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© Cambridge International Examinations 2013

CAMBRIDGE INTERNATIONAL EXAMINATIONS

International General Certificate of Secondary Education

MARK SCHEME for the October/November 2013 series

0580 MATHEMATICS

0580/11 Paper 1 (Core), maximum raw mark 56

This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for Teachers. Cambridge will not enter into discussions about these mark schemes. Cambridge is publishing the mark schemes for the October/November 2013 series for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level components and some Ordinary Level components.

Mark Scheme Syllabus Paper

IGCSE – October/November 2013 0580 11


Abbreviations

cao correct answer only

cso correct solution only

dep dependent

ft follow through after error

isw ignore subsequent working

oe or equivalent

SC Special Case

www without wrong working

Qu. Part Answers Mark Part Marks

1 121 042

1

2 250

1

3

86.7 or 86.74 to 86.75 1

4 (a)

(b)

42 000

10 381 cao

1

1

5 (a)

(b)

2

Both lines drawn

1

1

6 (a)

(b)

(4, 1)

Point plotted at (–1, 3)

1

1

7 3a – 4b

Final Answer

2 B1 for answer 3a ± jb or ka – 4b

or SC1 for answer reached in working then spoilt

8

5.293 cao 2 B1 for 5.29 or 5.292 to 5.2927

9

125 2 B1 for 55 or 125 in any other correct position on

diagram

or M1 for 180 – 55




10

7.7

2 M1 for 44 × 100

17.5 oe

11 (a)

(b)

6561 cao

1

1

1

12

4.8 oe 2 M1 for 5 + 19 = 3x + 2x oe or better

or B1 24 – 2x = 3x oe

or 5 = 5x – 19 oe

13 [Other angle could be] 84 2 M1 for 180 – (48 + 48)

or SC1 shows that two angles of 66 are needed to make

an isosceles triangle

14

(a)

(b)

6

2 oe

200 Final answer

1

1FT

FT 600 × their (a) providing their (a) is a probability

15

435, 445 cao 2 B1 for one value in correct place

or SC1 for both values correct but reversed

16 (a)

(b)

4

7 nfww

1

2

M1 for a correctly ordered list of at least 8 numbers

17

944 cao

3 M1 for 800 × 6 ×100

3 oe

A1 for 144

A1 FT Dependent on M1 scored

for their 144 + 800 evaluated

18

(a)

(b)

Ruled perpendicular line

through P

Correct ruled line drawn

with 2 correct sets of arcs

1

2

± 2°

B1 for correct line without correct arcs

or for 2 sets of correct arcs with no line

19

6.6 cao

3 M1 for sin 56 = 8

hoe or better

A1 for 6.63......

A1 FT Dependent on M1 scored

for their answer correctly rounded to 2sf




20

(a)

(b)

12

16

−

5

3

2

2

B1 for each correct component

B1 for each correct component

21

(a)

12

9 –

12

1 oe

[=] 12

8 oe [=]

3

2

M1

M1

Must be shown.

Both fractions must be shown

(b) 2

5 ×

25

4 oe

Cancelling shown

or 50

20oe [=]

5

2

M1

M1

Must be shown

Dependent and cancelling shown

or a fraction and then 5

2 must be shown

22 (a)

(b)

6b( a – 4c)

Final answer

n (j + k) or nj + nk oe

Final answer

2

2

B1 for answer 6( ab – 4bc ) or 3b( 2a – 8c )

or 2b( 3a – 12c ) or b( 6a – 24c )

M1 for one correct step of a two-step method

or SC1 for [m] = k + jn or [m] = j+ kn

23 (a)

(b)

(c)

(i) 11

(ii) subtract 4 oe

2, 6, 10 cao

3n – 4 oe

1

1

1

2

B1 for answer 3n ± k, where k is an integer




0580 MATHEMATICS






Abbreviations

cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working

Qu. Answer Mark Part Marks

1 3 + 5 × (4 – 2) 1

2

2

2

1

3 12 final answer 1

4 (a) 3.5 symbols in hot chocolate row 1

(b) 7 1

5 19% 0.7195 √0.038 sin 11.4 1/5 2 B1 for decimals [0.19], [0.2], 0.194…, 0.197…, 0.192… seen Or for four in correct order

6 (a) −447 1

(b) 2 1

7 15.7 or 15.70 to 15.71 2 M1 for 2 × π × 2.5

8

160

2 M1 for 18

8 × 360

9 (a) 1

(b) or or

1

Many other answers

10 8.54[4....] 2 M1 for 7.22 + 4.62 or better

11 10.1[0] Final answer 3 M1 for 1.3199 and 1.3401 seen

and M1 for 500 × 1.3199 or 500 × 1.3401 or for 500 × (their highest – their lowest) oe

12 10[.00] 3 M2 for 1.90 and 2.90 and 5.20 only or M1 for two of 1.90, 2.90, 5.20 in a list of three or two values from the table

or SC1 for 1.90, 2.90, 4.30 [from 2

20.540.3 +

]




13 (a) 5 cao 1

(b) 196 cao 1

(c) 97 cao 1

14 (a) (0, 5) 1

(b) –2 1

(c) y = –2x + k 1 k ≠ 5

15 (a) 26 1

(b)

10

3−c or

10

3

−

− c

oe final answer

2

M1 for one correct step of a two step method.

16 74.1 or 74.137 to 74.140 3 M1 for 10 × 6 and M1 for 0.5 × π × 32

17 [x =] 3, [y =] 4 3 M1 for correctly eliminating one variable A1 for [x =] 3 A1 for [y =] 4 If zero scored, SC1 for correct substitution and evaluation to find the other variable.

18 (a) x7 1

(b) 5y6 2 B1 for 5ym or ky6 in answer m ≠ 0, k ≠ 0

19 (a) Ruled line from (0, 0) to (5, 22.5) 2 B1 for (5, 22.5) or (0, 0) at the ends of the ruled line.

(b) (i) 17.5 to 18.5 1FT FT their straight line

(ii) 3.3 to 3.4 1FT FT their straight line

20 (a) Net completed 2 With one 2 by 5, one 3 by 5 and two 2 by 3 rectangles correctly positioned B1 for 2 correct rectangles correctly positioned

(b) 30 cm3

2

1

M1 for 3 × 2 × 5 Independent mark

21 (a) Angle bisector with correct arcs 2 B1 for correct line, with incorrect or no arcs or

correct arcs with incorrect or no line

(b) Perpendicular bisector with two correct pairs of arcs

2 B1 for correct line, with incorrect or no arcs or

correct arcs with incorrect or no line

(c) Arc centre C, radius 7cm Correct region shaded

1

1FT

FT their arc centre C




0580 MATHEMATICS






Qu. Answers Mark Part Marks

1 84 1

2 a(2a − 5) final answer 1

3 29 1

4 39 2 M1 for 52 × 45 ÷ 60 oe

5 (a) 2600 1

(b) [0].058 1

6 (a) 11

6

1

(b) Arrow to right of 0.5 1 Reasonable accuracy

7 Any two of (20, 8) (–4, 0) (12, 24) 2 B1 for one correct

8 (a) 9[h] 35[min] 1

(b) 19 25 1

9 (a) 3 1

(b) 3 1

10 22

9 , 0.41, 7

3 , 43%, 7

π

2

B1 for decimals [0.41] 0.429,

0.409. 0.449 [0.43], or for 4

in correct order

11 (a)

− 7

6

1

(b)

−

21

18

1FT

‘Their (a)’ × −3

12 (a) Negative 1

(b) Positive 1

13 [AB =] 5.3 to 5.7 cm

[Bearing] 130° to 134°

1

1

SC1 for correct length line and

bearing but starting at base of

North line

14 [x =] 1.75 or 14

3 or 4

7

2

M1 for first correct step 4x = 7,

x + 4

3 = 4

10 ,




15 7

22 − 5

7

35

225 their× oe − 35

77 their× oe or

35

77225 theirtheir ×−× oe

35

61 or 135

26 cao

B1

M1

A1

16

160

3 M1 for sin 15 = 628

][oe or better

A1 for 162.5[3…] or 163

or 162.54

B1 FT correct rounding

17 30.9 or 30.88 to 30.91 3 M2 for 12 × 12 − π × 6 × 6 or

4( 6 × 6 − 4

1π × 6 × 6)

M1 for 12 × 12 or π × 6 × 6 or

( 6 × 6 − 4

1π × 6 × 6)

18 (x =) 3, (y =) −2 3 M1 for correctly eliminating

one variable

A1 for [x = ]3

A1 for [y =] −2

If zero scored, SC1 for correct

substitution and evaluation to

find the other variable

19 (a)

7.5 × 10–2

2 M1 for 0.075 or 3/40 80

6

0.75 × 10–1 or 75 × 10–3 oe

(b) 9.3 × 107 2 M1 for 93 000 000 or 93 × 106

or 0.93 × 108 oe

20 (a) Circle, radius 3 cm, centre A, not inside the

rectangle

2 M1 for arc or full circle centre

A radius 3 cm

or for an incorrect size circle at

A outside rectangle

(b) One line of symmetry with correct arcs

E.g.

2

B1 for correct ruled line (must

reach or cross two sides)

B1 for 2 pairs of correct

intersecting arcs




21 (a) 11x − 7y final answer 2 B1 for 11x ± my or nx − 7y

(b) 3a − 2b final answer 2 B1 for 8a −12b or −5a + 10b

or 3a ± pb or qa −2b

22 (a) (i) 1000 [m] 1

(ii) 80 [m/min] 2 M1 for 1600 ÷ 20

(iii) 20 [min] 1

(b) (i) Ruled line from (11 10, 1600) to (11 35, 0) 2 M1 for 1600 ÷ 64 soi

(ii) 11 35 1FT their line at the axis if on the

grid and not before 11 10.




0580 MATHEMATICS

0580/21 Paper 2 (Extended), maximum raw mark 70





Abbreviations



dep dependent



oe or equivalent

SC Special Case



1 86.7 or 86.74 to 86.75 1

2 5.293 cao 2 B1 for 5.29 or 5.292 to 5.2927

3 125 2 B1 for 55 or 125 in any other correct position

on diagram or M1 for 180–55

4 7.7 2 M1 for 44 ×

100

5.17 oe

5 4.8 oe 2 M1 for 5 + 19 = 3x + 2x oe or better

or B1 for 24 – 2x = 3x oe

or 5 = 5x – 19 oe

6 (a) 6

2 oe

1

(b) 200 1FT FT 600 × their (a) providing their (a) is a

probability

7 435, 445 cao 2 B1 for one value in the correct place

or SC1 for both values correct but reversed

8

134

3 M2 for 53

1001.20

×

×

oe

or M1 for 1.20100

53=

××x

or 3% = 4.02 oe

If 0 scored SC1 for answer of figs 134

9 (a) 2+n

n

oe final answer

1

(b) n2–1 oe final answer 2 B1 for any quadratic in final answer

10 [±]22

ac − oe final answer

3

M1 for correct square

M1 for correct re-arrangement

M1 for correct square root




11 150 3 M1 for m3 to cm3 or cm3 to m3

12 (a) 110 1

(b) 79 2 B1 for DAC = 42 or ACB = 79 or ACD = 28

13 (a) 4

5 oe

1

(b) 4y6 2 B1 for ky6 or y6 or 4yk or 4 as final answer

14 1

52

−

−

t

t final answer

3 B1 for 1

)1(3

−

−

t

t or better

B1 for 3(t – 1) – (t + 2) oe or better

15 (a) 12

1

12

9− oe

[=]12

8oe [=]

3

2

M1

M1

Must be shown

Both fractions must be shown

(b) 25

4

2

5× oe

Cancelling shown or 50

20oe [=]

5

2

M1

M1

Must be shown

Dependent and cancelling shown or a

fraction and then 5

2must be shown

16 (a)

6

9

1

(b) 10.8 or 10.81 to 10.82

2FT M1 for 22 )6()9( theirtheir +

A1 for 10.8 or FT correctly evaluated

(c) (17, 13) 1FT FT their 9 and 6.

(8 + their 9, 7 + their 6) correctly evaluated

17 (a) (a + b)(1 + t) 2 B1 for 1(a + b) + t(a + b)

or a(1 + t) + b(1 + t)

(b) (x – 6)(x + 4) 2 SC1 for answer of (x + a)(x + b) where

ab = –24 or a + b = –2

18

486 cao

4

M1 for πππ 243422

2

1=+× rr or better

A1 for [r =] 9

M1 for ( )33

4

2

1 their][ rπ×




19

(a) 40

2 M1 for 6060

1000144

×

×

oe

(b) 3.5

2FT FT 140 ÷ their (a)

M1 for dist ÷ their (a)

or dist ÷ 40

or dist ×1000144

6060

×

×

or B1 for 140 seen

20 (a) (i) Accurate bisector of angle B with

correct arcs

2

B1 for correct line or correct arcs

(ii) Accurate perpendicular bisector of

BC with correct arcs

2

B1 for correct line or correct arcs

(b) correct region shaded 1

21

(a) 73.7 or 73.73 to 73.74

3 M1 for 223

20×

+

or B1 for BX = 8

M1 for tan [ ] = 8

6

their or better

(b) 120

2 M1 for 12202

1××

oe

22

(a) (i) 50

5 oe

1

(ii)

50

11 oe

1

(b) 16

11 oe

1

(c) 2450

380 oe

2 M1 for 49

19

50

20×

(d)

1




0580 MATHEMATICS






Abbreviations



dep dependent



oe or equivalent

SC Special Case


soi seen or implied


1 19% 0.7195 038.0 sin 11.4 1/5 2 B1 for decimals [0.19], [0.2], 0.194…, 0.197…,

0.192… seen

Or for four in correct order

2 (a) –447 1

(b) 2 1

3 15.7 or 15.70 to 15.71 2 M1 for 2 × π × 2.5

4

160

2 M1 for 36018

8× oe

5 (a) 1

(b) Some possible answers:

1

6 [±] 4−y final answer 2 M1 for first move completed correctly

M1 for second move completed correctly on answer

line

7

170

2 M1 for 10)2212(2

1×+× oe

8

3619 to 3620

2 M1 for 312×π××

3

4

2

1or better

9 decagon 3 M1 for 360 ÷ 36 oe

A1 for 10

10 10.1[0] 3 M1 for 1.3199 and 1.3401 seen

and M1 for 500 × 1.3199 or 500 × 1.3401

or for 500 × (their highest – their lowest) oe

11

120

3 M1 for d

kv =

A1 for k = 600




12 p = 71.4025 cao

q = 73.1025 cao

3 B1 for 8.45 and 8.55 seen

M1 for their LB2 [π] or their UB2 [π]

If 0 scored, SC1 for one correct.

13 10[.00] 3 M2 for 1.90 and 2.90 and 5.20 only

or M1 for two of 1.90, 2.90, 5.20 in a list of three or

two values from the table

or SC1 FOR 1.90, 2.90, 4.30

+

2

20.540.3from

14 52 3 B2 for AOB = 104

or B1 for OAB or OBA = 38

15 (8, 2) 3 M1 for correctly eliminating one variable

A1 for x = 8

A1 for y = 2

If 0 scored, SC2 for correct substitution and correct

evaluation to find the other value.

16 x <6.8 4 B3 for 6.8 with wrong inequality or equal as answer.

Or

M1 for first move completed correctly

and M1 for second move completed correctly

and M1 for third move completed correctly

17 (a)

3026

511

2

SC1 for one correct row or column

(b)

−

−

24

16

8

1 oe

2 B1 for

−

−

24

16k

or B1 for

dc

ba

8

1

18 (a) (1.5, 12.5) oe 2 B1 for either coordinate

(b) y = 3x + 8 oe 3 B2 for y = mx + 8 or y = 3x + c or 3x + 8

or B1 for gradient (or m) = 3 and B1 for c = 8

If 0 scored, SC1 for 23 = their m × 5 + c

or for 2 = their m × –2 + c

or for 12.5 = their m × 1.5 + c

(c) Most common methods:

Correctly substituting P (3, 17) into

y = 3x + 8

Showing the gradient of AP or BP = 3

Other methods possible.

1




19 (a) –2a – 2c oe 2 M1 for BO = –a – c or for any correct route or correct

unsimplified expression

(b) 2a + c 2 M1 for any correct route or correct unsimplified

expression

(c) –a – c oe 2FT FT their (a) or correct answer

Or M1 for a correct non direct route from O to E or for

correct unsimplified expression or for correct FT

unsimplified

20 (a) 4.05 to 4.2 1

(b) 2.6 to 2.75 2 B1 for 9.6 seen

(c) 2.05 to 2.25 2 B1 for [UQ] 5.0 to 5.1 and [LQ] 2.85 to 2.95 seen

(d)

48

5

2

M1 for 5

21

(a) 37.2 or 37.17 to 37.19

3 M2 for sin[ ] = 6

65sin4×

or M1 for 65sin

6

sin[]

4= oe

(b) 11.7 or 11.72 to 11.74 3 M1 for [B =] 160 – 65 – their (a)

M1 for 2

1 × 4 × 6 × sin their 77.8




0580 MATHEMATICS






Abbreviations



dep dependent



oe or equivalent

SC Special Case



1 39 2 M1 for 52 × 45 ÷ 60 oe

2 Any two of (20, 8) (–4, 0) (12, 24) 2 B1 for one correct

3

–8

2 M1 for 2x = –16 or 5.72

1−=+ x oe or better

4 tan 100, cos 100, 1/100, 100–0.1 2 B1 for decimals –0.1[[7..], –5.[67..], [0.01],

0.6[3..] or for three in the correct order

5 (a) 600 000 1

(b) 79.2 2 M1 for 22 × 60 × 60 ÷ 1000 oe

6

25[.00]

3 M2 for 30 × 120

100oe

or M1 for 30 associated with 120%

e.g. 1.2x = 30

7 5 3 M2 for (x – 5)(x – 1)

or

M1 for evidence of a factorisation which gives

the correct coefficient of x or positive prime

constant term e.g. (x – 7)(x + 1), (x – 4)(x – 2),

(x – 3)(x – 1)

8 1.6 oe 3 M1 for m = kx3

A1 for k = 25

9 (a) a2 + 2ab + b2 2 B1 for a2 [+] ab [+] ab [+] b2 or better seen

(b) 22 1

10

160

3 M1 for sin 15 = 628

[]oe or better




11 (a)

−

24

13

1

(b)

− 24

12

10

1oe

2 B1 for

dc

ba

10

1or B1 for

− 34

12k

12

(a) 7.5 × 10–2

2 M1 for 0.075 or 40

3or

80

6or 0.75 × 10–1 oe

(b) 9.3 × 107 2 M1 for 93 000 000 or 93 × 106 or 0.93 ×108 oe

13 (a) 24 2 M1 for MOC = 48

(b) 24 2 M1 for ACM = 66

or

B1 for 48 – their (a)

14 (a) 8q–1 or q

8

2

B1 for 8qk or kq–1

(b) 1/5 or 0.2

2 M1 for 5–2,2

5

1or [0].04 seen oe

15 (a) Circle, radius 3 cm, centre A, not

inside the rectangle

2 M1 for arc or full circle centre A radius 3 cm

or for an incorrect size circle at A outside

rectangle

(b) One line of symmetry with correct

arcs. E.g.:

2 B1 for correct ruled line (must reach or cross two

sides)

B1 for 2 pairs of intersecting arcs

16

(a) 8.61 or 8.609 to 8.6102

4 M1 for 120sin32

1 2×π××

M1 for [ ]23360

30 2××π×

M1 for area of triangle + 2 sectors

(b) 430 or 431 or 430.4 to 430.41 1FT FT their (a) × 50




17 (a) triangle at (0, 3) (2, 3) and (2, 4) 3 B1 for each correct vertex

If 0 scored then M1 for correct reflection in the

y axis or correct translation of their first stage 3

right 2 up

(b) reflection in y axis 2 B1 for reflection

B1 for y axis or x = 0

18 (a) 19–19.1 1

(b) 3 2 M1 for 47 seen

(c) 4.9 to 5.7 2 B1 for [UQ] 21.7 to 22.2 and [LQ] 16.5 to 16.8

(d)

50

45 oe

2 B1 for 45 seen or

SC1 for 50

5isw

19 (a) 75 2 B1 for [g(6) =] 36

(b) 3.5 –6.5 3 M1 for (2x + 3)2 = 100

M1 for 2x + 3 = [±]10

If 0 scored, SC1 for one correct value as answer

(c)

2

3−x oe final answer

2 M1 for x = 2y + 3 or y – 3 = 2x or 2

3

2+= x

y

or better

(d) 5 1




0580 MATHEMATICS

0580/31 Paper 3 – Core maximum raw mark 104





Abbreviations



dep dependent



oe or equivalent

SC Special Case



1 (a) (i)

(ii)

(iii)

(iv)

(b)

(c) (i)

(ii)

36 cao

5, 2, 3, 4, 3, 8, 1, 4

fully correct bar chart

26 – 30 cao

7 (hours) 25 ( minutes) cao

238.48

75

1

2

3FT

1

1

2

2

B1 for 6 or 7 frequencies correct

or 8 correct tallies if frequency column

blank

or 8 correct frequencies in tally column

B1 for a correct linear scaled frequency

axis

B2FT for correct height and equal width

of bars

or

B1FT for correct height of at least 5 bars

or all bars correct height but unequal

widths or gaps

SC2 for a fully correct bar chart but linear

scale not marked

M1 for 167 × 1.428 soi by 238.47(6) or

238.5 or 238

M1 for 107.1 ÷ 1.428

2 (a) (i)

(ii)

(b) (i)

(ii)

(iii)

(c) (i)

2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30,

40, 60.

60

60

49

2

Any correct example

1

2

1

1

1

1

Award mark for any one from list.

B1 for any common factor on answer line,

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30

Calculation and correct answer must be

seen




(ii)

(d) (i)

(ii)

(iii)

Any correct example

>

>

<

1

1

1

1

Calculation and correct answer must be

seen

3 (a) (i)

(ii)

(b) (i)

44 – 46

231 – 235

Fully correct drawing with arcs

52250 to 60500 nfww

1

1

3

3FT

B2 for correct triangle without arcs

B1 for 1 correct length side

Or arc of 6cm or 8cm

M2 for 2

1 × 550 ×

(their correct height × 50)

Or 2

1 × 11 × their correct height in cm

or

B1 for their correct height in cm

or their correct height × 50 seen

If 0 scored then SC1 for 2

1 × 550 ×

(50 × k)

4 (a) (i)

(ii)

(b) (i)

(ii)

Translation

−

−

8

7

Enlargement

[Scale factor] 0.5

[Centre] (0, 0)

D at ( –2, 4) (–4 , 4) (–3 , 6)

E at ( –4, 2) ( –4 , 4) ( –6 ,3)

1

1

1

1

1

1

2

Accept 7 left and 8 down

B1 for correct orientation, incorrect centre

or 90° rotation clockwise about (0,0).




5 (a) (i)

(ii)

(b) (i)

(ii)

(iii)

(c)

230

252

9

3.5

4

x = 1.5 or 3/2

y = –5

2

2

1

2

3

4

M1 for 130 + 4 × 25 or better

M1 for 4n = 1138 – 130 or better

Or (1138 – 130) / 4 or better

M1 for 8y = 24 + 4 or better

Or y – 4/8 = 24/8 or better

M1 for first correct step

M1FT for second correct step

M1 for correctly equating one set of

coefficients.

M1 for correct method to eliminate one

variable.

A1 for x = 1.5

A1 for y = –5

6 (a)

(b) (i)

(ii)

(c)

(d) (i)

(ii)

252.56

510

170

102

136

34.5

63.6 or 63.61 – 63.63

127 or 127.2…

2

2

3

3

2

1FT

M1 for (30 + 30 + 17) × 3.28 or better oe

M1 for 30 × 17

M2 for 2 correct areas clearly identified

or M1 for 408 ÷ (5 + 3 + 4) soi by 34 or

one correct area clearly identified

SC2 for three correct answers in incorrect

places

M2 for 221730 + soi by 1189

or M1 for 302 + 172 soi by 1189

M1 for 4.52 × π or 20.25 π

FT for their (d)(i) × 2




7 (a)

(b)

(c)

(d) (i)

(ii)

14, 4, 2, 8, 14

8 points correctly plotted

Smooth and correct curve through all

correct points

x = 0.5 or x = 2

1

y = 9 ruled

–2.15 to –2.25

3.15 to 3.25

3

P3FT

C1

1

1

1FT

1FT

B2 for 4 correct

B1 for 2 or 3 correct

P2FT for 6 or 7 points correctly plotted

P1FT for 4 or 5 points correctly plotted

8 (a) (i)

(ii)

(iii)

(b) (i)

(ii)

(c)

(d) (i)

(ii)

July or Jul

10.9

– 9.6

150 ÷ 360

90 oe

250

11682

4.48 × 106 cao

9.82

1

1

1

1

3

3

1

3

Accept 150 × 90

360, 150 × 4

M1 for their 150/360 × 600 or their

150 × 150/90

and B1 for 150 seen as angle

M2 for 885 × 15 × 0.88 oe

M1 for 885 × 0.88 oe

or 885 × 15 × 0.12 oe

M2 for 4480000

44800004920000− × 100 oe

or

−1

4480000

4920000× 100 oe

or

B1 for 440000 or 0.44 or 1.098(….)

or 109.8(…..)




9 (a) (i)

(ii)

(iii)

(b) (i)

(ii)

(c)

Chord

Radius

12

Tangent [meets] radius [at] 90 [°]

66

Angles [in] triangle 180 or

Angle [in a] semi–circle [= 90]

Octagon

360 ÷ 8 [= 45]

(180 – their 45) ÷ 2

67.5

15

1

1

1

1

2

1

1

M1

M1FT

A1

2

M1 for BCD identified as 90

or 180–24–90

alternative method

M1 for (8–2) × 180 [=1080]

or 6 × 180 [=1080]

M1FT for (their 1080 ÷ 8) ÷ 2

or their 1080 ÷ 16

A1 for 67.5

M1 for 360 / 24




0580 MATHEMATICS






Abbreviations cao correct answer only cso correct solution only dep dependent ft follow through after error isw ignore subsequent working oe or equivalent SC Special Case www without wrong working

Question. Answers Mark Part Marks

1 (a) Scalene [triangle]

(b) Congruent

(c) (i) translation

−

2

6

(ii) rotation

180°

[Centre] ( 0,0 )

(d) Image (1, –2), (4, –2), (2, –3)

(e) Image (2, 4), (8, 4), (4, 6)

(f) 6

1

1

1

1

1

1

1

1

2

2FT

Accept 6 left and 2 up.

SC1, 1, 1 for

Enlargement, [SF=] –1,(0,0)

B1 for 2 times enlargement, incorrect centre

M1 for 0.5 × their base × their height




2 (a) (i) 9

5

(ii) 60

(b) 1080

(c) 0.85 × 3450

Or 3450 – 0.15 × 3450

(d) 32

2

2

3

2

3

B1 for 144

80 or better or 0.556 or 0.555… or

answer 9

4

M1 for 144 ÷ (6+5+1) or 144÷12

M1 for 2 ÷ 5 × 5200 soi by 2080

And M1 for

their 2080 + 24×175 – 5200 or better

B1 for 0.85 or for 0.15 × 3450

M2 for 1002500

25003300×

−

oe

or ( 2500

3300 – 1 ) × 100 oe

Or

B1 for 800 or 2500

25003300− or

2500

3300 or

1.32 or 132 or 0.32

3 (a) (i) 4n + 21, final answer

(ii) 5n + 3 = 3n + 27

[n =] 12

(iii) 126

(b) (i) yellow

(ii) arrow pointing at 0.5

(iii) 20

4 o.e. or 0.2 or 20%

(iv) 20

16 o.e. or 0.8 or 80%

1

1

2

1FT

1

1

1

1FT

M1 for 5n – 3n = 27 – 3 or better

SC1 for 4 out of 20 and 16 out of 20




4 (a) (i) 370 to 380

(ii) [0]36 to [0]40

(iii) Intersecting arcs:

Arc centre A radius 10.5 cm

Arc centre B radius 7 cm

(iv) 300 to 310

(b) 11 25

(c) 4200

(d) 13.1

(e) 8515

2

1

2

1FT

3

1

2

1

B1 for 7.4 to 7.6 seen

B1 for one correct arc

or C correct with no arcs

M2 for 525 ÷ 700 × 60 or better soi

Or M1 for 525 ÷ 700 soi by 0.75

B1 for 13 100 or 13.107 or 13.100

Or B1FT their conversion to 4 or more sig

figs seen and then correctly rounded to 3 sig

figs

5 (a) –1 –1.25 2.5 1

(b) 10 correctly plotted points

Two correct smooth curves through

all correct points and not across

y-axis

(c) 1.15 to 1.35

(d) (i) Line x = –3.5 ruled

(ii) (5, –3) plotted

(iii) line y = –3 ruled

2

P3FT

C1

1FT

1

1

1FT

B1 for two correct

P2FT for 8 or 9 correctly plotted

P1FT for 6 or 7 correctly plotted




6 (a) (i) 26

(ii) 16

(iii) 17 –3

(b) (i) 9 17

(ii) odd

(c) (i) 23

(ii) 5n + 3 oe final answer

(iii) 19

1

1

2

2

1

1

2

2

B1 for each

B1 for one correct in correct position

or FT for fourth term

B1 for 5n + k , jn + 3 j ≠ 0

Or 5n + 3 oe not as final answer

M1FT for their (c)(ii) = 98 if linear soi

7 (a) 23

(b) [Affected by an] extreme value oe

(c) 40.9

(d) (i) 6 points correctly plotted

(ii) positive

(iii) line of best fit ruled and

continuous

(iv) No, [estimate unreliable as]

outside range [of data]

2

1

2

P2

1

1

1

M1 for clear attempt to find middle

If zero scored then SC1 for 40

M1 for

(36+38+42+36+45+42+32+40+40+46+56+38)

÷ 12 implied by 491 ÷ 12

If zero scored then SC1 for 26.25 or 26.3

P1 for 4 or 5 correctly plotted

dep on at least 11 points on graph




8 (a) 7

Pentagon

(b) (i) trapezium

(ii) 125°

(iii) 32°

(c) (i) 90°

angle [in a] semicircle [=90°]

(ii) 55°

(iii) 93°

1

1

1

1

2

1

1

1

3

M1FT for 180 – 125 – 23 or better

or 180 – their 125 – 23 or better

M2 for 90 – 52 or 180 – 90 – 52 or 38

If M0 then B1 for angle CAD = 90° indicated

9 (a) (i) 7

(ii) –32

(iii) –11

(b) (i) 1.05 × 107

(ii) 4 580 000

(iii) Kaliningrad

(iv) 2.7 × 105

1

1

1

1

1

1

2

Allow –7

B1 for figs 27

10 (a) 3.5

(b) 2n – 18 or 2 ( n – 9 ) final answer

(c) 5p2(2 + p) final answer

2

2

2

M1 for 6x – 12 = 9 or better

or x – 2 = 6

9 or better

B1 for 8n – 8 or –6n –10 or 2n or –18

M1 for any correct incomplete factorisation

or 5p2(2 + p) seen in working




0580 MATHEMATICS

0580/33 Paper 3 – Core, maximum raw mark 104





Abbreviations



dep dependent



oe or equivalent

SC Special Case


Qu. Part Answers Mark Part Marks

1 (a)

(b)

(c)

(d)

240 900

[Total] 1640

(i) 600 ÷ 5 × 17

(ii) 30

43.1

261.36 cao

1,1

1FT

M2

2

2

3

500 + their 2 costs

M1 for 600 ÷ 5 or 17 ÷ 5

M1 for 2040 ÷ 17 × 3

Or 120 × 3, soi by 360

M1 for 1002040

20402920×

−

oe

or 100)12040

2920( ×− oe

or 1001002040

2920−× oe

M1 for 1500 × 1.0553 oe

M1FT for their 1761.36 – 1500

If only 1 scored SC1 for correctly rounding to

2 decimal places from at least 3 decimal places

SC2 if only 1761.36 seen

2 (a)

(b)

Kite

(i) Rotation

90° clockwise (or 270° anti-

clockwise) oe

[centre] origin oe

(ii) Translation

−

−

10

2

1

1

1

1

1

1

Accept 2 left and 10 down oe




(c)

(iii) Enlargement

[Scale Factor] –3

[centre] (–3, 4)

(i) [x2 =] 32 + 12

[x =] 2213 + or [x = 19 +

or 10 and = 3.162…

(ii) 9.15

(iii) 27.45 to 27.5

1

1

1

M1

M1dep

3

1FT

M1 for 32 + 12 or better

Needs a value to 3 or more decimal places

B1 for 2 or 1.41 or better seen

M1 for 2 x 3.16 + 2 x their 1.41...

soi by 9.14

If zero scored SC1 if answer in range 8.6 to 9.6

their (c)(ii) ×3

3 (a)

(b)

(i) 28

(ii) 25 or 49 or 9 or 1

(iii) 2

(iv) 19 or 29

(i) 5

(ii) 27

1

1

1

1

1

2

B1 for 8

1 or 216 seen

4 (a)

(b)

(c)

(i) 40

(ii) 140

(i) [w =] 90

(ii) [x =] 24

(iii) [y =] 66

[z =] 66

[Angle between] tangent [and]

diameter/radius [=] 90°

2

1FT

1

1

1FT

1FT

1

M1 for 360 ÷ 9

180 – their (a)(i)

180 – (their w + their x)

(90 – their x) or their y

5 (a)

(i) 1, 7, 1

(ii) 8 points correctly plotted

Correct smooth curve through all 8

correct points

1, 1, 1

P3FT

C1

P2FT for 6 or 7 correct

P1FT for 4 or 5 correct




(b)

(c)

(d)

–1.1 to –1.3 and 4.1 to 4.3

(i) Line x = 1.5 drawn

(ii) x = 1.5 oe

(i) Ruled continuous line drawn

(ii) 1

(iii) [y =] x + 2

1FT,

1FT

1

1FT

1

2

1FT

Equation of their line in (c)(i)

M1 for run

rise for their line

their (d)(ii) + their 2

6 (a)

(b)

(c)

(d)

(i) 18

(ii) 7

(iii) 25

Alison with reference to [higher] mean

and

Bethan with reference to [higher] median

(i) [Frequencies] 3, 2, 1

[Angles] 72°, 48°, 24°

(ii) Two correct sectors on pie chart

3 ‘correct’ labels

5

2

2

1

2

1FT

1FT

1

2

2FT

1

2

M1 for evidence of ordering

M1 for sum of 15 items ÷ 15 soi

Strict FT

Strict FT

B1 for 1 correct or

M1 for one frequency ÷ 15 × 360

or × 24

B1FT for 1 correct sector

Only ft if (c)(i) angles total 144

Independent

B1 for 0.4 or 40% or 15

6 or any equivalent

fraction

7 (a)

(b)

(c)

[Angle DCE =] 36.9 or 36.8699 to 36.9

1.875 or 1.88

3.75

3

2

1FT

B1 for [DE =] 0.75 soi

M1 for than DCE = 0.1

DEtheir

M1 for 0.5 × (1.5 + 2.25) × 1.0 oe

their (b) × 2




(d)

3 rectangles and 1 trapezium correctly

placed on the grid with correct scale and

size.

4

B1 for rectangle to right 6 by 8 squares

B1 for an accurate and correctly placed

trapezium

B1 for a rectangle to left 9 by 8 squares

B1 for rectangle 5 by 8 squares and further to

the left

8 (a)

(b)

(c)

(d)

(e)

Octagon

[Pattern 3] 20 and 22

[Pattern 4] 26, 29

[Pattern 7] 44, 50

(i) 6n + 2 oe final answer

(ii) 140 oe

7n + 1 oe final answer

n – 1 final answer

1

1

1, 1

1, 1

2

1FT

2

2FT

B1 for 6n + a or bn + 2 b ≠ 0

ft linear expression in (c)(i)

B1 for 7n + c or dn + 1 d ≠ 0

B1FT for n + j or kn 1 k ≠ 0

9

(a)

(b)

(c)

(i) [r =] h

V

π

3

(ii) [r =] 15

1413

x

x

π

[r =] 2.99…

18.9 or 18.8 or 18.849 to 18.852

1.9 [cents] cao

2

M1FT

A1

2

3

B1 for [r2 =] h

Vor

V 33

π

seen or better

their formula

M1 for 2 × π × 3 oe

M1 for 2,15 (or 215) ÷ 113

A1 for 0.019 (0…) or 1.9 (0…) soi




0580 MATHEMATICS






Abbreviations



dep dependent



oe or equivalent

SC Special Case


art anything rounding to

soi seen or implied

Qu Answers Mark Part Marks

1 (a) (i)

5

2 cao

1

(ii) 3 : 2 cao 1

(b) (i) 1.22

2

M1 for 86.38 – 28 × 1.56

(ii) 1.3 [0] nfww 3 M2 for 1.56 ÷ 1.2 oe

or M1 for 1.56 = 120% soi

(c) 33.6[0] 2 M1 for (667 – 314.2) ÷ 10.5 oe

2 (a) 3 correct lines on grid

(0, 0) to (40, 5)

(40, 5) to (100, 5)

(100, 5) to (120, 0)

2 Allow good freehand

SC1FT for 2 lines correct, FT from an incorrect

line

(b)

40

5 oe

1

(c) 3.75 4 M2 for 0.5 × 40 × 5 + 60 × 5 + 0.5 × 20 × 5 oe

[450]

or M1 for evidence of a relevant area = distance

and M1dep their area (or distance) ÷ 120





3 (a) (i) 204 or 204.2 to 204.23 2 M1 for 135××π implied by answer in range

204.1 to 204.3

(ii) 12 cao

3 M2 for 22513 − or states 5, 12, 13 triangle

or M1 for 132 = 52 + h2 or better

(iii) 314 or 314.1 to 314.2

2 M1 for ×××2

53

1π their (a) (ii) implied by

answer in range 314 to 314.3

(iv) 3.14 × 10–4 or 3.141 to

3.142 × 10–4

2FT FT their (a) (iii) ÷ 1003 correctly evaluated and

given in standard form to 3 sig figs or better

or M1 FT for their (a) (iii) ÷ 1003

or SC1 for conversion of their m3 into standard

form only if negative power

(b) 138 or 138.3 to 138.5

4 M3 for 36026

10×

π

π

oe or

36013

135

2×

×

××

π

π (i)(a)or their oe

or M2 for a correct fraction without × 360

or M1 for 132××π oe [81.6 to 81.8] seen

or 2

13×π oe [530.6 to 531.2] seen

4 (a) 45.[0] or 45.01 to 45.02 nfww 4 M2 for 552 + 702 – 2.55.70 cos 40

or M1 for correct implicit equation

A1 for 2026. ….

(b) 84.9 or 84.90 to 84.92 4 B1 for angle BDC = 40 soi

M2 for 32sin

)40(sin70 their

or M1 for correct implicit equation

(c) (i) 4060 or 4063 to 4064 nfww

3

M2 for 2

1 ( )40sin 70 × 55 + 2

1

( ))3240180(sin)(70 −−× theirbtheir oe

or M1 for correct method for one of the triangle

areas

(ii) 1020 or 1015 to 1016

2FT

FT their (c) (i) ÷ 4 oe correctly evaluated

or M1 their (c) (i) ÷ figs 4 oe

(d) 35.4 or 35.35… nfww

2 M1 for sin 40 = 55

distance or better

or for 2

1 (55 × 70 sin 40) = (70 × distance) ÷ 2

or better





5 (a) (i) Correct reflection to (4, 8)

(2, 9) (4, 9)

2

SC1 for reflection in line x = 5

or reflection in y = k

Ignore additional triangles

(ii) Correct rotation to (4, 2), (4, 3)

(6, 3)

2

SC1 for rotation 180˚ with incorrect centre

Ignore additional triangles

(iii) Shear, x-axis oe invariant,

[factor] 2

3 B1 each (independent)

(iv)

10

21

2FT

FT their shear factor

B1FT for one correct column or row in 2 by 2

matrix but not identity matrix

or SC1FT for

12

01

(b) (i) p + 2s final answer

2 M1 for recognising OQ as position vector soi

(ii) s +

2

1p final answer

2 B1 for s + kp or ks + 2

1p

or correct route (k ≠ 0)

(c) parallel and OQ = 2SR oe 1

6 (a) (i) 1.4 to 1.6 1

(ii) 1.15 to 1.25 1

(iii) – 1 1

(iv) – 2.25 to – 2.1

– 0.9 to – 0.75

2.2 to 2.35

3 B2 for 2 correct or B1 for one correct

or B1 for y = x drawn ruled to cut curve 3 times

(b) (i) – 15 2 B1 for [h(3) =] 8 seen

or M1 for 1 – 2(x2 – 1) or better

(ii)

2

1 x−

or 22

1 x

− oe final answer

2

M1 for2 x = 1 – y or x = 1–2y or better

(iii) – 2, 2

3 M1 for x2 – 1 = 3 or better

B1 for one answer

(iv)

8

1 oe nfww

3 M2 for 8x = 1 or 8x – 1 = 0

or M1 for 1 – 2(3x) [= 2x]





7 (a) 24.7 or 24.66 to 24.67 4 M1 for midpoints soi

(condone 1 error or omission)

(5, 15, 25, 35, 45, 55)

and

M1 for use of ∑fx with x in correct interval

including both boundaries (condone 1 further

error or omission)

and

M1 (dependent on second M) for ∑fx ÷ 120

(b) (i) 50, 90, 114 2 B1 for 2 correct

(ii) Correct curve

or ruled polygon

3 Ignore section to left of t = 10

B1 for 6 correct horizontal plots

and B1FT for 6 correct vertical plots

If 0 scored SC1 for 5 out of 6 correct plots

and

B1FT for curve or polygon through at least 5 of

their points dep on an increasing curve/polygon

that reaches 120 vertically

(iii) 21.5 to 23

15 to 16.5

24 to 26

4

B1

B1

B2 or B1 for 72 or 72.6 seen

(c) (i) 50, 30 2 B1 each

(ii) Correct histogram

3FT B1 for blocks of widths 0 – 20, 30 – 60 (no

gaps)

B1FT for block of height 2.5 or their 50 ÷ 20

and B1FT for block of height 1 or their 30 ÷ 30





8

(a) ( ) ( )( )1184112

−−− or better

p = –(– 11), r = 2(8) or better

– 0.67, 2.05 final answers

B1

B1

B1B1

Seen anywhere or for

2

16

11

−x

Must be in the form r

qp + or

r

qp −

or B1 for 16

11

16

11

8

112

+

+

SC1 for – 0.7 or – 0.672 to – 0.671 and 2.0 or

2.046 to 2.047

or answers 0.67 and – 2.05

(b) 132

3 M1 for xky = oe or kyx = oe

A1 for k = 6 oe or better or for k = 0.1666 to

0.167

[k = 6 implies M1A1] oe

(c) 20 with supporting algebraic working

6 B2 for 195.0

5.14

5.2=

−+xx

oe

or B1 for 5.2

x

or 5.

5.14−x

M1dep on B2 for first completed correct move

to clear both fractions

M1 for second completed correct move to

collect terms in x to a single term

M1 for third completed correct move to collect

numeric term[s] leading to ax = b

SC1 for 20 with no algebraic working

9 (a) y = 2 oe

y = 2x oe

y = – 2

1 x + 5 oe

1

2

2

M1 for y = kx, 0≠k or gradient 2 soi

M1 for gradient – ½ soi or y = kx + 5oe

or x + 2y = k 0≠k oe

If L2 and L3

both correct but interchanged then

SC3

(b) y ≥ 2 oe

y ≤ 2x oe

y ≤ – 2

1 x + 5 oe

3

B1 for each correct inequality, allow in any

order

After 0 scored, SC1 for all inequalities reversed

(c) (i) 4 [bushes], 3 [trees]

2

M1 for any correct trial using integer

coordinates in region

or 30x + 200y = 720 seen

(ii) 2 [bushes], 4 [trees]

860

2

1

M1 for any correct trial using integer

coordinates in region





10 (a) (i) 1 + 2 + 3 + 4 + 5 = 15 1

(ii) Correct substitution equating to

sum

e.g. ( )

3122

=+

kand k = 2 stated

with no errors seen

2 M1 for using a value of n in ( )k

nn 1+

e.g. ( )

3122

=+

k

or for a verification using k = 2

e.g. ( )

32

122=

+

(iii) 1830 1

(iv) 30

2 M1 for ( )2

1+nn

= 465 or better

(v) n – 8 1

(b) (i) 225, 15 2 B1 either

(ii)

( )4

122

+nn

oe

1

(iii) 36100

2 M1 for ( )4

1191922

+ oe or 1902




0580 MATHEMATICS






Abbreviations



dep dependent



oe or equivalent

SC Special Case



soi seen or implied

Correct answer Mark Part marks

1 (a) (i) 3216 Final answer 2 M1 for (18900 – 5500) × 0.24 oe

(ii) 1307 Final answer 2FT FT (18900 – their (a)(i)) ÷ 12 correctly

evaluated

M1 for (18900 – their (a)(i)) ÷ 12

(b) 4.5[%] nfww

2 M1 for 10018900

]18900[50.19750×

−

or 18900

1890050.19750 −

(c) A by 31.05…

or 31.04 to 31.05

or 31.[0]

31.1[0]

5 M1 for 1500 × 4.1/100 × 3 [+ 1500] oe

M1 for 1500 × 1.0333 [– 1500] oe

A1 for 1684.5 or 184.5 or 1653[.45..] or

153[.45..]

and M1dep for subtraction of their amounts or

their interests

2 (a) 36.9° or 36.86 to 36.87 2 M1 for tan[DBC] = 1.8/2.4 oe

(b) (i) 1.8² + 2.4² leading to 9

2

M1 for 1.8² + 2.4² or better

(ii) [cosABD) =]

346.62

6.8346.6222

××

−+

127 or 126.8…

M2

A2

M1 for correct cos rule but implicit version

A1 for –0.599…

After 0 scored, SC2 nfww for answer 127 or

126.8 to 126.96 from other methods or no

working shown

(c) 39.6 or 39.7 or 39.59 to 39.68 3 M2 for ½ (2.4 + 8.6) × 1.8 × 4 oe

Or M1 for )6.84.2(2

8.1+ oe soi by 9.9 to

9.92




3 (a) 10

74 −x

final answer nfww

3 M2 for 52

)13(2)12(5

×

+−− xx

or 25

)12(5

×

−x–

25

)13(2

×

+x

or M1 for attempt to convert to common

denominator of 10 or multiple of 10 with one

error in numerator

(b) x² + 9 final answer nfww 4 B3 for 4x² – 6x – 6x + 9 – 3x² +12x or correct

answer given and

then spoilt

or B1 for 4x² – 6x – 6x + 9 seen and B1 for

– 3x² +12x or – (3x² – 12x) seen

(c) (i) (2x – 1)(x + 3) isw solving 2 M1 for (2x + a)(x + b) where ab = –3 or

2b + a = 5 with integers a and b

(ii)

)3(2

12

−

−

x

x

or 62

12

−

−

x

x

final answer nfww

3

M2 for 2(x + 3)(x – 3) or (2x – 6)(x + 3) or

(2x + 6)(x – 3) seen

or M1 for 2(x² – 9) seen

4 (a) (i) 90 ÷ (42/360 × π × 82) o.e.

3.836 to 3.837

M3

A1

M2 for 42/360 × π × 82 × h = 90

or M1 for 42/360 × π × 82

(ii) 131 or 130.75 to 130.9 nfww 5 M2 for 42/360 × π × 2 × 8 × 3.84 oe

[22.48 to 22.53]

or M1 for 42/360 × π × 2 × 8 oe soi

[5.86 to 5.87]

and M1 for 2 × (8 × 3.84)

[61.37 to 61.44]

and M1 for 2 × (42/360 × π × 82)

[46.88 to 47]

(b) 2.42 or 2.416 to 2.419

3 M2 for 3.84 × 390

5.22oe or h = 3

3

90

5.2284.3 ×

or M1 for 390

5.22oe or 3

5.22

90oe seen

or 3

384.3

h =

5.22

90oe




5 (a) 7, 11.5, 4.5 1,1,1

(b) Correct curve cao

5

B3FT for 10 correct plots, on correct vertical

grid line and within correct 2 mm square

vertically

Or B2FT for 8 or 9 correct plots

Or B1FT for 6 or 7 correct plots

and B1 indep for two separate branches on

either side of y-axis

(c) (i) 0.69 < x < 0.81 1

(ii) –2.3 < x < –2.2

–0.8 < x < –0.6

0.35 < x < 0.5

3

B1 for each correct

After 0 scored, allow SC1 for drawing line

y = 7.5 long enough to cross curve at least once

(d) (i) y = 10 – 3x ruled correctly

–0.55 < x < –0.45

0.35 < x < 0.45

B2

B1dep

B1dep

long enough to cross curve twice.

B1 for ruled line gradient –3 or y intercept at

10 but not y = 10

Or B1 for ‘correct’ but freehand

Dependent on at least B1 scored for line

After 0 scored, SC2 for –0.5 and 0.4 [from

solving equation]

(ii) 10 1 –2

or –10 –1 2

3 B2 for 2 – x – 10x2 [= 0] oe

Or B1 for 01012

2=−−

xx

oe Correctly

eliminating – 3x

Or B1 for 2 – x – 3x3 = 10x2 – 3x3 oe Correctly

clearing fractions




6 (a) (i) 110

1 oe

2 M1 for 10

1

11

1×

(ii)

110

6 oe

55

3

2 M1 for 10

2

11

3×

(iii)

110

8 oe

55

4

2FT FT their (a)(ii) + 10

1

11

2× correctly evaluated

or M1 their (a)(ii) + 10

1

11

2×

(b) (i)

990

6 oe

165

1

2 M1 for 9

1

10

2

11

3××

(ii)

990

336 oe

165

56

2 M1 for 9

6

10

7

11

8××

(iii)

990

198 oe

5

1

5 M4 for

××+

××

9

9

10

1

11

23

9

8

10

2

11

33 oe

or M3 for

××

××

9

9

10

1

11

23

9

8

10

2

11

33 or

oe

Or

M1 for 9

8

10

2

11

3×× oe seen and M1 for

××9

9

10

1

11

2 oe seen




7 (a) 14 10 or 2 10 pm final answer 2 M1 for (0)8 10 oe or answer 14 hours and

10 minutes or answer 2 10 [am]

(b) 5 hours 45 minutes cao 2 M1 for 345 [mins] seen or for 805 /7 × 3 oe or

5.75 seen

(c) (i) 798 or 798.2 to 798.4….

2 M1 for 10712 / 60

2513 or 10712 ÷ 13.4…

(ii) 1.82 × 105

or 1.815 × 105 to 1.816 × 105

4 B3 for 182000 or 181500 to 181600 seen

or M2 for 10712000/59 oe

or M1 for figs 10712/figs 59 soi by figs 182 or

figs 1815 to 1816

and B1 FT for their number of litres correctly

converted to standard form rounded to 3sf or

better

(d) 8600 3 M2 for 10148 ÷ 1.18 oe

or M1 for 10148 associated with 118[%]

8 (a) (i) –6 1

(ii) 2.75 oe 2 M1 for [g(x) =] 0.5 or 7/14

Or

++

+ 1

75

1

72

xx

oe

(b)

4

3−x or

4

x

– 4

3 Final answer

2

M1 for y – 3 = 4x or better or x = 4y + 3 or

better

or 4

y=

4

3 + x or flowchart with – 3 then ÷ 4

(c) (i) 5

2 M1 for 4x = 23 – 3 or x + 4

3 =

4

23 or better

(ii) x² + 5x – 7 = 0

)1(2

)7)(1(455 2−−±−

oe

1.14 and –6.14 final answers

B1

B1

B1

B1

B1

May be implied by correct values in formula

B1 for )7)(1(452 −− or better [53]

If in form r

qp +

orr

qp −

, B1 for –5 and

2(1) or better

No recovery of full line unless seen

Or SC1 for 1.1 or 1.140…. and –6.1

or – 6.140 …

Or answers –1.14 and 6.14




9 (a) (i) Reflection

x = –2 oe

2

B1 for either

(ii) Translation

−

2

7 oe

2

B1 for either

(iii) Stretch

x-axis oe invariant

[factor] 3

3

B1 for each

(b) (i) Triangle with coords at (8, 2)

(7, 3) and (7, 5)

2 B1 for rotation about (6, 0) but 90°

anticlockwise

Or for rotation 90° clockwise around any point

(ii) Triangle with coords at

(–2, –5) (–6, –5) and (–8, –7)

2 B1 for 2 correct points or for enlargement of

SF –2 any centre

(iii) Triangle with coords at (1, –1)

(4, –6) and (3, –5)

2 B1 for 2 correct points or coordinates of

2 points shown

(c)

− 12

01

2

B1 for one row or one column correct but not

identity matrix.

Or SC1 for

−

10

21

10 (a) 48 and 57, 9n + 3 oe

(b) 56 and 50, 86 – 6n oe

(c) 125 and 216, n3 oe

(d) 130 and 222 n3 + n oe

1 2

1 2

1 1

1 1FT

B1 for 9n + k oe

B1 for k – 6n oe

FT their (c) + n dep on expression in n in (c)




0580 MATHEMATICS






Abbreviations



dep dependent



oe or equivalent

SC Special Case



soi seen or implied


1 (a) (i) 45 2 M1 for 5 × 63 ÷ 7

(ii) 20 2 M1 for 5 × 56 ÷ 14

(iii)

23.4 or 23.38 to 23.41

3 M2 for 1009.413

8.48–9.413×

×

×

or 1009.4

138.48–9.4×

÷

Or

M1 for 9.413

8.48–9.413

×

×

or 1009.413

8.48×

×

or 76.6[…]

(b) 128 4 Using fractions (percentages / decimals):

M1 for 8

3

4

3×

=

32

9 or 5.37

100

75× [= 28.125%]

A1 for 32

9 or 28.125[%]

M1 for 36 ÷ 32

9 oe

or 36 × 125.28

100 oe

Partial percentages

M1 for (Remaining) 5.37

36100 ×

[= 96]

A1 for 96

M1 for 96 ÷ 100

75 oe

SC1 for 288




2 (a)

119.94[…] nfww

3 M2 for 26sin

122sin62×

or M1 for 122sin

AC =

26sin

62 oe

SC2 for correct answer from alternative methods

(b) 109 or 108.7 to 108.8 nfww 4 M2 for 119.9..2 + 552 – 2 × 119.9.. × 55cos65

A1 for 11827[·…] or 11834 to 11835[·…]

or M1 for implicit version

(c) 1970 or 1969 to 1970.4 2 M1 for ½ × 119.9.. × 62 × sin 32

(d) 22300 or 22310 to 22320 3 M2 for (their (c) + 0.5 × 55 × 119.9.. × sin65) × 4.5

or

M1 for their (c) + 0.5 × 55 × 119.9.. × sin65

3 (a) 9 – 2x, 7 – 2x oe 2 B1 for each, accept in any order

(b) x(9 – 2x)(7 – 2x)

4x3 – 32x2 + 63x

M1FT

A1

Correct expansion and simplification with no errors

(c) 24 20 2 B1 for each correct value

(d) Correct curve 3 B2FT for 5 correct plots

or

B1FT for 3 or 4 correct plots

(e) 0.65 to 0.75 ≤ x ≤ 2 oe 2 B1 for 0.65 to 0.75 seen

(f) (i) 36 to 37 1

(ii) 1.2 to 1.4 1

4 (a) 48 and 84

66 and 66

2 B1 for each pair

(b) 540 2 M1 for 3 × 180 or (2 × 5 – 4) × 90

or 5 × (180 – 360 ÷ 5) oe

(c) 1620 2 M1 for 7 × 360 – their 540 – 360

(d) (i) 2x + 5 + 3y – 20 + 4x – 5 + x + y –

10 = 360 oe

1 Allow partial simplification but not 7x + 4y – 30 = 360

(ii) 2x + 5 + 3y – 20 = 180 1

(iii) [x =] 30, [y =] 45 nfww 4 M1 for correct multiplication

M1 for correct elimination

A1 x = 30 or y = 45

If 0 scored SC1 for correct substitution to find the

other variable

(iv) 65, 115, 115, 65 1 Accept in any order




5 (a) (i) 3.81 or 3.812 to 3.813 or

3h 49min nfww

4 M1 for midpoints soi (condone 1 error or omission

and

M1 for use of ∑fx with x in correct interval including

both boundaries (condone 1 further error or omission)

and

M1 (dep on 2nd M1) for ∑fx ÷ 80 (305 ÷ 80)

(ii) Correct histogram 4 B1 for each correct block

and

B1 for correct widths

(b) (i) 5

2 ,

4

1 ,

4

3 ,

4

1 oe

2 B1 for 5

2 or both

4

1s in correct place

(ii) 20

18 nfww

10

9

3 M2 FT for 1 – their 5

2 × their

4

1

or 5

3 ×

4

3 +

5

3 × their

4

1 + their

5

2 ×

4

3 oe

or

M1 FT for their 5

2 × their

4

1

or 5

3 × their

4

1 + their

5

2 ×

4

3 oe

(iii) 125

27 [0.216]

2 M1 for 5

3 ×

5

3 ×

5

3

6 (a) 329.7 to 330 3 M2 for ½π(122 + 8.752 – 3.252) oe

or M1 for ½π122 or ½π8.752 or ½π3.252

SC2 for answer 1318 to 1320

(b) 2970 or 2967 to 2969.[…] 4 M3 for ½π(24 + 17.5 + 6.5) × 35 + their (a)

or

M2 for ½π(24 + 17.5 + 6.5) × 35

or

M1 for ½π × 24 or ½π × 17.5 or ½π × 6.5

SC3 for 3955 to 3960 dep on SC2 in (a)

(c) 11.5 or 11.6 or 11.53 to 11.55 3FT M1 for their (a) × 35

A1 for 11500 or 11530 to 11550




(d) (i) 40

20=

h

r or

4020

hr=

1 Accept 20 : 40 = r : h leading to 40r = 20h [r = h/2]

40

20 =

2

1 and

2

1=

h

r

(ii)

35.3 or 35.31 to 35.34

3 M2 for 31211545

π

×their oe or 2 × their r

or

M1 for their 11545 = hh

×

×π×

2

23

1 oe

or their 11545 = rr 23

1 2××π× oe

7 (a) (i) 2

3 or 1.5

2

M1 for )4(8

)4(14

−−

−−

oe

(ii) y = 2

3x + 2 oe

2 B1 for y = their 2

3x + c o.e.

or y = mx + 2, m ≠ 0

SC1 for 2

3x + 2

(iii)

18

12

1

(iv) 21.6 or 21.63[…] 2 M1 FT for their 122 + their 182 oe

(b) (i) (a) 3b – 4a 1

(b)

5

1(6b – 8a) oe simplified

2 M1 for 5

1(12a + 6b) – 4a or AR = AO + OR

(c) 6a + 3b oe simplified 1

(ii)

OR is parallel to OT

1 Dep on OT correct

(iii) 4

9 or 2.25

2 M1 for

2

2

3




8 (a) ( )

2

–2

t

uts oe nfww

3

M1 for a correct rearrangement to isolate the a term

and

M1 for a correct multiplication by 2

and

M1 for a correct division by t2

(b) 36.75 cao 3 M2 for 15.5 + 2.5 × 8.5

B1 for two of 15.5, 2.5, 8.5 seen

(c) (i) 5

16 or better [3.2]

1

(ii) 11.2 4 M2 for ½(25 + 10)16 (= 280)

or M1 for appreciation of distance from area

and M1 for their 280 ÷ 25 (dep on M1)

9 (a) 15 18 3n + 3 or 3(n + 1)

6 10

25 36 (n + 1)2

9 B2 for 15, 6, 25

or B1 for two correct values

B3 for 18, 10, 36

or B1 for each correct value

B2 for 3n + 3 oe

or M1 for 3n + k, for any k

B2 for (n + 1)2 oe

or M1 for a quadratic expression

(b) 14 2 M1 for (n + 1)(n + 2) = 240 or better

or 15 × 16 = 240

(c) (i) ½ + p + q = 9 1

(ii) [p = ] 3

[q = ] 2

11

5 B2 for 4p + 2q = 23

or B1 for ½ × 23 + p × 22 + q × 2 oe

M1 for correct multiplication and subtraction of their

equations

A1 for [p = ] 3 or [q = ] 2

11

If 0 scored then SC1 for either correct




10 (a) 3+x

x

cao

3

B1 for (x + 3)(x – 3)

B1 for x(x – 3)

(b) 2

3 and –5

7

M2 for 15(x + 1) – 20x = 2x(x + 1)

or M1 for multiplication by one denominator only

or )1(

20)1(15

+

−+

xx

xx

and B2 for 2x2 + 7x – 15 [= 0]

or B1 for 15x + 15 – 20x or 2x2 + 2x

and M2 for (2x – 3)(x + 5) or their correct factors or

formula

or M1 for (2x + a)(x + b)

where ab = –15 or a + 2b = 7

A1 for x = 2

3 and –5

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