MATHEMATICS 0580/04

PMTCambridge IGCSE *0123456789*MATHEMATICS0580/04Paper 4 (Extended)For examination from 2020SPECIMEN PAPER2 hours 30 minutesYou must answer on the question paper.You will need:Geometrical instrumentsINSTRUCTIONS Answer all questions. Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. Write your name, centre number and candidate number in the boxes at the top of the page. Write your answer to each question in the space provided. Do not use an erasable pen or correction fluid. Do not write on any bar codes. You should use a calculator where appropriate. You must show all necessary working clearly. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles indegrees, unless a different level of accuracy is specified in the question. For π, use either your calculator value or 3.142.INFORMATION The total mark for this paper is 130. The number of marks for each question or part question is shown in brackets [ ].This document has 20 pages. Blank pages are indicated. UCLES 2017[Turn over

PMT21(a) K r i s t i a n a dn St e pha ni e s ha r e s omK r i s t i a n r e c e i ve s 72.(i) W o r k outhow(ii) K r i s t i a n s pe ndsC a l c ul a t e t he(iii) K r i s t i a n a l s o buysm uc h S45%t e phaofpr i c e ofe m oney i n t he: 2.ni e r e c e i ve s .hi s 72 on at her a tio3c omc o m puta m e a l f orput .[ 2] .[ 1]e r ga m e .e r ga m e . 8.40 .C a l c ul a t e t he f r a c t i on of t he 72 K r i s t i a n ha s l e f t a f t e r buyim e a l.G i ve youra ns w e r i n i t s l ow e s t t e r m s .(iv) S t e pha in e uysba okb in a s a l e f orT h i s s a l e pr i c e i s a f t e r a r e du c t i on of C a l c ul a t e t heU C L E S 2017ngt hec ompute r ga m e a ndt he.[ 2] .[ 3] 19.20 .or i gi na l pr i c e o f t he20%.058/bok.04/S P / 20

PMT3(b) B or i s i n ve s t s 50 aC a l c ul a t e t het a r a t e ofva l ueoft he2%pe r ye a r s i m pl e i nt e r e s t .i n ve s t m e nta t t hee n d of10 yea rs. .(c) M a r l e n e i nveC a l c ul a t e t hes t s 50 at a r a t e ofva l ueoft he1.9%i n ve s t m e ntpe r ye a r c oma t t hee n d ofpound i10 yeF i nd theva l ueoft a r a t e of x% ep r ey a r c om oundp ia r s , t he av l ue of t he i nve s t m e nti s 6U C L E S 2017.[ 2]a rs.nt e r e s t .38.0, cor r e c t t o t hene a r e s t c e nt .x.x . [ 3]nt e r e s t . .(d) H a ns i n ev s t s 50 aA t t he e dn of01 ye.058/04/S P / 20.[ 3][ T urn over

PMT42(a) 02 sT het udec umnt s e s t i m a t e t he volu a t i ve f r e ueq cn y dil um e , V ma gr a m s owh3, ofa c l a s s r om.s t he i r r e s lu t s .2025020180160140120C mu lu a t i vef r e que cn y10806040200V05010150V ol umU s e t hegr a ph to f i nd a(i) t hem e di a n,303e (m350404505 0)n e s t i m a t e of.(ii) t he(iii) t he(iv) t heh penum60ti nt e r quar t i l e r a ngeU C L E S 2017[ 1],.m3[ 2].m3[ 1]r c e nt i l e ,be r ofs t udent s w hoe s t i m a t e t ha t t hevolume i s gr e a t e r t ha n 30. 3m058/04/S P / 20m3.[ 2]

PMT5(b) T ehT he20s t udet a bl e s how2A r e a ( AmF r e quent s a l s o e s t i m a t e t hes t he i r r e s ul t s .)20 nc y32A 60t ot a l a r e a , A m2, ofA 1060 t hew i ndow10 6480s i n t heA 150c l a s s r om150 24.A 250(i) C a l c lu a t e a n e s t i m a t e fo t he m e a n.Y o u m su t s howa l l yourw or ki g.n.(ii) C o m pl e t e t hehi s t ogra mt o s how t hei nf or m a t i on in t hem2[ 4]t a bl e .2F r e ueq nc y1de ns i t y00105020150A re a (m2250A)[ 4](iii) T w o s t ude nt s a r e c osh e n a t r a ndomt o be m or e t ha n 10m 2.f r omt hosF i n d t he rp bao ib l i t y t ha t oneo f t he t w o s t udea nd t eh ot eh r s t deu tn e s t i m a t e s t he a r e a t o bee s t udent s t ha t e s t i m a t e d t hent s e s t i m a t e s t he150m 2 ro l e s s . .U C L E S 2017058/04/S P / 20a r e a t o bea r e a oft h e w i ndowsgr e a t e r t ha n 150m.[ 3]2[ T urn over

PMT63f ( x) 20x x, x(a) C om0pl e t e t het a bl e .x 10 8 5 2 1.6f ( x) 12 10.5 9 12 14.11.614.258121012[ 2](b) O n t hegr i d, dra w t hegr a ph ofy f ( x)f or x –1.6 a–10y x 10.nd –4–6–8–10–12–14–16–18 [ 5]U C L E S 2017058/04/S P / 20

PMT7(c) U s i ng yourgr a ph, sol vet hee quat i on f( x) 1 1.x .(d) k i s a pr i m e numF i nd theposbe r a nd f( x) k ha s no ss i bl e va l ue s ofol ut i onsorx .[2].k.(e) T hegr a di e ntW r i t e dowoft hen t hegr a ph ofc ordi na t e s of.y f ( x) at the point (2, 12) is 4.t heot he r pointon they f ( x) where the gradient is 4.gr a ph of( .,.(f)(i) T h e e quaS howt i on f( x) x2[ 2]c a nb.)[ 1]x3 px2 q 0.e w r itte na st ha t p 1 and q 20.[ 2](ii) O n t he(iii) U s i ng yourgr i d opsi t e , drgr a phs, s ol vea w t het hegr a ph ofy x2t i onx3 – x2 – 20 e quaf or0.–4 x 4. x .U C L E S 2017058/04/S P / 20[ 2].[ 1][ T urn over

PMT8(iv)yN O T T OS C A L E0T h e id a gr a m s hows a sketch ofP i s t eh oip tn ( n, 0) .W r i t e down t heva l uexPoft hey x3 – x2 – 20.gr a ph ofn. n .U C L E S 2017058/04/S P / 20[ 1]

(a) (i) D r a w t he(ii) D r a w t he (b) D e s c r i beU C L E S 2017r e f l e c t i on ofr ot a t i on off ul l y t het r i a ngt r i a ngll e T i n t hee T a boutl i nesingle t r a ns f or m a t i on t( –2, –1)x 0.[ 2]t hr ough 90 ha t m a pst r i a nglc l oc kwe T onto t r i a nglis e .[ 2]e U.058/04/S P / 20[ 2][ T urn over

PMT105(a)xc mT heT heN O T T OS C A L Epe r i m e t e r fo t he r e c t a ng l e i s 08 c m .a r e a of t he r e c t a ngl e i s A c m 2 .(i) S howt ha tx2 – 40x A 0.[ 3](ii) W he n A 30, sol vet hee quax2 – 40t i onx A 0 by fa c t or i s i ng.x .(iii) W eh n A 20, sS h ow a l l yourx A 0 su i ng tx2 – 40a ns w e r s c or r e c t t o 2 deol ev t he e uaq t i onw or ki ng a dn ig ve your x .U C L E S 2017058/04/S P / 20heorx .[qua rd a t i c f or m ul a .c i m a l pl a c e s .3]orx .[4]

PMT11(b) A c a r c o m lp e t e s a 02kmj our ne y a t a n a ev r a g e s pe e d ofx km / h.T he c a r c mo lp e t e s the return journey of 02mka t a n a ev r a ge s pe e d of(i) S howt ha t t hedi f f e r e nc e2000hours.x (x 10)be t w e e nt hetim et a ke nf ore a c hof( x 10)km/ h.t hetw oj ourne ysis[ 3](ii) F i nd tG i veyourhedi f f e r e cn e be t w e e n t he t i m e t a ke n f ora sn w e r i n minutes a nd seconds.e a c h oft het w o j our .U C L E S 2017058/04/S P / 20ne ysw he n x 80.m in.s [ 3][ T urn over

PMT126MRQTN O T T OS C A L ErOOPQR i s a r e c t a ngl e a nd O i s t he ro i gi n.M i s t he m i d poi nt of RQ a nd PT : TQ 2 :OP p a nd OR r.(a) F i nd, in t e r m s of(i)orr, i n i t s s i m pl e s t f or mMQ .[ 1]MT .[ 1]OT .[ 1]MT ,OT .(b) RQ a ndF i nd tG i vep a nd/1.MQ,(ii)(iii)PpOT a r e e xt e ndeheyourposd a nd me e t a t U.i t i on vec t or fo U i n t e r m s ofa ns w e r i n i t s s i m pl e s t f or m .p a ndr. U C L E S 2017058/04/S P / 20.[ 2]

PMT13(c) MT fF i nd the2 kp a ndkposi t i veMT va l ueof180 .k. k .U C L E S 2017058/04/S P / 20.[ 3][ T urn over

PMT147f ( x) 2 x 1(a) S ol vet h e e quat i on fx) x2 4g(h(x) 2x( x) g( 1) .x .(b) F i nd f[ 2] 1( x) .f(c) F i nd gf.– 1( x) .[ 2]( x) i n i t s s i m pl e s t f or m .(d) S ol vet h e e quat i on h1 2h (x)W r i t e dow( x) 0.5 .U C L E S 2017.[ 1]kxn t heva l ueofk.k . [ 3] 1x .(e).058/04/S P / 20.[ 1]

PMT158T hegr i d s how s t hegr a ph ofy c osx f or x 360 0 y.10.5090 180 360 x270 –0.5–1(a) S lo ev t h e e qua t i on 3cso x 1 f orG i ve oy ru a ns w e r s c or r e c t t o 1 de0 x 360 .c i m a l pl a c e . (b) O n t heU C L E S 2017s a m e gr i d, ske t c h t hegr a ph ofy s i n x f or058/04/S P / 200 x 360 .a nd . [4][ 2][ T urn over

PMT169DC32 70 mNOT TOSCALE40 A55 mBT eh di a gr a m s hows a t r a ep z i umABCD.AB i s pa r a l l e l t o DC.AB 5 m , BD 70 m , a gln e ABD 40 a nd angle BCD 32 .(a) C a l c ul a t e AD.AD . m[ 4]BC . m[ 4] (b) C a l c ul a t e BC.U C L E S 2017058/04/S P / 20

PMT17(c) C a l c ul a t e t hea r e a ofABCD.(d) C a l c ul a t e t hes hort e s t di s t a nc e f r omU C L E S 2017[ 3]A t o BD. 2m058/04/S P / 20m[ 2][ T urn over

PMT1810 (a) S owhf i urg[ T het ha t t hee s.vol umvolume , V, ofe ofa s phea m e t a l s pher e ofr e w i t h r a di usr a di usris V 15c mi s 14140c m3, c or r e c t t o 4 s i gni f i c a nt4 3πr .]3[ 2](b) (i) T h e s phe r e i s pl a c e d i ns i de a n e m pt y c yl i ndrT h e t a nk i s f i l l e d w i t h w a t e r .i c a l t a nk ofr a di us25c ma nd hei ght60c m .2 5 c mN O T T OS C A L E60C a l c ul a t e t hevolume ofc mw a t e r ne e de d t o f i l l t het a nk.(ii) T hes pher e i s r e m oved f r omc m3[ 3]t h e t a nk.N O T T OS C A L EdC a l c ul a t e t hede pt h, d, ofw a t e r i n t het a nk. d .U C L E S 2017058/04/S P / 20c m[ 2]

PMT19(c) T he12di a gr a mbe l ows hows a s ol i d c i r c ul a r c on e a nd as ol i d s phere .N O T T OS C A L Exc mrc m5 xc mT ehT heT heS how[ T eh[ T hec no e ah s r a id us 5 x c m a nd hei g ht 21 x c m .s ph e r e ha s r a di su r c m .c on e ha s t eh s a m e total s ur f a c e a r e a a s t h e s phet h a t r2 re .45 2x.2c u r ve d s ru f a c e a r e a , A, of a c neow i t h r a d i us r a dn s l a nts u r f a c e a r e a , A, fo a s phe r e w i t h r a di su r i s A 4 πr2 ].he i ghtl i s A πrl.] [ 5]U C L E S 2017058/04/S P / 20[ T urn over

PMT2011A c ur ve(a) F i nd tha s e quahet i onc ory x3 – 6di na t e s ofx2 16.t het w o t ur n i ng point s .( . , .)(b) D e t e r m i ne w he t he r e a c h oft he t ur ni ng poiG i ve r e a s onsf or ourya sn w e r s .nt s i s a m a xi m umora nd (a m i ni m um.,.)[ 6].[ 3]Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Everyreasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, thepublisher will be pleased to make amends at the earliest possible opportunity.Cambridge Assessment International Education is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University ofCambridge Local Examinations Syndicate (UCLES), which itself is a department of the University of Cambridge. U C L E S 2017058/04/S P / 20

MATHEMATICS 0580/04 Paper 4 (Extended) For examination from 2020 SPECIMEN PAPER 2 hours 30 minutes You must answer on the question paper. You will need: Geometrical instruments INSTRUCTIONS Answer all questions. Use a black or dark blue