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w w w
* 4 4 6 4 8 3 0 8 9 1 *
MATHEMATICS (SYLLABUS D) Paper 1
m co s. er ap eP em tr .X
Cambridge International Examinations Cambridge Ordinary Level
4024/12 May/June 2015
2 hours
Candidates answer on the Question Paper. Additional Materials:
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 a 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 in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 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 80.
This document consists of 19 printed pages and 1 blank page. DC (AC/FD) 97054/2 © UCLES 2015
[Turn over
2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1
(a) Evaluate
1.3 + 2.9 . 0.2
Answer............................................. [1]
1 1 (b) Evaluate2 # . 4 5
Answer���������������������������������������������� [1]
2
Writethesenumbersinorderofsize,startingwiththesmallest.
©UCLES2015
13 7 5 0.7 0.64 20 12 8
Answer...............,...............,...............,...............,...............[2] smallest
4024/12/M/J/15
3 3
b
12
4b
Thediagramshowsatrapeziumwithlengthsincentimetres. Theareaofthetrapeziumis120cm2.
Findthevalueofb.
Answerb=...................................... [2]
4
Abagcontainsredcounters,bluecountersandyellowcounters. Thereare60countersinthebag.
Theprobabilitythatacountertakenatrandomfromthebagisredis
2 . 5 5 . Theprobabilitythatacountertakenatrandomfromthebagisblueis 12
Howmanyyellowcountersareinthebag?
Answer��������������������������������������������� [2]
©UCLES2015
4024/12/M/J/15
[Turn over
4 5
FarizatravelsfromLondontoAstana. ThetimeinAstanais5hoursaheadofthetimeinLondon,sowhenitis1000inLondon thelocaltimeinAstanais1500.
ShefliesfromLondontoMoscowandthenfromMoscowtoAstana. TheflightleavesLondonat1225andtakes4hourstoreachMoscow.
1 Farizawaits4 hoursinMoscowfortheflighttoAstana. 2
ShearrivesinAstanaat0525localtime.
HowlongdidtheflightfromMoscowtoAstanatake?
Answer...............hours...............minutes[2] 6
Bywritingeachnumbercorrecttoonesignificantfigure,estimatethevalueof 29.3 2 . 2.04 # 0.874
Answer��������������������������������������������� [2]
©UCLES2015
4024/12/M/J/15
5 7
yisinverselyproportionaltothesquareofx.
Giventhaty=24whenx=2,findywhenx=8.
Answery=..................................... [2]
8
TheVenndiagramshowsthesetsA,BandC. A
B q
p s
t
r u
v C
Listtheelementsof
(a) A∪B,
w
Answer............................................ [1]
(b) B′∩C. Answer............................................ [1]
©UCLES2015
4024/12/M/J/15
[Turn over
6 9
(a) Write0.00000521instandardform. Answer��������������������������������������������� [1]
(b) Givingyouranswerinstandardform,evaluate(6 # 10 7) # (5 # 10 -3) .
Answer��������������������������������������������� [1]
10 Thesetwotrianglesarecongruent. Thelengthsareincentimetres,correcttothenearest0.1cm. q°
5.6
p 62°
3.8
5.6
41°
5.1
Findpandq.
Answerp=...........................................
q=..................................... [2]
©UCLES2015
4024/12/M/J/15
7 11
y 8 7 6 5 4 3 2 1 0
1
2
3
4
5
6
7
8
x
Thediagramshowstheline y = 2x + 1.
ThepointPhascoordinates(a,b)whereaandbarebothpositiveintegers. Thevaluesofaandbsatisfytheinequalitiesa 1 2 ,b 1 7 andb 2 2a + 1.
WritedownallthepossiblecoordinatesofP.
Answer................................................................................................................................................. [2]
©UCLES2015
4024/12/M/J/15
[Turn over
8 12 Omarhasapackofnumbercards. Hepicksthesefivecards. _2
_4
_2
4
1
(a) Writedownthemodeofthefivenumbers. Answer���������������������������������������������� [1]
(b) Hetakesanothercardfromthepack.
(i) Ifthemeanofthesixnumbersis -1 ,whatnumberdidhepick?
Answer���������������������������������������������� [1]
(ii) Ifthedifferencebetweenthehighestandlowestofthesixnumbersis12, whatarethetwopossiblenumbershecouldhavepicked?
Answer�������������������� or....................[1]
13 (a) Express60asaproductofitsprimefactors.
Answer��������������������������������������������� [1]
(b) Findthesmallestpossibleintegermsuchthat60misasquarenumber.
Answerm=.................................... [1]
(c) Thelowestnumberthatisamultipleofboth60andtheintegernis180.
Findthesmallestpossiblevalueofn.
Answern=..................................... [1]
©UCLES2015
4024/12/M/J/15
9 14 IntriangleABC,AB=5cmandAC=6cm. (a) ConstructtriangleABC. LineBCisdrawnforyou.
B
C
[2] (b) Measure BAtC inyourtriangle. Answer�������������������������������������������� [1]
©UCLES2015
4024/12/M/J/15
[Turn over
10 15
c = 8a - 3b
(a) Findcwhena = 3andb = - 4 . Answerc=�������������������������������������� [1]
(b) Rearrangetheformulatomakebthesubject.
Answerb=..................................... [2]
16 (a) Evaluate
(i) 2 0 + 2 3 ,
J1N 2 (ii) K O . L9P
Answer�������������������������������������������� [1]
1
Answer�������������������������������������������� [1]
-2
(b) Simplify ^4x 2h .
Answer�������������������������������������������� [1]
©UCLES2015
4024/12/M/J/15
11 J4 0N O representsthetransformationT. 17 Thematrix K 0 1 L P (a) DescribefullythetransformationT. Youmayusethegridbelowtohelpyouanswerthisquestion.
Answer............................................................................................................................................... ....................................................................................................................................................... [2]
(b) ThetransformationTmapstriangleAontotriangleB. TheareaoftriangleBisxcm2.
Find,intermsofx,theareaoftriangleA.
Answer������������������������������������ cm2[1]
©UCLES2015
4024/12/M/J/15
[Turn over
12 18 (a) Factorisecompletely p 2 q - pq .
Answer�������������������������������������������� [1]
(b) (i) Factorise 5x 2 + x - 4 .
Answer�������������������������������������������� [1]
(ii) Hencesolve 5x 2 + x - 4 = 0 .
Answerx=................ or................[1]
19
(a)
Luisworksinanoffice. Fornormaltimeheispaid$8perhour. Forovertimeheispaidthesamerateasnormaltimeplusanextra50%. Onemonthheworks140hoursnormaltimeand10hoursovertime.
Workouthowmuchheispaidforthatmonth’swork.
Answer$........................................ [2]
(b) Sarainvests$240inanaccountthatpays3%peryearsimpleinterest. Sheleavesthemoneyintheaccountfor5years.
WorkouthowmuchmoneySarahasattheendof5years.
Answer$........................................ [2]
©UCLES2015
4024/12/M/J/15
13 20 Thetimestakenfor200peopletocompletea5kmracewererecorded. Theresultsaresummarisedinthecumulativefrequencydiagram. 200 180 160 140 120
Cumulative frequency 100 80 60 40 20 0 16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
Time (minutes)
(a) Usethediagramtoestimate
(i) themediantime, Answer������������������������������minutes[1]
(ii) theinterquartilerangeofthetimes.
Answer������������������������������minutes[2]
(b) Itwasfoundthattherecordingofthetimeswasinaccurate. Thecorrecttimeswerealloneminutemorethanrecorded.
Writedownthemedianandinterquartilerangeofthecorrecttimes.
AnswerMedian=........................minutesInterquartilerange=........................minutes[1]
©UCLES2015
4024/12/M/J/15
[Turn over
14 J 1 21 (a) Expressasasinglematrix 3 K L-2
3N J 4 O-K 5P L-1
0N O. 2P
Answer [2]
J3 - 2N O A= K L p - 1P ThedeterminantofAis2.
(i) Findp.
(b)
Answerp=..................................... [1]
(ii) FindA–1.
Answer [1]
©UCLES2015
4024/12/M/J/15
15 22 Thescaleofamapis1:25000.
(a) Thescalecanbewrittenas1cm:dkm.
Findd.
Answerd=..................................... [1]
(b) Thedistancebetweentwovillagesis8km.
Findthedistance,incentimetres,betweenthetwovillagesonthemap.
Answer���������������������������������������cm[1]
(c) Thedistancebetweenthepeaksoftwomountainsismeasuredonthemapas76mm.
Calculatethedistance,inkilometres,betweenthetwopeaks.
Answer������������������������������������� km[2]
©UCLES2015
4024/12/M/J/15
[Turn over
16 23 (a) Solvetheinequalities. - 4 G 2x - 5 1 7
Answer�������������������������������������������� [2]
(b) Solvethesimultaneousequations. 3x+4y=3 2x–y=13
Answerx=...........................................
y=..................................... [3]
©UCLES2015
4024/12/M/J/15
17 1 24 [Volume of a cone = rr 2 h , curved surface area of a cone = rrl ] 3 4 [Volume of a sphere = rr 3 , surface area of a sphere = 4rr 2 ] 3
h r
Thesolidisformedfromahemisphereofradiusrcmfixedtoaconeofradiusrcmandheighthcm. Thevolumeofthehemisphereisonethirdofthevolumeofthesolid.
(a) Findhintermsofr.
Answerh=..................................... [2]
(b) Theslantheightoftheconecanbewrittenasr k cm,wherekisaninteger.
Findthevalueofk.
Answerk=..................................... [2]
(c) Findanexpression,intermsofrandπ,forthetotalsurfacearea,incm2,ofthesolid.
Answer������������������������������������ cm2[1]
©UCLES2015
4024/12/M/J/15
[Turn over
18 25
C A a O
b
D
B
1 Inthediagram,AisthemidpointofOCandBisthepointonODwhereOB = OD. 3
OA = a andOB = b .
(a) Express,assimplyaspossible,intermsof aandb
(i) AB, Answer�������������������������������������������� [1]
(ii) CD. Answer............................................ [1]
(b) EisthepointonCDwhereCE:ED=1:2.
(i) Express BE ,assimplyaspossible,intermsofaand/orb.
Answer�������������������������������������������� [2]
(ii) WhatspecialtypeofquadrilateralisABEC? Answer�������������������������������������������� [1]
©UCLES2015
4024/12/M/J/15
19 26 (a) Thefirstfourtermsofasequence,S,are89,83,77,71.
(i) FindanexpressionforSn,thenthtermofthissequence.
AnswerSn=.................................... [2]
(ii) FindthesmallestvalueofnforwhichSn<0.
Answern=...................................... [1]
(b) Thenthtermofadifferentsequence,T,isgivenbyTn = n 2 - 4n .
(i) FindandsimplifyanexpressionforTn + 1 - Tn .
Answer............................................ [2]
(ii) ThedifferencebetweenTp + 1 andTp is75.
Findthevalueofp.
Answerp=..................................... [1]
©UCLES2015
4024/12/M/J/15
20 BLANK PAGE
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.
©UCLES2015
4024/12/M/J/15
* 4 4 6 4 8 3 0 8 9 1 *
MATHEMATICS (SYLLABUS D) Paper 1
m co s. er ap eP em tr .X
Cambridge International Examinations Cambridge Ordinary Level
4024/12 May/June 2015
2 hours
Candidates answer on the Question Paper. Additional Materials:
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 a 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 in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 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 80.
This document consists of 19 printed pages and 1 blank page. DC (AC/FD) 97054/2 © UCLES 2015
[Turn over
2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1
(a) Evaluate
1.3 + 2.9 . 0.2
Answer............................................. [1]
1 1 (b) Evaluate2 # . 4 5
Answer���������������������������������������������� [1]
2
Writethesenumbersinorderofsize,startingwiththesmallest.
©UCLES2015
13 7 5 0.7 0.64 20 12 8
Answer...............,...............,...............,...............,...............[2] smallest
4024/12/M/J/15
3 3
b
12
4b
Thediagramshowsatrapeziumwithlengthsincentimetres. Theareaofthetrapeziumis120cm2.
Findthevalueofb.
Answerb=...................................... [2]
4
Abagcontainsredcounters,bluecountersandyellowcounters. Thereare60countersinthebag.
Theprobabilitythatacountertakenatrandomfromthebagisredis
2 . 5 5 . Theprobabilitythatacountertakenatrandomfromthebagisblueis 12
Howmanyyellowcountersareinthebag?
Answer��������������������������������������������� [2]
©UCLES2015
4024/12/M/J/15
[Turn over
4 5
FarizatravelsfromLondontoAstana. ThetimeinAstanais5hoursaheadofthetimeinLondon,sowhenitis1000inLondon thelocaltimeinAstanais1500.
ShefliesfromLondontoMoscowandthenfromMoscowtoAstana. TheflightleavesLondonat1225andtakes4hourstoreachMoscow.
1 Farizawaits4 hoursinMoscowfortheflighttoAstana. 2
ShearrivesinAstanaat0525localtime.
HowlongdidtheflightfromMoscowtoAstanatake?
Answer...............hours...............minutes[2] 6
Bywritingeachnumbercorrecttoonesignificantfigure,estimatethevalueof 29.3 2 . 2.04 # 0.874
Answer��������������������������������������������� [2]
©UCLES2015
4024/12/M/J/15
5 7
yisinverselyproportionaltothesquareofx.
Giventhaty=24whenx=2,findywhenx=8.
Answery=..................................... [2]
8
TheVenndiagramshowsthesetsA,BandC. A
B q
p s
t
r u
v C
Listtheelementsof
(a) A∪B,
w
Answer............................................ [1]
(b) B′∩C. Answer............................................ [1]
©UCLES2015
4024/12/M/J/15
[Turn over
6 9
(a) Write0.00000521instandardform. Answer��������������������������������������������� [1]
(b) Givingyouranswerinstandardform,evaluate(6 # 10 7) # (5 # 10 -3) .
Answer��������������������������������������������� [1]
10 Thesetwotrianglesarecongruent. Thelengthsareincentimetres,correcttothenearest0.1cm. q°
5.6
p 62°
3.8
5.6
41°
5.1
Findpandq.
Answerp=...........................................
q=..................................... [2]
©UCLES2015
4024/12/M/J/15
7 11
y 8 7 6 5 4 3 2 1 0
1
2
3
4
5
6
7
8
x
Thediagramshowstheline y = 2x + 1.
ThepointPhascoordinates(a,b)whereaandbarebothpositiveintegers. Thevaluesofaandbsatisfytheinequalitiesa 1 2 ,b 1 7 andb 2 2a + 1.
WritedownallthepossiblecoordinatesofP.
Answer................................................................................................................................................. [2]
©UCLES2015
4024/12/M/J/15
[Turn over
8 12 Omarhasapackofnumbercards. Hepicksthesefivecards. _2
_4
_2
4
1
(a) Writedownthemodeofthefivenumbers. Answer���������������������������������������������� [1]
(b) Hetakesanothercardfromthepack.
(i) Ifthemeanofthesixnumbersis -1 ,whatnumberdidhepick?
Answer���������������������������������������������� [1]
(ii) Ifthedifferencebetweenthehighestandlowestofthesixnumbersis12, whatarethetwopossiblenumbershecouldhavepicked?
Answer�������������������� or....................[1]
13 (a) Express60asaproductofitsprimefactors.
Answer��������������������������������������������� [1]
(b) Findthesmallestpossibleintegermsuchthat60misasquarenumber.
Answerm=.................................... [1]
(c) Thelowestnumberthatisamultipleofboth60andtheintegernis180.
Findthesmallestpossiblevalueofn.
Answern=..................................... [1]
©UCLES2015
4024/12/M/J/15
9 14 IntriangleABC,AB=5cmandAC=6cm. (a) ConstructtriangleABC. LineBCisdrawnforyou.
B
C
[2] (b) Measure BAtC inyourtriangle. Answer�������������������������������������������� [1]
©UCLES2015
4024/12/M/J/15
[Turn over
10 15
c = 8a - 3b
(a) Findcwhena = 3andb = - 4 . Answerc=�������������������������������������� [1]
(b) Rearrangetheformulatomakebthesubject.
Answerb=..................................... [2]
16 (a) Evaluate
(i) 2 0 + 2 3 ,
J1N 2 (ii) K O . L9P
Answer�������������������������������������������� [1]
1
Answer�������������������������������������������� [1]
-2
(b) Simplify ^4x 2h .
Answer�������������������������������������������� [1]
©UCLES2015
4024/12/M/J/15
11 J4 0N O representsthetransformationT. 17 Thematrix K 0 1 L P (a) DescribefullythetransformationT. Youmayusethegridbelowtohelpyouanswerthisquestion.
Answer............................................................................................................................................... ....................................................................................................................................................... [2]
(b) ThetransformationTmapstriangleAontotriangleB. TheareaoftriangleBisxcm2.
Find,intermsofx,theareaoftriangleA.
Answer������������������������������������ cm2[1]
©UCLES2015
4024/12/M/J/15
[Turn over
12 18 (a) Factorisecompletely p 2 q - pq .
Answer�������������������������������������������� [1]
(b) (i) Factorise 5x 2 + x - 4 .
Answer�������������������������������������������� [1]
(ii) Hencesolve 5x 2 + x - 4 = 0 .
Answerx=................ or................[1]
19
(a)
Luisworksinanoffice. Fornormaltimeheispaid$8perhour. Forovertimeheispaidthesamerateasnormaltimeplusanextra50%. Onemonthheworks140hoursnormaltimeand10hoursovertime.
Workouthowmuchheispaidforthatmonth’swork.
Answer$........................................ [2]
(b) Sarainvests$240inanaccountthatpays3%peryearsimpleinterest. Sheleavesthemoneyintheaccountfor5years.
WorkouthowmuchmoneySarahasattheendof5years.
Answer$........................................ [2]
©UCLES2015
4024/12/M/J/15
13 20 Thetimestakenfor200peopletocompletea5kmracewererecorded. Theresultsaresummarisedinthecumulativefrequencydiagram. 200 180 160 140 120
Cumulative frequency 100 80 60 40 20 0 16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
Time (minutes)
(a) Usethediagramtoestimate
(i) themediantime, Answer������������������������������minutes[1]
(ii) theinterquartilerangeofthetimes.
Answer������������������������������minutes[2]
(b) Itwasfoundthattherecordingofthetimeswasinaccurate. Thecorrecttimeswerealloneminutemorethanrecorded.
Writedownthemedianandinterquartilerangeofthecorrecttimes.
AnswerMedian=........................minutesInterquartilerange=........................minutes[1]
©UCLES2015
4024/12/M/J/15
[Turn over
14 J 1 21 (a) Expressasasinglematrix 3 K L-2
3N J 4 O-K 5P L-1
0N O. 2P
Answer [2]
J3 - 2N O A= K L p - 1P ThedeterminantofAis2.
(i) Findp.
(b)
Answerp=..................................... [1]
(ii) FindA–1.
Answer [1]
©UCLES2015
4024/12/M/J/15
15 22 Thescaleofamapis1:25000.
(a) Thescalecanbewrittenas1cm:dkm.
Findd.
Answerd=..................................... [1]
(b) Thedistancebetweentwovillagesis8km.
Findthedistance,incentimetres,betweenthetwovillagesonthemap.
Answer���������������������������������������cm[1]
(c) Thedistancebetweenthepeaksoftwomountainsismeasuredonthemapas76mm.
Calculatethedistance,inkilometres,betweenthetwopeaks.
Answer������������������������������������� km[2]
©UCLES2015
4024/12/M/J/15
[Turn over
16 23 (a) Solvetheinequalities. - 4 G 2x - 5 1 7
Answer�������������������������������������������� [2]
(b) Solvethesimultaneousequations. 3x+4y=3 2x–y=13
Answerx=...........................................
y=..................................... [3]
©UCLES2015
4024/12/M/J/15
17 1 24 [Volume of a cone = rr 2 h , curved surface area of a cone = rrl ] 3 4 [Volume of a sphere = rr 3 , surface area of a sphere = 4rr 2 ] 3
h r
Thesolidisformedfromahemisphereofradiusrcmfixedtoaconeofradiusrcmandheighthcm. Thevolumeofthehemisphereisonethirdofthevolumeofthesolid.
(a) Findhintermsofr.
Answerh=..................................... [2]
(b) Theslantheightoftheconecanbewrittenasr k cm,wherekisaninteger.
Findthevalueofk.
Answerk=..................................... [2]
(c) Findanexpression,intermsofrandπ,forthetotalsurfacearea,incm2,ofthesolid.
Answer������������������������������������ cm2[1]
©UCLES2015
4024/12/M/J/15
[Turn over
18 25
C A a O
b
D
B
1 Inthediagram,AisthemidpointofOCandBisthepointonODwhereOB = OD. 3
OA = a andOB = b .
(a) Express,assimplyaspossible,intermsof aandb
(i) AB, Answer�������������������������������������������� [1]
(ii) CD. Answer............................................ [1]
(b) EisthepointonCDwhereCE:ED=1:2.
(i) Express BE ,assimplyaspossible,intermsofaand/orb.
Answer�������������������������������������������� [2]
(ii) WhatspecialtypeofquadrilateralisABEC? Answer�������������������������������������������� [1]
©UCLES2015
4024/12/M/J/15
19 26 (a) Thefirstfourtermsofasequence,S,are89,83,77,71.
(i) FindanexpressionforSn,thenthtermofthissequence.
AnswerSn=.................................... [2]
(ii) FindthesmallestvalueofnforwhichSn<0.
Answern=...................................... [1]
(b) Thenthtermofadifferentsequence,T,isgivenbyTn = n 2 - 4n .
(i) FindandsimplifyanexpressionforTn + 1 - Tn .
Answer............................................ [2]
(ii) ThedifferencebetweenTp + 1 andTp is75.
Findthevalueofp.
Answerp=..................................... [1]
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