Cambridge International Examinations Cambridge International General Certificate of Secondary Education
* 3 2 9 1 7 5 4 8 5 5 *
0580/21
MATHEMATICS
May/June 2015
Paper 2 (Extended)
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.
This document consists of 12 printed pages. DC (AC/FD) 101622/2 © UCLES 2015
[Turn over
2 1
At noon the temperature was 4 °C. At midnight the temperature was –5.5 °C. Work out the difference in temperature between noon and midnight.
Answer ........................................... °C [1] __________________________________________________________________________________________ 2
Use your calculator to work out
10 + 0.6 # (8.3 2 + 5) .
Answer ................................................ [1] __________________________________________________________________________________________ 3
Write 270 000 in standard form.
Answer ................................................ [1] __________________________________________________________________________________________ 4
Expand and simplify.
x (2x + 3) + 5(x – 7)
Answer ................................................ [2] __________________________________________________________________________________________ 5
Paul and Sammy take part in a race. The probability that Paul wins the race is
9 35 .
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] __________________________________________________________________________________________
© UCLES 2015
0580/21/M/J/15
3 6
Rice is sold in 75 gram packs and 120 gram packs. The masses of both packs are given correct to the nearest gram. Calculate the lower bound for the difference in mass between the two packs.
Answer ............................................. g [2] __________________________________________________________________________________________ 7
Simplify.
6uw–3 × 4uw6
Answer ................................................ [2] __________________________________________________________________________________________ 8
The point A has co-ordinates (– 4, 6) and the point B has co-ordinates (7, –2). Calculate the length of the line AB.
Answer AB = ....................................... units [3] __________________________________________________________________________________________ 9
Without using a calculator, work out
1 45 ' 37 .
Show all your working and give your answer as a fraction in its lowest terms.
Answer ................................................ [3] __________________________________________________________________________________________ © UCLES 2015
0580/21/M/J/15
[Turn over
4 10
12 Speed (metres per second)
0
0
1
2
3
4
5
6
Time (minutes) 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] __________________________________________________________________________________________ 11
Find the nth term of each sequence. (a) 4,
8,
12,
16,
20,
.......
Answer(a) ................................................ [1] (b) 11,
20,
35,
56,
83,
.......
Answer(b) ................................................ [2] __________________________________________________________________________________________ © UCLES 2015
0580/21/M/J/15
5 12
p is inversely proportional to the square of (q + 4). p = 2 when q = 2. Find the value of p when q = –2.
Answer p = ................................................ [3] __________________________________________________________________________________________ 13
A car travels a distance of 1280 metres at an average speed of 64 kilometres per hour. Calculate the time it takes for the car to travel this distance. Give your answer in seconds.
Answer .............................................. s [3] __________________________________________________________________________________________
© UCLES 2015
0580/21/M/J/15
[Turn over
6 14 Q
b
NOT TO SCALE
R
a
P
S
M
PQRS is a quadrilateral and M is the midpoint of PS. PQ = a, QR = b and SQ = a – 2b. (a) Show that PS = 2b. Answer(a)
[1] (b) Write down the mathematical name for the quadrilateral PQRM, giving reasons for your answer.
Answer(b) .............................................................. because ............................................................... ............................................................................................................................................................. [2] __________________________________________________________________________________________
© UCLES 2015
0580/21/M/J/15
7 15
y 9 8 7 6 5 4 3 2 1 –4 –3 –2 –1 0
1
2
3
4
5
6
7
8
x
Write down the 3 inequalities which define the unshaded region.
Answer ................................................. ................................................. ................................................. [4] __________________________________________________________________________________________ 16
Georg invests $5000 for 14 years at a rate of 2% per year compound interest. Calculate the interest he receives. Give your answer correct to the nearest dollar.
Answer $ ................................................ [4] __________________________________________________________________________________________
© UCLES 2015
0580/21/M/J/15
[Turn over
8 17
(a) Write 30 as a product of its prime factors.
Answer(a) ................................................ [2] (b) Find the lowest common multiple (LCM) of 30 and 45.
Answer(b) ................................................ [2] __________________________________________________________________________________________ 18
Solve the simultaneous equations. You must show all your working.
5x + 2y = –2 3x – 5y = 17.4
Answer x = ................................................ y = ................................................ [4] __________________________________________________________________________________________
© UCLES 2015
0580/21/M/J/15
9
B
19
E 8 cm
A
10 cm
y cm
x cm
6 cm
C
D
NOT TO SCALE
9 cm
F
Triangle ABC is similar to triangle DEF. Calculate the value of (a) x,
Answer(a) x = ................................................ [2] (b) y.
Answer(b) y = ................................................ [2] __________________________________________________________________________________________ 20
Factorise completely. (a) yp + yt + 2xp + 2xt
Answer(a) ................................................ [2] (b) 7(h + k)2 – 21(h + k)
Answer(b) ................................................ [2] __________________________________________________________________________________________
© UCLES 2015
0580/21/M/J/15
[Turn over
10 21
9 cm
NOT TO SCALE
4 cm
The diagram shows a toy. The shape of the toy is a cone, with radius 4 cm and height 9 cm, on top of a hemisphere with radius 4 cm. Calculate the volume of the toy. Give your answer correct to the nearest cubic centimetre. [The volume, V, of a cone with radius r and height h is V = 13 πr 2h.] [The volume, V, of a sphere with radius r is V = 43 πr 3.]
Answer ......................................... cm3 [4] __________________________________________________________________________________________
© UCLES 2015
0580/21/M/J/15
11 22
(a) Calculate
f
3 -1
7 -2 pf 4 4
(b) Calculate the inverse of
1 p. 2
f
5 6
Answer(a)
f
p
[2]
Answer(b)
f
p
[2]
3 p. 4
__________________________________________________________________________________________
Question 23 is printed on the next page.
© UCLES 2015
0580/21/M/J/15
[Turn over
12 23
f(x) = 5 – 3x (a) Find f(6).
Answer(a) ................................................ [1] (b) Find f(x + 2).
Answer(b) ................................................ [1] (c) Find ff(x), in its simplest form.
Answer(c) ................................................ [2] (d) Find f –1(x), the inverse of f(x).
Answer(d) f –1(x) = ................................................ [2]
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.
© UCLES 2015
0580/21/M/J/15
Cambridge International Examinations Cambridge International General Certificate of Secondary Education
* 4 3 1 1 3 5 7 7 9 9 *
0580/23
MATHEMATICS
May/June 2015
Paper 2 (Extended)
1 hour 30 minutes Candidates answer on the Question Paper. Additional Materials:
Electronic calculator Tracing paper (optional)
Geometrical instruments
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.
This document consists of 12 printed pages. DC (CW/SW) 101618/2 © UCLES 2015
[Turn over
2 1
Ahmed and Babar share 240 g of sweets in the ratio 7 : 3. Calculate the amount Ahmed receives.
Answer ............................................. g [2] 2
Factorise completely.
9x2 – 6x
Answer ................................................ [2] 3 NOT TO SCALE
5 cm
x° 2 cm Calculate the value of x.
Answer x = ................................................ [2] 4
An equilateral triangle has sides of length 6.2 cm, correct to the nearest millimetre. Complete the statement about the perimeter, P cm, of the triangle.
Answer ........................... P ........................... [2]
© UCLES 2015
0580/23/M/J/15
3 5
Factorise
2x2 – 5x – 3.
Answer ................................................ [2] 6
Find the 2 × 2 matrix that represents a rotation through 90° clockwise about (0, 0). Answer
7
f
p
[2]
James buys a drink for 2 euros (€). Work out the cost of the drink in pounds (£) when £1 = €1.252 . Give your answer correct to 2 decimal places.
Answer £ ................................................ [3]
© UCLES 2015
0580/23/M/J/15
[Turn over
4 8
Without using a calculator, work out
1 78 ÷ 59 .
Show all your working and give your answer as a fraction in its lowest terms.
Answer ................................................ [3] 9
Solve the equation.
3(x + 4) = 2(4x – 1)
Answer x = ................................................ [3] 10
In a sale, the cost of a coat is reduced from $85 to $67.50 . Calculate the percentage reduction in the cost of the coat.
Answer ............................................ % [3]
© UCLES 2015
0580/23/M/J/15
5 11 C
NOT TO SCALE
100° A
30° 24 cm
B
Use the sine rule to calculate BC.
Answer BC = .......................................... cm [3] 12 10
NOT TO SCALE
Speed (m/s)
0
u
3u Time (seconds)
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] (b) Find the acceleration in the first u seconds. Answer(b) ........................................ m/s2 [1] © UCLES 2015
0580/23/M/J/15
[Turn over
6 13
Simplify. (a) 12x12 ÷ 3x3
Answer(a) ................................................ [2] 1
(b) (256y 256) 8
Answer(b) ................................................ [2] 14
Solve the equation.
2x2 + x – 2 = 0
Show your working and give your answers correct to 2 decimal places.
Answer x = ......................... or x = ......................... [4] __________________________________________________________________________________________
© UCLES 2015
0580/23/M/J/15
7 15
The circumference of a circle is 30 cm. (a) Calculate the radius of the circle.
Answer(a) .......................................... cm [2] (b)
The length of the arc of the semi-circle is 15 cm. Calculate the area of the semi-circle.
Answer(b) ......................................... cm2 [2]
© UCLES 2015
0580/23/M/J/15
[Turn over
8 16
(a) In this part, you may use this Venn diagram to help you answer the questions. F
S
In a class of 30 students, 25 study French (F), 18 study Spanish (S). One student does not study French or Spanish. (i)
Find the number of students who study French and Spanish.
Answer(a)(i) ................................................ [2] (ii)
One of the 30 students is chosen at random. Find the probability that this student studies French but not Spanish.
Answer(a)(ii) ................................................ [1] (iii)
A student who does not study Spanish is chosen at random. Find the probability that this student studies French.
Answer(a)(iii) ................................................ [1] (b)
P
Q
R On this Venn diagram, shade the region R © UCLES 2015
(P
Q )′.
0580/23/M/J/15
[1]
9 17 200
150
Cumulative 100 frequency
50
0
1
2
3
4
5
6
7
8
9
10
Time (seconds) 200 students take a reaction time test. The cumulative frequency diagram shows the results. Find (a) the median, Answer(a) .............................................. s [1] (b) the inter-quartile range,
Answer(b) .............................................. s [2] (c) the number of students with a reaction time of more than 4 seconds. Answer(c) ................................................ [2]
© UCLES 2015
0580/23/M/J/15
[Turn over
10 18
P NOT TO SCALE
8 cm D
C
20 cm
M
A
B
20 cm
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. Calculate the total surface area of the pyramid.
Answer ......................................... cm2 [5]
© UCLES 2015
0580/23/M/J/15
11 19 M
B
P NOT TO SCALE
X
b
O
A
a
OAPB is a parallelogram. O is the origin, OA = a and OB = b. M is the midpoint of BP. (a) Find, in terms of a and b, giving your answer in its simplest form, (i)
BA,
Answer(a)(i) BA = ................................................ [1] (ii)
the position vector of M.
Answer(a)(ii) ................................................ [1] (b) X is on BA so that
BX : XA = 1 : 2.
Show that X lies on OM. Answer(b)
[4] Question 20 is printed on the next page. © UCLES 2015
0580/23/M/J/15
[Turn over
12 20 R NOT TO SCALE
9 cm
P
10 cm
Q
The area of triangle PQR is 38.5 cm2. Calculate the length QR.
Answer QR = .......................................... cm [6]
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.
© UCLES 2015
0580/23/M/J/15
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 Cambridge O Level components.
® IGCSE is the registered trademark of Cambridge International Examinations.
Page 2
Mark Scheme Cambridge IGCSE – May/June 2015
Syllabus 0580
Paper 21
Abbreviations 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
1
9.5
1
2
7.37 or 7.371...
1
3
2.7 × 105
1
4
2 x 2 + 8 x − 35 final answer
2
Part Marks
B1 for 2 correct terms in final answer or M1 for 2 x 2 + 3 x or 5 x − 35
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
24u 2 w3 final answer
2
B1 for 2 correct elements in final answer
8
13.6 or 13.60...
3
M2 for
9
9 5
their
9 7 9×7 or × 5 3 5×3
21 1 or 4 cao 5 5
10
2520
(− 4 − 7 )2 + (6 − (− 2 ))2
oe
or M1 for (− 4 − 7) oe or (6 − (− 2)) oe 63 35
B1
or
M1
or their
63 15 or equivalent division with ÷ 35 35 fractions with common denominators
A1
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
© Cambridge International Examinations 2015
Page 3
Mark Scheme Cambridge IGCSE – May/June 2015
Question. Answer 11 (a) (b)
12
Mark
Syllabus 0580
Paper 21
Part Marks
4n oe final answer
1
3n 2 + 8 oe final answer
2
M1 for a quadratic expression as final answer or 3n 2 + 8 oe in working
18
3
M2 for 2(2 + 4)2 = p(–2 + 4)2 oe M1 for p =
k (q + 4)2
A1 for k = 72 72
13
3
M2 for
1280 60 × 60 × 64 1000
M1 for working out distance ൊ speed e.g. figs 1280 ÷ 64 or figs
1280 their speed
or for working out km/h to m/s conversion e.g. 64 ×
1000 oe 60 × 60
1280 60 × 60 oe or their × 1000 64
14 (a) (b)
a + 2b − a or a − ( a − 2b) oe
1
Parallelogram
1
PM equal and parallel to QR
1
SC1 for answer trapezium with reason PM parallel to QR
or PM or PS parallel to QR and MR found = a so 2 pairs of parallel sides 15
y<8
1
y [ 6 – x oe and y [ x + 2 oe
3
B2 for either y [ 6 – x oe or y [ x + 2 oe or SC2 for y = 6 – x oe and y = x + 2 oe or SC1 for y K 6 – x or y = 6 – x or y K x + 2 or y = x + 2
© Cambridge International Examinations 2015
Page 4
Mark Scheme Cambridge IGCSE – May/June 2015
Question. Answer
Mark
1597 cao
16
4
Syllabus 0580
Paper 21
Part Marks B3 for 1597.39.. or 1597.3[9...] or 1597.4 or 6597 or B2 for 6597.3[9...] or 6597.4 2 or B1 for 50001 + 100
14
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) (b)
18
2× 3× 5
2
B1 for 2, 3, 5 as prime factors
90
2
B1 for 90k or for listing multiples of each up to 90 or 2 × 32 × 5
Correctly equating one set of coefficients
M1
Correct method to eliminate one variable
M1
Dependent on the coefficients being the same for one of the variables Correct consistent use of addition or subtraction using their equations
x = 0.8
A1
If zero scored SC1 for 2 values satisfying one of the original equations
y = −3
A1
or if no working shown, but 2 correct answers given
19 (a)
(b) 20 (a)
(b)
6 oe 8
7.5
2
M1 for [ 10] ×
12 cao
2
M1 for 9 ×
2
B1 for y ( p + t ) + 2 x( p + t ) or
( p + t )( y + 2 x )
final answer
8 10 oe or 9 × 6 their (a)
p( y + 2 x ) + t ( y + 2 x )
7(h + k )(h + k − 3) final answer
2
(
)
B1 for 7 (h + k ) − 3(h + k ) or (h + k )(7(h + k ) − 21) 2
© Cambridge International Examinations 2015
Page 5
Mark Scheme Cambridge IGCSE – May/June 2015
Question. Answer
Mark
285 cao
21
4
Syllabus 0580
Paper 21
Part Marks × π × 4 2 × 9 , 48π
M1 for
1 3
M1 for
128 π 1 4 × × π × 43 , 3 2 3
A1 for 284.8 to 284.9,
272 π 3
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)
(b)
22 17 18 7
2
M1 for a 2 × 2 matrix with 2 correct elements
1 4 − 3 2 − 6 5
2
M1 for
4 − 3 1 a b or k soi 2 c d − 6 5
or det = 2 soi −13
1
(b)
−3x − 1 or 5 − 3(x + 2)
1
(c)
9x − 10 cao
2
M1 for 5 − 3( 5 − 3x)
(d)
5− x final answer oe 3
2
M1 for correct first step e.g.
23 (a)
y + 3 x = 5 or
y 5 = − x or y − 5 = −3 x or 3 3
better or for interchanging x and y, e.g. x = 5 − 3 y , this does not need to be the first step
© Cambridge International Examinations 2015
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 Cambridge O Level components.
® IGCSE is the registered trademark of Cambridge International Examinations.
Page 2
Mark Scheme Cambridge IGCSE – May/June 2015
Syllabus 0580
Paper 22
Abbreviations 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
5.34 × 107
1
2
9 [h] 30 [min] cao
1
3
1 or 0.25 4
1
(a)
7
1
(b)
Any number except 3, 7 or 20
1
5
0.2 oe
2
M1 for 1 – (0.15 + 0.3 + 0.35)
6
8 × 103 or 8000 nfww
2
M1 for w + 4 × 103 = 1.2 × 104 oe or 5w + 20 × 103 = 6 × 104 oe
7
Parallel
1
Same length
1
2n2 + 3 oe final answer
2
4
8
M1 for a quadratic expression as final answer or 2n2 + 3 oe in working
9
23 oe, must be fraction 90
2
M1 for 25.5& - 2.5& oe e.g. 2.55r – 0.25r or B1 for
k 90
10
7
2
B1 for 120.5 or 113.5 seen
11
1 − 2 − 1 oe 5 11 3
2
− 2 − 1 soi M1 for k 11 3
or
1 a b 5 c d
or det = 5 soi
© Cambridge International Examinations 2015
Page 3
8 3
12
13
Mark Scheme Cambridge IGCSE – May/June 2015
B1
4 3 × their oe 5 8
M1
3 cao 10
A1
(a)
11
1
(b)
8
2FT
or
Syllabus 0580
Paper 22
40 3 15 accept or 15 8 40
12 40 ÷ their or equivalent division with 15 15 fractions with common denominators or
FT 30 – 2 × their (a) or M1 for 4 × 7 = 2(x – 1) + FG oe or 4(x – 4) = 2(x – 1) + FG oe or 2 × 7 + 2(x – 4) = 2(x – 1) + FG oe Allow x to be their (a) in each
684
14
3
M2 for 0.95 × 4 × 3 × 60 or M1 for 0.95 × 4 [× 3] or 4 × 3 × 60 or 0.95 × 3 × 60 or 0.95 × 4 × 60
2 x − 23 final answer ( x + 2)( 2 x − 5)
15
3
B1 for a common denominator of (x + 2)(2x – 5) B1 for 3(2x – 5) – 4(x + 2) or better or SC2 for final answer
2x − 7 ( x + 2)( 2 x − 5)
or SC1 for numerator of 2x – 7 in final answer 16
(a) (i)
0.5 or – 0.5 or
1 1 or − 2 2
(a)(ii) 4
17
1
1
(b)
1.37 or 1.37[4…]
1
(a)
[y =] 2x + 3 cao
3
(b)
−
1 oe 2
1FT
M2 for correct unsimplified equation or B1 for gradient = (11 – 3) ÷ (4 – 0) or better and B1 for c = 3 –1 ÷ their m
© Cambridge International Examinations 2015
Page 4
18
Mark Scheme Cambridge IGCSE – May/June 2015
78
(a)
3
M2 for 5 × 12 +
Syllabus 0580
Paper 22
1 × 12 × (8 – 5) or 2
1 × 6 × (5 + 8) × 2 oe 2 or M1 for 5 × 12,
1 × 12 × (8 – 5) , 2
1 × 6 × (5 + 8) or 12 × 8 – (…) 2 (b) 19
1170
1FT
(a)
1
Correct circle, radius 4 cm centre C
(b)
2
B2 for correct bisector with 2 pairs of correct arcs or B1 for correct bisector with no/wrong arcs
1
Correct complete boundary and correct shading. Dep on at least B1 in (b)
C
(c) A
20
15 × their (a)
B
(a) (i) 4
1
(ii) {3, 9}
1
(iii) fewer than 6 numbers from {1, 3, 5, 7, 9, 11} or ∅
1
(b)
ξ A
B
1
C
21
(a)
m=2
2
n = –10
B1 for m = 2 B1 for n = –10 If 0 scored SC1 for (x + 2)2 in working or x2 + 2mx + m2 + n and equating coefficients 2m[x] = 4[x] or m2 + n = –6
(b)
1.16 or 1.16[2…] from completing square
2FT
FT dep on negative n B1 for (x + their m)2 = –their n or SC1 for correct answer from using formula or for both answers 1.16 and –5.16 whatever method used
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Page 5
22
23
24
Mark Scheme Cambridge IGCSE – May/June 2015
Syllabus 0580
Paper 22
(a)
44
2
M1 for 48 soi
(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
(a)
0.4 or
(b)
1430
(c)
11.9 or 11.91 to 11.92
(a)
9x2
(b)
2 5
1 3
1FT
M2 for correct, complete, area statement 1 1 e.g. 120 × 10 + × 20 × 8 + × 30 × 10 oe 2 2 or M1 for one area calculation 1 1 e.g. 10 × 120 or × 20 × 8 or × 30 × 10 2 2 their (b) ÷ 120
1
x−5 3
2
M1 for correct first algebraic step e.g. 5 y y – 5 = 3x or = x + or better 3 3 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
© Cambridge International Examinations 2015
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 Cambridge O Level components.
® IGCSE is the registered trademark of Cambridge International Examinations.
Page 2
Mark Scheme Cambridge IGCSE – May/June 2015
Syllabus 0580
Paper 23
Abbreviations 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
3 x(3 x − 2) final answer
2
B1 for 3(3x 2 − 2 x) or x(9 x − 6)
3
66.4[2…]
2
M1 for cos […= ]
4
18.45 18.75
1 1
If 0 scored, SC1 for 6.15 and 6.25 seen or for correct answers reversed
5
(2 x + 1)( x − 3)
2
B1 for (2 x + a)( x + b) , where ab = – 3 or a + 2b = – 5
6
0 1 −1 0
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
15 8
B1
or
15 9 × oe 8 5
M1
or
27 3 or 3 cao 8 8
A1
their
2 oe 5
135 72
135 40 ÷ or equivalent division with 72 72 fractions with common denominators
9
2.8 oe
3
M2 for 12 + 2 = 8 x − 3 x or better or M1 for 3x + 12 or 8 x − 2
10
20.6 or 20.58 to 20.59
3
M2 for
85 − 67.5 67.5 × 100 or 1 − × 100 85 85
or M1 for
67.5 85 − 67.5 × 100 or 85 85
If zero scored SC1 for
© Cambridge International Examinations 2015
67.5 − 85 × 100 85
Page 3
Mark Scheme Cambridge IGCSE – May/June 2015
Question
Answer 12.2 or 12.18 to 12.19
11
Syllabus 0580
Mark 3
Paper 23
Part Marks M2 for
24 sin 30 sin 100
or M1 for correct implicit equation e.g.
12
(a)
5
3
sin 100 sin 30 = 24 BC
M2 for
u × 10 + 2u × 10 = 125 oe 2
or M1 for evidence that area represents distance e.g.
13
u × 10 , 2u × 10 or 3u × 10 2
FT 10 ÷ their u correctly evaluated
(b)
2
(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 )
1FT
2
2
1 − 4(2)(−2)
14
p+ q p− q If in form or r r
B1
1 If completing the square B1 for x + oe 4
B1
1 1 B1 for x = − + 1 + 4 4
p = – 1, r = 2(2) or 4
– 1.28 0.78
15
1 1 or x = − − 1 + 4 4 B1 B1
2
2
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
(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 0.5 × π × (30 ÷ 2π)2
© Cambridge International Examinations 2015
Page 4
Mark Scheme Cambridge IGCSE – May/June 2015
Question 16
(a) (i)
Answer 14
Mark 2
M1 for any two of 1, 11, 14, 4 correctly placed on Venn diagram or for 1 + 25 − x + x + 18 − x = 30 oe
25 − their (a )(i ) their 11 or from 30 30 diagram
(ii)
11 oe 30
1FT
FT
(iii)
11 oe 12
1FT
FT their diagram e.g.
(b)
18
Paper 23
Part Marks
or
17
Syllabus 0580
25 − their (a )(i ) 12
their 11 12
1
(a)
6
1
(b)
2
2
M1 for 7 identified as the UQ or 5 identified as the LQ or both lines drawn from the 150 and 50 across and down to the horizontal axis
(c)
180
2
M1 for answer 20 or line or mark on graph indicating 20
912 or 912.2…
5
M4 for 4 × 0.5 × 20 × or better or
82 + 102 + 20 × 20
M3 for 4 × 0.5 × 20 ×
82 + 102 or better
or M1 for and
82 + 102
M1 for 0.5 × 20 × and M1 for 20 × 20
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82 + 102
Page 5
Mark Scheme Cambridge IGCSE – May/June 2015
Question 19
(a) (i) (ii) (b)
Answer –b + a b+
Mark
Paper 23
Part Marks
1
1 a 2
1 1 3
[OX =] b + 1 3
Syllabus 0580
(–b + a) oe
a + 2 b oe 3
A1
2 statements from: 1 a 2
OM = b +
M1
B2
oe
B1 for any one of these statements
or [OX =]
2 ( 3
b+
1 a) 2
oe
or OX = 2 OM oe 3
20
9.37 or 9.370 to 9.371
6
M2 for sin[P] =
38.5 0.5 × 9 × 10
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)=
9 2 + 10 2 − RQ 2 2 × 9 × 10
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 ÷ 12 × 10 or 7.7 or M1 for
1 2
× 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)2 + 7.72)
© Cambridge International Examinations 2015
