Ebenhaezer Study Club

Cambridge International Examinations

Cambridge International General Certificate of Secondary Education

MATHEMATICS 0580/42
Paper 4 (Extended) May/June 2017
MARK SCHEME
Maximum Mark: 130

Published

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.

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Mark schemes should be read in conjunction with the question paper and the Principal Examiner Report for
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This document consists of 7 printed pages.

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Ebenhaezer Study Club
0580/42 Cambridge IGCSE – Mark Scheme May/June 2017
PUBLISHED

Question Answer Marks Part marks

1(a)(i) 600 ÷ (11+ 9) × 11 [ =330] M1 Could be in separate steps

with no errors seen

1(a)(ii) 270 1

1(b)(i) 372 cao nfww 3 B2 for answer 371.7…

8
 1.5 
or M1 for 330 × 1 +  oe not spoiled
 100 

After zero scored, SC1 for answer 42 or 41.7…

1(b)(ii) 12.6 or 12.7 or 12.63 to 12.73 2 their (b)(i) − 330 their (b)(i)
M1 for or × 100 soi by 112.7
330 330
or 113
After zero scored, SC1 for answer 12%

1(c)(i) 99 1
cao final answer
280

1(c)(ii) 27.5[0] 3 100 − 10

M2 for 24.75 ÷ oe
100
or M1 for recognising 24.75 as 90[%] oe

1(d)(i) 32 cao 2  20  15 
M1 for  1 −  1 −  [x]oe
 100  100 
or for 0.15 × 0.8 [x] oe

1(d)(ii) 13 cao 2  20  15 
M1 for  1 −  1 −  × x = 40.84 – 32 oe seen
 100  100 
  their (d)(i)  
or for their (d)(i) +  1 −    x = 40.84 oe
  100 

2(a)(i) Image at (8, 1), (10, 5), (8, 5) 2 6 k 

B1 for translation   or  
k   −5 
or 3 correct points not joined

2(a)(ii) Image at (4, 10), (4, 8), (8, 8) 2 B1 for rotation 90˚ anticlockwise but different centre
or for rotation 90˚ clockwise about (4, 10)
or 3 correct points not joined

2(a)(iii) Image at (6, 3), (6, 5), (7, 5) 2 1

B1 for enlargement factor but incorrect centre
2
or 3 correct points not joined

2(b) Reflection 1

y = − x oe 1 If zero scored, M1 for correct use of matrix product

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Ebenhaezer Study Club
0580/42 Cambridge IGCSE – Mark Scheme May/June 2017
PUBLISHED

Question Answer Marks Part marks

2(c)(i)(a)  13  2 B1 for each in a 2 by 1 matrix

  or SC1 for (13 [,] 16)
16 

2(c)(i)(b)  2 10  2 B1 for answer any 2 by 2 matrix

 
 3 15 

2(c)(i)(c) 1  4 −3  2  4 −3 
  oe isw B1 for k   oe soi (k ≠ 0 )
2  −2 2   −2 2 
or for determinant = 2 oe soi

2(c)(ii) NM or MP or N² oe or P² oe 1

3(a)(i) 175.5 nfww 4 M1 for at least four of

50, 125, 175, 225, 325 soi

M1 for Σfx with x inside or on boundary of each interval

their Σfx
M1 (dep on second M1) for
200

3(a)(ii) Fully correct histogram 4 B1 for each correct bar

If zero scored, B1 for 0.2, 1.32, 0.7, 0.16 seen

3(b)(i) Fully correct cumulative 3 B1 for correct horizontal plots

frequency diagram B1 for correct vertical plots

B1FT dep on at least B1 earned for points joined with

smooth increasing curve or polygon
If zero scored, SC1 for 4 correct plotted points

3(b)(ii)(a) 170 to 175 1

3(b)(ii)(b) 152 to 158 2 M1 for 42 to 48 written

4(a) –1.75 to –1.7 1

1.7 to 1.75 1

4(b)(i) Correct ruled solid tangent at 1

(–1.5, 3.5)

4(b)(ii) –7 to –5 2 dep dep on close attempt at ruled solid tangent at x = –1.5 in

part (b)(i)
M1 for rise/run dep on close attempt at ruled solid tangent
at x = –1.5

4(c)(i) 1 1

4(c)(ii) Correct curve 3 B2 for 4 or 5 correct points

or B1 for 2 or 3 correct points

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0580/42 Cambridge IGCSE – Mark Scheme May/June 2017
PUBLISHED

Question Answer Marks Part marks

4(d)(i) –0.95 to –0.8 1

1.1 to 1.45 1

4(d)(ii) their (–0.95 to –0.8 )< x < 1FT correct or FT their (d)(i)
their( 1.1 to 1.45) oe

4(e)(i) 0.125 oe and 0.03125 oe and 1

0.000976 to 0.000977 oe

4(e)(ii) 0 1 accept zero, nought, etc

5(a)(i) 94.2 or 94.3 or 94.24 to 94.26 2 M1 for π × 3 × 10

5(a)(ii) 9.54 or 9.539… 3 M2 for 102 − 32

or M1 for h 2 + 32 = 102 oe

5(a)(iii) 89.9 or 89.90 to 89.92… 2 1

M1 for × π × 32 × their (a)(ii)
3

5(b) 108 or 107.9 to 108.1 nfww 4 π × 3 × 10 their (a)(i)

M3 for 2
× 360 oe or × 360 oe or
π × 10 π × 102
2× π ×3
× 360 oe
2 × π × 10

x
or M2 for × π × 102 = their (a)(i) oe
360
x
or × 2 × π × 10 = 2 × 3 × π oe
360

x
or M1 for × π × 102 seen
360
x
or × 2 × π × 10 seen
360

5(c) 46.6 to 46.8 4 their (b) 1

M3 for × π × 102 − × 10 × 10 × sin(their (b)) oe
360 2

their (b)
or M1 for × π × 102 or their (a)(i) soi
360
1
and M1 for × 10 × 10 × sin(their (b)) soi
2

6(a) 1 6 1
, correctly placed
3 7

4 3 1
, correctly placed
7 7

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Ebenhaezer Study Club
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Question Answer Marks Part marks

6(b) 2 2 2 1
oe M1 for ×
21 3 7

6(c)(i) 15 3 2 6 1 3
oe M2 for × + × oe
21 3 7 3 7

2 6 1 3
or M1 for × oe or × oe seen
3 7 3 7

6(c)(ii) 50 2FT FT (70 × their (c)(i)) rounded up or down to integer

M1 for 70 × their (c)(i)

6(d) 10 2 2 1 1 1 1
oe M1 for × × × × [×k ] oe nfww
243 3 3 3 3 3
where k is positive integer less than 5

7(a)(i) 1 9 3 M2 for [2](4x + 7) = [2](6x – 2) oe

4.5 or 4 or final answer
2 2
or M1 for 2(2x + 6) + 2(2x + 1) oe
or 4(3x – 1) oe
or M1 for correctly reaching ax = b from their linear
equation

7(a)(ii) (2 x + 6)(2 x + 1) = (3x − 1) 2 M1 May be seen in different stages

5 x 2 − 20 x − 5 [= 0] oe B3 B1 for 4x² + 2x + 12x + 6 or better

B1 for 9x² – 3x – 3x + 1 or better

−(−20) ± (−20) 2 − 4(5)( −5) M2 FT their 3 term quadratic provided formula used or
complete the square
2(5)
−(−20) + q
oe M1 for (−20) 2 − 4(5)(−5) oe or if in form
2(5)
−(−20) − q
or FT± their quadratic
2(5)
or for completing the square
M2 for 2 ± 1 + 22
or M1 for (x – 2)²

4.24 or 4.236… cao B1

7(b)(i) ( x + 5)( x − 1) final answer 2 B1 for x(x – 1) + 5(x – 1)

or x(x + 5) –[1](x + 5))
or for ( x + a )( x + b) where ab = – 5
or a + b = 4

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Ebenhaezer Study Club
0580/42 Cambridge IGCSE – Mark Scheme May/June 2017
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Question Answer Marks Part marks

7(b)(ii) 5( x + 1) − 8 x = x( x + 1) M2 Could be seen in different stages

or 5 x + 5 − 8 x = x 2 + x M1 for 5(x + 1) – 8x seen or for common denominator of
x(x + 1) for LHS or both sides soi

–5 and 1 cao A2 A1 for x 2 + 4 x − 5 [= 0] oe

8(a) 66[.0] or 66.03 to 66.04 2 9

M1 for tan = oe
4

8(b) 1 2 2 M1 Any alternative method must be full and complete and

32 + 42 or 6 +8 result in exactly 5
2

8(c) 60.9 or 60.94 to 60.95 2 9

M1 for tan = oe
5

8(d) 5.83 or 5.84 or 5.827 to 5.840 6 M1 for [PB or PC = ] 92 + 52 or [XC =] 92 + 52 – 7.5

3
M1 for angle BPX = 2 × invsin oe
their PB

B1 for [ PB or PC =] 106 = 10.29 to 10.30

or XC = 2.79 to 2.8[0]
or angle BPX = 33.9 or 33.86 to 33.90…

M2 for
( their PB )2 + 7.52 − 2 × their PB × 7.5 × cos ( their BPX )
oe

or M1 for correct implicit equation

9(a)(i) 100 1

9(a)(ii) 92.3 or 92.29… to 92.31 3 10

M2 for 200 ÷ (2 + ) oe
60

or M1 for 200 ÷ their time interval

10
or M1 for soi oe
60

9(b)(i) 240 nfww 3 V  30 20 

M2 for  +  = 100 oe
2  60 60 

or M1 for any correct relevant area seen in terms of V

9(b)(ii) 2 2FT FT for their (b)(i) ÷ 1080 to 3 sf or better

oe
9 1000
M1 for their (b)(i) × soi
3600

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Ebenhaezer Study Club
0580/42 Cambridge IGCSE – Mark Scheme May/June 2017
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Question Answer Marks Part marks

10(a) –11 1

10(b) 7 2 M1 for 3x – 2 = 19 or better

10(c) 25 2 M1 for 3 × 3x − 2 oe

10(d) 9 x 2 − 8 x + 2 final answer 3 M1 for (3x − 2) 2 + 3x − 2 + x oe

B1 for ( 3 x − 2 ) =  9 x 2 − 6 x − 6 x + 4 oe
2
 

10(e) x+2 2 y 2
oe final answer M1 for x = 3y – 2 or y + 2 = 3x or = x − or better
3 3 3

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