Cambridge International Examinations Cambridge Ordinary Level

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  ...
Author: Alisha Thornton
2 downloads 1 Views 1009KB Size
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 © 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) I fthedifferencebetweenthehighestandlowestofthesixnumbersis12,  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

Suggest Documents