maths specimen paper - nazarbayev university
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Foundation Year Programme
Entrance Tests
MATHEMATICS
SPECIMEN PAPER
for
NUFYP SET 2017
V1.0 October 2016
Mathematics
SPECIMEN for NUFYP SET 2017 60 minutes
Instructions to Candidates
Please read this page carefully, but do not open the question paper until you are told that you may do so.
A separate answer sheet is provided for this section. Please check you have one.
You require a soft pencil and an eraser.
Please check that the title of the paper you are taking matches the title on the answer sheet.
Please complete the top section of the answer sheet in soft pencil with your personal details.
There are 30 questions in this paper. Each question is worth one mark. There are no penalties for incorrect responses, only marks for correct answers, so you should attempt all 30 questions.
Answer in soft pencil on the answer sheet provided. For each question, choose the one answer you consider correct and record your choice on the separate answer sheet. If you make a mistake, erase thoroughly and try again.
Speed as well as accuracy is important in this paper. Work quickly, or you might not finish the paper.
Any rough work should be done on this question paper.
Calculators are NOT permitted.
Please wait to be told you may begin before turning this page.
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1 Thesymboldefinesamathematicalbinaryoperationsuchthat forall
positiveintegers.
Whatisthevalueof 23 2?
A 2 3
B
C
D 4
E √
2 Solvetheinequality:
8 2
A 4
B 2and 4
C 2and 4
D 2and 4
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3 Thesumofthetwovaluesof thatsatisfythesimultaneousequations 3 1 0and3 7 5is
A 8.5
B 7.5
C 1.5
D 3.5
E 4.5
F 5
4 Thealgebraicfraction isequalto5 21
Whichoneofthefollowingisequivalentto intermsof ?
A
B
C
D
E
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5 Usingtheformula:
calculatethevalueof when:
1.2 10
3.0 10
A 2 10
B 4 10
C 2 10
D 4 10
6 Evaluate1
43
051
81
932
A
B
C 9
D
E
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7 Given
2
Rearrangetheformulatomake thesubject.
A
B
C 2
D
8 Thesumoftherootsofaquadraticequationis7,theproductoftherootsis9.
Whatistheequation?
A x 7 9 0
B x 7 9 0
C x 7 9 0
D x 7 9 0
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9 Therootsoftheequation2 11 0differby2.
Thevalueof is
A
B
C
D
10 Thelongestsideofaright‐angledtriangleis6 √5units.
Oneoftheshortersidesis3 2√5units.
Whatisthelengthofthethirdside?
A 2√3
B 70 24√5
C 12
D 3 √5
E 14 7.5√5
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11 Giventhat isasolutiontothesimultaneousequations:
4 10 47
2 5
Whatisthevalueof when 0?
A 4
B 1
C 0
D 1
E 3
F 7
G 8
12 Fiverunnerscompetedinarace:Fred,George,Hermione,Lavender,andRon. FredbeatGeorge.
HermionebeatLavender.
LavenderbeatGeorge.
RonbeatGeorge.
Assumingtherewerenoties,howmanypossiblefinishingorderscouldtherehavebeen,givenonlythisinformation?
A 1
B 6
C 12
D 18
E 24
F 120
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13 Simplify:
4
A 2
B 2
C 4
D 4
E 6
F 6
14 Whichoftheexpressionsbelowhasthelargestvaluefor0 1?
A
B
C
D√
E √
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15 Thediagramshowsaquadrantofacircle,centreO,radius20cm.
ThechordABhasbeendrawn.
diagram not to scale
Whatfractionofthequadrantisshaded?
A
B
C
D
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16 Whatistheequationofthestraightlinepassingthrough 4,1 whichisparalleltothelinegivenbytheequation3 2 12?
A 3 14 2
B 2 11 3
C 2 14 3
D 3 2 5
E 2 3 10
17 Foranyrealnumbers , ,and where ,considerthesethreestatements:
1.
2. 2
3.
Whichofthesestatementsmustbetrue?
A Allthreestatements
B Onlystatements1and2
C Onlystatements2and3
D Onlystatements1and3
E Onlystatement1
F Onlystatement2
G Onlystatement3
H Noneofthestatements
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18 Thecross‐sectionofatriangularprismisanequilateraltrianglewithside2 cm. Thelengthoftheprismis cm.
LetthetotalsurfaceareaoftheprismbeTcm2.GiventhatthevolumeoftheprismisTcm3,whichoneofthefollowingisanexpressionfor intermsof ?
A
B√
C√
D√
E√
19 AshapeisformedbydrawingatriangleABCinsidethetriangleADE.
BCisparalleltoDE.
AB 4cmBC cmDE 3 cmDB – 4 cm
CalculatethelengthofDE.A 5cmB 7cmC 9cmD 4 2√7cmE 7 2√7cm
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20 Acubehasunitlengthsides.Whatisthelengthofalinejoiningavertextothemidpointofoneoftheoppositefaces thedashedlineinthediagrambelow ?
diagram not to scale
A √2
B
C
D √3
E √5
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21 Thediagramshowsthreesimilarright‐angledtriangles.
diagram not to scale
Whatistheareaofthelargesttriangle?
A cm2
B cm2
C 5cm2
D 15cm2
E cm2
1cm
3cm
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22 The termofasequenceis
Whatisanexpressionforthedifferencebetweenthe 1 termandthe term?
A
B
C
D
E
23 Giventhat and arenon‐zerointegers,theexpression
isanintegerif
A 0
B 0
C 0and 0
D 0and 0
E 0and 0
F 0and 0
G 0
H 0
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24 Forwhatvaluesofthenon‐zerorealnumber doesthequadraticequation2 2haverealdistinctroots?
A Allvaluesof
B 2
C 2
D 2
25 Acirclehasadiameterof20cm.
ThelineACisadiameterofthecircle.
BisapointonthecircumferenceofthecirclewithAB 12cm.
ThepointDliesonthearcAContheoppositesidetopointB.
Whatisthesineof∠BDC?
A 0.6
B
C 0.8
D √
E√
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26 Asquarepieceofmetalhasasemi‐circularpiececutoutofitasshown.Theareaoftheremainingmetalis100cm2.
diagram not to scale
Whichofthefollowingisacorrectexpressionofthelengthofthesideofthesquareincm?
A 10
B 10
C 20
D 20
E 20
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27 Twoidenticalcopiesofaright‐angledtriangleareplacedontopofeachothertomakeaquadrilateralABCDasshownbelow.
diagram not to scale
Theperpendicularsidesofthetrianglesareintheratio1: 3
Whatfractionoftheareaofthequadrilateraliscoveredbybothtriangles?
A
B
C
D
E
F
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28 Giventhat 0and1 3and2 11
Whatistherangeofpossiblevaluesof ?
A 0
B 2
C 0 2
D 0 10
E 2 10
29 Theweightofananimalincreasesby50%eachyearfor3years.Itthendeclinesinweightby20%ayearfor2yearsandthendeclinesbyafurther25%inthenextyear.
Whatisthepercentageincreaseintheanimal’sweightattheendof6yearscomparedtoitsoriginalweightatthestartofthisperiod?A 5%B 20%
C 62%
D 85%
E 115%
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30 Ifyoulookataclockandthetimeis9.45,whatistheanglebetweenthehourandtheminutehands?
A 0°
B 7.5°
C 15°
D 22.5°
E 30°
END OF TEST
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BLANK PAGE
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