This document consists of 12 printed pages.

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.

2

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

3

0580/21/M/J/15© UCLES 2015 [Turn over

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

0580/21/M/J/15© UCLES 2015

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

5

0580/21/M/J/15© UCLES 2015 [Turn over

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

6

0580/21/M/J/15© UCLES 2015

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

7

0580/21/M/J/15© UCLES 2015 [Turn over

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

8

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

9

0580/21/M/J/15© UCLES 2015 [Turn over

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

0580/21/M/J/15© UCLES 2015

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

11

0580/21/M/J/15© UCLES 2015 [Turn over

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

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.

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