.p.h gains M1,A1,U0.
200 / 240 = 0·83(33...) gains M1,A1,U0.
4.Use overlay
Position at 135° from ship A.
Position at 215° from ship B.
Position marked OR two intersecting lines.
M1
M1
A1
± 2° (use overlay). Allow the M marks for dots,
crosses
or any unambiguous indication that the correct
bearings
have been offered.
F.T. if at least M1 and two intersecting lines. (Lines
must originate from ship A and ship B respectively)
5.
(Annual cost of units) 15000×4.028(p)
60420(p) or (£)604.2(0)
(Fixed charge per year £6.98 × 12 =) (£)83.76
(cost of units + fixed charge per year – 48) ÷12
(£639.96÷12 or 63996÷12)
(Monthly payment=) (£)53.33 or 5333(p)
B1
M1
A1
M1
A1
M1
A1
B1
8
Alternative mark scheme- Monthly cost
(Monthly cost of units=)15000÷12×4.028(p)
(£)50.35 or 5035(p)
(Monthly discount=)(48÷12=)(£)4
(£)604.2(0) ÷12 + 6·98 – 4 .
(=£50·35+6·98 – 4)
(Monthly payment=)(£)53.33 or 5333(p)
6. (cost of room) (5 x 24 = ) (£)120
(total cost of meals) 27 x 154
(£)4158
(total money spent) 120 + 4158 + 356 + 165
(£)4799
(total money collected from tickets) 154 x 35
(£)5390
(Money given to charity) (£)591
B1
M1
A1
M1
A1
M1
A1
B1
FT ‘their 120’ and ‘their 4158’ but not 24 and 27.
FT ‘their correct total collected’ – ‘their total
money spent’
Unsupported correct answer implies all previous
marks.
Alternative method
(cost of room) (5 x 24 = ) (£)120 B1
(Difference in meal and ticket price) 35 – 27 M1
= (£)8 A1
(Total money from this difference) 8 x 154 M1
= (£)1232 A1
(total money spent) 120 + 356 + 165 M1
(£)641 A1
(Money given to charity) (£)591 B1
7(a) 44, 76, 80
(b) Correct cumulative frequency diagram, points
plotted at upper bounds and joined by a curve or
straight line
(c)
Median ≈ 58 reading from graph
Low quartile ≈ 55.5 reading from graph
Upper quartile ≈ 61 reading from graph
Interquartile range ≈ 5.5
(d) Range ends correctly indicated
(50(cm) and 68(cm))
Median line correctly indicated (approx. 58 )
UQ and LQ correctly indicated (approx. 61 & 55.5)
B1
B2
B1
B1
B1
B1
B1
B1
B1
10
Accuracy: nearer the intersection of correct lines
than any others
FT only if cumulative in (a)
B1 for points correct but not joined, OR
B1 correct apart from 0.5 translation, OR
B1 if one error in plotting but joined correctly
FT from their cumulative entries. Not cumulative
means no FT. Accuracy of readings ±0.5
FT their UQ – their LQ correctly evaluated.
Independent FT
In (d) FT consistent previous misread of scale
Whiskers should be shown
If incorrect then FT their median
If incorrect then FT their UQ and LQ reading
8. (Salary received) (£)30000 × 0·7
= (£)21000
(Cost of petrol) 8000 × (£)6·25
40
= (£)1250
(New salary received) = (£)14000
(Loss) (£)21000 - (£)1250 - (£)14000
= (£)5750
Organisation and communication Accuracy of writing
M1
A1
M1
A1
B1
M1
A1
OC1 W1 9
Or F.T. 2/3 × ‘their 21000’.
F.T. their three stated values.
(Look for ‘19750 - 14000’ or ‘21000 - 15250’)
9. Taxable income (52250 – 9205=)(£)43045
40% tax to be paid on (£)10790
0.2 x 32255 (=6451)
0.4 x 10790 (=4316)
(£) 6451AND (£)4316
Claudia’s tax should be (£)10767
B1
B1
M1
M1
A1
A1
FT ‘taxable income’ – 32255, i.e.
‘their 52250 -9205’ – 32255 correctly evaluated
FT 0.4 × (‘their 43045’ – 32255) provided
‘their 43045’ > 32255, also
FT (52250 – 32255 =) giving 0.4 × 19995 (=7998)
FT sum of ‘their 6451’ + ‘their 4316’ provided at
least 1 of these values is correct and M2 awarded
(Note: 6451 + 7998 = 14449)
10. (a) Suitable uniform scales starting at zero, with axes
labelled.
Correct grouped frequency diagram. [Heights of
80,60,52,32,16]
(b) Sight of the mid-points 0.5, 1.5, 2.5, 3.5 & 4.5
Sum of mid-points × freq = 444
÷ 240
= 1.8(5) (hours) or equivalent.
1 < t ≤ 2 (hours)
B1
B2
B1
M1
m1
A1
B1
B1 for 1 error in heights of bars.
If no marks awarded, SC1 for a frequency polygon
with
all correct heights.
FT their mid-points provided they are within the
limits
of each group, including the limits themselves.
ISW. Accept 1.9. Allow 2 if 1.85 has been seen.
Allow 1 to 2 hours.
11.TRUE
FALSE
TRUE
FALSE
TRUE
B2 B1 for any 4 correct
12. (Volume of block =) 10 × 8 × 5 (=400) (cm3)
(Density of metal =) 1100 ÷ 400 OR 1.1 ÷ 400 OR 1.1 ÷
0.0004
= 2.75 OR 0.00275 OR 2750
Appropriate unit g/cm3 kg/cm3 kg/m3
B1
M1
A1
U1
FT 1100 or 1.1 ÷ ‘their volume’ provided it is a
product. Volume may be given in another metric
unit.
13. (a) (Vol. cuboid =) 182 × 10 OR (Vol. cylinder =) π × 122
× 7
(Vol. cuboid) = 3240
(Vol. cylinder) = 3166(·7..)
(Larger volume in the cuboid by) 73(.3…)
cm3
(b) (S. Area cuboid =) 4×18x10+2x182
OR (S. Area cylinder =) 2×π×12×7+2×π×122
= 1368 (cm2)
= 1432(·5... cm2)
.:Square based tin uses less metal
M1
A1
A1
B1
U1
M1
A1
A1
A1
Accept 3165 to 3168 inclusive OR 1008 π for vol. of
cylinder
FT their values, if M1 gained.
For sight of cm3 anywhere within the answer.
Accept 1431 to 1433.2 inclusive OR 456 π for ‘S.
Area cylinder’
FT if at least M1A1 gained
14. 26.7 = π x d or 26.7 = 2 x π x r or r = 26.7/π Diagonal = 8.495… to 8.5(0…) (cm)
diagonal2 = side2 + side2
side2 = diagonal2/2
side length = 6(.0096…cm)
Perimeter = 24.(….cm)
M1
A1
M1
A1
A1
B1
6
Accept rounded or truncated
FT their diagonal
Do not FT from inappropriate truncation or
incorrect rounding (e.g. from d = 8.4)
Answer here for A1 should round to 6.01
FT provided both M marks awarded for 4 x ‘their
side length’
EAS Practice Papers SET2 Mathematics – Numeracy Unit 2 –Higher Tier
SET 2 – Numeracy U2 HT Mark Comments
1.Use overlay
Position at 135° from ship A.
Position at 215° from ship B.
Position marked OR two intersecting lines.
M1
M1
A1
± 2° (use overlay). Allow the M marks for dots,
crosses
or any unambiguous indication that the correct
bearings
have been offered.
F.T. if at least M1 and two intersecting lines. (Lines
must originate from ship A and ship B respectively)
2(a) 44, 76, 80
(b) Correct cumulative frequency diagram, points
plotted at upper bounds and joined by a curve or
straight line
(c)
Median ≈ 58 reading from graph
Low quartile ≈ 55.5 reading from graph
Upper quartile ≈ 61 reading from graph
Interquartile range ≈ 5.5
(d) Range ends correctly indicated
(50(cm) and 68(cm))
Median line correctly indicated (approx. 58 )
UQ and LQ correctly indicated (approx. 61 & 55.5)
B1
B2
B1
B1
B1
B1
B1
B1
B1
10
Accuracy: nearer the intersection of correct lines
than any others
FT only if cumulative in (a)
B1 for points correct but not joined, OR
B1 correct apart from 0.5 translation, OR
B1 if one error in plotting but joined correctly
FT from their cumulative entries. Not cumulative
means no FT. Accuracy of readings ±0.5
FT their UQ – their LQ correctly evaluated.
Independent FT
In (d) FT consistent previous misread of scale
Whiskers should be shown
If incorrect then FT their median
If incorrect then FT their UQ and LQ readings
3. (Salary received) (£)30000 × 0·7
= (£)21000
(Cost of petrol) 8000 × (£)6·25
40
= (£)1250
(New salary received) = (£)14000
(Loss) (£)21000 - (£)1250 - (£)14000
= (£)5750
Organisation and communication Accuracy of writing
M1
A1
M1
A1
B1
M1
A1
OC1 W1 9
Or F.T. 2/3 × ‘their 21000’.
F.T. their three stated values.
(Look for ‘19750 - 14000’ or ‘21000 - 15250’)
4. Taxable income (52250 – 9205=)(£)43045
40% tax to be paid on (£)10790
0.2 x 32255 (=6451)
0.4 x 10790 (=4316)
(£) 6451AND (£)4316
Claudia’s tax should be (£)10767
B1
B1
M1
M1
A1
A1
FT ‘taxable income’ – 32255, i.e.
‘their 52250 -9205’ – 32255 correctly evaluated
FT 0.4 × (‘their 43045’ – 32255) provided
‘their 43045’ > 32255, also
FT (52250 – 32255 =) giving 0.4 × 19995 (=7998)
FT sum of ‘their 6451’ + ‘their 4316’ provided at
least 1 of these values is correct and M2 awarded
(Note: 6451 + 7998 = 14449)
5. (a) Suitable uniform scales starting at zero, with axes
labelled.
Correct grouped frequency diagram. [Heights of
80,60,52,32,16]
(b) Sight of the mid-points 0.5, 1.5, 2.5, 3.5 & 4.5
Sum of mid-points × freq = 444
÷ 240
= 1.8(5) (hours) or equivalent.
1 < t ≤ 2 (hours)
B1
B2
B1
M1
m1
A1
B1
B1 for 1 error in heights of bars.
If no marks awarded, SC1 for a frequency polygon
with
all correct heights.
FT their mid-points provided they are within the
limits
of each group, including the limits themselves.
ISW. Accept 1.9. Allow 2 if 1.85 has been seen.
Allow 1 to 2 hours.
6.TRUE
FALSE
TRUE
FALSE
TRUE
B2 B1 for any 4 correct
7. (Volume of block =) 10 × 8 × 5 (=400) (cm3)
(Density of metal =) 1100 ÷ 400 OR 1.1 ÷ 400 OR 1.1 ÷
0.0004
= 2.75 OR 0.00275 OR 2750
Appropriate unit g/cm3 kg/cm3 kg/m3
B1
M1
A1
U1
FT 1100 or 1.1 ÷ ‘their volume’ provided it is a
product. Volume may be given in another metric
unit.
8. (a) (Vol. cuboid =) 182 × 10 OR (Vol. cylinder =) π × 122 ×
7
(Vol. cuboid) = 3240
(Vol. cylinder) = 3166(·7..)
(Larger volume in the cuboid by) 73(.3…)
cm3
(b) (S. Area cuboid =) 4×18x10+2x182
OR (S. Area cylinder =) 2×π×12×7+2×π×122
= 1368 (cm2)
= 1432(·5... cm2)
.:Square based tin uses less metal
M1
A1
A1
B1
U1
M1
A1
A1
A1
Accept 3165 to 3168 inclusive OR 1008 π for vol. of
cylinder
FT their values, if M1 gained.
For sight of cm3 anywhere within the answer.
Accept 1431 to 1433.2 inclusive OR 456 π for ‘S.
Area cylinder’
FT if at least M1A1 gained
9. 26.7 = π x d or 26.7 = 2 x π x r or r = 26.7/π Diagonal = 8.495… to 8.5(0…) (cm)
diagonal2 = side2 + side2
side2 = diagonal2/2
side length = 6(.0096…cm)
Perimeter = 24.(….cm)
M1
A1
M1
A1
A1
B1
6
Accept rounded or truncated
FT their diagonal
Do not FT from inappropriate truncation or
incorrect rounding (e.g. from d = 8.4)
Answer here for A1 should round to 6.01
FT provided both M marks awarded for 4 x ‘their
side length’
10(a) 5.2/100 x 450 or 0.05 x 450 or 23.4(0)
(1 + 0.052)4 x 450
(£) 551.16
Conclusion, e.g. ‘Yes as more than £550’
(b)(i) 0.068
(ii) Greater AND a reason, e.g. ‘interest is accumulated
through the year (each three months)’
(iii) Use of n = 4
(1 + 0.068/4)4 -1
AER 6.98(%)
(iv) Explanation, based on need for fair comparison of
interest rates
B1
M1
A1
E1
B1
E1
B1
M1
A2
E1
11
May be embedded in further calculation
Method of adding on different amounts , 4 year
period, following attempts to calculate 5.2%
Example of working without truncation or
rounding:
(450+23.4(0) =473.4(0)
473.4(0) + 24.6168 = 498.0168, 498.01 or 498.02
498.0168 + 25.8968736 = 523.9136736
523.9136736 + 27.24351.. = 551.15718…)
Accept 551.15(7….)
B1 and SC1 for depreciation 363.45(099..), but no
FT for a conclusion
Simple interest answer of 543.6(0) is awarded only
the B1
FT from their compounded amount provided M1,
and FT from simple interest from an answer of
543.6(0) being < 550
CAO
Correct substitution in the formula given
A1 for 0.06975373… rounded or truncated, or
incorrect rounding or truncation of the AER
percentage. Mark final answer (box takes priority)
Allow ‘percentage of interest paid annually’, must
mention ‘year’ or ‘annual’
11. Π × 1.82 × 142/360 OR Π × 3.62 × 142/360
Π × 3.62 × 142/360 - Π × 1.82 × 142/360
Answer 12(cm2) or answers in the range
12.03 to 12.05 (cm2)
B1
M1
A1
3
Seen in working
Or equivalent
12(a) 0
(b) Tangent drawn at t = 3.5
Method, difference y / difference x
Evaluated estimated answer from their reasonable tangent
(c)(i) Finding v values: (0,) 14, 29, 26, 30
Split into 4 areas and attempt to sum
Correct substitution into trapezium rule
168 (metres)
(c)(ii) 0.168(km)
B1
B1
M1
A1
B1
M1
M1
A1
B1
The values used must be correct, do not allow 27/3.5
May not be from a tangent, but must be from use of
differences, e.g. curve used to form a ‘right-angled
triangle’
(Approximately 3.3 (m/min2)
Sight of (0,) 14, 29, 26, 30
Sight of the sum of 4 products or an attempt
substitution of their 5 values in the trapezium rule
Or equivalent. (14 + 43 + 55 + 56) or (0+28+
58+52+30)
FT their values for v provided at least 3 values are
correct, OR 2 areas correct in sum of 4 possible
FT their (i)/1000 evaluated correctly