Download 4024 June 2015 Question Paper 12

Cambridge International Examinations
Cambridge Ordinary Level
* 4 4 6 4 8 3 0 8 9 1 *
MATHEMATICS (SYLLABUS D)
4024/12
May/June 2015
Paper 1
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
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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.
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7
5
0.7 0.64
20
12
8
Answer...............,...............,...............,...............,...............[2]
smallest
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3
3
b
12
4b
Thediagramshowsatrapeziumwithlengthsincentimetres.
Theareaofthetrapeziumis120cm2.
Findthevalueofb.
Answerb=...................................... [2]
4
Abagcontainsredcounters,bluecountersandyellowcounters.
Thereare60countersinthebag.
Theprobabilitythatacountertakenatrandomfromthebagisredis
2
.
5
5
.
Theprobabilitythatacountertakenatrandomfromthebagisblueis
12 Howmanyyellowcountersareinthebag?
Answer��������������������������������������������� [2]
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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]
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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]
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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]
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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]
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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]
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14 IntriangleABC,AB=5cmandAC=6cm.
(a) ConstructtriangleABC.
LineBCisdrawnforyou.
B
C
[2]
(b) Measure B AtC inyourtriangle.
Answer�������������������������������������������� [1]
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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]
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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]
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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]
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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]
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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]
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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]
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23 (a) Solvetheinequalities.
- 4 G 2x - 5 1 7
Answer�������������������������������������������� [2]
(b) Solvethesimultaneousequations.
3x+4y=3
2x–y=13
Answerx=...........................................
y=..................................... [3]
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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]
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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]
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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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