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Write your Centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen.You may use an HB pencil for any diagrams or graphs.Do not use staples, paper clips, glue or correction fluid.DO NOT WRITE IN ANY BARCODES.
Answer all questions.If working is needed for any question it must be shown below that question.Electronic calculators should be used.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For π, use either your calculator value or 3.142.
At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question.The total of the marks for this paper is 70.
The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate.
5 Paul and Sammy take part in a race. The probability that Paul wins the race is
35
9 . The probability that Sammy wins the race is 26%.
Who is more likely to win the race? Give a reason for your answer.
Answer ........................... because .............................................................................................................. [2]__________________________________________________________________________________________
A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 metres per second. It continues at this speed for 1 minute. It then decelerates for 3 minutes until it stops at the next station. The diagram shows the speed-time graph for this journey.
Calculate the distance, in metres, between the two stations.
Answer ............................................ m [3]__________________________________________________________________________________________
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
Cambridge International ExaminationsCambridge International General Certificate of Secondary Education
*4311357799*
MATHEMATICS 0580/23
Paper 2 (Extended) May/June 2015
1 hour 30 minutes
Candidates answer on the Question Paper.
Additional Materials: Electronic calculator Geometrical instruments Tracing paper (optional)
READ THESE INSTRUCTIONS FIRST
Write your Centre number, candidate number and name on all the work you hand in.Write in dark blue or black pen.You may use an HB pencil for any diagrams or graphs.Do not use staples, paper clips, glue or correction fluid.DO NOT WRITE IN ANY BARCODES.
Answer all questions.If working is needed for any question it must be shown below that question.Electronic calculators should be used.If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For π, use either your calculator value or 3.142.
At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question.The total of the marks for this paper is 70.
The syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge International Level 1/Level 2 Certificate.
Answer BC = .......................................... cm [3]
12
Speed (m/s)
0 u 3uTime (seconds)
NOT TOSCALE
10
A car starts from rest and accelerates for u seconds until it reaches a speed of 10 m/s. The car then travels at 10 m/s for 2u seconds. The diagram shows the speed-time graph for this journey.
The distance travelled by the car in the first 3u seconds is 125 m.
(a) Find the value of u.
Answer(a) u = ................................................ [3]
Show your working and give your answers correct to 2 decimal places.
Answer x = ......................... or x = ......................... [4]__________________________________________________________________________________________
The diagram shows a solid pyramid on a square horizontal base ABCD. The diagonals AC and BD intersect at M. P is vertically above M. AB = 20 cm and PM = 8 cm.
Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity.
To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cie.org.uk after the live examination series.
Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.
20R
QP
9 cm
10 cm
NOT TOSCALE
The area of triangle PQR is 38.5 cm2.
Calculate the length QR.
Answer QR = .......................................... cm [6]
® IGCSE is the registered trademark of Cambridge International Examinations.
CAMBRIDGE INTERNATIONAL EXAMINATIONS
Cambridge International General Certificate of Secondary Education
MARK SCHEME for the May/June 2015 series
0580 MATHEMATICS
0580/21 Paper 2 (Extended), maximum raw mark 70
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 May/June 2015 series for most Cambridge IGCSE
®, Cambridge International A and AS Level components and some
cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied
Question. Answer Mark Part Marks
1 9.5 1
2 7.37 or 7.371... 1
3 2.7 × 105 1
4 35822
−+ xx final answer 2 B1 for 2 correct terms in final answer
or M1 for xx 322+ or 355 −x
5 Sammy and correct reason with 25.7% oe shown
2 B1 for 25.7% or 0.257... seen or conversion of 26% to fraction and common denominator
6 44 2 B1 for 75.5 or 119.5 seen
7 3224 wu final answer 2 B1 for 2 correct elements in final answer
8 13.6 or 13.60... 3 M2 for ( ) ( )( )22
2674 −−+−− oe
or M1 for ( )74 −− oe or ( )( )26 −− oe
9 5
9
their 3
7
5
9× or
35
79
×
×
5
21 or
5
14 cao
B1
M1
A1
or 35
63
or their 35
15
35
63÷ or equivalent division with
fractions with common denominators
10
2520
3
M2 for 12 × (1 + 6) ÷ 2 oe
or M1 for 1 area correct If zero scored B1 for top speed = 720 m per min or total time = 360 sec
16 1597 cao 4 B3 for 1597.39.. or 1597.3[9...] or 1597.4 or 6597
or B2 for 6597.3[9...] or 6597.4
or B1 for
14
100
215000
+
If B1 scored or B0 scored and an attempt at compound interest is shown SC1 for their 6597[...] – 5000 evaluated correctly provided answer positive and SC1 for their final answer rounded correctly to nearest $ from their more accurate answer
17 (a) 532 ×× 2 B1 for 2, 3, 5 as prime factors
(b) 90 2 B1 for 90k or for listing multiples of each up to 90
or 2 × 32 × 5
18 Correctly equating one set of coefficients
Correct method to eliminate one variable
x = 0.8
y = −3
M1
M1
A1
A1
Dependent on the coefficients being the same for one of the variables Correct consistent use of addition or subtraction using their equations If zero scored SC1 for 2 values satisfying one of the original equations
or
if no working shown, but 2 correct answers given
19 (a) 7.5 2 M1 for [8
6]10 × oe
(b)
12 cao 2 M1 for 6
89× oe or
(a)
109
their×
20 (a) ( )( )xytp 2++ final answer 2 B1 for ( ) ( )tpxtpy +++ 2 or
( ) ( )xytxyp 22 +++
(b) ( )( )37 −++ khkh final answer 2 B1 for ( ) ( )( )khkh +−+ 372
If A0 then B1 for their final answer rounded correctly to nearest whole number from their more accurate answer dependent on at least M1
22 (a)
718
1722 2 M1 for a 2 × 2 matrix with 2 correct elements
(b)
−
−
56
34
2
1 2
M1 for
dc
ba
2
1 or
−
−
56
34k soi
or det = 2 soi
23 (a) −13 1
(b) −3x − 1 or ( )235 +− x 1
(c) 9x − 10 cao 2 M1 for 5 − 3( 5 − 3x)
(d) 3
5 x−
final answer oe 2 M1 for correct first step e.g.
53 =+ xy or xy
−=
3
5
3 or xy 35 −=− or
better
or
for interchanging x and y, e.g. yx 35 −= , this does
not need to be the first step
® IGCSE is the registered trademark of Cambridge International Examinations.
CAMBRIDGE INTERNATIONAL EXAMINATIONS
Cambridge International General Certificate of Secondary Education
MARK SCHEME for the May/June 2015 series
0580 MATHEMATICS
0580/22 Paper 2 (Extended), maximum raw mark 70
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 May/June 2015 series for most Cambridge IGCSE
®, Cambridge International A and AS Level components and some
(b) 24 2 M1 for 40 or 16 or both lines drawn from 15
and 45 across and down to the horizontal
axis
(c) 5 2 M1 for answer 55 or line or mark on graph
indicating 55
23 (a) 0.4 or 5
2 1
(b) 1430 3 M2 for correct, complete, area statement
e.g. 120 × 10 + 2
1× 20 × 8 +
2
1× 30 × 10 oe
or M1 for one area calculation
e.g. 10 × 120 or 2
1× 20 × 8 or
2
1× 30 × 10
(c) 11.9 or 11.91 to 11.92 1FT their (b) ÷ 120
24 (a) 9x2 1
(b)
3
5−x
2 M1 for correct first algebraic step e.g.
y – 5 = 3x or 3
5
3+= x
y or better
or
for interchanging x and y, e.g. x = 3y + 5, this
does not need to be the first step
(c) 9x + 20 cao final answer 2 M1 for 3(3x + 5) + 5
® IGCSE is the registered trademark of Cambridge International Examinations.
CAMBRIDGE INTERNATIONAL EXAMINATIONS
Cambridge International General Certificate of Secondary Education
MARK SCHEME for the May/June 2015 series
0580 MATHEMATICS
0580/23 Paper 2 (Extended), maximum raw mark 70
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 May/June 2015 series for most Cambridge IGCSE
®, Cambridge International A and AS Level components and some
cao correct answer only dep dependent FT follow through after error isw ignore subsequent working oe or equivalent SC Special Case nfww not from wrong working soi seen or implied
Question Answer Mark Part Marks
1 168 2 M1 for 240 ÷ (7 + 3) or better
2 )23(3 −xx final answer 2 B1 for )23(3 2xx − or )69( −xx
3 66.4[2…] 2 M1 for cos […= ] 5
2 oe
4 18.45 18.75
1
1
If 0 scored, SC1 for 6.15 and 6.25 seen or for correct answers reversed
5 )3)(12( −+ xx 2 B1 for ))(2( bxax ++ , where ab = – 3 or a + 2b = – 5
6
− 01
10 2 B1 for one correct column
7 1.60 cao 3 B2 for 1.597…. or 1.6 or M1 for 2 ÷ 1.252
8
8
15
5
9
8
15×their oe
8
33or
8
27cao
B1
M1
A1
or 72
135
or 72
40
72
135÷ or equivalent division with
fractions with common denominators
9 2.8 oe 3 M2 for xx 38212 −=+ or better or M1 for 28or123 −+ xx
13 (a) 4x9 final answer 2 B1 for answer kx9 or 4xk (k 0≠ )
(b) 2y32 final answer 2 B1 for answer ky32 or 2yk (k 0≠ )
14 )2)(2(412 −− B1 If completing the square B1 for 2
4
1
+x oe
If in form
r
qp + or
r
qp −
p = – 1, r = 2(2) or 4
B1 B1 for 2
4
11
4
1
++−=x
or 2
4
11
4
1
+−−=x
– 1.28 0.78
B1
B1
If 0 scored for the last two B marks then SC1 for – 1.3 and 0.8 or – 1.281 to – 1.280 and 0.781 or 0.7807 to 0.7808 or 1.28 and – 0.78 or – 1.28 and 0.78 seen in the working
15 (a) 4.77 or 4.774 to 4.775 2 M1 for 30 ÷ [2]π
(b) 35.7 or 35.8 or 35.74 to 35.82 2 M1 for 0.5 × π × (their (a))2
or M1 for 0.5 × 10 × 9 × sin = 38.5 M3 for √(92 + 102 – 2×9×10 × cos (their P)) or M2 for 92 + 102 – 2×9×10 × cos (their P) or M1 for a correct implicit expression
e.g. cos(their P)= 1092
109222
××
−+ RQ
Note: 87.8, 87.81[…] or 87.7[55…] score 4 marks
or M is foot of perpendicular from R to PQ M2 for perp.ht = 38.5 ÷
2
1 × 10 or 7.7
or M1 for 2
1 × 10 × […] = 38.5
M1 for PM = √(92 – 7.72)[ = 4.659… or 4.66] M1 for QM = 10 – their 4.659…[ = 5.34…] M1 for QR = √((their QM)