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MO8/5/MATS Ù / SP 2 / ENGfi 21 /þ(
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tnternationa I Bacca laureaten
Baccatauréat nternationa I
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Bachillerato lnternacional
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MATHEMATICAL STUDIES
STANDARD LEVEL
PAPER 2
Thursday 8 May 2008 (morning)
I hour 30 minutes
INSTRUCTIONS TO CAN DIDATES
.
.
.
Do not open this examination paper until instructed to do so.
Answer all the questions.
Unless otherwise stated in the question, all numerical answers must be given exactly or correct
to three significant figures.
220A-74M
9 pages
@
lntemat¡onal Saccalaureate Organizatíon 2@8
MO8/5/}4ATSD/SP2ÆNG
3
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page. You are advised lo show all working, where possible. Where an
answer is wong, some mark may be givenþr correcl melhod, provided tltß ß shown by writlen working.
SolulÌons þund from a graphic dßplay calcalator should be supported by suilable working, e.g. if graphs
are used tofind a solution, you should sketch lhese as parl ofyour answen
Please slart each qtteslion on a new
1.
[Maximummark:17J
(a)
Sketch the graph of the function
clearly the uis intercepts and any
/(x)
: Ult.,for -l0S¡110.
o
".
n,"Iel
Indicating
[6 marksJ
(b)
Write down the equation of the vertícal asyrrptote.
(c)
On the same diagram sketch the graph
(d)
Using your graphical display calculator write down the coordinates of one of the
points of intersection on the graphs of f and g, g.ving your answer correct to
five decimal places.
(e)
(Ð
of g(x)
: x * 0.5
: x+ 0.5.
Write down the gradientofthe line g(x)
Thc linc Z passcs through thc point with coordinatos (-2, -3) and is perpendicular
to the line g(x)- Find the equation of
I-
Þ\
v -- -+
d)
(Jro't3, , Bf Ò18\
[2 nørksJ
[2 morksJ
[3 marlcsJ
[I
markJ
[3 marksJ
e)
a)
22A8-1404
-Z= 2+l
-l= t
t= -x- {
Turn over
-42.
nA tÆ
M08/5/ÙIATSD/SP2ÆNG
[Mmimum mark: 20J
(i)
A goup of SÂstudents completed
The following datâ rvas collected.
a questionnaire for a lvfathematical Studies project.
18 students own a digitat camera
15 students own an rpod (Ð
26 students own a cell phone (C)
I student owns
5 students own
2 students owu
3 students own
all th¡ee
@)
items
r
;
digiøl camera and an ipod but not a
a cell phone and an ipod but not ô digi
a cell phg5 and a digital cæmlrabp!not an ipod
a
(a)
Represent this information on a Venn diagrarn.
[4 narksJ
(b)
calculaæ the number ofstudents uÀo o\ur none of the iæms mentíoned above.
[2 marlæJ
(c)
If a student is chosen atrandorrl write down
the probability tttat iúe ótudent
owns a digital camera only.
(d)
chosen
]1,,*o çt9den!,?re
both own a cell þhone only.
(e)
ar random, calcul4te the probability
tþat
p
markJ
th. ey
[3 marlesJ
If
a student o\ryn¡i an ipod, write down the probability that the shrde,nt also
owns a digital c¿unera.
a")
\^-=
Ð3
n
a
cì >lo
2
C.2to
[2 marksJ
(Thß question continues on theþllowingpage)
E'ls
9
2208-74ô4
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MO8/5IN4ATSD/SP2ÆNG
5
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(fuestion 2 continued)
(iÐ Cl
and Kate both wish to go to the cinema but one of them has to stay at home to
baby-sit.
The probability that Kate goes !o the cinem¿ is 0.2. If Kate does not go Claire goes.
If Kate goes to the cinema the probability that she is late home is 0.3.
If Claire goes to the cinemo the probability that sho is lote home is 0.6.
(a)
Copy and complete the probability tree diagram below
[3 marksJ
Late
0.3
Kate
,1
,lp
Not
Late
.ã
,4
(b)
Not Late
Calculate the probability that
late; G aX'l)
(Ð
Kate goes to the cinema and is not
(iÐ
the person who goes to the cinema arrives home late.
[2 mørlaJ
[j
narksJ
(,Ð1,¡) + (,ù(.r)
I
b + , +ß
: sLl
22,08-',t404
Turn over
-63.
M08/5/\4A[SD/SP2ÆNGÆZ
I
/)ü
[Maximummark: l3J
(Ð
The graph below represents the temperature (2" Celsius) in'lVashington measured
at midday during a period of thirteen consecutive daysstarting at-Day 0.
These points also lie on the graph of the function
I(¡) : a *åcos (cx"), 0S x<12,
where a, b and ce lR.
T
23
22
2t
-/
20
-19
t8
I
l6
0
,-;¿ ,/
I
I
0
(a)
2
4
Find the value
(Ð
q;
(iÐ
b.
8
10
12x
of
[2 marksJ
c:30.
O)
Showthat
G)
using the graph, or otherwise, write down the part ofthe domain for which
the midday temperature is less than 18.5"-
fl
markJ
[2 marksJ
(Ihis question continues on theþllowing page)
t) -l(<l= \1 +âcos(cx\
t'l = rq + Tcñ(bt)
7 = ;-'eos (t"q)
-\
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(s
3Òo
Ge
b
s Ô-'
c)
(tlt ts,tù
3,rg< x < &,s2
-84.
MO8/5/}4ATSD/SP2ÆNGÆZ ID(X
[Maxirrummark: l9J
(Ð
Mal is shopping for a school trip. He buys 50 tins of beans and 20 packets of
cereal. The total cost is 260 Austalian dollars (AUD).
(a)
.;i
Write down an equation showing this infonnatio4 taking å to be the cost
of onetin of beans and c to be the cost of one þackeüof cereal inAItD.
b+ toc = bb
I
Write down another equation to represent this information.
markJ
(c) Findthecostofone tiuoft¡ezurs. 4 *tl>
(d) (Ð Sketch the graphs of these rwo equations.
two
graphs.
\+ao¿ =ebD
[]
Stephen thinks ttrat Mal has not bought enough so he buys 12 more tins of beans
and 6 more packets of cereal., He piys 66 AúD.
O)
(ü)
5D
[2 marlcsJ
f.l z )
\ rt¿l
[4 marksJ
The niangular faces,of a sguare based pyramid, AÐCDE, are all inclincd at 70'
base. The edges of the b se ABCD are all l0 cm and M is the centre.
G is the mid-point of
ùo the
CD.
E
@iagram not to scale)
v
B
ur
¡)-fo"..-? o" --
fM
A
<
x :,1.3 ,73't3811
G
D
(a)
Uging the letters on the diagram d¡aw a triangle showing the position
ofa
70" angle.
(b)
Show that the height of the pyramid is l3-7 cm, to 3 significant figures.
(c)
Calculate
5'+
(iÐ the size of angle DEC.
(Ð
2208-',t404
thelengthofEG;
(d)
Find the total surface area of
G)
Find the volume of the
p
markJ
[2 marksJ
?
81t ; l4,berw
\*c
"13"?3
3"1
,V
o
thep¡.ramid.
pyramid.
qfl
[4 marksJ
ne 7 e.n-t
?
emo
a-
[2 marhJ
[2 marlcsJ