Download Test of Mathematics for University Admission Specimen Paper 2

TEST OF MATHEMATICS
FOR UNIVERSITY ADMISSION
SPECIMEN
60 minutes
PAPER 2
INSTRUCTIONS TO CANDIDATES
Please read these instructions 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 paper. Please check you have one.
You also require a soft pencil and an eraser.
This paper is the second of two papers. There are 20 questions on this paper.
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.
There are no penalties for incorrect responses, only points for correct answers, so
you should attempt all 20 questions. Each question is worth one mark.
Any rough work should be done on this question paper. No extra paper is allowed.
Please complete the answer sheet with your candidate number, centre number, date
of birth, and full name.
Calculators must NOT be used. There is no formulae booklet for this test.
Please wait to be told you may begin before turning this page.
This question paper consists of 15 printed pages and 5 blank pages.
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BLANK PAGE
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1. Theradiusofthecircle2
2
8
A
12
15
0is
B
C
D
√37
E
√67
2.
Thegradientofthecurve
A
atthepointwhere
√
2is
√2
B
3√2
C
4√2
D
√2
E
6√2
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4
Considerthefollowingattempttosolveanequation.Thestepshavebeennumberedfor
reference.
3.
x+5 = x+3
(1)
2
x + 5 = x + 6x + 9
2
(2)
x + 5x + 4 = 0
(3)
( x + 4) ( x + 1) = 0
x = −4 or x = −1
Whichoneofthefollowingstatementsistrue?
A Both 4and 1aresolutionsoftheequation.
B Neither 4nor 1aresolutionsoftheequation.
C
Onesolutioniscorrectandtheincorrectsolutionarisesasaresultofstep 1 .
D Onesolutioniscorrectandtheincorrectsolutionarisesasaresultofstep 2 .
E Onesolutioniscorrectandtheincorrectsolutionarisesasaresultofstep 3 .
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4.
Asetoffivecardseachhavealetterprintedontheirfrontandanumberprinted
ontheirback,asfollows:
Whichoneofthefivecards A,B,C,DorE providesacounterexampletothe
followingstatement?
Everycardthathasavowelonitsfronthasanevennumberonitsback.
5.
Usingtheobservationthat2
approximately
A
B
C
D
E
F
2
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3 ,itispossibletodeducethatlog 2is
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6.
Theareaofarectangleismeasuredtobe5600cm correctto2significant
figures.
Thewidthoftherectangleismeasuredtobe80cmcorrecttothenearest
centimetre.
Whichoneofthefollowingexpressionsgivesthegreatestpossibleheightofthe
rectangle?
A
70.5cm
B
75cm
C
D
E
F
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cm
.
cm
cm
.
cm
7
7.Whichoneofthefollowingisasketchofthegraph
1?
4
4
3
3
2
2
1
1
0
0
–4 –3 –2 –1
0
–4 –3 –2 –1
0 1 2 3 4 5 6
–1
–1
–2
–2
–3
–3
–4
–4
A
B
4
4
3
3
2
2
1
1
0
0
–4 –3 –2 –1
0
0 1 2 3 4 5 6
–4 –3 –2 –1
–1
–1
–2
–2
–3
–3
–4
–4
D
C
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1
2
3
4
5
6
2
3
4
5
6
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8.
Considerthefollowingstatementaboutthepositiveinteger :
Statement * :Thesumofthefourconsecutiveintegers,thesmallestofwhichis ,
isamultipleof6.
Whichoneofthefollowingistrue?
A
B
C
D
E
Statement * istrueforallvaluesof .
Statement * istrueforallvaluesof whichareodd,butnotforany
othervaluesof .
Statement * istrueforallvaluesof whicharemultiplesof3,butnot
foranyothervaluesof .
Statement * istrueforallvaluesof whicharemultiplesof6,butnot
foranyothervaluesof .
Statement * isnottrueforanyvalueof .
9.
ConsiderthestatementaboutFred:
* Everydaynextweek,Fredwilldoatleastonemathsproblem.
Ifstatement * isnottrue,whichofthefollowingiscertainlytrue?
A
Everydaynextweek,Fredwilldomorethanonemathsproblem.
B
Somedaynextweek,Fredwilldomorethanonemathsproblem.
C
OnnodaynextweekwillFreddomorethanonemathsproblem.
D
Everydaynextweek,Fredwilldonomathsproblems.
E
Somedaynextweek,Fredwilldonomathsproblems.
F
OnnodaynextweekwillFreddonomathsproblems.
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10.
Whichoneofthefollowingisasketchofthegraphof
4
–1
1
0
–1
–2
0 1
2
3 4
5
6
7
8
9 10
–2
5
6
7
8
9 10
01
2
3 4
5
6
7
8
9 10
0 1 2
3 4
5
6
7
8
9 10
–3
–4
3
2
1
0
0 1
2
3 4
5
6 7
8
9 10
–1
–2
–3
–3
–4
C
D
3
5
4
2
1
0
3
2
–1
3 4
4
3
1
0
2
B
5
4
–1
–2
0 1
–5
A
2
1
0
1?
3
2
5
3
2
1
0
log 2for
–1
01
2
3 4
5
6 7
8
9 10
–2
–3
–2
–4
–3
–5
E
F
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10
11.
A
tan
B
log
100
C
sin
D
log 10
E
12.
Whichoneofthefollowingnumbersislargestinvalue?
Allanglesaregiveninradians. √2
Apolynomial
1
hasthepropertythat 1
2.
Whichoneofthefollowingcanbededucedfromthis?
A
1
2forsomepolynomial
.
B
1
2forsomepolynomial
.
C
1
2forsomepolynomial
.
D
1
2forsomepolynomial
.
E
2
1forsomepolynomial
.
F
2
1forsomepolynomial
.
G
2
1forsomepolynomial
.
H
2
1forsomepolynomial
.
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13.
Fiverunnerscompetedinarace:Fred,George,Hermione,Lavender,andRon.
FredbeatGeorge.
HermionebeatLavender.
LavenderbeatGeorge.
RonbeatGeorge.
Assumingtherewerenoties,howmanypossiblefinishingorderscouldthere
havebeen,givenonlythisinformation?
A
1
B
6
C
12
D
18
E
24
F
120
14.
Thegraphofthepolynomialfunction
,
issketched,where , , , , ,and arerealconstantswith
0.
Whichoneofthefollowingisnotpossible?
A
Thegraphhastwolocalminimaandtwolocalmaxima.
B
Thegraphhasonelocalminimumandtwolocalmaxima.
C
Thegraphhasonelocalminimumandonelocalmaximum.
D
Thegraphhasnolocalminimaorlocalmaxima.
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15.
Foranyrealnumbers , ,and where
1
2
3
,considerthesethreestatements:
2
Whichofthestatements1,2,and3mustbetrue?
A
none
B
1only
C
2only
D
3only
E
1and2only
F
1and3only
G
2and3only
H
1,2and3
16.
Thesequence
isgivenbytherule:
2
1 for
Whatis
A
150
B
250
C
D
5150
E
4 1
F
4
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17.
Let beasetofpositiveintegers,forexample couldconsistof3,4,and8.
Apositiveinteger iscalledan ‐numberifandonlyifforeveryfactor of with
1,thenumber isamultipleofsomenumberin .
Sointheaboveexample,9isan ‐number;thisisbecausethefactorsof9greater
than1are3and9,andeachoftheseisamultipleof3.
Positiveinteger isthereforenotan ‐numberifandonlyif
A
forevery positive factor of with
1,
thereisanumberin whichisnotafactorof .
B
forevery positive factor of withm 1,
thereisnonumberin whichisafactorof .
C
forevery positive factor of with
1,
everynumberin isafactorof .
D
forsome positive factor of with
1,
thereisanumberin whichisnotafactorof .
E
forsome positive factor of with
1,
thereisnonumberin whichisafactorof .
F
forsome positive factor of with
1,
everynumberin isafactorof .
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18.
Agroupoffivenumbersaresuchthat:

theirmeanis0

theirrangeis20
Whatisthelargestpossiblemedianofthefivenumbers?
A
0
B
4
C
4 D
6 E
8
F
20
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19.
Thepositiverealnumbers , ,and aresuchthattheequation
hasthreerealroots,onepositiveandtwonegative.
Whichoneofthefollowingcorrectlydescribestherealrootsoftheequation
?
A
Ithasthreerealroots,onepositiveandtwonegative.
B
Ithasthreerealroots,twopositiveandonenegative.
C
Ithasthreerealroots,buttheirsignsdifferdependingon , ,and .
D
Ithasexactlyonerealroot,whichispositive.
E
Ithasexactlyonerealroot,whichisnegative.
F
Ithasexactlyonerealroot,whosesigndiffersdependingon , ,and .
G
Thenumberofrealrootscanbeoneorthree,butthenumberofroots
differsdependingon , ,and .
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20.
Fivelogicianseachmakeastatement,asfollows:
MrP: Ofthesefivestatements,anoddnumberaretrue.
MsQ: Bothstatementsmadebywomenaretrue.
MrR: MyfirstnameisRobertandMrP’sstatementistrue.
MsS: Exactlyonestatementmadebyamanistrue.
MrT: Neitherstatementmadebyawomanistrue.
Howmanyofthefivestatementscanbesimultaneouslytrue?
A
none
B
1only
C
2only
D
3only
E
4only
F
noneor1only
G
1or2only
H
2or3only
END OF TEST
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