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DC (AC/FD) 101622/2© UCLES 2015 [Turn over
Cambridge International ExaminationsCambridge International General Certificate of Secondary Education
*3291754855*
MATHEMATICS 0580/21Paper 2 (Extended) May/June 2015
1 hour 30 minutesCandidates 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.
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0580/21/M/J/15© UCLES 2015
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 52#+ + .
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
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]__________________________________________________________________________________________
g s
7 37
2.7 105
n n
2 43 5 35
it8oc 35
0.25710.26
Sammy as 0.26302571or
26 79 35
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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.
AnswerAB = ....................................... units [3]__________________________________________________________________________________________
9 Without using a calculator, work out 15
4
7
3' .
Show all your working and give your answer as a fraction in its lowest terms.
Answer................................................ [3]__________________________________________________________________________________________
I 19.5 75.5
44
24mW
Cl5tC8F
13.6
f f x 3 Gfs 4754
4
4
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10
00 1 2 3
Time (minutes)
Speed(metres per
second)
4 5 6
12
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]__________________________________________________________________________________________
loTI
I hIa
Catt xh 126 11 12 42ms x
mins
42 601520
fIuif44h
Yuta I Gaff 9 as't Ytf 676 C 8
Brits
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12 p is inversely proportional to the square of (q + 4). p = 2 when q = 2.
Find the value of p when q = –2.
Answerp = ................................................ [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]__________________________________________________________________________________________
P I k thx5andsoCqt451hs72R72subp2andof2henceChT2K 10 71CGT fft45 18
A 1280M 1.28km
house 64km h
Time ftpfgfO.o2hours
002 60 60
72
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14
Q
P
a
b
M S
R NOT TOSCALE
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]__________________________________________________________________________________________
a Itv
PJ a la 21724
Parallelogram PM is parallelto QR
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15
–4 –3 –2 –1 0 1x
1
2
2 3 4 5 6 7 8
y
3
4
5
6
7
8
9
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]__________________________________________________________________________________________
y48y G x
YZoctz100 2 40290
5000 40254 foot 402
6597.3938156597 5000
1597
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0580/21/M/J/15© UCLES 2015
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
Answerx = ................................................
y = ................................................ [4]__________________________________________________________________________________________
30It 30 2 3 5
30 306090
45 45900 LCM 90
C 3 33 5
15 69 6 Ssct2y2
15 283 87 y 3Joe G 2
3Iy 93 sx 4
y 39,1 3a 4154 500.83
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19
8 cm 10 cm 6 cm
NOT TOSCALE
x cm
9 cmy cmA
B
C D
E
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]__________________________________________________________________________________________
SF Eg 13
10
74 7 T
9 x 4 312
Y Pt E t 2xCptE
ItE Cy t 2oD
Hht k h t k 3
Hhth htK D
10
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21
4 cm
9 cm
NOT TOSCALE
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 = 3
1πr2h.] [The volume, V, of a sphere with radius r is V =
3
4πr3.]
Answer ......................................... cm3 [4]__________________________________________________________________________________________
1281TVolumeof sphere tzxIzxTX
473 3
481TVolume ofcone Iz XIX 42 9
272173
or
285
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22 (a) Calculate 3
1
7
4
2
4
1
2-
-f fp p.
Answer(a) f p [2]
(b) Calculate the inverse of 5
6
3
4f p.
Answer(b) f p [2]
__________________________________________________________________________________________
Question 23 is printed on the next page.
1
26 2 7 4 3 1 7 2
1 2 4 4 1 1 4 2
IIta
inverse ad.tlcat
csxHToxssfIss7 tzfs's
12
0580/21/M/J/15© UCLES 2015
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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.
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]
s 3467 1 613
fCxt2 5 3GHzs Soc G
I 30C
f tho 5 36 3 75 15 9 d 9 10
yes Soc y S3
apple.yttgqfg.gg hence5 X
3g S KJ