maths specimen paper - nazarbayev university

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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©UCLES 2016 Standard ATS Sample Material

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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2

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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3

[Turn over

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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4

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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5

[Turn over

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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6

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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7

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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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8

15 Thediagramshowsaquadrantofacircle,centreO,radius20cm.

ThechordABhasbeendrawn.

diagram not to scale

Whatfractionofthequadrantisshaded?

A

B

C

D

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9

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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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10

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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11

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20 Acubehasunitlengthsides.Whatisthelengthofalinejoiningavertextothemidpointofoneoftheoppositefaces thedashedlineinthediagrambelow ?


A √2

B

C

D √3

E √5

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12

21 Thediagramshowsthreesimilarright‐angledtriangles.


Whatistheareaofthelargesttriangle?

A cm2

B cm2

C 5cm2

D 15cm2

E cm2

1cm

3cm

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13

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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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14

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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15

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26 Asquarepieceofmetalhasasemi‐circularpiececutoutofitasshown.Theareaoftheremainingmetalis100cm2.


Whichofthefollowingisacorrectexpressionofthelengthofthesideofthesquareincm?

A 10

B 10

C 20

D 20

E 20

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16

27 Twoidenticalcopiesofaright‐angledtriangleareplacedontopofeachothertomakeaquadrilateralABCDasshownbelow.


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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18

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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maths specimen paper - nazarbayev university

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