MI
o/5/MATSD
I SP1 /
tf4 nA
ENG
lnternational Baccalaureaten
Bacca lauréat lnternationa I
BachiIlerato I nternacionaI
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22107403
MATHEMATICAL STUDIES
STANDARD LEVEL
PAPER
1
Wednesday 5 Mdy 2oí ti (afternoon)
t hour
Candidate session number
30 mínutes
INSTRUCTIONS TO CANDIDATES
.
.
.
.
.
Write your session number in the boxes above.
Do not open this examlnatíon paper until instructed to do so.
A graphÍc display calculator is required for this paper.
Answer all the questÍons in the spaces provided.
Unless otherwise stated in the question, all numerical answers must be glven exactly or correct
to three significant figures.
17 pages
2210-7403
ilililililililll
01 17
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I
nternational Baccalaureate Organizatlon
201 0
_2_
Mmimtn
I
mar,þs:llrilt.be
givenþr conzclonswerc.
an answeris
rworking. WorHng
Wherc
A slripping container is a cr$oid wirh,dimensions
(a)
:calculat€
_/
Mlois/tfArSD/SplÆNG tTZtlW
16
* rÍ n
the exact volurne ofthe container. Give
Jim $timator ¡[6 rtirnensions of the container as 15
estänatc the voh¡me of the container. '
yo'r
and
bøgiven
theþox,
suitable working,
rl^.
¡¡nswer as a
frçrioa
m,2 mand 3 m ond r¡sos th"ç,s., to
(b) Calculate the percentage e,tror in Jim's estimated volume of. ùo.so¡tainer. , , i
Wordng:
a) r==,rårrW!ry
I
ù
+
t00)
= Åo,f
Answen:
(a)
(b)
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[s nar,lal
4
,u3
40,5?o
[j.narfuJ
-32.
M I O/5/T4ATSD/SP I ÆNG ITZI
|)cl,
The sets P, Q aad Ua¡e defined as
y
= {Real Numbers}, p={PositiveNumbers} and Q={Rational Numbers}.
o
q
ì
-a
5x lo
.ìl
tí
-,
Write down in the correct region on the Ve,nn diagram the nr¡mbers
aa
+,
7
5xlo-2, sin(60'), o, ۋ',
-rc.
[6naru
Working:
2210-7403
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til
Turn over
-43.
I O/s/T\,f AT
SD/SP{ ÆNGÆZ
I
/)O(
p údq.
Considerbvo propositions
(a)
M
Complete the trr¡th table below.
p
q
T
T
T
F
F
T
F
F
[4 narlcsJ
I'
-r
f
r
F
I
P+-ll
-rp
-tPÐq
F
F
-T
I
T
1
F
r
a
-r
-t
f-
(b) Decide whether the com¡lound proposition
(p+-q)e(-,p+
q)
is a tautology. Staæ the reason for your decision.
VorHng:
[2 narksJ
( r=r-6)êÉ'f )ß)
Ç
f
f
F
Answer:
(b)
T
il
-?
o
2210-7403
-54.
M I O/5/}{ATSD/SP
I
ÆNGÆZ I DO(
The stem and leaf diagram below shows tbe lengtbs of 2?melal compoaents in cm.
Leaf
Stem
I
2
Key: ll2mþaos
l.2cm
3
4
5
6
'
0,t
'r
.1r
ti'
' rl''-É'
(a)
Wríteilownthemodallengthofthemstalicompoú€Nrts.
(b)
Find the median length ofthe metal components.
[2 narksJ
(c)
Calculate the interquartile range of the lenglhs of the meøl compononts.
þnarksJ
'"j' '"'
'l
tlturtcl
l|brking:
b) 3,ln +
c)
4.
1
3,bl
l-2,,+ = l,'/
Answers
(a)
o)
(c)
2210-7403
4,r,il c
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Turn over
-65.
The volume of a sphere is V
=rÆ
Ml0/5IMA*XSD/SPIÆNGÆZl/)ü
, where ,S is its suffase a¡ea.
The surface a¡ea of a sphere is 500 cm2.
(a)
(b)
Calculate the volume of tho sphere. Give your a$¡\4'er corect to two decimal,
places.
'Wriùe
neZ
p markJ
dovm your answer to (a) conect to the nea¡est integer.
(o) Write down your aruwer to (b) b Qe-form ¿xlg"r
[3 nartuJ
wüere ,lS,ø,<10 rod,,
[2 marlcsJ
.
Working:
o.,l v
<oo?
3bTf
= )o{1,305--zl3
Answers
(a)
(b)
(c)
2210-7403
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t,otl x /Òt
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¡
-76.
MIOis/lvfAISD/SPIÆNGn
lß.
(l)
A fitness club has 60 members. 35 of the mer¡bers attend the club's aerobics course
and28 members attend the club's yoga cor¡rse (y). 17 members aftend both corûses.
AVenn diagram is used to illustrate this situation.
YzY
A
(a)
fl marhJ
lVrite down the value of g.
(b) Find the value ofp.
(c)
Calculate the number of members of the fitress club who aüond neithor the
aerobics course
(d)
[2 narksJ
(l)
nor the yoga course
Shade, on yor¡r Venn diagram, A'
ñY
(I).
[2 narksJ
[l
.
mark]
Working:
Answers:
(a)
2210-7403
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07 17
l1
(b)
t3
(c)
t4
Turn over
-87
The diagram
.shows a hiangle ABC in which A c
Triangle ABM is equilateral.
M I O/5/T\{ATSD/SP I ÆNG
-
17
rr^ DU
cm. M is the midpoint df AC.
ts
díøgram not to scøle
$
g,<
(a)
O)
11o"*
S/¡ite dorw
(Ð
the length
(iÐ
the size ef angle BMC;
(üÐ
the size of angle MCB.
ofBM in cm;
[3 marksJ
Calculat€,the.lengù ofBC incm.
[3 marløJ
Working:
a)
¿\
ò¿)
t-li ¡
r)
Eu =g'l
t ïoo- loo" = | 20,
Tsosoùs I ta¿o _l1r:îr
- X=7O Ansvters:
(a)
,l r-w¡
/zoo
(Ð
(iÐ
(üi)
(b)
2210-7403
300
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--
lt'1
-98.
M I 0/5 /I4Ar SD/SP I ÆNGÆZ l /)O(
Maria travels to school either by walking or by bicycle. The probability she cycles to
school is 0.75.
If she walks, the probability that she is late for school is 0.1.
If she cycles, the probability that she is læe for school is 0-05.
(a)
Complete the tree diagram below, showing the appropriate
Dj
probabilities.
[3 narksJ
Late
rüalk
a
qrq
,þf
Not late
Late
0J5
Not l¿te
(b)
[j
Find the probability that Maria is late for school.
marksJ
Working
?Ct^lò -- ¿ af)c'
ù
+ (¡àf'os)
Answers:
(b) ôb45 6ß lo,0,l7o
'
22tO-7403
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Turn over
-109.
M I O/5/}4ATSD/SP I ÆNG
NZI
IW
120 Mathematics students in.a school sat an exarnination. Their scores (given as a
percentage) \r/ere surnmarized on a cumulative frequency diagram. This diagrirm is
given bel
I
ll
90
80
C)
)
c)
70
I
Er
o
d
)É
-(-)
50
3
20
I
I
20
30
0
80
100
Examination Score
(This Eteslion conlinues on theþllowing page)
22tO-7403
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1017
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M I O/5/T\4AT SD/
SP I
ÆNGÆZ
I
/)ü
(Question 9 continued)
(a)
Complete the grouped frequency table for the students.
Examination
Score x (%o)
0<x320
20<x<40
'40<xS60
l4
26
fl
Frequency
O)
'Write
[3 narksJ
¡ 180
60<
,
llo
80 <
it
¡ Sl00
("
p'narkJ
down the mid-interval value of the 40 < x 160 inten¡al.'
,!
(c)
Calculaþ an estimate of the mean oramination score of the students.
[2 narksJ
Working:
4) 1z-+o =Sg
llr)'qg -- t(o
'("
/ Ao -l t4 --
b) to
.)ú
rù
3 oI.rò
ro/r+\
t?O
,/
t'7
6
Answers:
(b)
(c)
2210-7403
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1117
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ã
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Turn over
- J210.
M l 0/5/T\{Ar SD/SP,I ÆNc
nzt txx
o:ut a ,¿2 test to determine whether or not a person,s choice
of one of the three professions; engineering medicine or law.is influenced by the
Tony wants to carry
person's sex (gender).
(a)
Staæ the
(b)
Wriùe do$,n the number of degrees ofûeedom.
of
nullbypotþrsis,Ho, fsr this t€st.
the 400 people Tony inten:rriewed,22a wöre.màle and l'g0 wetr,"fèüald¡,i,
80 ofthe people had chosen engineering as a profession.
(c)
a
'
,.
I
Calculate the oçected nr¡mber of female engineers.
[2martuJ
Tony rued a 5 % level of significance fo¡ his test and obtained
correct to 3 sigûdficaûtfigures.
(d)
apvalue of 0.0634
State Tony's conclusion to the test. Give a reason for this conolusion.
[2matrsJ
WorHng:
Y--ò
B)
c-)
2
Ç
l'ln
Gu{ lßo >7Ç
,loo
v
q0ò
r8a
z2Ð
Answers:
(a)
o)
(c)
2
v
,o
(d)
2210-7403
1217
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-13-
M I O/5/I4AISD/SP I ÆNG
NA
IW
11. The diagram below shows the graph of the functions:
f
(x) = p cos(qx), where p,q e Q. and
g(Ì)
= sin(¡)
-I
v
2
I
(in degrees)
-1
--2
(a)
'Write
(b)
Write down the value
(c)
Calculate the value of 4.
(d)
down the period of
f
[I mark]
(x)
fl
ofp.
markJ
[2 marlæJ
Use your graphic display calculator to find any solutions
l@)= g(x) in the interval 180" <¡ < 360".
to the
equation
[2 marksJ
Worlcing:
¿)
T=
'ffi
Answers
(a)
(b)
(c)
(d)
2210-7403
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1317
2,+D
o
l.'l'
/,f
74rlu
Turn over
-t412'
Ml'0/5/ÀÁarsD/sP I ÆNc tflZt
tw
Susi havels from Singapore to Thailand and changes 1500
Singapore dollms (SGD)
to Thai baht (THB). The excharge rare is l sGD uu¡ zt.or+64
THB.
(a)
Calculate the number of Thai baht Susi buys. Give your ans\r/er
correct to the
neare¡t baht.
[2 ngrksJ
Susi leaves Thailand áùd bavels to Indonesia She has 20
000 TIIB and uses theòe to
buy Indonesim nrpiah (ÞR). The exohange rate is 3.2ggs2THB
buys 1000IÐR.
(b)
Calculâte the. total nr¡mber of Indonesian. rupiah Susi reoeives,
neÐrNt thousari ù rupiah.
corrrst to the
[2 narksJ
Swi' wanté' to'find'thra¡þroeinate exohange.rate betweem siryoBore
dsilars and
Indonesian rupiah andgsos the exchangg rates
forlEi!frt¡
(c) --'-.nea.rcst
ah.
tho
rry¡4
Worh.ng
4)
[2 marløJ
I s60 -- 2r.0 3
\ soo SG!b
TI-| ß
, Zt,oiq 6Lt Tt+S
ì SEO
\")
=
3t
gfl ,qb
rTttB -- too¿ r$ R
þoooT¡*ß . tOooJDR
?.)1
3s
c-) iv ,ozt 6
-' B,
2210-7401
do this.
"83
3, z?61>
tFl- ß
, loo2tÞR
Answers:
(a) 4t
(b)
2
o
(c)
Ò
-1513.
M I O/sA4ATSD/SP I ÆNGÆZ I DO(
,In a research proj-ept on the relation between the gender of 150 science students at
college and their degree subjecf the following set of data is collected.
Degree Subject
Gender
Biology
Physics
Chemistry
Male
40
t6
35
Female
l5
24
20
qt
Find the probability that a student chosen at random
(a)
is male;
[2 narb]
(b)
is either male or studies Chemistry;
[2 narksJ
(c)
studies Physics, given that the student is male.
[2 narksJ
Working:
Ð
ù
+
'lfl
Ltl
@
@
Answers:
(a)
*
(b)
(c)
2210-'t403
rlilllHillilllr
1
517
Turn over
- l6t4.
A quadrati'c function,
f (x)= ax2 +bx , is represented
M l O/s/ì4ArsDi sP I ÆNG/IZ I ÆO(
by,the mappiúg diagram below.
.Í
Í(x)
(a)
use the mapping diagram to write down two equations in terms of
(b)
Find the value
a and,b.
[2 marlæJ
of
(Ð a;
(iÐ
(c)
Working:
a)
b.
[2 marksJ
Calculate the¡-coordin¿ûe ofthevertex ofthe graph
Í â- -l>
-Ll
-vb'
g
=â
¿f
of f(x).
[2 marbJ,
q
_1,-4
( r,r\
+b
q(.r)=
74
-+
(b)
a Yb
N-- e-
(Ð
(iÐ
À= (.
(c) - J.l
2210-7403
t
-17
15.
The fi.¡nction
(a) (Ð
f (x)= 5-3(2")
is defined fo¡ x
-
M I O/5/TVIATSD/SP
I
ÆNG NZT
Iß.
)0
Onthearesbelowsketchthe gaphof
/(r)
andshowthebehaviourofthe
curve as¡.r rncreases.
(iÐ
[4 marks]
Write down the coordinates of any intercepts with the axes.
T
5
=-l
X
(b)
Draw the line y = 5 on your sketch.
(c)
Write down the number of solutions to the eqtration
[I
/(t)
p narkl
=5
Answers:
(a)
(iÐ
(c)
!
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markJ
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