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1 2 3 4 5 6 A B C D E F G P a ys Emissions en 1990 Emissions en 2001 V ariation en tre 2001 et 1990 (en % ) V ariation prévue en tre 1990 et 2010 en % ) Emissions prévues en 2010 V ariation prévue en tre 2001 et 2010 (en % ) Belgi que 141,3 150,2 6,3 -7,5 Dane mark 69,5 69,4 -0,1 -21 54,9 -20,9 Espa gne 289,8 382,8 32,1 15 333,3 -12,9 Italie 509,2 545,4 7,1 -6,5 -12,7 P ortu gal 61,4 83,8 36,5 27 78 -6,9
1.
Table
r e ading
E.154
The
table
b elo w
sho ws
greenhouse
gas
emissions
in
the
Europ ean
Union
in
millions
of
tonnes
of
CO
2
.
equiv alen t
In
the
last
column,
the
Ky oto
Proto col
targets
for
greenhouse
gas
emission
reductions
or
maxim um
allo w able
in- creases
ha v e
b een
indicated
for
eac h
coun try .
F or
example :
German y
m ust
reduce
its
emissions
b y
at
least
21
%
be- t w een
the
y ears
1990
and
2010 ;
Spain
can
increase
them
b y
a
maxim um
of
15
%
bet w een
the
y ears
1990
and
2010.
Some
data
ha v e
b een
deleted,
and
w e
prop ose
to
reco v er
some
of
them
in
the
follo wing
Q
.
C
.
M
.
.
For
information
:
to
express
the
emissions
of
eac h
greenhouse
gas
in
tonnes
of
CO
2
equivalen t,
the
emissions
of
eac h
gas
are
w eigh ted
b y
a
co efficien t
taking
in to
accoun t
its
w arming
p o w er
compared
with
that
of
CO
2
.
This
co efficien t
is
1
for
CO
2
,
21
for
CH
4
,
310
for
N
2
O
,
23
900
for
SF
6
,
140
to
11
700
for
HF Cs
and
2100
to
9
200
for
PF Cs.
Émissions
en
1990
Emissions
en
2001
Variation
en tre
1990
et
2001
(en
%
)
Variation
prévue
en tre
1990
et
2010
(en
%
)
Allemagne
1218
-18.3
-21
Autriche
78.4
9.6
-13
Belgique
141.3
150.2
6.3
-7.5
Danemark
69.5
69.4
-0.1
-21
Espagne
289.8
382.8
32.1
15
Finlande
77.3
4.7
France
558.6
0.4
Grèce
132.2
23.5
25
Irlande
53.4
70
13
Italie
545.4
7.1
-6.5
Luxemb ourg
6.1
-44.2
-28
Pa ys-Bas
219.7
4.1
-6
Portugal
61.4
83.8
36.5
27
Roy aume
Uni
657.2
-12
-12.5
Suède
70.5
-3.3
4
Ensemble
De
l’Union
europ éenne
4108.3
-2.3
-8
Source
:
Europ ean
En vironmen t
Agency ,
2003.
Part
A
Q.C.M.
each
question
has
three
statemen ts
iden tified
b y
the
letters
a
,
b
,
c
of
whic h
only
one
is
correct.
In
T able
1,
pro vided
in
the
app endix,
the
candidate
m ust
cir- cle
the
correct
answ er
for
eac h
question.
No
justification
is
required.
A
correct
answ er
earns
1
p oin t
;
an
incorrect
answ er
deducts
0.5
p oin ts
;
no
answ er
earns
or
deducts
no
p oin ts.
If
the
total
is
negativ e,
the
mark
is
reduced
to
zero.
1
F or
the
Europ ean
Union
as
a
whole,
the
quan tit y
of
green-
house
gases
emitted
b et w een
1990
and
2001
w as
m ulti- plied
b y :
a
0.977
b
1.023
c
0.023
2
Greenhouse
gas
emissions
in
Austria
for
the
y ear
2001
accoun ted
for
around
0.1
million
tonnes
of
CO
2
equiva- len t
:
a
85.9
million
tonnes
of
CO
2
;
b
153.7
million
tonnes
of
CO
2
equivalen t
;
c
88
million
tonnes
of
CO
2
equivalen t.
3
The
p ercen tage
c hange
in
greenhouse
gas
emissions
in
Ire- land
b et w een
1990
and
2001
is
equal
to
0.1
%
to
within
:
a
23.7
%
b
31.1
%
c
16.6
%
4
Greenhouse
gas
emissions
in
Luxem b ourg
for
the
y ear
1990
amoun ted
to
around
0.1
million
tonnes
of
CO
2
equivalen t
:
a
8.8
million
tonnes
of
CO
2
;
b
13.8
million
tonnes
of
CO
2
equivalen t
;
c
10.9
million
tonnes
of
CO
2
equivalen t.
Part
B
We
wish
to
kno w,
for
certain
coun tries
that
ha v e
not
y et
reac hed
their
Ky oto
Proto col
targets
in
2001,
the
rate
of
re- duction
to
b e
applied
to
2001
greenhouse
gas
emissions
in
order
to
reac h
the
quan tities
forecast
for
2010.
Greenhouse
gas
emissions
are
expressed
in
millions
of
tonnes
of
CO
2
.
equiv alen t
In
the
columns
D
,
F
and
G
,
the
results
are
rounded
to
the
ten th.
The
con ten ts
of
some
cells
are
hidden.
1
a
Whic h
form ula
w as
en tered
in
cell
F2
and
then
copied
do wn
to
cell
F6
?
b
What
form ula
do es
cell
F6
contain?
c
Complete
the
column
F
of
table
2
giv en
in
the
app endix.
A
result
rounded
to
0.1
million
tonnes
of
CO
2
equiva- len t
will
b e
giv en.
2
a
Belgium
w an ts
to
meet
the
targets
set
under
the
Ky oto
Proto col.
Justify
that
it
will
ha v e
to
reduce
its
greenhouse
gas
emissions
b et w een
2001
and
2010
b y
appro ximately
13
%
b
What
form ula
has
b een
en tered
in
cell
G2
and
then
copied
do wn
to
cell
G6
?
c
Whic h
coun try ,
listed
in
T able
2,
will
ha v e
to
ac hiev e
the
highest
rate
of
emissions
reduction
b et w een
2001
https:/ /c hingmath.fr
sacados/154
1 2 3 4 5 6 A B C D E F G P a ys Emissions en 1990 Emissions en 2001 V ariation en tre 2001 et 1990 (en % ) V ariation prévue en tre 1990 et 2010 en % ) Emissions prévues en 2010 V ariation prévue en tre 2001 et 2010 (en % ) Belgi que 141,3 150,2 6,3 -7,5 Dane mark 69,5 69,4 -0,1 -21 54,9 -20,9 Espa gne 289,8 382,8 32,1 15 333,3 -12,9 Italie 509,2 545,4 7,1 -6,5 -12,7 P ortu gal 61,4 83,8 36,5 27 78 -6,9
1 2 3 4 5 6 7 8 A B C D E F G Désignation de l’ article Prix unitaire ( H T ) T V A à 5 ; 5% T V A à 19 ; 6 % Prix unitaire TTC Quan tités Prix T otal T T C radiateur 1 ; 20 m 49,00 4 radiateur 0 ; 80 m 37,00 2 thermostat 17,34 3 c haudière 66,75 1 main d’o euvre 25,50 65 T otal
and
2010
to
meet
its
Ky oto
Proto col
targets?
E.146
The
F
.
M
.
I
(international
monetary
fund)
,
created
in
1945,
has
ˇ
as
its
main
mission
to
help
coun- tries
with
balance-of-pa ymen ts
problems
that
are
unable
to
b orro w
on
the
financial
mark ets
on
affordable
terms
ı.
1
Its
outstanding
loans
in
2003
were
85.3
billion
dollars
in
2003
,
whereas
for
the
financial
y ear
2006
it
w as
only
27
billion
dollars.
Express
this
c hange
using
a
p ercen tage,
rounded
to
the
nearest
h undredth.
2
Of
the
y ear’s
2006
outstanding
loans,
African
coun tries
accoun t
for
7
%
of
the
F
.
M
.
I
’s
outstanding
loans.
The
Demo cratic
Republic
of
Congo
is
the
coun try
most
in- debted
to
the
F
.
M
.
I
with
a
slate
represen ting
29.1
%
of
African
outstandings.
a
F aîtes
a
diagram
represen ting
this
situation
b
Determine
the
amoun t
of
outstanding
loans
dedicated
to
African
coun tries.
c
What
is
the
amoun t
of
outstanding
R
.
D
.
C
.
?
taken
from
Jeune
Afrique
2006
E.156
new
Caledonia
-
Marc h
2004
-
9
p oin ts
A
priv ate
individual
is
fitting
out
the
house
he
has
just
b ough t
:
he
is
ha ving
a
new
gas
heater
installed.
He
mak es
a
mo del
of
the
future
bill
on
the
basis
of
the
informa- tion
pro vided
b y
his
installer ;
the
latter
giv es
him
the
prices
HT
(excluding
tax)
.
T o
obtain
the
prices
TT C
(inclusive
of
al l
taxes)
,
he
m ust
add
to
the
price
HT
the
amoun t
of
the
TV
A
(value-added
tax)
;
this
TV
A
is
expressed
as
a
p er- cen tage
of
the
price
HT
:
it
is
5.5
%
for
supplies
(radiators,
thermostat,
b oiler)
and
19.6
%
for
lab or.
The
unit
price
for
lab or
is
coun ted
b y
the
hour.
The
table,
pro vided
in
App endix
1,
to
b e
returned
with
the
cop y ,
represen ts
elemen ts
of
the
spreadsheet
on
whic h
the
in- dividual
has
created
his
in v oice
mo del.
Throughout
the
exer cise
wil l
b e
r ounde d
to
the
hundr e dth
1
F rom
the
information
pro vided
on
the
attac hed
table
:
a
Calculate
the
amoun t
of
TV
A
for
a
radiator
of
1.20
m
b
Calculate
the
price
HT
of
the
thermostat.
c
Calculate
the
price
HT
of
the
b oiler
d
Complete
the
cells
C
2
,
B
4
and
B
5
of
the
table
with
the
missing
n umerical
v alues
2
What
form ula
can
b e
en tered
in
cell
C2
,
b efore
automati- cally
cop ying
it
do wn
to
line
5,
to
obtain
the
amoun ts
of
TV
A
?
Complete
cells
C3
and
C4
of
the
table
with
the
missing
n umerical
v alues.
3
What
form ula
can
b e
en tered
in
cell
E2
,
b efore
automat- ically
cop ying
it
do wn
to
line
5,
to
obtain
unit
prices
TT C
?
4
Calculate
the
price
TT C
per
hour
of
lab or
and
fill
in
cell
E6
of
the
table
with
the
missing
n umerical
v alue.
5
What
form ula
can
b e
en tered
in
cell
G2
,
b efore
automat- ically
cop ying
it
do wn
to
line
6,
to
obtain
prices
TT C
?
Then
complete
column
G
of
the
table
with
the
missing
n umerical
v alues.
6
a
The
installer
giv es
a
discoun t
of
4
%
on
the
price
HT
of
the
b oiler :
whic h
table
cells
will
the
n umerical
con ten t
c hange?
b
By
ho w
m uc h
will
the
final
bill
fall?
c
Will
this
amoun t
b e
the
same
if
the
discoun t
of
4
%
is
made
on
the
price
TT C
of
the
b oiler?
Justify
answ er
E.149
In
2004,
in
a
medium-sized
to wn,
a
census
w as
tak en
of
y oung
p eople
aged
10
to
15
who
regularly
pla y ed
a
team
sp ort
(soccer,
handball)
or
an
individual
sp ort
(tennis,
judo)
.
It
is
assumed
that
eac h
y oung
p erson
coun ted
in
this
w a y
pla ys
just
one
sp ort.
The
cit y
has
b een
divided
in to
four
sec- tors
:
north,
south,
east,
w est.
The
results
are
group ed
in
the
table
giv en
in
appendix
I
(to
b e
c omplete d
and
r eturne d
with
the
c opy)
1
a
W e
w an t
to
calculate
the
totals
p er
ro w.
What
for- m ula
should
w e
write
in
cell
F2
to
obtain
b y
cop ying
it
do wn
to
F6
the
total
n um b er
of
y oung
p eople
p er
line?
b
W e
w an t
to
calculate,
b y
sector,
the
frequencies
of
y oung
p eople
practicing
an
individual
or
team
sp ort,
relativ e
to
the
census
p opulation.
What
form ula
should
w e
write
in
cell
B7
to
obtain,
b y
cop ying
it
to
the
righ t
to
F7
,
these
frequencies?
In
the
fol lowing
questions,
p er c entages
wil l
b e
r ounde d
to
the
tenth.
2
Complete
the
table
giv en
in
appendix1
(to
b e
r eturne d
with
the
c opy)
3
Can
w e
sa y
that
less
than
a
third
of
the
teenagers
who
resp onded
to
this
surv ey
seem
to
b e
more
attracted
to
an
individual
sp ort
than
to
a
team
sp ort?
Justify
the
answ er
with
a
calculation
4
Assuming
that
ev ery
y ear
the
n um b er
of
teenagers
pla y- ing
team
sp orts
increases
b y
5
%
and
that
the
n um b er
of
teenagers
practicing
an
individual
sp ort
decreases
b y
10
%
,
calculate :
a
the
n um b er
of
teenagers
pla ying
a
team
sp ort
in
2005
in
this
cit y ;
b
the
n um b er
of
teenagers
practicing
an
individual
sp ort
in
2005
in
this
cit y ;
c
the
p ercen tage
c hange
b et w een
2004
and
2005
in
the
n um b er
of
teenagers
who
will
practice
a
sp ort
in
this
cit y .
https:/ /c hingmath.fr
chapExoCorrec/146 sacados/146 sacados/156 1 2 3 4 5 6 7 8 A B C D E F G Désignation de l’ article Prix unitaire ( H T ) T V A à 5 ; 5% T V A à 19 ; 6 % Prix unitaire TTC Quan tités Prix T otal T T C radiateur 1 ; 20 m 49,00 4 radiateur 0 ; 80 m 37,00 2 thermostat 17,34 3 c haudière 66,75 1 main d’o euvre 25,50 65 T otal chapExoCorrec/149 sacados/149
1 2 3 4 5 6 7 A B C D E F Nord Sud Est Ouest TOT AL F o otball 150 125 75 250 600 Handball 50 75 30 85 240 T ennis 35 30 15 50 130 Judo 70 50 20 100 240 TOT AL 305 280 140 485 1210 F réquence en %
1 2 3 4 5 6 7 8 9 10 11 12 13 A B C D tableau 1 c haîne bleue c haîne jaune T otal nom bre d’inciden ts p our lesquels l’alarme a fonctionné 46 72 nom bre d’inciden ts p our lesquels l’alarme n’a pas fonctionné T otal 52 tableau 2 p ourcen tage d’inciden ts p our lesquels l’alarme a fonctionné 96% p ourcen tage d’inciden ts p our lesquels l’alarme n’a pas fonctionné T otal 100 % 100 % tableau 3 c haîne bleue c haîne jaune T otal p ourcen tage d’inciden ts p our lesquels l’alarme a fonctionné 39% 61% 100% p ourcen tage d’inciden ts p our lesquels l’alarme n’a pas fonctionné 67% 33% 100% T aux de défaillance du système d’alarme en % 0 1 2 3 4 5 6 7 8 9 10 11 12 Coût mo y en d’une in terv en tion en euros 500 1000 1500 2000 2500
E.186
A
compan y
has
t w o
pro duction
lines
:
blue
line,
y ello w
line.
An
alarm
system
detects
inciden ts
that
ma y
o ccur
on
eac h
of
these
t w o
lines.
In
order
to
monitor
the
effectiv eness
of
this
alarm
system,
w e
observ ed,
o v er
a
p erio d
of
one
mon th,
the
n um b er
of
triggers
of
this
system,
as
w ell
as
these
failures
(i.e.
incidents
o c curring
without
the
alarm
b eing
trigger e d)
.
The
results
w ere
tak en
from
a
spreadsheet
(table
1)
.
Some
cells
in
this
table
ha v e
b een
mask ed.
There
w ere
52
inciden ts
on
the
blue
c hain,
46
of
whic h
w ere
detected
b y
the
alarm
system.
F or
the
y ello w
c hain,
the
alarm
system
w as
triggered
72
times,
i.e.
in
96
%
of
inciden ts
on
this
c hain.
1
a
Calculate
the
total
n um b er
of
inciden ts
on
the
y ello w
c hain.
b
Complete
T able
1.
c
What
form ula
has
b een
en tered
in
cell
D2
knowing
that
it
has
b een
copied
do wn
to
D4
?
2
In
T able
2,
whose
cells
are
in
p ercen tage
format,
w e
seek
to
obtain
the
p ercen tages
in
relation
to
the
n um b er
of
inciden ts
observ ed
on
eac h
c hannel.
a
Calculate
the
p ercen tage
of
inciden ts
on
the
blue
c hain
for
whic h
the
alarm
did
not
w ork.
The
result
will
b e
rounded
to
0.1
%
.
b
Complete
T able
2.
c
What
form ula
has
b een
written
in to
cell
B7
,
then
copied
do wn
in to
cells
B8
and
B9
?
3
W e’re
in terested
in
T able
3.
a
In
cell
C13
,
w e
find
the
n um b er
33
%
.
Giv e
an
in ter- pretation
of
this
n um b er.
b
What
form ula
has
b een
en tered
in
cell
B12
,
then
copied
throughout
T able
3?
4
An
alarm
system’s
failure
rate
is
the
p ercen tage
of
in- ciden ts
in
whic h
the
alarm
failed
as
a
prop ortion
of
all
inciden ts
on
the
line
as
a
function
of
the
alarm
system’s
failure
rate.
The
compan y
considers
that
the
alarm
system
is
not
ef- fectiv e
when
the
a v erage
cost
of
an
in terv en tion
b ecomes
greater
than
1
500
e
.
a
A t
what
failure
rate
is
the
alarm
system
no
longer
con- sidered
effectiv e?
The
result
will
b e
giv en
to
the
near- est
0.2
%
.
b
Is
the
alarm
system
effectiv e
for
the
blue
c hain?
for
the
y ello w
c hain?
Justify
https:/ /c hingmath.fr
1 2 3 4 5 6 7 A B C D E F Nord Sud Est Ouest TOT AL F o otball 150 125 75 250 600 Handball 50 75 30 85 240 T ennis 35 30 15 50 130 Judo 70 50 20 100 240 TOT AL 305 280 140 485 1210 F réquence en % sacados/186 1 2 3 4 5 6 7 8 9 10 11 12 13 A B C D tableau 1 c haîne bleue c haîne jaune T otal nom bre d’inciden ts p our lesquels l’alarme a fonctionné 46 72 nom bre d’inciden ts p our lesquels l’alarme n’a pas fonctionné T otal 52 tableau 2 p ourcen tage d’inciden ts p our lesquels l’alarme a fonctionné 96% p ourcen tage d’inciden ts p our lesquels l’alarme n’a pas fonctionné T otal 100 % 100 % tableau 3 c haîne bleue c haîne jaune T otal p ourcen tage d’inciden ts p our lesquels l’alarme a fonctionné 39% 61% 100% p ourcen tage d’inciden ts p our lesquels l’alarme n’a pas fonctionné 67% 33% 100% T aux de défaillance du système d’alarme en % 0 1 2 3 4 5 6 7 8 9 10 11 12 Coût mo y en d’une in terv en tion en euros 500 1000 1500 2000 2500
I M C 10 I M C 12 I M C 14 I M C 16 I M C 18 I M C 20 I M C 22 I M C 24 I M C 26 I M C 28 I M C 30 Taille 1 1.05 1.1 1.15 1.2 1.25 1.3 P oids 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
E.203
The
three
parts
of
the
exercise
are
indep enden t.
Before
c hildren
start
elemen tary
sc ho ol,
do ctors
and
n urses
from
the
Ministry
of
Education
carry
out
a
health
c hec k
and
measure
the
heigh t
(in
meters)
and
w eigh t
(in
kilo gr ams)
of
eac h
c hild.
These
t w o
parameters
are
used
to
calculate
the
b o dy
mass
index
(BMI)
,
whic h
is
an
indicator
of
p ossible
o v erw eigh t.
Part
I
The
graph
in
App endix
2
sho ws
differen t
curv es
of
b o dy
sur- face
area
S
giving
the
BMI
as
a
function
of
w eigh t
(betwe en
16
and
32
kilo gr ams)
and
heigh t
(betwe en
1
meter
and
1.3
meters)
of
the
c hild.
This
app endix
m ust
b e
returned
with
the
cop y
with
all
the
construction
lines
necessary
to
solv e
part
I.
1
Giv e
a
rounded
v alue
for
the
BMI
of
a
c hild
w eighing
19
kilograms
and
measuring
1.09
meters.
2
Giv e
a
rounded
v alue
for
the
w eigh t
of
a
c hild
with
a
BMI
of
20
and
a
heigh t
of
1.22
meters.
3
What
is
the
w eigh t
range
for
a
c hild
measuring
1.25
me-ters
with
a
BMI
b et w een
12
and
16
?
Part
I I
BMI
is
calculated
using
the
follo wing
form ula
:
BM I
=
P
T
2
P
denotes
the
c hild’s
w eigh t
(in
kilo gr ams)
and
T
their
heigh t
(in
meters)
.
1
The
w eigh t
and
heigh t
of
a
sample
of
15
six-y ear-old
b o ys
w ere
recorded
in
order
to
calculate
their
BMI.
These
data
are
pro vided
in
the
app endix.
Without
using
a
calculator,
determine
the
median
heigh t,
the
first
and
third
quar- tiles
asso ciated
with
heigh t,
and
sp ecify
the
in terquartile
range.
Explain
y our
approac h.
2
Calculate
the
BMI
of
a
c hild
w eighing
19
kilograms
and
measuring
1.09
meters.
Whic h
question
in
P art
2
do es
this
result
corresp ond
to?
3
Based
on
the
do cumen t
pro vided
in
the
app endix,
is
a
6-y ear-old
b o y
measuring
1.20
meters
tall
and
w eighing
26
kilograms
o v erw eigh t?
Justify
y our
answ er.
4
When
a
c hild
is
o v erw eigh t
but
not
ob ese,
they
are
said
to
b e
mo derately
o v erw eigh t.
What
BMI
condition
w ould
apply
to
a
6-y ear-old
b o y
to
b e
considered
mo derately
o v erw eigh t?
5
Using
the
sample
in
the
app endix,
calculate
the
p ercen t- age
of
b o ys
who
are
o v erw eigh t.
What
p ercen tage
of
these
b o ys
are
mo derately
o v erw eigh t?
Part
I I I
During
a
surv ey
conducted
during
the
1999-2000
sc ho ol
y ear,
the
p ercen tages
of
6-y ear-old
c hildren
who
w ere
o v erw eigh t
or
not
o v erw eigh t
w ere
recorded
according
to
their
place
of
residence.
These
results
are
presen ted
in
the
app endix.
1
Calculate
the
p ercen tage
of
o v erw eigh t
c hildren
in
rural
areas.
2
Calculate
the
p ercen tage
of
ob ese
c hildren
in
rural
areas.
3
Clearly
state
whether
the
follo wing
statemen ts
are
true
or
false,
or
whether
the
data
do es
not
allo w
for
a
clear
conclusion
:
In
the
P aris
metrop olitan
area,
there
are
more
than
3
ob ese
c hildren
for
ev ery
10
o v erw eigh t
c hildren.
The
n um b er
of
o v erw eigh t
c hildren
in
to wns
with
few er
than
50
000
inhabitants
is
v ery
sligh tly
lo w er
than
the
n um b er
of
o v erw eigh t
c hildren
in
to wns
with
b et w een
50
000
and
200
000
inhabitants.
Weigh t
(P)
15
18
19
20
22
23
23
23
Height
(T)
1.05
1.05
1.09
1.10
1.02
1.17
1.15
1.16
IMC
13.61
16.33
16.53
21
;
15
16.80
17.39
17.09
Weigh t
(P)
24
24
25
25
26
27
27
Size
(T)
1.20
1.20
1.25
1.30
1.20
1.24
1.30
IMC
16.67
16.67
16.00
14.79
18
;
06
17.56
15.98
International
thresholds
for
b o dy
mass
index
(BMI)
to
define
o v erw eigh t
and
ob esit y
in
c hildren
Age
BMI
for
o v erw eigh t
BMI
for
ob esit y
(in
ye ars)
Boys
Girls
Boys
Girls
5
ans
17.42
17.15
19.30
19.17
5
y ears
and
a
half
17.45
17.
20
19.47
19.34
6
ans
17.55
17.35
19.78
19.65
6
y ears
and
a
half
17.71
17.53
20.
23
20.08
Lecture
:
for
a
6-y ear-old
b o y
measuring
120
cm
,
the
o v er- w eigh t
BMI
is
17.55,
whic h
corresp onds
to
a
w eigh t
of
25.272
kg
;
ab o v e
this,
he’s
considered
o v erw eigh t.
The
threshold
for
ob esit y
is
19.78
,
whic h
corresp onds
to
a
w eigh t
of
28.483
kg
.
F or
a
girl
of
the
same
age
and
heigh t,
the
threshold
for
o v erw eigh t
is
24.977
kg
et
that
for
ob e- sit y
29.296
kg
.
Source
:
COLE
et
al.
British
medical
journal
2000.
320
https:/ /c hingmath.fr
sacados/203 France - Septembre 2006 - 12 points
I M C 10 I M C 12 I M C 14 I M C 16 I M C 18 I M C 20 I M C 22 I M C 24 I M C 26 I M C 28 I M C 30 Taille 1 1.05 1.1 1.15 1.2 1.25 1.3 P oids 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Cyclomotoristes Usagers de v oitures de tourisme Moto cyclistes Nom bre de p ersonne 500 1000 1500 2000 2500 3000 12 ans 13 ans 14 ans 15 ans 16 ans 17 ans 18 ans 19 ans 20 ans 21 ans 22 ans 23 ans 24 ans
Typ e
of
agglomeration
meration
%
of
c hildren
without
b eing
o v erw eigh t
%
c hildren
who
are
o v erw eigh t
%
c hildren
with
mo derate
o v erw eigh t
%
c hildren
who
are
ob ese
rurales
87.2
9.2
moins
de
50
000
habitants
86.9
13,
1
9.9
3.2
entre
50
000
et
200
000
habitants
86,
8
13.2
9.7
3.5
entre
200
000
et
2
000
000
habitants
85.7
14,
3
10.2
4.1
agglo-mération
parisienne
83.4
16.6
11,
6
5
E.1772
Les
t w o
parts
are
indep enden t
Part
A
In
2003,
on
a v erage,
ev ery
da y
in
F rance,
almost
49.1
p eople
aged
12
to
18
w ere
victims
(injure d
or
kil le d)
of
road
acci- den ts.
Mop eds
ha v e
the
highest
a v erage
n um b er
of
victims
(26.0
victims
p er
day)
,
follo w ed
b y
passenger
cars
(12.8
vic- tims
p er
day)
,
p edestrians
(5.0
victims
p er
day)
and
cyclists
(2.5
victims
p er
day)
.
The
table
b elo w
giv es
the
breakdo wn
of
road
acciden t
victims
aged
12
to
18
b y
age
and
user
category
for
2003.
Age
Pié-tons
Cyclis
te
Cyclo
moto
ristes
Moto
cycliste
Usagers
de
v oiture
de
tourisme
Autres
usagers*
Total
12
ans
330
147
49
22
247
24
819
13
ans
263
165
122
23
279
26
878
14
ans
234
135
1
010
35
292
37
1
743
15
ans
260
139
1
701
57
396
27
2
580
16
ans
269
111
2
549
136
610
25
3
700
17
ans
223
111
2
457
259
925
39
4
013
18
ans
248
115
1
605
214
1
940
59
4
181
Total
1
827
923
9
493
745
4
689
237
17
914
*
Users
of
vans,
he avy
go o ds
vehicles,
tr ansp ort
in
c om- mum.
.
.
Data
from
:
http://eduscol.education.fr/D0187/default.htm
1
Mop ed
riders
a
Chec k
that
in
2003,
ev ery
da y
in
F rance
there
w as
an
a v erage
of
26.0
mop ed
riders
aged
12
to
18
killed
in
road
acciden ts.
b
Calculate
the
p ercen tage,
among
mop ed
riders,
of
ac- ciden ts
in v olving
under-13s,
rounded
to
0.1.
c
Calculate
the
p ercen tage
of
injured
mop ed
riders
un- der
18
y ears
of
age
out
of
all
injured
riders,
rounded
to
0.1.
2
Motorcyclists
a
In
2003
there
w ere,
all
ages
com bined,
16
629
motor- cyclists
in v olv ed
in
road
acciden ts.
Is
the
follo wing
statement
true
or
false?
Justify
the
answ er :
ˇAmong
motorcyclists
in v olv ed
in
acciden ts
in
2003,
less
than
one
in
t w en t y
w as
a
y oung
p erson
aged
b e- t w een
12
and
18ı.
b
All
ages
com bined,
there
w ere
18
518
motorcyclists
killed
in
road
acciden ts
in
2002
and
16
629
in
2003.
Calculate
the
p ercen tage
c hange
in
the
n um b er
of
mo- torcyclists
in v olv ed
in
road
acciden ts
b et w een
2002
and
2003.
Round
the
result
to
0.1.
Part
B
The
graph
b elo w
giv es,
for
the
12-24
age
group,
the
n um b er
of
road
acciden t
casualties
in
2003
b y
age
for
three
categories
of
user
:
mop ed
riders,
motorcyclists
and
passenger
car
users.
Victimes
of
acciden ts
in v olving
mop eds,
motorcycles
or
passenger
cars
1
a
Indicate
the
ages
for
whic h,
in
2003
the
n um b er
of
passenger
car
casualties
exceeded
2
000.
the
n um b er
of
mop ed
casualties
is
appro ximately
equal
to
1
000.
b
With
the
precision
allo w ed
b y
the
graph,
determine
the
n um b er
of
mop ed
riders
aged
20
who
w ere
victims
of
a
road
acciden t.
2
a
A t
what
age
is
the
maxim um
n um b er
of
passenger
car
acciden t
victims?
b
What
phenomenon(s)
can
explain
the
fact
that
as
age
increases,
the
n um b er
of
passenger
car
acciden t
victims
increases
rapidly
and
then
gradually
decreases?
https:/ /c hingmath.fr
chapExoCorrec/1772 sacados/1772 France - Septembre 2006 - 9 points
Cyclomotoristes Usagers de v oitures de tourisme Moto cyclistes Nom bre de p ersonne 500 1000 1500 2000 2500 3000 12 ans 13 ans 14 ans 15 ans 16 ans 17 ans 18 ans 19 ans 20 ans 21 ans 22 ans 23 ans 24 ans
Un concert 100 500 700 900 1100 1300 1500 G
N N N N
N N N N
E.4745
In
a
cit y ,
a
concert
hall
has
sc heduled
40
concerts
during
the
2004/2005
season.
The
exp ected
audience
n um b ers
are
sho wn
in
the
histogram
in
App endix
3.
F or
example,
the
manager
b eliev es
that
six
concerts
will
attract
b et w een
500
and
700
sp ectators
during
the
2004/2005
season.
1
Complete
the
follo wing
staffing
table
:
Classe
[100;500[
[500;700[
[700;900[
[900;1100[
[1100;1300[
[1300;1500[
Numb er
2
Use
the
calculator
to
determine
the
mean
and
standard
deviation
of
this
series.
2.
Medians
and
quartiles
E.1958
Giv e
the
range,
median,
first
and
third
quartile
of
the
follo wing
series
:
34
38
39
41
42
43
44
45
45
47
47
48
49
50
51
51
52
52
53
54
55
55
55
55
55
55
55
56
56
57
58
58
58
59
59
59
60
62
62
62
62
63
64
65
66
66
66
66
67
68
68
73
74
74
75
75
79
81
81
85
E.4740
Giv e
the
range,
median,
first
and
third
quartile
of
the
follo wing
series
:
34
38
39
41
42
43
44
45
45
47
47
48
49
50
51
51
52
52
53
54
55
55
55
55
55
55
55
56
56
57
58
58
58
59
59
59
60
62
62
62
62
63
64
65
66
66
66
66
67
68
68
73
74
74
75
75
79
81
81
85
E.196
Consider
four
statistical
series
whose
c har- acter
v alues
ha v e
b een
represen ted
on
a
graduated
line
b y
p oin ts
(two
individuals
do
not
have
the
same
char acter
value)
Series
1 :
Series
2 :
Series
3 :
Series
4 :
1
Determine
the
total
n um b er
in
eac h
series.
2
Plot
the
first
quartile,
median
and
third
quartile
on
eac h
of
the
graduated
lines.
E.1920
Determine
the
range,
median,
first
and
third
quartile
of
the
follo wing
statistical
series
:
0,250
0,260
0,290
0,290
0,300
0,300
0,310
0,310
0,320
0,320
0,320
0,320
0,330
0,330
0,330
0,340
0,340
0,340
0,340
0,350
0,350
0,350
0,350
0,305
0,360
0,360
0,370
0,370
0,370
0,370
0,380
0,380
0,380
0,390
0,390
0,390
0,390
0,400
0,400
0,410
0,410
0,420
0,420
0,420
0,430
0,430
0,450
0,460
0,470
0,470
E.4737
On
a
graduated
line,
a
teac her
has
or- dered
the
grades
of
these
four
classes
of
10th
graders.
Here
are
their
represen tations
:
Series
1 :
Series
2 :
Series
3 :
Series
4 :
The
aim
of
the
exercise
is
to
divide
eac h
of
the
classes
in to
four
parts
ˇ
of
equal
size
ı
represen ting
:
The
w eak est
quarter
The
medium-lo w
quarter
The
medium-strong
quarter
The
strong
quarter
1
Sho w
the
median
v alue
of
the
series
on
eac h
of
the
grad- uated
lines.
2
Complete
the
splitting
of
the
series
b y
re-splitting
eac h
part
in
half.
3
Can
y ou
giv e
a
qualitativ e
judgmen t
of
these
classes?
https:/ /c hingmath.fr
chapExoCorrec/4745 sacados/4745 Un concert 100 500 700 900 1100 1300 1500 G sacados/1958 chapExoCorrec/4740 sacados/4740 sacados/196 N N N N sacados/1920 Extrait Liban -- juin 2004
chapExoCorrec/4737 sacados/4737 N N N N
0 2 4 6 8 10 12 14 16 18 20 Classe 2 - A Classe 2 - B Classe 2 - C Classe 2 - D
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 A B C D E F P a ys Prix H T T axe in térieure Prix hors T V A TV A en % Prix T T C Luxem b ourg 0,325 0,253 0,578 15,00 0,665 Grèce 0,324 0,251 0,575 18,00 0,679 P ortugal 0,306 0,292 0,598 17,00 0,700 Espagne 0,330 0,297 0,627 16,00 0,727 Belgique 0,307 0,305 0,612 21,00 0,740 Autric he 0,340 0,289 0,629 20,00 0,755 Irlande 0,342 0,327 0,669 21,00 0,809 F rance 0,301 0,392 0,693 19,60 0,829 P a ys-Bas 0,340 0,358 0,698 19,00 0,831 Danemark 0,340 0,358 0,698 19,00 0,831 Suède 0,330 0,347 0,701 25,00 0,846 Finlande 0,354 0,347 0,701 25,00 0,876 Allemagne 0,309 0,470 0,779 16,00 0,904 Italie 0,351 0,403 0,754 20,00 0,905 Ro y aume Uni 0,302 0,693 0,995 17,50 1,169 Moyenne
E.4739
1
Here
are
the
scores
of
four
groups
of
studen ts
on
the
mo c k
exam.
Fill
in
the
b o xes
for
the
differen t
indicators
b elo w
:
Group
1
Group
2
Group
3
Group
4
Notes
5
-
6
-
10
10
-
11
12
-
12
14
6
-
8
-
8
8
-
10
-
11
14
-
15
8
-
8.5
8.5
-
9
11
-
11
12
-
12
6
-
6
-
7
8
-
10
-
11
11
-
15
Av erage
Range
Median
2
Compare
qualitativ ely
in
ligh t
of
the
indicators
calcu- lated
previously :
a
Group
1
and
group
2
b
Group
2
and
group
4
c
Group
1
and
group
3
3.
Mustache
b ox
E.1970
Consider
four
statistical
series
whose
c har- acter
v alues
ha v e
b een
represen ted
on
a
graduated
line
b y
p oin ts
(two
individuals
do
not
have
the
same
char acter
value)
Series
1 :
Series
2 :
Series
3 :
Series
4 :
Dra w
the
b o x
plots
corresp onding
to
eac h
of
these
series
di- rectly
on
the
graduated
lines.
E.4751
On
a
graduated
line,
a
teac her
has
or- dered
the
grades
of
these
four
classes
of
10th
graders.
Here
are
their
represen tations
:
1
Dra w
the
b o x
diagram
for
eac h
of
these
classes.
2
Compare
these
statistical
series
qualitativ ely .
E.167
On
1
er
January
2005,
the
table
b elo w
giv es
the
prices,
in
euros,
p er
liter
of
diesel
in
fifteen
Europ ean
coun tries.
The
table
sho ws
:
price
HT
(price
excluding
tax)
the
amoun t
of
domestic
tax
eac h
coun try
adds
to
the
pre-tax
price
;
the
rate
of
TV
A
applied
after
adding
the
domestic
tax ;
the
price
TT C
(price
inclusive
of
al l
taxes)
Prix
diesel
in
Europ e
at
1
er
January
2005
Example
:
In
the
UK,
the
price
of
diesel
excluding
tax
is
0.302
euro
plus
domestic
tax
of
0.693
e
.
Then
to
the
price
ex- cluding
TV
A
of
0.995
e
is
applied
a
TV
A
of
17.5
%
,
leading
to
a
price
TT C
1.169
e
.
Part
A
-
T able
w ork
The
table
is
a
spreadsheet.
The
columns
D
and
F
required
the
https:/ /c hingmath.fr
chapExoCorrec/4739 sacados/4739 sacados/1970 chapExoCorrec/4751 sacados/4751 0 2 4 6 8 10 12 14 16 18 20 Classe 2 - A Classe 2 - B Classe 2 - C Classe 2 - D sacados/167
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 A B C D E F P a ys Prix H T T axe in térieure Prix hors T V A TV A en % Prix T T C Luxem b ourg 0,325 0,253 0,578 15,00 0,665 Grèce 0,324 0,251 0,575 18,00 0,679 P ortugal 0,306 0,292 0,598 17,00 0,700 Espagne 0,330 0,297 0,627 16,00 0,727 Belgique 0,307 0,305 0,612 21,00 0,740 Autric he 0,340 0,289 0,629 20,00 0,755 Irlande 0,342 0,327 0,669 21,00 0,809 F rance 0,301 0,392 0,693 19,60 0,829 P a ys-Bas 0,340 0,358 0,698 19,00 0,831 Danemark 0,340 0,358 0,698 19,00 0,831 Suède 0,330 0,347 0,701 25,00 0,846 Finlande 0,354 0,347 0,701 25,00 0,876 Allemagne 0,309 0,470 0,779 16,00 0,904 Italie 0,351 0,403 0,754 20,00 0,905 Ro y aume Uni 0,302 0,693 0,995 17,50 1,169 Moyenne
0,310 0,320 0,330 0,340 0,350 0,360 0,6 0,7 0,8 0,9 0,10 0,11 0,12
0 1 2 3 4 5 6 7 8 9 10 11 12 13 Station I Station U
use
of
form ulas
to
b e
filled
in.
1
What
form ula
w as
en tered
in
D2
,
then
recopied
to
D16
to
obtain
the
price
excluding
TV
A
?
2
What
form ula
w as
en tered
at
F2
,
then
recopied
to
F16
to
obtain
the
price
TT C
?
3
W e
w an t
to
obtain
in
cell
B17
the
a v erage
price
b efore
tax.
What
form ula
can
b e
en tered
in
this
cell?
Part
B
-
Study
of
prices
b efore
tax
The
statistical
series
made
up
of
prices
b efore
tax
has
b een
studied
and
the
c haracteristics
giv en
b elo w
ha v e
b een
ob- tained
:
mean
:
X
≈
0.324
:
standard
deviation :
ff
≈
0.019
first
and
third
quartiles :
Q
1
=0.306
and
Q
3
=0.34
;
median
:
M
e
=0.325
1
Using
the
graded
axis
b elo w,
construct
the
b o x
plot
for
this
series.
The
first
and
third
quartiles,
median,
maxi- m um
and
minim um
of
the
series
will
b e
sho wn.
2
Giv e
the
n um b er
of
coun tries
whose
price
HT
of
diesel
b elongs
to
the
in terv al
[
x
−
ff
;
x
+
ff
]
.
Part
C
-
Price
study
TT C
We
are
no w
in terested
in
the
TT C
price
of
diesel
fuel
in
these
fifteen
coun tries.
1
Calculate
the
mean
x
of
this
series.
The
result
will
b e
rounded
to
the
thousandth.
2
Read
from
the
diagram
b elo w,
the
median,
first
and
third
quartile
of
this
series
of
TT C
diesel
prices.
V alues
will
b e
giv en
with
the
precision
p ermitted
b y
the
diagram.
3
Q.C.M.
Answ er
the
t w o
questions
b elo w
b y
c ho osing
the
correct
answ er
from
the
three
prop osals.
No
justification
is
re- quired.
T o
answ er,
cop y
the
c hosen
answ er
on
y our
cop y .
A
cor- rect
answ er
earns
0.5
poin t,
a
wrong
answ er
deducts
0.25
p oin t
and
no
answ er
adds
or
deducts
no
p oin ts.
A
nega- tiv e
p oin t
total
is
reduced
to
zero.
a
The
median
of
the
series
of
fifteen
prices
TT C
is
:
The
8
e
value
;
the
half-sum
of
the
7
e
and
the
8
e
value
;
the
half-sum
of
the
8
e
and
the
9
e
value.
b
The
first
quartile
of
the
series
of
fifteen
TT C
prices
is
:
the
3
e
value
;
la
4
e
value
;
the
half-sum
of
the
3
e
and
the
4
e
value.
4
A
journalist
writes
:ıIn
Europ e,
taxes
on
diesel
harmonize
prices
within
the
Europ ean
Union.ı
Confirm
or
den y
this
statemen t
b y
arguing.
Part
D
-
Study
of
prices
in
F rance
Q.C.M.
Answ er
the
t w o
questions
b elo w
b y
c ho osing
the
correct
an- sw er
from
the
three
prop osals
(where
the
r esults
have
b e en
r ounde d
to
1
%
)
.
No
justification
is
required.
T o
answ er,
cop y
the
c hosen
answ er
on
y our
cop y .
A
correct
answ er
earns
1
p oin t,
a
wrong
answ er
deducts
0.5
poin t
and
no
answ er
adds
or
deducts
no
p oin ts.
A
negativ e
p oin t
total
is
reduced
to
zero.
1
In
F rance,
the
domestic
tax
on
diesel
represen ts
:
230
%
of
the
price
HT
;
57
%
price
HT
;
130
%
of
price
HT
.
2
In
F rance,
the
o v erall
p ercen tage
of
taxes
applied
to
price
HT
to
obtain
price
TT C
is
:
175
%
150
%
64
%
E.169
lebanon
ffl
June
2006
ffl
11
p oin ts
In
a
region
of
eastern
F rance,
air
p ollution
is
monitored
daily ,
hour
b y
hour,
b y
a
net w ork
of
21
measuring
stations.
Among
these,
let’s
consider
the
station
noted
U
,
whic h
is
lo cated
in
an
urban
area,
the
station
I
,
in
an
industrialized
area
and
the
station
R
,
in
a
rural
mid-moun tain
area.
Part
A
In
this
part,
w e
compare
the
measuremen ts
obtained
at
sta- tions
U
and
I
for
sulfur
dio xide
(
SO
2
)
,
one
of
the
p ollutan ts
measured.
Concen trations
of
this
p ollutan t
are
expressed
in
million ths
of
a
gram
p er
cubic
meter
of
air
(in
this
exer cise,
this
unit
is
note d
µ
=
g
)
.
The
b o x
plots
dra wn
b elo w
relate
to
hourly
measuremen ts
of
the
p ollutan t
at
stations
U
and
I
,
for
the
da y
of
No v em b er
16,
2004.
The
ends
of
the
diagrams
corresp ond
to
the
minim um
and
maxim um
v alues.
F or
example,
at
station
U
,
the
maxim um
v alue
recorded
w as
8
µg
=
m
3
1
F or
eac h
of
the
t w o
stations,
indicate
the
median
and
calculate
the
in terquartile
range
as
w ell
as
the
range
of
the
measuremen t
series
2
Indicate,
b y
graphical
reading
and
sp ecifying
the
statis- tical
parameters
used,
on
whic h
station(s),
on
that
da y :
a
measuremen t
disp ersion
w as
greatest
b
at
least
half
the
measuremen ts
w ere
less
than
or
equal
to
5?
c
75
%
of
measuremen ts
at
least
w ere
less
than
or
equal
to
6?
Part
B
In
this
part,
station
R
.
is
considered
The
table
b elo w
giv es
the
hourly
readings,
for
the
same
da y
of
No v em b er
16,
2004,
what
concerns
the
p ollu- tan t
ozone
(
O
3
)
.
Concen trations
are
expressed
in
million ths
of
a
gram
p er
cubic
meter
of
air.
https:/ /c hingmath.fr
0,310 0,320 0,330 0,340 0,350 0,360 0,6 0,7 0,8 0,9 0,10 0,11 0,12
chapExoCorrec/169 sacados/169 Liban -- Juin 2006 -- 11 points
0 1 2 3 4 5 6 7 8 9 10 11 12 13 Station I Station U
station R station U station I 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 concen tration en millionième de grammes par mètres cub e d’air 0 10 20 30 40 50 60 70 80 90 100
0 1 2 3 4 5 3 e quartile: 2,42 Médiane: 2,06 1 er quartile: 1,63 Fondus de la glisse Glisse plaisir
Heure
1
h
2
h
3
h
4
h
5
h
6
h
7
h
8
h
9
h
10
h
11
h
12
h
Concen-tration
78
79
77
59
57
65
65
67
68
67
59
54
Heure
13
h
14
h
15
h
16
h
17
h
18
h
19
h
20
h
21
h
22
h
23
h
24
h
Concen-tration
64
68
78
74
72
72
76
77
76
74
77
76
1
What
are
the
minim um
and
maxim um
v alues
of
this
se- ries?
2
Determine,
with
justification,
the
median
and
quartiles
Q
1
and
Q
3
of
this
series.
3
Construct
the
b o x
diagram,
taking
half
a
cen timetre
as
the
graphical
unit.
Part
C
The
graph
b elo w
giv es,
for
the
p ollutan t,
the
a v erage
daily
results
for
No v em b er
2004
at
stations
U
,
I
and
R
.
1
a
On
whic h
da ys
in
No v em b er
w as
the
ozone
concen- tration
at
least
30
µg
=
m
3
for
station
U
?
b
Whic h
da ys
of
the
same
mon th
w as
it
at
most
60
µg
=
m
3
for
station
R
?
2
Station
I
sensor
read
58
µg
=
m
3
on
No v em b er
11
and
45
µg
=
m
3
on
No v em b er
13.
On
No v em b er
12,
the
sensor
w as
out
of
order.
The
tec hnician
decided
to
replace
the
missing
v alue
with
one
obtained
using
linear
in terp ola-
tion.
What
v alue
did
he
obtain?
Justify
the
answ er,
sp ecifying
the
pro cedure
follo w ed.
E.159
Part
A
The
table
b elo w
giv es
the
breakdo wn
of
225
cross-coun try
skiers
from
t w o
sp orts
clubs
:
the
ˇ
Fondus
de
la
glisse
ı
and
the
ˇ
Glisse
plaisir
ı,
according
to
their
a v erage
time
on
a
t yp- ical
race.
Times
are
group ed
in to
half-hour
amplitude
bands.
Club
Time
in
heures
TOTAL
[0.5
;1[
[1
;1.5[
[1.5
;2[
[2
;2.5[
[2.5
;3[
[3
;3.5[
[3.5
;4[
Fondu
de
glisse
6
21
37
45
22
7
0
138
Glisse
plaisir
0
0
1
10
44
29
3
87
TOTAL
6
21
38
55
66
36
3
225
1
Of
the
ˇ
Fondus
club
runners
at
glisse
ı,
what
p ercen tage
ha v e
an
a v erage
time
in
the
[1.5
;
2[
?
2
Of
all
the
riders,
what
p ercen tage
ha v e
a v erage
times
in
the
range
[1.5
;
2[
?
3
Lucas
claims
that
more
than
half
the
riders
ha v e
an
a v- erage
time
strictly
under
2.5
h
.
Is
he
righ t?
Justify
y our
answ er
with
a
calculation.
Part
B
We’re
in terested
in
the
club
ˇ
Glisse
plaisir
ı.
1
Belo w
is
an
extract
from
the
ranking
of
the
87
runners
in
this
club
according
to
their
a v erage
time
o v er
this
race.
Using
this
extract,
determine
the
median,
first
and
third
quartile
of
the
series
of
a v erage
times
of
these
87
runners.
Coureur
n
o
1
2
·
·
·
19
20
21
22
23
24
25
·
·
·
38
39
40
Temps
h
1.98
2.01
·
·
·
2.69
2.7
2.7
2.74
2.75
2.76
2.77
·
·
·
2.87
2.87
2.88
Coureur
n
o
41
42
43
44
45
46
·
·
·
63
64
65
66
67
·
·
·
86
87
Temps
h
2.89
2.89
2.89
2.89
2.89
2.9
·
·
·
3.08
3.1
3.1
3.11
3.11
·
·
·
3.6
3.67
2
The
b o x
plot
of
the
a v erage
time
series
of
the
ˇ
Fondus
de
la
Glisse
ı
club
runners
is
giv en.
The
ends
of
the
whisk ers
corresp ond
to
the
minim um
and
maxim um
times.
Construct
on
the
same
dra wing,
with
the
precision
al- lo w ed
b y
the
scale,
the
b o x
diagram
of
the
series
of
a v er- age
times
of
the
riders
of
the
ˇ
Glisse
plaisir
ı
club.
3
Using
the
t w o
b o x
plots,
compare
the
results
of
skiers
from
the
t w o
clubs.
Argue.
Part
C
To
study
p erformances,
t w o
friends
Théo
and
Clémen t
recorded
in
a
table
their
times
ac hiev ed
during
8
training
sessions
on
this
t ypical
race.
The
table
w as
created
using
a
spreadsheet
program.
The
table
cells
are
in
the
format
:
n um- b er,
2
decimal
places.
https:/ /c hingmath.fr
station R station U station I 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 concen tration en millionième de grammes par mètres cub e d’air 0 10 20 30 40 50 60 70 80 90 100 chapExoCorrec/159 sacados/159 Asie - Juin 2006 - 8 points
0 1 2 3 4 5 3 e quartile: 2,42 Médiane: 2,06 1 er quartile: 1,63 Fondus de la glisse Glisse plaisir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 A B C D E F T emps de Clémen t T emps en heure/min utes/secondes T emps de Théo T emps en heure/min utes/secondes temps en secondes temps en heures heures min utes secondes 1er en traînemen t 2 25 57 8757 2,43 2≥ème en traînemen t 2 23 26 8606 2,39 3≥ème en traînemen t 2 20 39 8439 2,34 4≥ème en traînemen t 2 27 7 8827 2,45 5≥ème en traînemen t 2 24 19 8659 2,41 6≥ème en traînemen t 2 21 37 8497 2,36 7≥ème en traînemen t 2 25 21 8721 2,42 8≥ème en traînemen t 2 19 56 8396 2,33 T emps mo y en : 2 23 33 8613 2,39 temps en secondes temps en heures heures min utes secondes 1er en traînemen t 2 50 3 10203 2,83 2≥ème en traînemen t 2 49 18 10158 2,83 3≥ème en traînemen t 2 48 27 10107 2,81 4≥ème en traînemen t 2 47 59 10079 2,80 5≥ème en traînemen t 2 49 39 10179 2,83 6≥ème en traînemen t 2 48 26 10106 2,81 7≥ème en traînemen t 2 50 3 10203 2,83 8≥ème en traînemen t 2 48 47 10127 2,81 T emps mo y en : 2 49 12 10145 2,82
0 1 2 3 4 5 6 7 8 9 10
We
read
that
Clémen t
put
in
for
his
1
er
training
:
2
hours
25
min utes
57
seconds,
or
2.43
hours.
1
a
Whic h
form ula
has
b een
written
in to
cell
E4
,
then
copied
do wn
to
E11
?
b
Whic h
form ula
w as
written
in to
cell
F4
,
then
copied
do wn
in to
form ula
F11
?
c
What
form ula
w as
en tered
in
cell
E12
to
calculate
Clé- men t’s
a v erage
time?
2
The
t w o
friends
w an t
to
join
one
of
the
t w o
clubs
next
y ear.
They
compare
their
a v erage
times
with
those
of
skiers
in
b oth
clubs.
They
w ould
lik e
to
b e
in
the
same
club
and
b e
in
the
top
quarter
of
skiers.
Is
their
wish
ac hiev able?
Explain
y our
answ er.
E.172
new
Caledonia
ffl
Marc h
2006
ffl
10
p oin ts
W e
w an t
to
tile
a
rectangular
ro om
of
6
m
in
length
and
4
m
in
width,
therefore
of
area
24
m
2
,
using
tiles
of
2
col- ors
:
red
and
gra y .
What’s
more,
there
are
t w o
t yp es
of
tile
in
eac h
color :
patterned
tiles
and
plain
tiles.
So
there
are
a
total
of
4
tile
patterns.
Parts
A
,
B
and
C
of
this
exercise
are
indep enden t.
Part
A
1
Eac h
tile
is
a
square
of
0.2
m
side.
What
is
the
minim um
n um b er
of
tiles
required
to
tile
the
ro om?
2
F or
installation
purp oses,
it
is
necessary
to
buy
at
least
672
tiles,
of
whic h
25
%
in
red,
the
rest
in
grey .
It
is
also
planned
to
la y
1
=
3
patterned
tiles
for
eac h
color,
the
rest
b eing
plain.
Calculate
the
minim um
n um b er
of
tiles
of
eac h
pattern
to
b e
purc hased
and
complete
the
table
b elo w.
Rouges
Gris
Total
Motifs
56
Unis
Total
504
3
Tiles
are
sold
in
pac ks
of
15
of
the
same
mo del.
a
Calculate
the
minim um
n um b er
of
pac ks
of
eac h
kind
required
and
complete
the
table
b elo w
:
Rouges
Gris
Total
Motifs
4
Unis
Total
47
b
Justify
that
the
minim um
total
n um b er
of
pac k ets
re- quired
is
indeed
equal
to
47.
Part
B
In
pac ks
of
15
tiles,
w e
studied,
out
of
a
batc h
of
1
000
packs,
the
n um b er
of
pac ks
con taining
n
defective
tiles
(
n
being
a
numb er
b etwe en
0
and
15)
and
w e
obtained
the
follo wing
ta- ble
:
n
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Nombre
de
paquets
comp or- tan t
n
carreaux
défec- tueux
30
80
170
440
190
70
20
0
0
0
0
0
0
0
0
0
1
Determine
the
median
of
this
statistical
series.
2
a
Determine
first
quartile
Q
1
b
Recall
the
definition
of
the
third
quartile
Q
3
.
Calcu- late
it.
c
Dra w
a
b o x
plot
of
this
series
in
the
reference
frame
b elo w.
https:/ /c hingmath.fr
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 A B C D E F T emps de Clémen t T emps en heure/min utes/secondes T emps de Théo T emps en heure/min utes/secondes temps en secondes temps en heures heures min utes secondes 1er en traînemen t 2 25 57 8757 2,43 2≥ème en traînemen t 2 23 26 8606 2,39 3≥ème en traînemen t 2 20 39 8439 2,34 4≥ème en traînemen t 2 27 7 8827 2,45 5≥ème en traînemen t 2 24 19 8659 2,41 6≥ème en traînemen t 2 21 37 8497 2,36 7≥ème en traînemen t 2 25 21 8721 2,42 8≥ème en traînemen t 2 19 56 8396 2,33 T emps mo y en : 2 23 33 8613 2,39 temps en secondes temps en heures heures min utes secondes 1er en traînemen t 2 50 3 10203 2,83 2≥ème en traînemen t 2 49 18 10158 2,83 3≥ème en traînemen t 2 48 27 10107 2,81 4≥ème en traînemen t 2 47 59 10079 2,80 5≥ème en traînemen t 2 49 39 10179 2,83 6≥ème en traînemen t 2 48 26 10106 2,81 7≥ème en traînemen t 2 50 3 10203 2,83 8≥ème en traînemen t 2 48 47 10127 2,81 T emps mo y en : 2 49 12 10145 2,82 chapExoCorrec/172 sacados/172 0 1 2 3 4 5 6 7 8 9 10
Nombre de paquets 0 10 20 30 40 50 60 Prix à payer 100 200 300 400 500 600 700 800 900 1000
0 10 20
Part
C
We
note
(in
eur os)
a
the
price
of
a
pac k et
of
tiles
and
b
the
fixed
deliv ery
c harge
whatev er
the
n um b er
of
pac k ets
deliv- ered.
The
graph
calculates
the
price
paid
b y
the
customer
as
a
func- tion
of
the
n um b er
of
tile
pac ks
purc hased.
1
Graphically
determine
the
price
paid
b y
the
customer
for
the
purc hase
of
50
pac ks
of
tiles.
2
Calculate
the
price
a
of
a
pac k et
of
tiles
and
the
amoun t
b
of
the
deliv ery
c harge.
Then
calculate
the
price
paid
b y
the
customer
for
47
pac k ages
deliv ered.
E.170
A
comp etition
features
t w o
rounds.
30
participan ts
tak e
part.
Here
is
the
table
sho wing
the
scores
obtained
b y
the
participan ts
:
Notes
on
20
Effectifs
Proof
n
o
1
Proof
n
o
2
5
0
3
6
6
0
7
5
5
8
8
0
9
1
8
10
3
0
11
0
3
12
2
4
13
0
0
14
1
1
15
2
4
16
2
2
1
Determine
the
median,
first
and
third
quartile
of
eac h
of
the
t w o
series.
2
Construct
on
the
graduated
lines
b elo w
the
b o x
plots
corresp onding
to
the
t w o
series.
Statistical
series
E
1
-
b o x
plot
Statistical
series
E
2
-
b o x
plot
https:/ /c hingmath.fr
Nombre de paquets 0 10 20 30 40 50 60 Prix à payer 100 200 300 400 500 600 700 800 900 1000 sacados/170 Extrait Juin 2004 - Centres Etrangers
0 10 20 0 10 20
tranc he d’âge SAU Exploitation de 50 ha à 100 ha 24 42 47 54 65 Exploitation de moins de 10 ha 18 43 57 60 63
E.164
The
table
(incomplete)
belo wb elo w
giv es
the
distribution
of
the
800
farm
managers
in
a
region
ac- cording
to
their
age
and
the
Useful
Agricultural
Area
(UAA)
of
their
farm.
Area
is
expressed
in
hectares
(
ha
)
and
age
in
y ears.
0;10
10;30
30;50
50;100
Total
15;25
2
1
5
3
25;35
21
16
28
84
35;45
40
33
59
148
45;55
17
53
123
55;65
110
60
70
57
297
Total
190
180
270
800
Part
A
1
Complete
the
table
(the
c omplete d
c olumns
c orr esp ond- ing
to
a
Useful
A gricultur al
A r e a
of
10
shouldbecopiedontothecopy
;
30
and
30
;
50
)
.
2
P ercen tages
ask ed
in
this
question
will
b e
rounded
to
0.1
%
.
a
Among
farm
managers,
what
p ercen tage
are
in
the
age
range
25
;
35
.
b
Among
farm
managers,
what
p ercen tage
are
strictly
under
45
y ears
of
age
and
o wn
at
least
30
ha
of
Useful
Agricultural
Area?
c
Among
farm
managers
aged
55
or
o v er,
what
p ercen t- age
ha v e
a
Useful
Agricultural
Area
of
less
than
10
ha
?
d
Among
farm
managers
with
a
Useful
Agricultural
Area
of
less
than
10
ha
,
what
p ercen tage
are
aged
55
or
o v er?
Part
B
1
a
Ho w
man y
farm
managers
are
strictly
under
45?
Strictly
under
55?
b
Explain
wh y
the
median
age
of
farm
managers
is
nec- essarily
b et w een
45
and
55.
T o
determine
the
median
age,
the
distribution
of
ages
in
the
class
45
;
55
is
giv en
b y
the
follo wing
table
:
Age
45
46
47
48
49
50
51
52
53
54
Numb er
18
21
24
31
30
31
3
27
28
20
How
man y
farm
managers
are
45
y ears
old
or
y ounger?
Justify
that
the
median
age
is
51.
c
The
first
and
third
quartiles
of
the
age
series
are
42
and
58.
Construct
a
b o x
plot
of
this
series,
taking
as
extreme
v alues
18
and
65.
W e’ll
c ho ose
2
mm
as
the
scale
for
one
y ear.
2
The
b o x
plot
of
the
ages
of
farm
managers
from
50
ha
to
100
ha
and
that
of
farm
managers
under
10
ha
are
sho wn
b elo w.
A
journalist
wrote
:
ˇAs
a
whole,
heads
of
50
to
100
ha
are
y ounger
than
heads
of
less
than
10
ha
.ı
Commen t
on
this
statemen t
using
these
b o x
plots.
E.1824
In
India,
a
p opulation
census
is
tak en
ev ery
ten
y ears.
The
last
census
w as
carried
out
in
2001.
It
rev ealed
the
dis- tribution
of
India’s
p opulation
according
to
v arious
criteria
including
age,
gender,
place
of
residence,
and
to ok
sto c k
of
India’s
literacy .
(sourc e :
Census
of
india
2001)
A
literate
p erson
b eing
one
who
can
read
and
write,
c hildren
aged
0-6
ha v e
b een
excluded
from
the
statistics.
Here
is
an
extract
from
the
data
collected
on
the
p opulation
aged
7
and
o v er
(in
mil lions
of
inhabitants)
.
Population
aged
7
and
plus
(in
mil lions
of
inhabitants)
Hommes
Femmes
Total
Rural
318
301
619
Urban
en vironmen t
131
119
250
Total
449
420
869
Population
aged
7
and
o v er
non
alphab etic
(in
mil lion
inhabitants)
Hommes
Femmes
Total
Rural
91
161
252
Urban
en vironmen t
18
32
50
Total
109
193
302
1
The
follo wing
statemen ts
relate
to
India’s
p opulation
aged
7
and
o v er
in
2001.
F or
eac h
of
these
statemen ts,
sa y
whether
it
is
true
or
false,
justifying
the
answ er.
a
Less
than
one
in
four
men
is
non-literate.
b
A t
least
t w o-thirds
of
non-literates
are
w omen.
c
In
urban
areas,
one
in
fiv e
p eople
is
non-literate.
d
More
than
80
%
of
non-literate
w omen
liv e
in
rural
ar- eas.
2
In
an
article
published
b y
UNESCO,
w e
read
:
ˇRecen t
statistics
sho w
a
steady
decline
in
the
n um b er
of
non- literates
in
the
w orld :
literacy
is
progressing
slo wlyı.
a
Calculate
the
p ercen tage
(rounde d
to
the
unit)
of
lit- erates
among
India’s
inhabitan ts
aged
7
and
o v er,
in
2001.
b
India
is
made
up
of
35
states.
A
state’s
literacy
rate
is
said
to
equal
x
when
the
p er- cen tage
of
literate
inhabitan ts
in
that
state
is
x
%
.
The
follo wing
table
giv es
the
literacy
rate,
rounded
to
the
unit,
recorded
in
2001
in
eac h
of
India’s
35
states
:
https:/ /c hingmath.fr
sacados/164 tranc he d’âge SAU Exploitation de 50 ha à 100 ha 24 42 47 54 65 Exploitation de moins de 10 ha 18 43 57 60 63 chapExoCorrec/1824 sacados/1824
3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 1 0 0 1 0 5 Recensement 1991
1 3 5 7 9 11 13
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Seconde 1 Seconde 2 Seconde 3 Seconde 4 Seconde 5 Seconde 6
48
54
54
55
57
60
61
61
63
64
64
64
65
67
67
69
69
69
70
70
70
72
73
74
77
77
81
81
81
82
82
82
88
88
91
Thus,
in
2001,
in
one
of
India’s
states,
the
liter acy
r ate
is
e qual
to
48,
which
me ans
that
the
p er c entage
of
liter ate
inhabitants
in
this
state
is
e qual
to
48
%
.
Determine
the
median,
first
quartile
and
third
quartile
of
the
series
of
literacy
rates
found
in
the
2001
census
in
eac h
of
India’s
35
states.
3
The
literacy
series
recorded
in
the
1991
census
in
eac h
of
the
35
states
of
India
is
represen ted
b y
the
b o x
plot
giv en
in
appendix
2
where
v alues
37
and
90
are
the
minim um
and
maxim um
v alues
of
the
series.
a
Sho w
on
the
same
graph,
the
b o x
plot
of
the
series
of
literacy
rates
recorded
in
the
2001
census
in
eac h
of
India’s
35
states.
b
By
comparing
these
t w o
diagrams,
giv e
t w o
precise
argumen ts
for
asserting
that
literacy
has
clearly
pro- gressed
in
India
b et w een
1991
and
2001.
E.2028
A
car
ren tal
compan y
o wns
a
fleet
of
800
v ehicles
of
three
differen t
mak es
A
,
B
and
C
.
Within
eac h
brand,
the
compan y
has
t w o
v ehicle
mo dels
:
ˇEssenceı
or
ˇDieselı.
During
the
y ear,
eac h
v ehicle
ma y
b e
immobilized
to
undergo
main tenance,
adjustmen ts,
oil
c hanges,
repairs,
etc.
F or
all
500
v ehicles
ˇDieselı
of
the
compan y ,
w e
studied,
dur- ing
the
y ear
2005,
the
n um b er
of
da ys
of
immobilization.
The
follo wing
statistical
series
S
was
obtained
:
Nombre
de
journées
d’immobilisation
1
2
3
4
5
6
7
8
Nombre
de
v éhicules
concernés
11
34
86
121
120
88
28
12
1
Calculate
the
mean
x
of
the
series
S
(the
r esult
wil l
b e
r ounde d
to
the
ne ar est
0.1)
.
2
Determine
the
median
m
of
the
series
S
.
3
Determine
the
first
quartile
Q
1
of
the
series
S
.
The
third
quartile
Q
3
is
assumed
to
equal
6.
4
Using
the
axis
sho wn
in
app endix
,
to
b e
returned
with
the
cop y ,
dra w
the
b o x
plot
of
the
S
series.
5
Calculate
the
standard
deviation
of
the
series
S
(the
r e- sult
should
b e
r ounde d
to
the
ne ar est
hundr e dth)
.
4.
Mustache
b ox :
r e ading
E.4748
Belo w
are
the
b o x
plots
for
the
6
second- y ear
classes
in
a
high
sc ho ol
during
the
second-quarter
com- mon
assessmen t
:
1
Giv e
the
marks
corresp onding
to
the
median,
first,
third
quartile
of
the
Seconde
1
mark
series.
2
In
Seconde
2,
can
w e
sa y
that
at
least
one
in
t w o
studen ts
has
a
mark
of
10
or
less?
Justify .
3
In
whic h
Seconde
classes
can
w e
sa y
that
at
least
75
%
of
studen ts
ha v e
a
mark
of
13
or
b elo w?
Justify .
4
F or
Seconde
class
3,
giv e
the
in terquartile
range.
5
In
Seconde
5,
what
p ercen tage
of
studen ts
scored
10
or
ab o v e?
https:/ /c hingmath.fr
3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 5 1 0 0 1 0 5 Recensement 1991 sacados/2028 1 3 5 7 9 11 13 chapExoCorrec/4748 sacados/4748 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Seconde 1 Seconde 2 Seconde 3 Seconde 4 Seconde 5 Seconde 6
10 10.5 11 11.5 12 12.5 13 1881 à 1900 1901 à 1920 1921 à 1940 1941 à 1960 1961 à 1980 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 cm C B A 0 2 4 6 8 10 12 14 16 18 20 2 o A 2 o B 2 o C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 o 1 2 o 2 2 o 3
E.4744
The
P aris
Mon tsouris
meteorological
ob- serv atory
has
b een
con tin uously
recording
outdo or
temp era- tures
since
1872,
and
pro vides
ann ual
a v erages
based
on
these
readings.
The
aim
of
this
exercise
is
to
compare
these
a v er- ages
b y
t w en t y-y ear
p erio ds
b et w een
1880
and
2000.
T o
clar- ify
v o cabulary ,
w e’ll
call
ˇann ual
temp eratureı
the
a v erage
of
temp eratures
recorded
in
a
giv en
y ear
(days
and
nights)
,
expressed
in
degrees
Celsius
and
rounded
to
0.05
o
C
.
Sourc es
Mété o
F r anc e
The
do cumen t
b elo w
sho ws
b o x
plots
constructed
from
ann ual
temp eratures
o v er
eac h
t w en t y-y ear
p erio d
b et w een
1881
and
1980.
On
eac h
of
these
diagrams,
the
median,
first
and
third
quartiles
ha v e
b een
plotted.
The
ends
of
the
ˇmoustac hesı
mark
the
minim um
and
maxim um
of
this
series.
F or
eac h
of
the
follo wing
prop ositions,
indicate
whether
it
is
true,
false
or
undecidable
(in
the
c ase
wher e
the
do cument
would
not
al low
us
to
know
whether
the
pr op osition
is
true
or
false)
.
Justify
the
answ er.
1
The
maxim um
ann ual
temp erature
w as
12.65
o
C
pendan t
a
cen tury ,
from
1881
to
1980.
2
The
ann ual
temp erature
range
w as
2.25
o
C
during
one
cen tury ,
from
1881
to
1980.
3
During
one
cen tury ,
from
1881
to
1980,
at
least
thirt y
y ears
had
their
ann ual
temp erature
b elo w
11.5
o
C
.
4
1961
w as
the
coldest
y ear
o v er
the
p erio d
1901-1980.
E.4747
A
p étanque
b oules
factory
designs
com- p etition
b oules
of
differen t
masses
and
diameters.
The
three
masses
offered
are
700
g
,
720
g
and
745
g
and,
for
eac h
of
these
masses,
three
diameters
are
prop osed
:
71
mm
,
75
mm
,
79
mm
.
A
regional
c hampion
decides
to
buy
720
g
balls,
but
hesitates
o v er
the
diameter.
T o
mak e
his
c hoice.
He
places
a
jac k
at
9
meters,
p oin ts
200
times
with
eac h
of
the
balls
of
differen t
diameters
and
measures
the
distance
to
the
jac k.
Here
are
the
decile-pruned
b o x
plots
represen ting
this
test.
The
ends
of
the
diagram
are
the
first
and
nin th
decile
resp ectiv ely .
Here
are
some
of
the
pla y er’s
feelings
after
the
test
:
1
"
With
the
79
mm
ball,
I
managed
some
v ery
go o d
thro ws,
but
also
some
v ery
bad
ones.
"
2
"
With
the
71
mm
ball,
I
had
v ery
go o d
sensations,
half
m y
thro ws
w ere
within
16
cm
of
the
jac k
and
I
managed
some
v ery
nice
ones.
"
3
"
But
m y
preference
is
for
the
75
mm
ball,
with
whic h
I’m
more
consisten t.
"
Asso ciate
the
corresp onding
b o x
diagram
with
eac h
t yp e
of
ball.
Justify
y our
answ er.
E.4783
The
diagram
b elo w
sho ws
b o x
plots
of
the
a v erages
obtained
b y
studen ts
in
three
classes
of
second
y ear
at
a
sc ho ol :
1
a
Giv e
the
range
of
a v erages
for
the
class
2
o
B
.
b
Giv e
the
in terquartile
range
of
the
class
2
o
A
.
2
Sa y
whether
the
follo wing
statemen ts
are
true,
false
or
undecidable
:
a
A t
least
50
%
of
second
graders
at
this
sc ho ol
had
an
a v erage
ab o v e
9
.
b
A t
most
25
%
of
second
graders
at
this
sc ho ol
had
an
a v erage
b elo w
7
.
E.4827
A
sc ho ol
has
three
sophomore
classes.
The
b o x
plots
b elo w
represen t
their
scores
on
a
common
test
:
Based
on
their
scores,
w e
also
constructed
the
follo wing
three
tables
of
studen t
n um b ers
:
a
Note
0;4
4;8
8;12
12;16
16;20
Staff
4
4
10
3
1
b
Note
0;4
4;8
8;12
12;16
16;20
Staff
3
2
6
8
4
c
Note
0;4
4;8
8;12
12;16
16;20
Numb er
of
emplo y ees
6
4
5
5
2
Associate
eac h
b o x
plot
with
the
corresp onding
table
of
em- plo y ee
n um b ers.
https:/ /c hingmath.fr
chapExoCorrec/4744 sacados/4744 10 10.5 11 11.5 12 12.5 13 1881 à 1900 1901 à 1920 1921 à 1940 1941 à 1960 1961 à 1980 chapExoCorrec/4747 sacados/4747 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 cm C B A chapExoCorrec/4783 sacados/4783 0 2 4 6 8 10 12 14 16 18 20 2 o A 2 o B 2 o C chapExoCorrec/4827 sacados/4827 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 o 1 2 o 2 2 o 3
0 10.5 11 11.5 12 12.5 13 13.5 14 10 20 30 40 50 60 70 80 90 100 110
5.
Cumulative
incr e asing
fr e quency
curve
E.4738
Here
is
the
table
sho wing
the
studen ts’
grades
in
the
middle
sc ho ol
diploma
exam :
Note
0
;
4
4
;
8
8
;
12
12
;
16
16
;
20
Numb er
5
32
61
80
15
Freq.
Cumulativ e
frequency
Ascending
1
What
is
the
mo dal
class
of
this
statistical
series?
2
Calculate
the
sc ho ol’s
a v erage
for
this
exam,
rounded
to
the
nearest
ten th.
3
a
Complete
the
table
b y
rounding
the
frequencies
to
the
nearest
thousandth.
b
Construct
an
orthonormal
co ordinate
system
where
the
scores
will
b e
represen ted
on
the
x-axis
(
1
cm
=2
points)
and
on
the
y-axis
(
1
cm
=8
students)
.
Plot
the
cum ulativ e
frequency
curv e
on
this
graph.
c
Deduce
the
v alue
of
the
median.
(Le ave
the
c onstruc- tion
lines
visible)
E.4750
66
Météo-F rance
w eather
stations
spread
across
F rance
ha v e
pro vided
ann ual
temp erature
data
for
eac h
y ear
b et w een
1901
and
2006.
The
cum ulativ e
frequency
p olygon
sho wn
b elo w
w as
ob- tained
:
1
Using
the
graph
ab o v e,
determine
the
v alues
for
this
sta- tistical
series
of
the
first
quartile,
the
median,
and
the
third
quartile.
2
a
Complete
the
follo wing
frequency
table
:
Temp érature
mo y enne
[10;10.5[
[10.5;11[
[11;11.5[
[11.5;12[
Numb er
of
y ears
Temp érature
mo y enne
[12;12.5[
[12.5;13[
[13;13.5[
Numb er
of
y ears
b
Using
the
calculator,
determine
the
mean
and
stan- dard
deviation
of
this
statistical
series
(results
should
b e
giv en
to
t w o
decimal
places)
.
https:/ /c hingmath.fr
chapExoCorrec/4738 sacados/4738 chapExoCorrec/4750 sacados/4750 0 10.5 11 11.5 12 12.5 13 13.5 14 10 20 30 40 50 60 70 80 90 100 110
0 10 20 30 40 50 60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 70 80 90 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Age F réquence
E.4784
In
an
am usemen t
park,
w e
studied
vis- itor
w aiting
times
at
the
en trance
to
a
household.
The
data
w as
compiled
in
the
table
b elo w
:
Waiting
time
(in
min)
0
;
5
5
;
10
10
;
20
20
;
30
30
;
60
Numb er
26
76
82
24
8
Frequency
F.C.C.
1
Complete
the
t w o
lines
for
frequencies
and
cum ulativ e
fre- quencies,
rounding
the
results
to
the
nearest
thousandth.
2
Construct
the
cum ulativ e
frequency
curv e
for
this
statis- tical
series
on
the
graph
b elo w
:
3
a
Graphically
determine
the
median
and
quartiles
of
this
statistical
series
(leave
the
c onstruction
lines)
.
b
Construct
the
b o x
plot
for
this
statistical
series
using
the
scale
:
1
cm
represents
5
min
expected
E.4825
The
2011
census
of
the
F renc h
p opula- tion
yielded
the
follo wing
headcoun t
table
:
Classe
d’âges
0;10
10;20
20;30
30;50
50;70
70;100
Effectif
(in
thousands)
8
054
7
981
8
077
17
372
15
630
8
234
Fréquence
F.
C.C.
1
Determine
the
frequency
of
the
F renc h
p opulation
repre- sen ted
b y
the
p opulation
aged
under
20
ans,
rounded
to
the
nearest
thousandth.
2
Complete
the
ro ws,
in
the
table
b elo w,
of
the
frequencies
and
increasing
cum ulativ e
frequencies
(fre quencies
wil l
b e
r ounde d
to
the
ne ar est
thousandth)
.
3
a
Plot
the
curv e
of
increasing
cum ulativ e
frequencies
in
the
frame
b elo w.
b
Determine
graphically
the
v alue
of
the
first
quartile,
median
and
third
quartile
of
this
statistical
series.
(construction
lines
should
b e
left
visible)
.
4
Plot
the
b o x
plot
using
the
p osition
indicators
for
this
se- ries
obtained
in
question
3
b
.
The
scale
will
b e
1
cm
for
10
ans.
https:/ /c hingmath.fr
chapExoCorrec/4784 sacados/4784 0 10 20 30 40 50 60 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 chapExoCorrec/4825 sacados/4825 0 10 20 30 40 50 60 70 80 90 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Age F réquence
155 0 160 165 170 175 180 185 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
E.4742
W e
consider
the
studen ts
in
a
junior
high
sc ho ol
class
and
study
their
heigh t.
Here
is
the
statistical
series
asso ciated
with
heigh t
in
cen time- ters
:
167
−
181
−
173
−
179
−
165
−
169
−
170
−
174
−
160
172
−
173
−
164
−
170
−
156
−
161
−
171
−
174
−
162
183
−
176
−
170
−
163
−
175
−
155
−
173
−
167
−
168
175
−
170
−
162
−
169
−
170
−
159
1
Complete
the
table
of
n um b ers
b elo w
and
the
asso ciated
lines
:
frequencies
will
b e
giv en
to
10
−
3
near.
Classe
[155;160[
[160;165[
[165;170[
[170;175[
[175;180[
[180;185[
Staff
Fréq
Fréq
cum
crois
san te
2
Consider
the
graph
b elo w
:
a
Dra w
the
cum ulativ e
frequency
p olygon.
b
Determine
the
p osition
of
the
first
quartile,
the
median,
and
the
third
quartile.
3
Plot
the
b o x
plot
corresp onding
to
this
statistical
series
using
the
follo wing
scale
:
1
cm
on
the
graduated
line
←→
2
cm
for
size.
E.221
Here
is
the
table
sho wing
the
distribution
of
studen ts’
scores
on
the
middle
sc ho ol
graduation
exam :
Score
0
;
4
4
;
8
8
;
12
12
;
16
16
;
20
Numb er
of
Studen ts
5
32
61
80
15
Fréquence
en
%
Fréquence
cum ulée
croissan te
1
Find
the
mo dal
class
for
this
statistical
series.
2
Calculate
the
sc ho ol’s
a v erage
score
on
this
exam,
rounded
to
the
nearest
h undredth.
3
a
Complete
the
ro ws
for
frequencies
and
cum ulativ e
frequencies
in
ascending
order
in
the
table
ab o v e.
b
Construct
an
orthonormal
co ordinate
system
where
the
x-axis
represen ts
(
1
cm
=2
points)
and
the
y-axis
represen ts
(
1
cm
=10
%
students)
.
Plot
the
cum ulativ e
frequency
curv e
on
this
co ordinate
system.
c
Determine
the
median
from
this
curv e.
(Le ave
your
c onstruction
lines
visible)
https:/ /c hingmath.fr
chapExoCorrec/4742 sacados/4742 155 0 160 165 170 175 180 185 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 chapExoCorrec/221 sacados/221
40 45 50 55 60 0 10 20 30 40 50 60 70 80 90 100
E.224
In
a
group
of
60
athletes,
resting
heart
rates
(FCR)
were
studied.
That
is,
the
n um b er
of
heartb eats
p er
min ute
after
a
long
p erio d
of
calm
and
rest.
Here
are
the
ages
and
F CRs
of
the
p opulation
Age
FCR
Age
FCR
Age
FCR
Age
FCR
42
42
50
50
37
52
41
54
41
43
35
50
42
52
31
55
61
45
24
50
21
52
50
55
51
45
23
50
40
53
32
55
41
46
52
50
34
53
22
55
27
46
36
51
35
53
42
55
33
46
31
51
28
53
52
55
40
48
35
51
55
53
18
57
55
48
60
51
49
53
51
59
31
48
29
52
31
53
22
59
32
48
30
52
35
53
23
59
35
48
49
52
38
54
53
59
44
49
32
52
53
54
50
59
40
50
40
52
42
54
28
59
36
50
47
52
54
54
47
60
The
CRF
of
the
study
p opulation
will
b e
tak en
as
the
study
c haracter
:
1
Giv e
the
median
of
this
statistical
series.
2
Complete
the
follo wing
table
:
Classe
[40
;
45[
[45
;
50[
[50
;
55[
[55
;
60]
Effectif
Fréquence
Fréq
cum
croissan te
Frequencies
will
b e
expressed
as
p ercen tages
to
the
near- est
0.1
%
.
3
a
Dra w
in
the
table
b elo w,
the
curv e
of
increasing
cu- m ulativ e
frequencies
in
the
frame
b elo w.
b
Lea ving
y our
constructions
on
the
figure,
giv e
the
ab- scissa
of
the
p oin t
on
the
curv e
with
ordinate
50
%
c
Giv e
an
in terpretation
of
this
result.
https:/ /c hingmath.fr
chapExoCorrec/224 sacados/224 40 45 50 55 60 0 10 20 30 40 50 60 70 80 90 100
45 55 65 75 85 0 10 20 30 40 50 60 70 80 90 100
0 10 20 30 40 0.1 0.2 0.3 0.4 0.5 Durée du tra jet (en min) F réquence (en %)
E.229
Jean,
a
video
game
en th usiast,
recorded
the
duration
in
seconds
of
the
40
games
he
pla y ed
:
49
52
57
57
57
58
58
59
60
60
60
62
63
63
63
63
64
64
64
64
65
65
66
67
69
69
70
70
72
74
74
75
75
76
77
78
79
80
80
80
1
Giv e
the
median
v alue
of
this
series.
That
is,
the
duration
suc h
that
:
The
n um b er
of
games
with
a
duration
less
than
this
represen ts
50
%
of
the
games
considered.
Th us,
that
the
games
represen ting
a
shorter
duration
also
represen t
50
%
2
a
Complete
the
table
b elo w
:
Classe
45; 50
50; 55
55; 60
60; 65
65; 70
70; 75
75; 80
80; 85
Eff.
Fréq.
Fréq
cum
croiss.
b
Construct
the
cum ulativ e
increasing
frequency
curv e
:
c
Find
the
v alue
of
the
median
from
this
graph
E.2016
Here
are
the
a v erage
mon thly
temp era- tures
recorded
b et w een
1994
and
2003
in
the
to wn
of
Sète
in
the
south
of
F rance
:
Mois
Janvier
Février
Mars
Avril
Mai
Juin
Temp érature
8.3
9.4
12.1
13.5
17.5
21.2
Mois
Juillet
Août
Sept.
Octob.
Nov em.
Decem.
Temp érature
23.4
22.8
18.6
15.7
10.8
8.5
1
Determine
the
a v erage
ann ual
temp erature
for
the
cit y
of
Sète.
2
Scien tists
estimate
a
global
temp erature
rise
of
1.5
o
C
in
2020.
a
Repro duce
the
previous
table,
accepting
the
scien tists’
predictions.
b
Then
calculate
the
a v erage
ann ual
temp erature
of
this
cit y
in
2020.
E.2065
W e
study
the
journey
made
b y
studen ts
in
the
second
grade
eac h
da y
to
get
from
their
homes
to
the
lycée.
The
time
(expresse d
in
minutes)
taken
for
this
journey
is
recorded
:
Temps
de
transp ort
par
jour
0
;
10
10
;
30
30
;
40
40
;
50
Nombre
d’élèv es
32
54
17
3
1
a
Recop y
the
ab o v e
table,
adding
the
frequencies
and
increasing
cum ulativ e
frequencies
expressed
as
p ercen t- ages
to
the
nearest
0.1
%
.
b
Determine
the
median
class
of
this
statistical
series.
2
Determine
the
a v erage
tra v el
time,
rounded
to
the
min ute,
p er
da y
of
a
second-grade
studen t
at
this
high
sc ho ol.
3
a
In
an
orthogonal
frame
of
reference
O
;
I
;
J
such
that
:
OI
=
0.2
cm
O J
=
0.1
cm
Plot
the
p olygon
of
increasing
cum ulativ e
frequencies.
b
Using
this
curv e,
determine
the
median
v alue
of
this
statistical
series.
E.230
By
studying,
on
a
class
basis,
the
tra v el
time
to
sc ho ol.
Here’s
ho w
long
it
tak es
:
5
;
15
;
15
;
25
;
5
;
38
;
37
;
20
;
3
;
15
;
7
;
2
;
30
;
10
16
;
2
;
5
;
5
;
20
;
25
;
25
;
30
;
3
;
11
;
25
;
8
;
13
1
Complete
the
table
b elo w,
rounding
frequencies
to
the
nearest
thousandth.
Classe
(en
min)
0
;
10
10
;
20
20
;
30
30
;
40
Effectif
Fréquence
Fréquence
Cum ulé
Croissan t
2
Construct
the
frequency
histogram
b elo w
:
3
Construct
the
cum ulativ e
increasing
frequency
curv e
:
https:/ /c hingmath.fr
chapExoCorrec/229 sacados/229
45 55 65 75 85 0 10 20 30 40 50 60 70 80 90 100 chapExoCorrec/2016 sacados/2016 chapExoCorrec/2065 sacados/2065
chapExoCorrec/230 sacados/230 0 10 20 30 40 0.1 0.2 0.3 0.4 0.5 Durée du tra jet (en min) F réquence (en %)
0 10 20 30 40 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Durée du tra jet (en min) F réquence (en %)
155 0 160 165 170 175 180 185 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
E.2363
The
graph
opp osite
sho ws
the
p olygon
of
increasing
cum ulativ e
frequencies
of
a
statistical
series
rep- resen ting
the
size
of
a
sample
of
high
sc ho ol
studen ts.
This
diagram
has
b een
dra wn
from
a
table
of
studen t
n um- b ers,
in
whic h
the
studen ts
ha v e
b een
sorted
in to
classes
:
[155
;
160[
;
[160
;
165[
;
[165
;
170[
[170
;
175[
;
[175
;
180[
;
[180
;
185[
1
a
Determine,
appro ximately ,
the
frequency
asso ciated
with
the
class
[155
;
160[
b
Determine,
appro ximately ,
the
frequency
asso ciated
with
the
class
[175
;
180[
2
Lea ving
the
construction
lines
on
the
graph
:
a
Determine
the
median
of
this
statistical
series.
b
Determine
the
first
and
third
quartile
of
the
series.
6.
Sampling
E.283
The
table
b elo w
sho ws
the
n um b er
of
couples
with
c hildren
under
25
still
living
at
home.
Numb er
of
c hildren
Numb er
of
couples
(in
thousands)
0
5420
1
3048
2
2880
3
1233
4
and
more
651
1
What
is
the
mo dal
class
of
this
statistical
series?
2
If
eac h
of
the
651
000
couples
in
the
"4 and
o v er" ro w
had
exactly
4
c hildren,
what
w ould
b e
the
a v erage
n um b er
of
c hildren
p er
couple?
3
Another
study
states
that
the
a v erage
n um b er
of
c hildren
under
25
still
living
with
their
paren t
is
1.18.
Calculate
the
a v erage
n um b er
of
c hildren,
among
the
651
000
cou- ples
with
4
or
more
c hildren,
living
still
living
in
their
household.
E.284
During
a
comp etition,
40
judokas.
are
w eighed
The
calculated
a v erage
w eigh t
is
72
kg
.
A
c hec k
of
the
scale
sho ws
that
it
w as
incorrectly
set
and
indicates
500
g
less
than
the
actual
w eigh t
on
eac h
of
the
w eighings.
What
is
the
actual
a v erage
w eigh t
of
the
40
judok as?
What
prop ert y
is
used
for
this
statemen t?
E.285
In
a
high
sc ho ol,
there
are
four
second-y ear
classes
con taining
30,
32
,28
and
27
pupils
re- sp ectiv ely .
The
a v erage
ph ysical
education
grades
for
these
classes
are
12,
11,
13
and
14
resp ectiv ely .
What
is
the
a v erage,
rounded
to
the
nearest
h undredth,
of
the
ph ysical
education
grades
for
all
four
of
the
lycée’s
second- y ear
classes?
https:/ /c hingmath.fr
0 10 20 30 40 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Durée du tra jet (en min) F réquence (en %) chapExoCorrec/2363 sacados/2363 155 0 160 165 170 175 180 185 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 chapExoCorrec/283 sacados/283 chapExoCorrec/284 sacados/284 chapExoCorrec/285 sacados/285
E.286
The
latest
F renc h
p opulation
census
b y
INSEE
(Institut
national
de
la
statistique
et
des
études
é c onomiques
-
http
://www.inse e.fr)
in
1999
giv es
us
the
fol- lo wing
table
:
Age
de
la
p opulation
Less
de
20
ans
de
20
ans
à
39
ans
de
40
à
59
ans
de
60
à
74
ans
de
75
à
99
ans
Fréquence
(%)
24.6
28.1
26
13.6
7.7
Calculate
the
a v erage
age
of
the
F renc h
p opulation
from
this
table
(It
is
assume d
that
p e ople
over
100
won ’t
influenc e
the
c alculations
to o
much)
.
E.287
Étude
du
tirage
du
January
prin ts :
02/01/2002
5
39
7
28
18
43
24
3
19
27
16
24
14
26
05/01/2002
3
19
27
16
24
14
26
9
34
13
25
7
28
6
09/01/2002
8
12
48
19
2
45
46
21
10
44
7
5
36
22
12/01/2002
42
12
3
45
26
47
2
20
29
31
48
17
34
16
16/01/2002
13
26
48
41
30
29
37
35
26
18
14
17
42
5
19/01/2002
46
3
17
44
25
37
2
29
1
27
45
17
40
21
23/01/2002
5
32
19
45
34
13
36
34
44
4
43
45
3
9
26/01/2002
23
40
33
10
14
3
4
18
24
7
41
27
47
44
30/01/2002
25
5
46
22
21
1
33
14
10
26
21
19
40
37
1
Dividing
the
results
in to
the
follo wing
fiv e
classes
:
[1
;
10[
,
[10
;
20[
,
[20
;
30[
,
[30
;
40[
and
[40
;
50[
,
dra w
up
a
table
sho wing
the
n um b ers
and
frequencies
frequencies
of
eac h
class
for
the
mon th
of
January
.
2
Y ou
are
giv en
the
n um b ers
in
eac h
class
for
the
dra ws
for
the
mon th
of
February
:
1
;
10
10
;
20
2
;
30
30
;
40
40
;
50
Effectifs
27
18
14
24
29
Give
the
frequency
distributions
for
the
whole
of
Jan uary
and
F ebruary .
3
Y ou
are
giv en
the
n um b ers
in
eac h
class
for
the
dra ws
in
the
mon th
of
March
:
1
;
10
10
;
20
2
;
30
30
;
40
40
;
50
Effectifs
22
27
24
30
23
Give
the
frequency
distributions
for
all
of
Jan uary ,
F ebru- ary
and
Marc h.
4
Do
y ou
agree
with
the
assertion
:
ˇPlus,
w e
increase
the
size
of
the
study
sam- ple,
the
more
the
frequency
of
eac h
class
stabilizesı
5
On
the
w ebsite
of
Française
des
Jeux
(http
://www.fdjeux.c om)
,
a
statistician
has
studied
since
the
game
first
app eared
the
frequency
distribution
b et w een
all
the
balls.
Here
are
his
results
:
1
;
10
10
;
20
2
;
30
30
;
40
40
;
50
Effectifs
(en
%
)
18.5
20.21
20.1
20.71
20.4
Can
y ou
giv e
an
explanation
as
to
wh y
the
frequency
of
the
class
[1
;
10[
is
significan tly
lo w er
than
the
frequencies
of
the
other
classes?
E.289
Here
are
the
dra ws
for
the
mon th
of
Jan- uary :
02/01/2002
5
39
7
28
18
43
24
3
19
27
16
24
14
26
05/01/2002
3
19
27
16
24
14
26
9
34
13
25
7
28
6
09/01/2002
8
12
48
19
2
45
46
21
10
44
7
5
36
22
12/01/2002
42
12
3
45
26
47
2
20
29
31
48
17
34
16
16/01/2002
13
26
48
41
30
29
37
35
26
18
14
17
42
5
19/01/2002
46
3
17
44
25
37
2
29
1
27
45
17
40
21
23/01/2002
5
32
19
45
34
13
36
34
44
4
43
45
3
9
26/01/2002
23
40
33
10
14
3
4
18
24
7
41
27
47
44
30/01/2002
25
5
46
22
21
1
33
14
10
26
21
19
40
37
Here
are
the
F ebruary
dra ws
:
02/02/2002
48
14
5
45
6
29
42
47
19
4
10
30
44
36
06/02/2002
33
18
14
10
7
3
36
2
45
12
43
38
41
30
09/02/2002
41
4
46
31
32
43
29
9
7
3
31
4
49
6
13/02/2002
44
12
37
31
24
2
45
2
39
23
38
17
13
37
16/02/2002
47
21
23
7
37
46
35
35
47
31
42
4
34
17
20/02/2002
6
46
4
19
8
42
40
16
2
24
4
45
44
37
23/02/2002
3
49
17
43
11
1
2
39
20
11
23
3
27
32
27/02/2002
43
29
45
6
32
24
25
18
4
37
42
46
23
14
Here
are
the
dra ws
for
Marc h
:
02/03/2002
10
39
1
37
40
48
29
32
29
49
23
45
22
30
06/03/2002
16
3
1
33
10
32
19
34
49
9
17
22
30
18
09/03/2002
22
30
38
15
25
20
48
8
21
25
48
34
31
39
13/03/2002
26
21
45
25
6
38
33
39
18
42
11
8
25
22
16/03/2002
12
34
39
17
40
15
44
31
33
26
40
3
37
18
20/03/2002
14
17
27
16
37
39
8
43
48
38
14
49
21
9
23/03/2002
2
47
39
13
36
9
12
10
8
42
3
46
5
1
27/03/2002
47
35
21
30
49
14
12
23
32
19
16
26
7
47
30/03/2002
48
25
40
13
24
16
4
10
2
1
4
9
36
22
https:/ /c hingmath.fr
chapExoCorrec/286 sacados/286 chapExoCorrec/287 sacados/287 sacados/289
148 13 18 815 20 959 25 559 30 221 35 57 45 31 55 210 70 Age (ans) 40 individus
7.
Gaussian,
normal
series
E.7860
One
compan y
claims
that
80
%
of
its
customers
are
satisfied
with
its
pro ducts.
1
A
consumer
asso ciation
wishes
to
v erify
this
claim
and
commissions
a
study
of
50
customers
of
this
compan y .
a
Determine
the
fluctuation
in terv al
at
the
threshold
of
95
%
.
b
The
study
obtains
a
satisfaction
rate
of
71
%
.
A ccord- ing
to
this
study ,
what
can
w e
sa y
ab out
the
compan y’s
affirmation
at
the
threshold
of
5
%
?
2
The
asso ciation
renews
its
study ,
this
time
fo cusing
on
100
customers.
This
new
study
still
obtains
a
satisfaction
rate
of
71
%
.
What
can
w e
sa y
ab out
the
compan y’s
assertion
at
the
threshold
of
5
%
.
E.188
An
In ternet
auction
site
wishes
to
carry
out
a
statistical
study
of
its
clien tele.
The
study
uses
a
sample
of
3.000
of
the
site’s
most
regular
customers.
Part
A
The
first
question
concerns
the
age
of
the
customers
consid- ered.
The
results
are
giv en
in
the
histogram
b elo w.
1
Complete,
without
justification,
table
3
in
the
app endix.
2
Using
the
calculator,
determine
without
justification
(re- sults
should
b e
r ounde d
to
the
tenth)
:
a
the
a v erage
age
of
the
auction
site’s
3.000
customers.
b
the
standard
deviation
ff
of
the
customer
age
series.
3
Can
w e
estimate
that
the
p ercen tage
of
individuals
who
ha v e
an
age
b elonging
to
the
range
[
m
−
ff
;
m
+
ff
]
is
greater
than
or
equal
to
75
%
.
Part
B
The
second
question
p osed
to
the
3.000
customers
concerns
a v erage
connection
time
in
min utes
o v er
a
one-w eek
p erio d.
1
The
study
sho w ed
that
the
series
of
a v erage
connection
times
follo ws
a
Gaussian
distribution
with
mean
—
∼
83.5
and
standard
deviation
s
∼
26.6
a
Determine
the
normal
range
at
95
%
of
this
series.
b
Ho w
man y
customers
can
w e
estimate
whose
a v erage
connection
time
p er
w eek
is
outside
this
range?
2
F or
this
series,
the
first
quartile
Q
1
is
65,
the
median
Me
is
85
and
the
third
quartile
Q
3
is
100.
a
What
is
the
minim um
n um b er
of
customers
whose
a v- erage
connection
time
p er
w eek
on
the
site
is
less
than
or
equal
to
65
min utes?
b
The
site
managers
hop ed
that
at
least
1.000
p eople
w ould
log
on
for
an
a v erage
of
1
hour
and
40
min utes
or
more
p er
w eek.
Has
this
goal
b een
ac hiev ed?
Annexe
Class
Centre
de
la
classe
Effectif
fréquence
(en
%
)
[13
;
18[
[18
;
20[
[20
;
25[
22.5
[25
;
30[
27.5
32
[30
;
35[
32.5
18.6
[35
;
45[
40
7.4
[45
;
55[
1.9
[55
;
70[
1
Total
×
3000
100
https:/ /c hingmath.fr
chapExoCorrec/7860 sacados/7860 sacados/188 148 13 18 815 20 959 25 559 30 221 35 57 45 31 55 210 70 Age (ans) 40 individus
0 10 20 30 40
E.195
F renc h
P olynesia
-
8
p oin ts
-
June
2005
The
follo wing
series
sho ws
the
n um b er
of
da ys
of
sno w- fall
p er
y ear
in
P aris
from
1900
to
1948.
The
49
v alues
in
this
series
are
not
listed
in
c hronological
order,
but
in
ascending
order.
1
-
5
-
6
-
6
-
6
-
7
-
7
-
7
-
8
-
8
9
-
10
-
10
-
11
-
11
-
11
-
12
-
12
-
12
-
12
13
-
13
-
13
-
14
-
14
-
14
-
14
-
15
-
16
-
17
17
-
17
-
18
-
18
-
18
-
18
-
19
-
19
-
20
-
20
20
-
23
-
26
-
29
-
29
-
31
-
32
-
32
-
34
1
a
Calculate
the
a v erage
n um b er
x
of
sno w
da ys
p er
y ear
in
P aris
b et w een
199
and
1948.
(the
r esult
wil l
b e
r ounde d
to
the
ne ar est
tenth.)
b
Determine
the
median,
Me
,
as
w ell
as
the
first
and
third
quartiles,
Q
1
and
Q
3
,
of
this
series.
Justify
eac h
answ er.
2
The
n um b er
of
da ys
of
sno wfall
p er
y ear
in
P aris
w as
also
recorded
from
1949
to
1997.
The
c haracteristics
of
this
new
statistical
series
are
pro vided
b elo w.
Minimum
First
quartile
Q
1
Médiane
med’
Troisième
quartile
Q
3
Maximum
Moy enne
x
1
7
12
18
36
13.3
a
Giv e
the
in terquartile
range
for
eac h
of
the
t w o
statis- tical
series
sho wing
the
n um b er
of
da ys
of
sno wfall
p er
y ear
in
P aris
for
the
p erio d
1900-1948
and
then
for
the
p erio d
1949-1997.
b
Build
on
the
appendix
the
b o x
plot
for
eac h
of
the
t w o
series
studied.
c
Compare
these
t w o
b o x
plots.
3
The
series
of
n um b ers
of
da ys
of
sno wfall
p er
y ear
in
P aris
o v er
the
p erio d
1900-1948
has
a
standard
deviation
of
s
,
and
the
series
of
n um b ers
of
da ys
of
sno wfall
p er
y ear
in
P aris
o v er
the
p erio d
1949-1997
has
a
standard
deviation
of
s
.
W e
assume
that
:
s
≈
7.82
;
s
≈
8.01
.
What
do es
it
mean
that
the
standard
deviation
is
higher
for
the
second
p erio d
than
for
the
first?
4
V arious
commen ts
ha v e
b een
made
in
the
press
ab out
these
w eather
records,
including
the
follo wing
:
ˇWin ters
with
less
and
less
sno w
o v er
the
course
of
the
cen turyı.
What
can
w e
mak e
of
this
commen t?
Perio d
1900-1948
P erio d
1949-1997
E.2024
The
P aris
Mon tsouris
meteorologi- cal
observ atory
has
b een
con tin uously
recording
outdo or
tem- p eratures
since
1872,
and
pro vides
ann ual
a v erages
based
on
these
readings.
The
aim
of
this
exercise
is
to
compare
these
a v erages
o v er
t w en t y-y ear
p erio ds
b et w een
1880
and
2000.
T o
clarify
the
v o cabulary ,
w e’ll
call
ˇann ual
temp eratureı
the
a v- erage
temp erature
recorded
in
a
giv en
y ear
(days
and
nights)
,
expressed
in
degrees
Celsius
and
rounded
to
0.05
o
C
.
Sourc es
Mété o
F r anc e
Part
A.
T emp eratures
at
the
end
of
the
XX
e
siècle
Documen t
2
in
App endix
1
sho ws
the
ann ual
temp erature
se- ries
for
the
y ears
1981
to
2000,
arranged
c hronologically
in
ascending
order.
1
Calculate
the
median,
first
and
third
quartiles
of
this
series.
Justify
eac h
answ er.
2
Dra w
the
b o x
plot
corresp onding
to
this
last
p erio d
on
do cumen t
I
in
app endix
1,
whic h
will
b e
returned
with
the
cop y .
Sho w
the
median,
first
and
third
quartiles,
minim um
and
maxim um
of
this
temp erature
series.
3
Determine
the
mean
of
the
ann ual
temp erature
series
from
1981
to
2000
using
the
calculator
(the
r esult
wil l
b e
r ounde d
to
0.05
o
C
)
Part
B.
A
cen tury
of
temp eratures
A
closer
analysis
of
ann ual
temp eratures
b et w een
1881
and
1980
sho ws
that
they
are
Gaussian
data
with
mean
m
=
11.49
o
C
and
standard
deviation
ff
=0.54
o
C
.
Recall
that
for
Gaussian
data,
the
in terv al
[
m
−
ff
;
m
+
ff
]
is
the
normalit y
range
at
68
%
.
1
Determine
the
normalit y
range
at
68
%
of
the
ann ual
temp erature
series
b et w een
1881
and
1980.
T o
ho w
man y
y ears
can
w e
estimate
the
n um b er
of
y ears
b et w een
1881
and
1980
whose
ann ual
temp erature
is
greater
than
m
+
ff
?
2
Do cumen t
I
in
App endix
1
sho ws
b o x
plots
constructed
from
ann ual
temp eratures
o v er
eac h
t w en t y-y ear
p erio d
b et w een
1881
and
1980.
On
eac h
of
these
diagrams,
the
median,
first
and
third
quartiles
ha v e
b een
plotted.
The
ends
of
the
ˇmoustac hesı
mark
the
minim um
and
maxi- m um
of
this
series.
F or
eac h
of
the
follo wing
prop ositions,
indicate
whether
it
is
true,
false
or
undecidable
(in
c ase
the
do cument
would
not
al low
to
know
whether
the
pr op osition
is
true
or
false)
.
Justify
the
answ er.
a
The
maxim um
ann ual
temp erature
w as
12.65
o
C
for
a
cen tury ,
from
1881
to
1980.
b
The
ann ual
temp erature
range
w as
2.25
o
C
for
one
cen- tury ,
from
1881
to
1980.
c
F or
a
cen tury ,
from
1881
to
1980,
at
least
thirt y
y ears
had
their
ann ual
temp erature
b elo w
11.5
o
C
.
d
1961
w as
the
coldest
y ear
o v er
the
p erio d
1901-1980.
Part
C.
Comparativ e
study
Making
reasoned
use
of
P arts
A
and
B
,
compare
the
temp er- atures
observ ed
in
P aris
in
the
last
t w en t y
y ears
of
the
XX
e
century
with
those
observ ed
o v er
the
previous
h undred
y ears.
Documen t
2 :
Ann ual
temp eratures
in
P aris
b et w een
1981
and
2000 :
sorted
in
c hronological
order
https:/ /c hingmath.fr
sacados/195 0 10 20 30 40 0 10 20 30 40 sacados/2024
10 11 12 13 1881 à 1900 1901 à 1920 1921 à 1940 1941 à 1960 1961 à 1980 1981 à 2000
0 2 4 6 8 10 12 14 16 18 20 Seconde 1 Seconde 2 Seconde 3 Seconde 4 Seconde 5 Seconde 6
Année
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
Temp é
rature
en
o
C
11.50
12.40
12.30
11.85
11.10
11.25
11.15
12.40
12.95
13.10
Année
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
Temp é
rature
en
o
C
11.75
12.30
11.85
13.10
12.85
11.40
12.90
12.40
13.05
12.90
sorted
in
ascending
order
Temp é
rature
en
o
C
11.10
11.15
11.25
11.40
11.50
11.75
11.85
11.85
12.30
12.30
Temp é
rature
en
o
C
12.40
12.40
12.40
12.85
12.90
12.90
12.95
13.05
13.10
13.10
Documen t
1 :
Ann ual
temp eratures
in
P aris
b y
t w en t y-y ear
p erio ds
E.165
The
results
obtained
b y
the
199
stu- den ts
from
six
classes
of
seconde
in
a
common
assignmen t
w ere
used
to
construct
the
six
b o x
plots
giv en
in
the
app endix.
The
results
obtained
b y
all
second-y ear
studen ts
are
giv en
in
the
follo wing
T able
1 :
Notes
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Effectifs
1
2
8
11
14
16
17
20
30
26
15
11
11
7
2
2
2
2
2
The
n um b ers
and
a v erages
for
the
second-y ear
classes
are
giv en
in
the
follo wing
T able
2 :
Seconde
1
2
3
4
5
6
Effectifs
34
33
34
33
32
33
Moy ennes
8.76
9.52
6.82
9.97
8.41
9.52
Part
A
Study
of
Seconde
classes
using
b o x
diagrams
1
Giv e
the
scores
corresp onding
to
the
median,
first,
third
quartile
of
the
Seconde
1
score
series.
2
In
Seconde
2,
can
w e
sa y
that
at
least
one
in
t w o
studen ts
has
a
mark
of
10
or
less?
Justify .
3
In
whic h
Seconde
classes
can
w e
sa y
that
at
least
75
%
of
studen ts
ha v e
a
mark
of
13
or
b elo w?
Justify .
4
Ho w
can
w e
explain
that
in
Seconde
5,
the
a v erage
mark
is
lo w er
than
the
median
mark?
5
F or
Seconde
3,
giv e
the
in terquartile
range.
6
In
Seconde
5,
ho w
man y
studen ts
scored
10
or
ab o v e?
Part
B
Study
of
all
Seconde
students
1
Determine
the
median,
first
and
third
quartile
of
the
grade
series
for
all
Seconde
studen ts.
On
the
axis
giv en
in
the
app endix,
construct
the
b o x
plot
for
this
series
2
a
Using
T able
1
ab o v e,
calculate
the
a v erage
score
x
of
Seconde
studen ts
(a
value
r ounde d
to
the
hundr e dth
wil l
b e
given)
.
b
Explain
the
metho d
for
calculating
this
a v erage
using
T able
2
ab o v e
exclusiv ely .
P erform
this
calculation.
3
It
is
assumed
that
the
grades
of
all
Seconde
studen ts
are
Gaussian
data
and
that
the
standard
deviation
ff
is
equal
to
3.45.
Commen t
s’app elle
l’in terv alle
x
−
2
ff
;
x
+2
ff
]
?
Giv e
the
p ercen tage
of
Secondes
studen ts
who
scored
outside
this
range?
https:/ /c hingmath.fr
10 11 12 13 1881 à 1900 1901 à 1920 1921 à 1940 1941 à 1960 1961 à 1980 1981 à 2000 sacados/165 0 2 4 6 8 10 12 14 16 18 20 Seconde 1 Seconde 2 Seconde 3 Seconde 4 Seconde 5 Seconde 6
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 cm C B A
1 2 3 4 5 6 7 8 9 10 11 12 13 A B C D E T ableau 2 : en p ourcen tage par rapp ort à l’e∑ectif total T ableau 1 : e∑ectif Masse (en g) \ Diamètre (mm) 71 75 79 T otal 700 2 157 3 123 1 803 7 083 720 3 003 4 122 2 310 9 435 745 2 124 2 982 1 923 7 029 T otal 7 284 10 227 6 036 23 547 Masse (en g) \ Diamètre (mm) 71 75 79 T otal 700 720 745 T otal 100 %
E.189
The
thr e e
p arts
ar e
indep endent
Part
A
A
p étanque
ball
factory
man ufactures
comp etition
balls
of
v arious
masses
and
diameters.
The
three
masses
offered
are
700
g
,
720
g
,
and
745
g
,
and
for
eac h
of
these
masses,
three
diameters
are
a v ailable :
71
mm
,
75
mm
,
79
mm
.
1
Ho w
man y
t yp es
of
balls
are
man ufactured
b y
this
com- pan y?
2
A
regional
c hampion
decides
to
buy
720
g
balls
but
is
un- sure
ab out
the
diameter.
T o
mak e
his
c hoice,
he
places
a
jac k
9
meters
a w a y ,
aims
200
times
with
eac h
ball
of
a
differen t
diameter,
and
measures
the
distance
to
the
jac k.
Here
are
the
b o x
plots,
trimmed
to
the
deciles,
rep- resen ting
this
test.
The
ends
of
the
plots
corresp ond
to
the
first
and
nin th
deciles,
resp ectiv ely .
Here
are
some
of
the
pla y er’s
impressions
after
the
test
:
With
the
79
mm
ball,
I
had
some
v ery
go o d
thro ws,
but
also
some
v ery
bad
ones.
With
the
71
mm
ball,
I
felt
great≠half
of
m y
thro ws
w ere
within
16
cm
of
the
jac k,
and
I
made
some
really
nice
ones
But
I
prefer
the
75
mm
ball,
whic h
allo ws
me
to
b e
more
consisten t.
Matc h
eac h
t yp e
of
ball
with
the
corresp onding
b o x
plot.
Explain
y our
answ er.
Part
B :
Ann ual
Sales
in
2004
Tables
1
and
2,
tak en
from
a
spreadsheet,
sho w
the
break- do wn
of
p étanque
ball
sales
for
the
y ear
2004
b y
diameter
and
mass.
Note:
Round
the
p ercen tages
to
the
nearest
ten th
of
a
p ercen t.
1
Calculate
the
p ercen tage,
rounded
to
0
;
1
%
,
of
720-gram
balls
with
a
diameter
of
75
mm
sold
in
2004.
2
Calculate
the
p ercen tage,
rounded
to
0
;
1
%
,
of
balls
with
a
diameter
of
75
mm
sold
in
2004.
3
Among
the
balls
of
700
g
sold
in
2004,
what
is
the
p er- cen tage,
rounded
to
0
;
1
%
,
of
balls
with
a
diameter
of
79
mm
?
4
The
table
of
p ercen tages
is
in
p ercen tage
format.
The
form ulas
b elo w
should
b e
en tered
in to
cell
B10
and
copied
to
the
rest
of
the
table.
Select
(or
the
c orr e ct
(s)
formula
(s))
.
a
=B3/E6
b
=B3/$E$6
c
=B$3/E6
d
=B3/23547
You
are
not
required
to
complete
the
table.
Part
C
:
Rejected
Balls
The
table
b elo w
sho ws
the
distribution
of
the
actual
masses
of
2
500
720-gram
comp etition
balls
that
w ere
man ufactured
:
Masse
(in
g
)
719,5
719,6
719,7
719,8
719,9
720
720,1
720,2
720,3
720,4
720,5
Sample
size
10
53
178
385
441
524
478
201
165
51
14
1
Calculate
the
mean
—
of
the
masses
of
these
2
500
balls.
Round
the
result
to
3
decimal
places.
2
Assume
that
the
data
follo w
a
Gaussian
distribution.
The
standard
deviation
s
of
this
set
is
equal
to
0
;
185
.
Determine
the
normal
range
at
95
%
for
this
set.
3
The
compan y
rejects
balls
that
fall
outside
the
normal- it y
range
as
unsuitable
for
comp etition.
Calculate
the
p ercen tage,
rounded
to
0
;
1
%
,
of
rejected
balls.
https:/ /c hingmath.fr
chapExoCorrec/189 sacados/189 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 cm C B A
1 2 3 4 5 6 7 8 9 10 11 12 13 A B C D E T ableau 2 : en p ourcen tage par rapp ort à l’e∑ectif total T ableau 1 : e∑ectif Masse (en g) \ Diamètre (mm) 71 75 79 T otal 700 2 157 3 123 1 803 7 083 720 3 003 4 122 2 310 9 435 745 2 124 2 982 1 923 7 029 T otal 7 284 10 227 6 036 23 547 Masse (en g) \ Diamètre (mm) 71 75 79 T otal 700 720 745 T otal 100 %
Un concert 100 500 700 900 1100 1300 1500 G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 A B C D E Classe milieux de nom bre de sp ectateurs sp ectateurs classes concerts 2004/2005 2005/2006 [0 ; 200[ 100 4 400 [200 ; 400[ 300 8 [400 ; 600[ 500 4 [600 ; 800[ 700 2 [800 ; 1000[ 900 6 5400 [1000 ; 1200[ 1100 10 11000 [1200 ; 1400[ 1300 6 7800 somme : 40 30400 31020 mo y enne : 775,5
E.192
There
are
t w o
concert
halls
in
a
cit y ,
eac h
of
whic h
programmed
40
concerts
during
the
2004
=
2005
season.
Salle
G
specializes
in
classical
m usic
and
Salle
J
in
jazz.
1
F or
the
v en ue
G
,
the
results
in
n um b er
of
exp ected
sp ec- tators
are
sho wn
b y
the
histogram
giv en
in
App endix
3.
F or
example,
the
manager
thinks
that
6
concerts
will
attract
b et w een
500
and
700
sp ectators
during
the
2004
=
2005
season.
a
Calculate,
using
class
middles,
the
mean
m
G
of
this
statistical
series.
b
The
data
in
this
series
are
considered
to
b e
Gaussian
(i.e.
they
appr oximately
fol low
a
normal
distribution)
.
The
normalit y
range
at
95
%
is
[302
;
1438]
.
Using
this
in terv al
find
the
mean
m
G
and
calculate
the
standard
deviation
ff
G
of
the
series.
2
Statistics
for
ro om
J
are
giv en
on
a
spreadsheet
made
using
a
table
(appendix
4)
?
Recall
that
C3
,
for
example,
denotes
the
address
of
the
cell
lo cated
at
the
in tersection
of
column
C
and
ro w
3
.
The
cells
A5
to
A11
contain
the
sp ectator
n um b er
classes,
all
with
amplitude
200.
The
cells
B5
to
B11
contain
the
class
middles.
The
cells
C5
to
C11
contain
the
n um b ers
of
concerts
corresp onding
to
the
classes
in
the
column
A
.
a
The
manager
w an ts
to
obtain,
using
the
table,
the
a v- erage
n um b er
of
sp ectators
p er
concert
for
the
season
2004
=
2005
.
In
the
cell
D5
figure
400
whic h
represen ts
the
n um b er
of
sp ectators
lik ely
to
ha v e
attended
the
four
concerts
relating
to
the
first
class.
What
form ula
has
the
manager
en tered
in
D5
,
kno wing
that
it
m ust
b e
recopied
to
D11
,
to
obtain
the
n um- b ers
relating
to
the
other
classes?
En ter
the
results
from
cells
D6
to
D11
on
App endix
4
(to
b e
r eturne d
with
c opy)
.
b
What
form ula
has
the
manager
en tered
in
D13
?
What
form ula
should
he
en ter
in
D15
to
get
the
a v erage
n um- b er
of
sp ectators
p er
concert
in
the
v en ue
J
?
En ter
this
n um b er
in
cell
D15
in
App endix
4.
3
Find,
for
the
series
concerning
ro om
J
,
the
resp ectiv e
classes
con taining
the
median
and
quartiles
of
the
n um- b er
of
sho ws.
4
T o
b o ost
attendance
during
the
2005
=
2006
season,
the
manager
decides
to
offer
subscriptions
for
sev eral
con- certs
during
the
y ear.
He
hop es
to
increase
b y
10
%
the
n um b er
of
sp ectators
at
eac h
concert
from
under
800.
a
Whic h
form ula
m ust
b e
en tered
in
cell
E5
(re c opie d
to
E8
)
to
find
the
exp ected
n um b er
of
sp ectators
in
2005
=
2006
for
these
first
4
classes?
En ter
the
4
results
in
the
table
in
App endix
4.
b
What
form ulas
need
to
b e
en tered
in
cellsen ter
in
the
cells
E13
and
E15
to
obtain
the
exp ected
n um b er
of
sp ectators
for
2005
=
2006
and
the
a v erage
p er
concert?
c
Calculate,
under
this
assumption,
the
relativ e
p ercen t- age
c hange
b et w een
the
exp ected
a v erage
in
2004
=
2005
and
that
exp ected
in
2005
=
2006
.
The
result
will
b e
rounded
to
the
nearest
0.1
%
.
https:/ /c hingmath.fr
sacados/192 Un concert 100 500 700 900 1100 1300 1500 G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 A B C D E Classe milieux de nom bre de sp ectateurs sp ectateurs classes concerts 2004/2005 2005/2006 [0 ; 200[ 100 4 400 [200 ; 400[ 300 8 [400 ; 600[ 500 4 [600 ; 800[ 700 2 [800 ; 1000[ 900 6 5400 [1000 ; 1200[ 1100 10 11000 [1200 ; 1400[ 1300 6 7800 somme : 40 30400 31020 mo y enne : 775,5
42 45 50 55 60 65 70
E.197
W e
studied
the
heart
rates
of
a
group
of
60
amateur
sp ortsmen
and
w omen
(cal le d
gr oup
I.)
,
prac- ticing
their
sp ort
2
to
4
times
a
w eek.
Heart
rate
is
the
n um b er
of
heartb eats
p er
min ute.
F or
eac h
of
these
athletes
in
the
I
group,
w e
measure
resting
he art
r ate
(RHR)
,
i.e.
the
lo w est
heart
rate
encoun tered
in
that
p erson,
measured
after
sev eral
trials
follo wing
a
long
p e- rio d
of
calm
and
rest.
The
results
of
this
study
are
summarized
in
the
table
b elo w,
where
the
resting
heart
rates
(RCF)
of
the
60
athletes
in
the
I
group
are
rank ed
in
ascending
order.
Age
FCR
Age
FCR
Age
FCR
Age
FCR
42
42
50
50
37
52
41
54
41
43
35
50
42
52
31
55
61
45
24
50
21
52
50
55
51
45
23
50
40
53
32
55
41
46
52
50
34
53
22
55
27
46
36
51
35
53
42
55
33
46
31
51
28
53
52
55
40
48
35
51
55
53
18
57
55
48
60
51
49
53
51
59
31
48
29
52
31
53
22
59
32
48
30
52
35
53
23
59
35
48
49
52
38
54
53
59
44
49
32
52
53
54
50
59
40
50
40
52
42
54
28
59
36
50
47
52
54
54
47
61
1
a
Determine
the
median
and
the
first
and
third
quar- tiles
of
the
FC R
series.
b
Construct
on
the
D
1
axis
giv en
in
App endix
(to
b e
r eturne d
with
c opy)
,
a
b o x
plot
for
this
series.
2
a
Complete
the
table
in
appendix
and
plot
a
graphi- cal
represen tation
of
the
FC R
series
of
the
60
athletes
in
the
I
group.
b
Calculate
the
mean
x
of
this
series.
3
a
It
is
assumed
that
the
FC R
of
the
athletes
in
the
I
group
are
Gaussian
data
with
a
standard
deviation
ff
equal
to
4.06
.
Déterminer
l’in terv alle
52
−
2
ff
;
52+2
ff
.
What
do
w e
call
this
in terv al?
b
Calculate
the
p ercen tage
of
athletes
whose
FC R
lies
within
this
in terv al.
W as
it
p ossible
to
predict
this
result?
Explain.
4
W e
wish
to
compare
the
FC R
of
athletes
in
the
I
group
with
the
FC R
of
a
group
of
60
p eople
doing
little
ph ys- ical
activit y
(cal le d
the
II
group)
.
The
FC R
study
of
p eople
in
the
II
group
yielded
the
follo wing
results
:
Mean
:
59.8
Median
:
60
Standard
deviation :
6.23
Third
quartile :
63
First
quartile :
57
Maxim um
v alue
:
70
a
On
the
D
2
axis
giv en
in
the
app endix,
dra w
a
b o x
diagram
for
the
FC R
of
the
p eople
in
the
II
group.
b
What
impact
do es
the
regular
practice
of
sp orts
activ- ities
seem
to
ha v e
on
an
individual’s
FC R
?
Axe
D
1
Axe
D
1
FCR
42
43
45
46
48
49
50
51
52
53
54
55
57
59
61
Nombre
d’individus
Table
E.190
A
compan y
wishes
to
purc hase
a
large
n um b er
of
motors.
Before
c ho osing
b et w een
M
1
or
M
2
motors,
it
wishes
to
compare
their
resp ectiv e
service
liv es.
Part
A
Comparison
of
the
lifetimes
of
a
sample
of
60
motors
of
t yp e
M
1
and
a
sample
of
60
motors
of
t yp e
M
2
.
1
Study
of
a
sample
of
60
motors
of
t yp e
M
1
.
In
the
table
giv en
in
do cumen t
1
of
app endix
2
is
the
life- time
in
mon ths
of
eac h
motor
of
a
sample
of
60
motors
of
t yp e
M
1
.
The
v alues
w ere
sorted
in
ascending
order
using
a
spreadsheet
program.
What
p ercen tage
of
M
1
motors
ha v e
a
service
life
of
4
y ears
or
more?
(result
wil l
b e
r ounde d
to
0.1%
)
.
2
a
Determine
the
median
and
then
the
first
and
third
quartiles
of
the
series
of
lifetimes
for
the
60
M
1
motors.
b
Represen t
this
series
b y
a
b o x
plot
on
do cumen t
2
in
app endix
2,
to
b e
handed
in
with
the
cop y .
The
me- dian,
first
and
third
quartiles
and
extremes
of
the
series
studied
will
b e
sho wn.
3
Study
of
a
sample
of
60
motors
of
t yp e
M
2
.
On
do cumen t
2
in
app endix
2
is
the
b o x
plot
represen t- ing
the
statistical
series
of
service
liv es
in
mon ths
of
a
sample
of
60
motors
of
t yp e
M
2
.
The
median
of
this
series
is
59
mon ths.
a
What
is
the
minim um
n um b er
of
motors
of
t yp e
M
2
whose
lifetime
is
greater
than
or
equal
to
59
mon ths?
b
What
is
the
minim um
p ercen tage
of
M
2
typ e
motors
with
a
service
life
less
than
or
equal
to
66
mon ths?
c
Compare
the
series
of
lifetimes
of
motors
of
t yp e
M
1
and
t yp e
M
2
using
their
b o x
diagrams.
Part
B
Study
of
a
sample
of
1000
motors
of
t yp e
M
2
A
statistical
series
on
a
sample
of
1000
motors
of
t yp e
M
2
show ed
that
the
series
of
mean
lifetimes,
expressed
in
mon ths,
is
Gaussian
with
mean
m
≈
59.6
and
standard
devia- tion
s
≈
0.8
.
1
Determine
the
range
of
normalit y
at
95
%
.
2
Ho w
man y
M
2
motors
with
a
life
of
less
than
58
mon ths
can
b e
estimated?
3
The
compan y
wishes
to
purc hase
motors
of
t yp e
M
2
such
that
at
least
99%
hav e
a
service
life
greater
than
or
equal
to
58
mon ths.
What
commen ts
can
y ou
mak e?
Annexe
Do cumen t
1
:
Lifetimes
in
mon ths
of
60
motors
of
t yp e
M
1
sorted
in
ascending
order
in
ro ws
:
https:/ /c hingmath.fr
sacados/197
42 45 50 55 60 65 70 42 45 50 55 60 65 70 chapExoCorrec/190 sacados/190
32 36 40 44 48 52 56 60 64 68 72 76 80 84 M 2
1 2 3 4 o 0,26 0,28 0,30 0,32 0,34 0,36 0,38 0,40 0,42 0,44
34
38
39
41
42
43
44
45
45
47
47
48
49
50
51
51
52
52
53
54
55
55
55
55
55
55
55
56
56
57
58
58
58
59
59
59
60
62
62
62
62
63
64
65
66
66
66
66
67
68
68
73
74
74
75
75
79
81
81
85
Documen t
2 :
bo x
plots
of
the
service
life
series
of
60
motors
of
t yp e
M
1
and
M
2
:
E.191
A
mouse
runs
do wn
a
pip e
(shown
in
the
figur e
b elow)
leading
to
exits
0,
1,
2,
3.
It
is
assumed
that
she
progresses
to w ards
the
finish
b y
ran- domly
heading
eac h
lev el
to
the
righ t
or
left
to
access
the
lev el
b elo w.
A
p ossible
route
can
therefore
b e
co ded
GGD
,
where
G
means
ˇ
going
to w ards
gauc heı
and
D
ˇaller
to w ards
droiteı,
on
eac h
of
the
three
lev els.
W e
are
then
in terested
in
the
n um b er
of
the
mouse
output.
Part
A
Theoretical
study
Find
all
p ossible
paths
(possibly
using
a
tr e e)
and
then
com- plete
the
theoretical
frequency
table
(appendix
1,
r eturn
with
c opy)
Part
B
Spreadsheet
sim ulation
Using
a
spreadsheet,
w e
run
a
sim ulation
of
100
mouse
pro- gressions
through
the
pip e
:
w e
obtain
the
frequencies
corre- sp onding
to
eac h
of
the
p ossible
mouse
outputs.
W e
then
note
the
frequency
corresp onding
to
the
output
n
o
1
obtained.
Running
50
sim ulations,
w e
obtain
50
frequencies
corresp ond- ing
to
the
output
n
o
1
.
(These
fr e quencies
ar e
r e c or de d
in
App endix
2)
1
The
series
of
50
frequencies
is
assumed
to
ha v e
mean
m
=0.364
and
standard
deviation
x
=0.051
,
results
giv en
with
3
decimal
places.
Calculate
the
p ercen tage
of
v alues
in
the
series
lying
within
the
in terv al
m
−
2
s
;
m
+2
s
.
Do es
this
result
corresp ond
to
what
w e
w ould
exp ect
from
a
Gaussian
or
normal
series?
Justify .
2
W e
then
run
t w o
series
of
50
sim ulations,
one
corresp ond- ing
to
500
mouse
progressions,
the
other
to
1000
progres- sions,
and
obtain
50
frequencies
of
the
output
n
o
1
for
eac h
series.
Dra w,
on
the
same
graph,
the
b o x
plot
that
corresp onds
to
the
series
of
50
sim ulations
p erformed
in
question
1
,
calculating
all
the
elemen ts
needed
to
build
this
t yp e
of
b o x.
3
a
Using
the
three
diagrams,
determine
whic h
series
ap- p ears
to
giv e
the
frequencies
closest
to
the
theoretical
frequency .
b
What
w ould
it
tak e
to
get
ev en
closer?
Output
n
o
0
1
2
3
Numb er
of
p ossible
paths
Theoretical
frequency
(in
%
)
Fréquences
theoretical
0,250
0,260
0,290
0,290
0,300
0,300
0,310
0,310
0,320
0,320
0,320
0,320
0,330
0,330
0,330
0,340
0,340
0,340
0,340
0,350
0,350
0,350
0,350
0,305
0,360
0,360
0,370
0,370
0,370
0,370
0,380
0,380
0,380
0,390
0,390
0,390
0,390
0,400
0,400
0,410
0,410
0,420
0,420
0,420
0,430
0,430
0,450
0,460
0,470
0,470
Fréquences
(arrange d
in
asc ending
or der)
obtenues
for
output
n
o
1
(for
50
simulations)
Boîtes
with
whisk ers
https:/ /c hingmath.fr
32 36 40 44 48 52 56 60 64 68 72 76 80 84 M 2 sacados/191 Liban - Juin 2004 - 8 points
1 2 3 4 o 0,26 0,28 0,30 0,32 0,34 0,36 0,38 0,40 0,42 0,44
Années 1980 1984 1988 1992 1996 2000 2004 Nombre d’habitants 100 200 300 400 500 600 700 800 900 1000 A B
E.168
Jean,
an
en th usiast
of
a
computer
game,
recorded
the
duration
in
seconds
of
the
40
games
he
pla y ed.
These
durations
w ere
rank ed
in
ascending
order
in
the
table
b elo w
:
49
55
57
57
57
58
58
59
60
60
60
62
63
65
65
66
67
69
69
70
70
72
74
74
75
75
63
63
63
64
64
64
64
76
77
78
79
80
80
82
So,
for
example,
there
w ere
three
games
pla y ed
in
60
seconds
eac h.
1
a
Determine
the
median,
then
the
first
and
third
quar- tiles
of
this
series
of
v alues.
b
Represen t
this
series
of
v alues
b y
a
b o x
plot
on
whic h
at
least
the
three
v alues
obtained
in
the
previous
ques- tion
will
app ear.
c
Calculate,
in
seconds,
the
a v erage
duration
of
the
40
games
(round
to
the
tenth)
2
The
man ufacturer
of
this
game,
after
surv eying
a
large
n um b er
of
pla y ers,
estimated
that
the
game
durations
constituted
Gaussian
data
with
a
mean
—
of
62
seconds
and
a
standard
deviation
ff
of
6
seconds.
The
man ufacturer
adv ertises
:
ˇ
You
have
a
95
%
chance
of
playing
every
game
lasting
b etwe en
50
se c onds
and
1
minute
14
se c onds.
ı
a
On
what
is
this
man ufacturer’s
claim
based?
b
Can
w e
sa y
that
95
%
of
the
40
games
pla y ed
b y
John
last
b et w een
50
seconds
and
1
min ute
14
seconds?
8.
Linear
interp olation
E.2023
The
graph
b elo w
sho ws
c hanges
in
the
n um b er
of
inhabitan ts
in
t w o
neigh b oring
comm unes,
named
A
and
B
,
from
1980
to
2004
(from
four
ye ars
to
four
ye ars)
.
Part
A
Reading
graphique
Answer
the
follo wing
questions
using
only
the
graph
ab o v e.
1
In
what
y ear
w as
the
p opulation
of
the
comm une
A
max-im um.
2
a
Sp ecify
the
y ears
in
whic h
the
comm unes
A
and
B
had
the
same
n um b er
of
inhabitan ts.
b
What
are
the
p erio ds
during
whic h
the
comm une
B
had
more
inhabitan ts
than
the
comm une
A
?
c
In
whic h
y ear
w as
the
difference
b et w een
the
n um b er
of
inhabitan ts
of
comm une
A
and
comm une
B
the
great- est?
3
Sp ecify ,
justifying
the
answ er,
during
whic h
four-y ear
p e- rio d
the
comm une
A
had
the
highest
p opulation
increase.
Part
B
We’re
in terested
in
p opulation
trends
in
these
comm unes
from
2000
to
2004.
The
follo wing
table
sho ws
the
n um b er
of
inhab- itan ts
in
these
t w o
comm unes
in
2000
and
2004.
Years
2000
2004
Commune
A
863
795
Commune
B
711
947
The
t w o
questions
are
indep enden t.
1
a
Justify
that,
from
2000
to
2004,
the
comm une’s
p op- ulation
A
fell
b y
appro ximately
7.9
%
.
b
Determine
the
p ercen tage
increase
in
the
comm une’s
p opulation
B
in
this
same
p erio d
(we’ll
give
the
r esult
r ounde d
to
0.1
%
)
.
c
If
w e
consider
the
p opulation
of
the
t w o
comm unes
com bined,
determine
the
p ercen tage
c hange
in
this
p opulation
during
this
p erio d
(we’ll
give
the
r esult
r ounde d
to
0.1
%
)
.
2
Estimate
b y
linear
in terp olation
on
the
in terv al
[2
000
;
2
003]
the
n um b er
of
inhabitan ts
in
the
m unici- palit y
B
in
2003.
9.
Old
statistics
ye arb o ok
E.144
A
moun tain
race
The
thr e e
p arts
ar e
indep endent.
The
app endix
is
to
b e
r e-
turned
with
the
c opy.
Part
A
:
T op ographical
study
The
route
of
a
moun tain
fo ot
race
is
giv en
in
the
app endix.
https:/ /c hingmath.fr
sacados/168 Antilles-Guyanes - Juin 2006 - 8 points
sacados/2023 Années 1980 1984 1988 1992 1996 2000 2004 Nombre d’habitants 100 200 300 400 500 600 700 800 900 1000 A B chapExoCorrec/144 sacados/144
0 1 2 3 4 5 6 7 5 10 15 20 25 30 35 40 Distances en km Marc Audrey Julien 1 2 3 4 5 6 A B C Année Nom bre de participan ts P ourcen tage d’év olution du nom bre de candidats par rapp ort à 2000 . 2000 142 0 % 2001 162 14 % 2002 182 28 % 2003 202 2004 222
Competitors
cross
a
first
hill
via
its
summit
S
1
.
The
finish
is
at
the
top
of
the
second
hill
S
2
.
P oin t
P
designates
the
lo cation
of
an
aid
station.
1
What
is
the
altitude
of
the
starting
p oin t?
F rom
the
aid
station?
2
A
runner
t wists
his
ankle.
He
giv es
his
p osition
using
a
cell
phone
as
follo ws
:
ˇ
I’m
on
the
desc ent
of
the
first
hil l
and
my
altimeter
in- dic ates
an
altitude
of
1
274
m
ı.
Indicate
in
color
on
the
map
the
minim um
searc h
area
for
this
runner
b y
rescue
w ork ers.
3
The
map
is
to
scale
1
=
50
000
.
Calculate
the
appro ximate
length
of
the
route
b et w een
the
starting
p oin t
and
the
summit
S
1
(we’ll
ne gle ct
the
differ enc e
in
altitude
b etwe en
the
starting
p oint
and
the
summit
ne gle ct
the
differ enc e
in
altitude
b etwe en
the
starting
p oint
and
the
summit
S
1
)
Part
B :
strok e
profile
The
graph
ab o v e
sho ws
the
running
profiles
of
three
runners
:
Julien,
Marc
and
Audrey .
1
Whic h
of
these
three
riders
arriv es
first?
2
What
happ ens
at
the
t w en tieth
min ute
of
the
race?
3
A t
the
score
of
5.5
km
,
what
is
Marc’s
time
lead
o v er
Julien?
4
A t
the
fifteen th
min ute
of
the
race,
what
distance
sepa- rates
Julien
and
Marc?
Part
C
:
Ev olution
of
the
n um b er
of
participan ts
The
table
b elo w,
extracted
from
an
automated
spreadsheet,
giv es
the
n um b er
of
participan ts
as
a
function
of
the
y ear
and
the
ev olution
of
this
n um b er
in
relation
to
the
y ear
2000.
The
column
C
is
in
p ercen tage
format.
P ercen tages
will
b e
rounded
to
1
%
.
1
What
t yp e
of
gro wth
in
the
n um b er
of
participan ts
is
this
o v er
the
p erio d
2000-2004?
Justify
y our
answ er.
2
a
What
is
the
p ercen tage
c hange,
rounded
to
1
%
,
in
the
n um b er
of
participan ts
from
2000
to
2003?
b
What
form ula,
to
b e
copied
do wn
using
only
cell
refer- ences,
has
b een
written
in
cell
C3
?
The
race
organizer
feels
that
the
increase
in
the
n um b er
of
participan ts
is
insufficien t.
It
is
therefore
launc hing
an
adv ertising
campaign
and
hop es
to
increase
participation
b y
15
%
per
y ear.
The
effects
of
this
campaign
should
b e
felt
as
early
as
2005.
a
Calculate
the
exp ected
n um b er
of
participan ts
in
2005.
b
What
t yp e
of
exp ected
gro wth
is
this
from
2005?
Jus- tify
y our
answ er.
c
Calculate
the
exp ected
n um b er
of
participan ts
in
2010.
Appendix :
to
b e
returned
with
cop y
This
top ograph y
of
the
place
where
the
p edestrian
race
tak es
place.
The
course
is
mark ed
in
b old.
https:/ /c hingmath.fr
0 1 2 3 4 5 6 7 5 10 15 20 25 30 35 40 Distances en km Marc Audrey Julien 1 2 3 4 5 6 A B C Année Nom bre de participan ts P ourcen tage d’év olution du nom bre de candidats par rapp ort à 2000 . 2000 142 0 % 2001 162 14 % 2002 182 28 % 2003 202 2004 222
1 2 3 4 5 6 7 A B C D E Année Nom bre de pa ys de l’UE ( en mil lions d’habitants) P opulation de l’UE ( en mil lions d’habitants) Augmen tation de la p opulation de l’UE (en % ) Sup er∏cie de l’UE (en k m 2 ) 1957 6 210,7 1 235 103 1973 9 279,7 1 588 829 1981 10 290 1 720 455 1986 12 341,9 2 317 515 1995 15 364,1 3 150 174 2004 25 439 3 888 717
E.152
The
Europ ean
Union,
noted
UE
,
grew
from
15
to
25
mem b er
coun tries
on
1
er
May
2004.
T able
2
giv es
indications
of
the
Europ ean
Union
at
eac h
c hange
in
the
n um b er
of
mem b er
coun tries.
It
w as
obtained
using
a
table.
1
In
this
question,
w e’re
in terested
in
the
EU’s
p opulation
increase.
a
What
form ula
can
b e
written
in
cell
D3
to
obtain,
b y
automatic
cop y
do wn,
the
p ercen tage
increase
in
the
EU
p opulation
at
eac h
date
of
c hange
in
the
n um b er
of
mem b er
coun tries,
compared
with
the
previous
date
of
c hange?
b
Complete
the
column
D
(results
wil l
b e
r ounde d
to
the
hundr e dth)
c
Calculate
the
p ercen tage
increase
in
EU
p opulation
from
1957
to
2004.
2
In
this
question,
w e’re
in terested
in
the
p opulation
den- sit y
of
EU
coun tries,
i.e.
the
n um b er
of
inhabitan ts
p er
km
2
(results
wil l
b e
r ounde d
to
the
unit)
.
The
table
b elo w
giv es
the
p opulation
densities
of
EU
coun tries
in
2004.
Pa ys
Finlande
Suède
Estonie
Lettonie
Densité
15
22
30
37
Pa ys
Irlande
Lituanie
Grèce
Espagne
Density
55
57
78
81
Pa ys
Chypre
Autriche
Slov énie
Hongrie
Densité
91
97
98
107
Pa ys
Slov aquie
France
Portugal
Danemark
Densité
110
118
123
Pa ys
Pologne
Rép.
T c hèque
Luxemb ourg
Italie
Densité
123
129
155
187
Pa ys
Allemagne
Roy aume
Uni
Belgique
Pa ys-Bas
Malte
Densité
231
248
338
388
1
266
a
Kno wing
that
F rance
has
61.2
million
inhabitan ts
in
2004
for
an
area
of
543
965
km
2
,
calculate
the
p opula- tion
densit y
of
F rance
in
2004
b
Determine
the
median
and
quartiles
of
this
densit y
se- ries,
then
mak e
a
b o x
plot
(the
maximum
wil l
not
b e
shown)
c
Calculate
the
a v erage
p opulation
densit y
of
the
EU
coun tries.
Note
that
the
mean
is
higher
than
the
me- dian.
Explain
wh y .
3
In
this
question,
w e
are
in terested
in
F rance’s
place
in
the
EU
in
2004
(results
wil l
b e
r ounde d
to
the
unit)
.
a
What
p ercen tage
of
the
EU
p opulation
do es
the
F renc h
p opulation
represen t
in
2004?
b
What
p ercen tage
of
the
surface
area
of
the
EU
repre- sen ts
the
surface
area
of
F rance
in
2004?
4
Answ er
true
or
false
to
the
follo wing
three
statemen ts
:
a
The
EU
p opulation
grew
b y
108
%
(to
the
ne ar est
unit)
bet w een
1957
and
2004.
b
The
surface
area
of
the
EU
increased
b y
a
factor
of
2
b et w een
1957
and
2004
c
A t
least
75
%
of
EU
coun tries
had
a
p opulation
densit y
of
150
or
more
in
2004.
E.2029
parts
1
and
2
are
indep enden t
P art
1
The
table
-
incomplete
-
b elo w,
giv es
the
v arious
results
for
cinema
attendance
in
F rance,
for
the
y ears
2004
and
2005.
Num b ers
of
admissions
in
millions
are
rounded
to
0.01
and
p ercen tages
to
0.1
%
.
Fréquen tation
totale
(millions
d’entr é es)
2004
2005
Evolution
2005/2004
en
%
Janvier
15.18
14.30
-5.8
Février
19.94
-16.0
Mars
15.34
14.17
-7.6
Avril
17.40
15.51
-10.8
Mai
13.77
-9.6
Juin
18.83
12.36
-34.4
Juillet
16.26
14.50
-10.8
Août
14.98
12.73
Septembre
9.83
8.29
-15.7
Octobre
17.17
14.93
-13.0
Nov em bre
15.10
14.85
-1.7
Décembre
20.07
23.49
+17.1
Année
195.33
175.65
-10.1
Sourc e :
Centr e
National
de
la
Cinémato gr aphie
http
://www.cnc.fr
According
to
the
latest
estimates
from
the
Researc h
Depart- men t,
cinema
attendance
reac hed
23.49
million
admissions
in
Decem b er
2005,
17.1
%
more
than
in
Decem b er
2004.
During
2005,
cinemas
ac hiev ed
175.65
million
admissions,
or
10.1
%
fewer
than
in
2004.
Search
for
missing
data.
1
V erify
that
the
n um b er
of
en tries
in
2005
for
the
mon th
of
F ebruary
is
16.75
million.
2
Calculate
the
p ercen tage
drop
in
attendance
b et w een
Au- gust
2004
and
August
2005.
3
Calculate
the
n um b er
of
admissions
in
Ma y
2004.
Part
2
A
surv ey
w as
carried
out
among
a
p opulation
of
sc ho olc hil-
https:/ /c hingmath.fr
sacados/152 Antilles-Guyane - Septembre 2005 - 11 points
1 2 3 4 5 6 7 A B C D E Année Nom bre de pa ys de l’UE ( en mil lions d’habitants) P opulation de l’UE ( en mil lions d’habitants) Augmen tation de la p opulation de l’UE (en % ) Sup er∏cie de l’UE (en k m 2 ) 1957 6 210,7 1 235 103 1973 9 279,7 1 588 829 1981 10 290 1 720 455 1986 12 341,9 2 317 515 1995 15 364,1 3 150 174 2004 25 439 3 888 717 sacados/2029 France - Septembre 2007 - 8 points
0 10 20
dren
to
find
out
their
preference
for
the
v ersions
of
foreign
films
they
see
at
the
cinema.
The
results
are
recorded
in
the
follo wing
table
:
Garçons
Filles
Total
Version
doublée
en
français
40.45
%
23
%
63.45
%
Version
orginale
sous-titrée
15.2
%
14.1
%
29.3
%
Sans
préférence
4.35
%
2.9
%
7.25
%
Total
60
%
40
%
100
%
This
sho ws
that
63.45
%
of
the
studen ts
surv ey ed
prefer
a
v er- sion
dubb ed
in
F renc h.
On
the
other
hand,
the
n um b er
of
girls
who
prefer
the
original
v ersion
with
subtitles
represen ts
14.1
%
of
the
total
p opula- tion
of
studen ts
surv ey ed.
Clearly
justifying
with
the
necessary
calculations,
sa y
whether
the
follo wing
statemen ts
are
true
or
false
:
1
ˇThe
prop ortion
of
girls
surv ey ed
who
ha v e
no
preference
for
the
v ersion
of
foreign
films
seen
at
the
cinema
is
the
same
as
that
of
b o ys
surv ey ed
who
ha v e
no
preference
for
the
v ers
ion
of
foreign
films
seen
at
the
cinema.ı
2
ˇAmong
the
studen ts
surv ey ed
who
prefer
the
orginal
v er- sion
with
subtitles,
there
are
more
50
%
bo ys.ı
E.194
A t
the
end
of
the
delib erations
of
an
examination
comprising
three
tests,
a
teac her
records
the
results
of
his
30
studen ts
in
tests
n
o
1
,
n
o
2
and
n
o
3
.
These
notes
are
group ed
together
in
the
follo wing
table
:
Notes
on
20
Effectifs
Proof
n
o
1
Proof
n
o
2
Proof
n
o
3
5
0
3
0
6
6
0
0
7
5
5
2
8
8
0
1
9
1
8
6
10
3
0
3
11
0
3
5
12
2
4
0
13
0
0
2
14
1
1
6
15
2
4
3
16
2
2
2
1
In
this
question,
w e
are
in terested
in
the
statistical
series
E
1
formed
b y
the
scores
of
the
test
n
o
1
.
a
Determine,
for
this
statistical
series,
the
minim um
and
maxim um.
b
Determine
the
median.
Justify .
c
Determine
the
1
er
and
3
e
quartiles.
Justify .
d
Dra w
the
b o x
plot
corresp onding
to
this
series
E
1
,
on
the
sheet
pro vided
in
the
app endix,
with
the
minim um
and
maxim um
for
extreme
v alues.
2
W e
are
no w
in terested
in
the
statistical
series
E
2
formed
b y
the
test
scores
n
o
2
.
a
Dra w
up
the
b o x
plot
corresp onding
to
this
series,
on
the
attac hed
sheet,
with
the
minim um
and
maxim um
as
extreme
v alues.
Sp ecify
the
v alues
used.
b
Calculate
the
arithmetic
mean
of
the
series
E
2
.
c
Giv e
the
v alue
of
the
standard
deviation
of
the
series
E
2
.
3
What
commen ts
can
y ou
mak e
comparing
the
t w o
b o x
plots
corresp onding
to
the
E
1
and
E
2
series?
4
W e
note
E
3
the
statistical
series
formed
b y
scores
on
the
n
o
3
test.
The
standard
deviation
of
the
series
E
3
is
assumed
to
b e
2.7.
a
Calculate
the
arithmetic
mean
of
the
series
E
3
.
b
Calculate
the
p ercen tage
of
studen ts
with
a
mark
less
than
or
equal
to
9
in
the
test
n
o
3
.
c
What
commen ts
can
y ou
mak e
comparing
the
results
of
the
n
o
2
test
with
those
of
the
n
o
3
test?
5
Kno wing
that
the
arithmetic
mean
in
the
n
o
1
test
is
9.13
and
that
this
test
n
o
1
is
assigned
co efficien t
3
and
the
tests
n
o
2
and
n
o
3
coefficien t
1,
what
is
the
arithmetic
mean,
out
of
20,
of
the
30
studen ts’
marks
in
this
exam?
Statistical
series
E
1
-
b o x
diagram
https:/ /c hingmath.fr
sacados/194 Centres Etrangers - Juin 2004 - 10 points
0 10 20
0 10 20
1 2 3 4 A B C D E F G H I J Année 1989 1990 1991 1992 1993 1994 1995 1996 Nom bre de sites colonisés en Méditerranée 1 3 8 23 30 38 48 77 Augmen tation par année =C2/$J
Les inscrits ...... Les abstentionnistes ...... Les votants ...... Personnes ayant voté ˇOUIı : ...... Personnes ayant voté ˇNonı : 1110 Personnes ayant voté blanc ou nul: ......
Statistical
series
E
2
-
b o x
diagram
E.2022
The
green
alga
Caulerpa
taxifolia
,
nativ e
to
tropical
seas,
w as
in tro duced
to
the
Mediterranean
in
the
early
1980s.
Its
adaptations
mak e
it
highly
comp etitiv e
with
Mediterranean
sp ecies.
Caulerpa
taxifolia
has
not
only
managed
to
surviv e
a
new
en vironmen t
(conditions
differ ent
fr om
those
in
tr op- ic al
waters)
,
but
it
is
proliferating
and
dev eloping
to
the
p oin t
of
raising
some
concerns
ab out
the
consequences
of
its
expansion.
Sources
:
GIF.
P osidonia
Part
A.
Study
of
the
ev olution
of
the
surface
co v ered
The
follo wing
table
sho ws
the
surface
area
co v ered
b y
algae
during
recen t
measuremen ts
in
the
Mediterranean
:
Année
1989
1992
1993
1996
1997
Surface
(en
ha)
1
427
1300
3052
4630
Is
the
gro wth
in
the
area
co v ered
b y
Caulerpa
exponen tial?
Justify .
Part
B.
Study
of
the
ev olution
of
the
n um b er
of
col- onized
sites
The
spreadsheet
in
App endix
2
presen ts
a
table
listing
the
n um b er
of
sites
colonized
b y
the
alga
in
the
Mediterranean
b et w een
1989
and
1996.
1
In
ro w
3
of
the
spreadsheet,
w e
w an t
to
sho w
the
p er- cen tage
increase
in
the
n um b er
of
colonized
sites
from
one
y ear
to
the
next.
The
cells
are
in
the
format
ˇp our- cen tageı.
What
form ula
should
b e
written
in
cell
D3
so
that
it
can
b e
copied
to
the
righ t?
Complete
the
do cu- men t
with
the
calculated
v alues,
rounded
to
1
%
.
2
Is
the
gro wth
in
the
n um b er
of
sites
colonized
b y
the
Caulerpa
exponen tial?
Justify
using
line
3
of
the
spread- sheet.
3
In
cell
C4
,
w e
ha v e
written
the
form ula
sho wn
on
the
w orksheet
in
App endix
2
and
then
copied
it
to
the
righ t.
The
cells
in
this
ro w
are
in
the
format
ˇp ourcen tageı.
What
is
the
form ula
written
in
cell
F4
?
4
Complete
line
4
of
the
spreadsheet
in
App endix
2,
to
b e
returned
with
the
cop y .
The
results
will
b e
rounded
to
0.1
%
.
What
do
these
results
represen t?
Part
C.
Study
of
the
ev olution
of
algal
size
In
the
summer
of
1996,
the
size
of
a
stolon
(long,
r o oting
stem)
of
Caulerpa
was
measured.
Its
size
on
July
15
w as
85
cm
,
its
size
on
August
24
w as
137
cm
.
During
this
fort y-da y
p erio d,
stolon
gro wth
w as
found
to
b e
linear.
Estimate
b y
in terp ola- tion
the
size,
to
the
nearest
cen timeter,
of
this
stolon
at
1
er
August
1996.
Numb er
of
sites
colonized
b y
the
green
alga
Caulerpa
taxifolia
,
in
the
Mediterranean
from
1989
to
1996
E.155
On
Ma y
29,
2005,
during
the
F renc h
referendum
on
the
Europ ean
Constitution,
a
p olling
firm
an- alyzed
exit
p olls
in
a
small
to wn.
In
this
to wn,
3,062
p eople
are
registered
to
v ote.
Among
these
p eople,
w e
distinguish
b et w een
v oters
and
non-v oters.
Among
the
v otes
cast
b y
v ot- ers,
w e
consider
ˇYESı
v otes,
ˇNOı
v otes,
and
in v alid
or
blank
v otes.
Throughout
this
exer cise,
al l
p er c entages
wil l
b e
r ounde d
to
0
;
1%
.
Part
A
1
Of
the
3,062
registered
v oters,
1,048
did
not
v ote.
The
referendum
turnout
rate
is
the
p ercen tage
of
v oters
out
of
the
total
n um b er
of
registered
v oters.
Determine
this
turnout
rate.
2
During
the
v ote,
2,000
p eople
rep orted
ha ving
v oted
ˇYESı
or
ˇNOı
in
the
referendum.
Their
p ercen tage
dis- tribution
is
giv en
in
the
follo wing
table
:
Percen tage
distribution
b y
age
group
Âge
YES
NO
18
-
24
y ears
7,1%
8,9%
25
-
34
ans
10,4%
12,7%
35
-
44
ans
11,0%
16,8%
45
-
59
ans
5,3%
8,7%
60
-
69
ans
6,3%
5,0%
70
y ears
and
older
4,4%
3,4%
a
Find
the
p ercen tage
of
p eople
under
25
who
v oted
ˇYESı
b
Determine
the
p ercen tage
of
p eople
b et w een
the
ages
of
18
and
24
c
Determine
the
p ercen tage
of
p eople
who
v oted
ˇYES.ı
d
Determine
the
n um b er
of
p eople
who
v oted
ˇYES.ı
3
Fill
in
the
data
in
the
table
b elo w
:
4
Among
registered
v oters,
determine
the
p ercen tage
of
p eople
who
v oted
ˇNO.ı
https:/ /c hingmath.fr
0 10 20 sacados/2022 1 2 3 4 A B C D E F G H I J Année 1989 1990 1991 1992 1993 1994 1995 1996 Nom bre de sites colonisés en Méditerranée 1 3 8 23 30 38 48 77 Augmen tation par année =C2/$J$2 chapExoCorrec/155 sacados/155 Les inscrits ...... Les abstentionnistes ...... Les votants ...... Personnes ayant voté ˇOUIı : ...... Personnes ayant voté ˇNonı : 1110 Personnes ayant voté blanc ou nul: ......
allemand % garçons % ∏lles % espagnol % garçons % ∏lles %
Part
B
Based
on
information
obtained
from
the
p olling
station
on
Ma y
29,
2005,
the
institute
also
compiled
the
results
presen ted
in
the
table
b elo w
:
Table
(F requencies
b y
ro w)
Percen tage
Distribution
of
Registered
V oters
b y
Age
Group
Âge
Voters
Non-voters
Total
18
-
24
y ears
100%
25
-
34
ans
55,0%
45,0%
100%
35
-
44
ans
68,0%
32,0%
100%
45
-
59
ans
77,3%
22,7%
100%
60
-
69
ans
89,8%
10,2%
100%
70
y ears
and
older
70,0%
30,0%
100%
The
results
are
giv en
as
a
p ercen tage
of
registered
v oters
in
eac h
age
group.
1
Among
the
550
registered
v oters
aged
18
to
24,
there
are
229
non-v oters.
What
is
the
absten tion
rate
in
this
age
group?
2
In
the
table
ab o v e,
what
do es
the
n um b er
77
;
3%
at
the
in tersection
of
the
45-59
-y ear-old
ro w
and
the
ˇv otersı
column
mean?
3
Of
all
p eople
aged
25
to
34,
378
did
not
v ote.
Ho w
man y
p eople
in
this
age
group
are
registered
at
this
p olling
place?
10.
Unclassified
financial
ye ars
E.121
Here
is
a
double-en try
table
sho wing
the
language
c hosen
as
an
option
in
a
class
of
34
studen ts
:
1
a
Complete
the
follo wing
table
:
Allemand
Espagnol
Total
Boys
10
17
Girl
Total
19
b
Determine
the
frequency
of
b o ys
practicing
German
relativ e
to
the
class
as
a
whole.
2
a
Determine
among
b o ys,
the
frequency
of
studen ts
practicing
Spanish.
b
Complete
the
follo wing
frequency
table
:
Allemand
Espagnol
Boys
Girl
Total
100
%
100
%
c
Complete
the
follo wing
frequency
tree
:
d
Find,
from
the
frequency
tree,
the
frequency
of
b o ys
practicing
German
(question
1
d
)
3
a
Determine
among
practitioners
of
German,
the
fre- quency
of
b o ys.
b
Complete
the
follo wing
table
:
Allemand
Espagnol
Total
Boys
100
%
Girl
100
%
c
Complete
the
follo wing
frequency
tree
:
https:/ /c hingmath.fr
sacados/121 allemand % garçons % ∏lles % espagnol % garçons % ∏lles %
garçons % allemand % espagnol % ∏lles % allemand % espagnol %
1 1 1 1 1 1 2 1 1 2 3 1 1 3 2 1 1 2 1 2 1 2 2 3 1 2 3 3 1 1 3 1 2 1 3 2 3 1 3 3 2 1 1 2 1 1 2 2 1 2 3 2 1 3 2 1 2 2 1 2 2 2 2 3 2 2 3 3 1 2 3 1 2 2 3 2 3 2 3 3 3 1 1 3 1 1 2 3 1 2 3 3 1 3 2 1 3 2 1 2 3 2 2 3 3 2 3 3 1 3 3 1 2 3 3 2 3 3 3 3
d
Find
the
frequency ,
from
this
tree,
of
b o ys
practicing
German
relativ e
to
the
whole
class
(question
1
d
)
E.160
A
man ufacturer
of
c ho colate
bars
has
prin ted,
in
large
quan tities,
the
same
n um b er
of
images
of
three
singers
Miss
Pinson,
Miss
Rossignol
and
Miss
Déci- b el.
Mlle
Pinson’s
image
is
n
o
1
Mlle
Rossignol’s
is
n
o
2
,
and
Mlle
Décib el’s
is
n
o
3
.
A
mac hine
randomly
inserts
a
picture
in to
eac h
c ho colate
bar
made.
There
are
as
man y
c ho colate
bars
con taining
the
image
of
eac h
singer.
Ev ery
da y ,
Aline
buys
a
c ho colate
bar.
She
w ould
lik e
to
ha v e
the
complete
collection
of
all
three
singers
and
w onders
ho w
man y
da ys
it
will
tak e
her
to
get
it.
Part
A
Aline
has
used
a
tree
to
list
the
differen t
images
that
can
b e
obtained
o v er
three
da ys.
This
tree,
partially
completed,
can
b e
found
opp o- site.
F or
example,
the
3
e
possibilit y
1
1
3
means
that
on
the
first
da y ,
the
c ho co- late
bar
con tains
the
image
of
Mll
Pinson,
on
the
second
da y
it
con tains
that
of
Miss
Pinson,
and
on
the
third
da y
that
of
Miss
Decib el.
1
Of
these
27
p ossibilities,
ho w
man y
are
there
that
result
in
a
complete
collection?
2
Are
there
more
than
25
%
cases
in
whic h
a
complete
col- lection
is
obtained?
Justify .
Aline
w an ts
to
obtain
the
complete
collection.
As
her
p o c k et
money
is
limited,
she
w ould
lik e
to
estimate
the
n um b er
of
da ys
she
can
exp ect
to
get
the
full
collection.
T o
do
this,
she’s
going
to
run
some
sim ulations.
Part
B
She
runs
a
sim ulation
b y
ha ving
her
calculator
displa y
a
ran- dom
list
of
n um b ers,
so
that
eac h
of
the
n um b ers
1,
2
and
3
has
the
same
c hance
of
app earing.
Here’s
the
list
she
gets
:
1-1-1-1-1-3-1-2-1-3.
A ccording
to
this
sim ulation,
for
the
first
fiv e
da ys,
Aline
dis- co v ers
in
her
c ho colate
bar
the
image
of
Mlle
Pinson,
on
6
e
day ,
miss
Décib el’s,
7
e
day ,
Miss
Pinson’s,
8
e
day
Miss
Rossig- nol’s
;
on
9
e
day
that
of
Mlle
Pinson,
and
on
10
e
that
of
Mlle
Décib el.
Aline
is
therefore
in
p ossession
of
the
complete
col- lection
at
8
e
day .
Imagine,
on
the
previous
mo del,
a
list
of
9
n um b ers
leading
to
the
complete
collection
obtained
at
5
e
day .
Part
C
To
get
a
clearer
idea,
Aline
runs
1000
sim ulations
using
her
calculator.
The
results
are
sho wn
in
the
follo wing
table
:
pt
Num b er
of
jours
nécessaires
at
obten tion
de
the
collection
complète
3
4
5
6
7
8
9
10
Effectifs
227
203
179
126
99
56
40
25
pt
Num b ers
from
jours
nécessaires
to
obten tion
de
the
collection
complète
11
12
13
14
15
16
17
18
Effectifs
18
12
4
3
3
2
1
2
This
means,
for
example,
that
of
the
1000
sim ulations,
203
are
situations
for
whic h
the
complete
collection
of
images
is
obtained
b y
4
e
day .
1
Determine
the
median,
first
and
third
quartile
of
this
statistical
series.
2
Aline
mak es
t w o
remarks
while
observing
these
sim ulated
results.
Remark
1
:
In
at
least
50
%
of
the
sim ulated
situations
the
complete
collection
is
obtained
no
later
than
the
.
.
.
da y .
Note
2
:
In
.
.
.
%
sim ulated
situations,
the
complete
im- age
collection
is
obtained
b y
7
e
day .
Complete
these
remarks.
3
Aline
sa ys
:
ˇAfter
18
da ys,
I’m
sure
I’ll
get
the
full
col- lectionı.
What
do
y ou
think
of
this
statemen t?
https:/ /c hingmath.fr
garçons % allemand % espagnol % ∏lles % allemand % espagnol % sacados/160 Inde - Avril 2005 - 8 points
1 1 1 1 1 1 2 1 1 2 3 1 1 3 2 1 1 2 1 2 1 2 2 3 1 2 3 3 1 1 3 1 2 1 3 2 3 1 3 3 2 1 1 2 1 1 2 2 1 2 3 2 1 3 2 1 2 2 1 2 2 2 2 3 2 2 3 3 1 2 3 1 2 2 3 2 3 2 3 3 3 1 1 3 1 1 2 3 1 2 3 3 1 3 2 1 3 2 1 2 3 2 2 3 3 2 3 3 1 3 3 1 2 3 3 2 3 3 3 3