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GCSE MARKING SCHEME

APPLICATIONS OF MATHEMATICS (LINKED PAIR PILOT) SUMMER 2015

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EAS Practice Paper Marking Scheme SET 2 Mathematics - Numeracy

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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)’


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


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


B1

2 taxis (Maximum 3 marks

available)

Taxi fare is (£)34 - (£)54

B1


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


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




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


B1


B1

2 taxis (Maximum 3 marks

available)

Taxi fare is (£)34 - (£)54

B1


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.


(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



The line must be fit for purpose, it should not pass

through the intersection of the axes

Ignore also joining point to point


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


(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


24 × (£)22

(implied by sight of (£)72 or (£) 528 respectively)


CAO

Attempt to find difference in price. FT ‘their (a)’


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



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


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 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.


(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



The line must be fit for purpose, it should not pass

through the intersection of the axes

Ignore also joining point to point


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


(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


24 × (£)22

(implied by sight of (£)72 or (£) 528 respectively)


CAO

Attempt to find difference in price. FT ‘their (a)’


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


Consideration of ‘+ 2 x (£)1’ can be implicit


C.A.O.

B1 for sight of 5 x 0.7 x (£)6 or (£)1.20



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


other numbers omitted or incorrectly placed, OR


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 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


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)


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)


(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.


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


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


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


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


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

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