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4
3
2
1
Outside the high school program
/ Sequence and spreadsheet (old 1L)
16 exercises (including 3 corrected)
a
Sequences, statistics and spreadsheets
(11 exercices)
1
2
3
4
5
6
7
8
9
A
B
C
D
E
Raison
de
la
suite
arithmétique
T
emps
n
écoulé
(en
dixième
de
seconde)
Abscisse
x
n
de
la
balle
(en
mètre)
Ordonnée
y
n
de
la
balle
(en
mètre)
0
0
2,5
1
2,8
2,4216
2
5,6
2,1864
3
1,7944
4
1,2456
5
14
0,54
x
0
y
i
j
1.
Se
quenc
es,
statistics
and
spr
e
adshe
ets
E.202
In
this
exer
cise,
al
l
times
ar
e
ex-
pr
esse
d
in
tenths
of
a
se
c
ond
and
distanc
es
in
meters.
The
tra
jectory
of
a
tennis
ball
is
mo
deled
b
y
a
curv
e
in
a
reference
frame
O
;
−
→
i
;
−
→
j
,
sho
wn
in
the
graph
b
elo
w.
One
unit
represen
ts
one
meter.
The
tennis
pla
y
er
hits
his
ball
at
time
0
in
M
0
co
ordinates
(
0
;
2.5
)
.
F
or
an
in
teger
n
,
the
p
osition
of
the
pla
y
er’s
ball
in
the
O
;
−
→
i
;
−
→
j
at
time
n
is
p
oin
t
M
of
co
ordinates
(
x
n
;
y
n
)
.
V
al-
ues
x
n
and
y
n
for
n
b
et
w
een
0
and
5
are
giv
en
b
y
the
table
in
the
app
endix,
extracted
from
a
spreadsheet.
This
table
m
ust
b
e
completed
during
the
exercise
and
returned
with
the
cop
y
.
Questions
1
to
4
are
to
a
large
exten
t
indep
enden
t
1
Study
of
the
sequence
of
n
um
b
ers
x
n
(abscissas
of
the
b
al
l’s
p
osition
at
time
n
)
a
Sho
w
that
the
v
alues
x
0
,
x
1
and
x
2
are
the
first
terms
of
an
arithmetic
sequence
whose
reason
r
will
b
e
de-
termined.
W
rite
the
found
v
alue
of
r
in
cell
E11
of
the
table
in
the
app
endix.
b
Assume
that
the
n
um
b
ers
x
n
are
the
terms
of
the
arith-
metic
sequence
with
first
term
x
0
and
reason
r
.
Justify
that
x
n
=
2.8
n
.
c
W
e
w
an
t
to
in
tro
duce
in
to
cell
B7
a
form
ula
recopied
to
B9
,
still
v
alid
if
w
e
c
hange
the
v
alue
of
r
.
Giv
e
this
form
ula.
d
Complete
the
t
w
o
missing
cells
in
column
B
of
the
table
in
the
app
endix.
e
The
ball
arriv
es
at
the
net,
lo
cated
12
meters
from
p
oin
t
O
,
at
time
t
.
Using
the
spreadsheet,
giv
e
a
frame
for
t
b
et
w
een
t
w
o
v
alues
a
ten
th
of
a
second
apart.
2
Study
of
the
sequence
of
n
um
b
ers
y
n
(or
dinates
of
the
b
al
l’s
p
osition
at
time
n
)
a
Sho
w
that
the
sequence
of
n
um
b
ers
y
n
is
neither
arith-
metic
nor
geometric.
b
The
la
ws
of
ph
ysics
allo
w
us
to
establish
the
relation-
ship
:
y
n
=
−
0.0784
·
n
2
+
2.5
Whic
h
table
form
ula
should
b
e
written
in
C4
so
that
it
can
b
e
copied
to
C9
?
3
Study
the
tra
jectory
of
the
ball.
The
net,
lo
cated
12
meters
from
the
p
oin
t
O
measures
ap-
pro
ximately
0.90
m
in
heigh
t.
Explain,
using
the
graph
recalled
in
the
app
endix,
wh
y
the
ball
passes
o
v
er
the
net.
4
When
the
ball
is
put
in
to
pla
y
,
the
serving
pla
y
er
is
al-
lo
w
ed
t
w
o
attempts
to
place
the
ball
in
the
opp
onen
t’s
service
b
o
x.
These
attempts
are
called
first
and
second
serv
es.
In
the
course
of
a
matc
h,
the
pla
y
er
has
missed
20
first
serv
es.
He
has
therefore
pla
y
ed
20
second
serv
es.
a
In
this
matc
h,
of
the
20
second
serv
es,
3
w
ere
successful
without
b
eing
caugh
t
b
y
the
opp
onen
t.
Of
the
second
serv
es,
what
p
ercen
tage
w
ere
successful
without
b
eing
caugh
t
b
y
the
opp
onen
t?
b
Of
these
20
second
serv
es,
65
%
w
ere
placed
in
the
opp
onen
t’s
service
b
o
x.
Calculate
the
n
um
b
er
of
suc-
cessful
second
serv
es.
c
The
20
missed
first
serv
es
corresp
ond,
for
the
first
serv
es
pla
y
ed,
to
a
failure
p
ercen
tage
of
26.7
%
(r
ounde
d
to
0.1
%
)
.
What
is
the
total
n
um
b
er
of
first
serv
es
the
pla
y
er
p
erformed
in
this
matc
h?
v
alues
of
x
n
and
y
n
Graphique
h
ttps:/
/c
hingmath.fr
sacados/202
1
2
3
4
5
6
7
8
9
A
B
C
D
E
Raison
de
la
suite
arithmétique
T
emps
n
écoulé
(en
dixième
de
seconde)
Abscisse
x
n
de
la
balle
(en
mètre)
Ordonnée
y
n
de
la
balle
(en
mètre)
0
0
2,5
1
2,8
2,4216
2
5,6
2,1864
3
1,7944
4
1,2456
5
14
0,54
x
0
y
i
j
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
A
B
C
D
E
F
Mon
tan
t
des
mensualités
de
Jules
160
T
aux
d’augmen
tation
des
mensualités
de
Léo
3
%
Somme
totale
rem
b
oursée
par
Jules
Mon
tan
t
des
mensualités
de
Léo
Somme
initiale
v
ersée
80
125
1
er
mois
2
e
mois
3
e
mois
560
137
4
e
mois
720
141
5
e
mois
880
145
6
e
mois
1040
149
7
e
mois
1200
154
8
e
mois
1360
158
9
e
mois
1520
163
10
e
mois
1680
168
11
e
mois
1840
173
12
e
mois
2000
Somme
totale
rem
b
oursée
2000
2000
E.1884
Jules
and
Léo
decide
to
buy
the
same
laptop.
They
don’t
ha
v
e
enough
money
to
pa
y
immedi-
ately
.
The
seller
offers
them
easy
pa
ymen
t
terms.
Including
in
terest,
eac
h
will
ha
v
e
to
pa
y
a
dep
osit
and
repa
y
a
total
of
2.000
euros
(including
dep
osit)
o
v
er
12
mon
ths
according
to
terms
to
b
e
defined.
Jules
c
ho
oses
to
pa
y
80
euros
at
the
time
of
purc
hase,
then
repa
ys
fixed
mon
thly
installmen
ts
of
160
euros
eac
h
of
the
follo
wing
12
mon
ths.
Léo
pa
ys
125
euros
up
fron
t,
then
his
mon
thly
pa
ymen
ts
in-
crease
b
y
3
%
eac
h
of
the
follo
wing
11
mon
ths.
So
his
first
mon
thly
pa
ymen
t
will
increase
b
y
3
%
compared
with
the
125
euros
initially
paid.
On
12
e
mon
th,
he
repa
ys
the
difference
b
et
w
een
the
2000
euros
o
w
ed
and
the
total
sum
he
has
already
repaid.
P
art
I
:
Jules
’s
c
hoice
Let’s
note
u
0
the
sum
paid
b
y
Jules
when
buying
the
com-
puter,
and
u
n
the
total
sum
repaid
b
y
Jules
after
n
mon
ths.
Th
us,
u
0
=
80
and
u
1
represen
ts
the
total
amoun
t
Jules
has
repaid
at
the
end
of
the
first
mon
th.
1
Calculate
u
1
and
u
2
.
2
a
What
is
the
nature
of
the
sequence
(
u
n
)
?
Justify
.
b
Express
u
n
in
terms
of
n
.
3
T
o
calculate
ho
w
m
uc
h
Jules
has
repaid
eac
h
mon
th,
w
e
use
a
spreadsheet.
The
spreadsheet
is
giv
en
in
App
endix
1.
What
form
ula
can
b
e
en
tered
in
cell
5
,
so
that
it
can
b
e
copied
do
wn
to
B16
?
P
art
I
I
:
Leo’s
c
hoice
W
e
note
v
0
the
sum
paid
b
y
Léo
to
purc
hase
the
computer,
and
v
n
the
amoun
t
of
Leo’s
mon
thly
pa
ymen
t
on
n
ième
mon
th
with
n
in
teger
b
et
w
een
1
and
11.
Th
us,
v
0
=
125
and
according
to
the
terms
of
the
con
tract,
v
1
=
129
rounded
to
the
nearest
euro.
1
Calculate
v
2
.
Round
to
the
nearest
euro.
2
What
is
the
nature
of
the
sequence
(
v
n
)
?
Justify
.
3
T
o
calculate
Leo’s
mon
thly
pa
ymen
ts,
w
e
also
use
the
spreadsheet
giv
en
in
App
endix
1.
What
form
ula
can
b
e
en
tered
in
cell
E5
,
so
that
it
can
b
e
copied
do
wn
to
E15
?
Answ
ers
pro
vided
ha
v
e
b
een
rounded
to
the
nearest
whole
n
um
b
er.
4
a
What
total
sum
has
Leo
repaid
at
the
end
of
11
e
mon
th.
What
is
the
12
e
mon
thly
pa
ymen
t?
b
What
form
ula
can
b
e
en
tered
in
cell
E16
to
directly
calculate
this
12
e
mon
thly
pa
ymen
t?
5
Starting
in
whic
h
mon
th
are
Leo’s
mon
thly
pa
ymen
ts
higher
than
Jules’
?
E.176
asia
ffl
June
2006
ffl
8
p
oin
ts
The
follo
wing
article
w
as
tak
en
from
a
w
eekly
newspap
er
:
ˇ
A
t
the
height
of
the
T
r
ente
Glorieuses,
when
pur
chasing
p
ower
gr
ew
by
4.2
%
p
er
ye
ar,
it
to
ok
only
sixte
en
ye
ars
for
an
employe
e
to
double
his
net
salary
(in
constan
t
francs)
.
A
t
the
same
time,
the
pur
chasing
p
ower
of
an
exe
cutive
was
e
quiva-
lent
to
just
over
twic
e
that
of
an
employe
e.
In
short,
lo
oking
at
the
e
asy
life
of
an
exe
cutive
family,
an
employe
e
house-
hold,
had
b
efor
e
its
eyes
its
futur
e
c
onsumption
level.
A
b
o
ar
d
his
Dauphine,
he
c
ould
dr
e
am
of
the
Peuge
ot
104!
In
the
’80s,
this
gr
owth
r
ate
r
ose
to
2
%
on
aver
age,
r
aising
hop
es
of
a
c
atch-up
over
mor
e
than
one
gener
ation.
T
o
my
son,
the
R
16
.
.
.
in
thirty-five
ye
ars!
Betwe
en
1990
and
2000,
this
r
ate
plunge
d
to
0.7
%
.
F
r
om
now
on,
a
c
entury
wil
l
b
ar
ely
suffic
e
to
achieve
such
a
r
esult.
The
Me
gane
for
the
gr
e
at-gr
andson.
.
.
Not
very
moti-
vating.
ı
The
aim
of
this
exercise
is
to
examine
the
accuracy
of
the
three
durations
announced
in
this
text
using
a
v
ariet
y
of
ap-
proac
hes.
P
art
A
-
Using
a
graph
This
part
lo
oks
at
the
follo
wing
extract
from
the
article
:
ˇ
When
pur
chasing
p
ower
gr
ew
by
4.2
%
p
er
ye
ar,
it
to
ok
an
employe
e
just
sixte
en
ye
ars
to
double
his
or
her
salary.
ı
In
the
T
ren
te
Glorieuses,
a
y
ear
noted
0
is
tak
en
as
the
refer-
ence
y
ear.
The
graph
b
elo
w
sho
ws
the
rate
of
increase
in
purc
hasing
p
o
w
er
as
a
function
of
the
n
um
b
er
of
y
ears
elapsed.
F
or
ex-
ample,
after
eigh
t
y
ears,
purc
hasing
p
o
w
er
has
increased
b
y
40
%
.
h
ttps:/
/c
hingmath.fr
sacados/1884
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
A
B
C
D
E
F
Mon
tan
t
des
mensualités
de
Jules
160
T
aux
d’augmen
tation
des
mensualités
de
Léo
3
%
Somme
totale
rem
b
oursée
par
Jules
Mon
tan
t
des
mensualités
de
Léo
Somme
initiale
v
ersée
80
125
1
er
mois
2
e
mois
3
e
mois
560
137
4
e
mois
720
141
5
e
mois
880
145
6
e
mois
1040
149
7
e
mois
1200
154
8
e
mois
1360
158
9
e
mois
1520
163
10
e
mois
1680
168
11
e
mois
1840
173
12
e
mois
2000
Somme
totale
rem
b
oursée
2000
2000
sacados/176
Asie - juin 2006 - 8 points
0
1
2
3
4
5
6
7
8
9
1011121314151617181920
1
2
3
4
5
6
7
8
9
10
11
12
13
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
A
B
Année
Co
e`cien
t
m
ultiplicateur
1
1,020
2
1,040
3
1,061
4
1,082
5
1,104
6
1,126
7
1,149
8
1,172
9
1,195
10
1,219
11
1,243
12
1,268
13
1,294
14
1,319
15
1,346
16
1,373
17
1,400
18
1,428
19
1,457
20
1,486
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
A
B
21
1,516
22
1,546
23
1,577
24
1,608
25
1,641
26
1,673
27
1,707
28
1,741
29
1,776
30
1,811
31
1,848
32
1,885
33
1,922
34
1,961
35
2,000
36
2,040
37
2,081
38
2,122
39
2,165
40
2,208
Jours
0
1
2
3
4
5
6
7
Concentration de radon
0
200
400
600
800
1000
1200
D
e
e
c
r
o
i
s
s
a
n
c
e
r
a
d
i
o
a
c
t
i
v
e
1
Is
the
gro
wth
in
purc
hasing
p
o
w
er
linear?
Justify
.
2
is
the
sixteen-y
ear
duration
announced
ab
o
v
e
correct?
P
art
B
In
this
part
w
e
are
in
terested
in
the
follo
wing
extract
from
the
article
:
ˇ
In
the
1980s,
this
gr
owth
r
ate
rises
to
2%
on
aver
age,
giving
hop
e
of
c
atching
up
over
mor
e
than
one
gener
ation.
T
o
my
son,
the
R16.
.
.
in
thirty-five
ans
ı.
W
e
prop
ose
to
study
the
ev
olution
of
purc
hasing
p
o
w
er
from
the
y
ear
1980,
tak
en
as
the
initial
y
ear
and
whic
h
will
b
e
noted
0.
The
table
b
elo
w
sho
ws
the
m
ultiplier
co
efficien
ts,
rounded
to
the
thousandth,
that
m
ust
b
e
applied
to
the
purc
hasing
p
o
w
er
of
y
ear
0
to
obtain
the
purc
hasing
p
o
w
er
after
n
y
ears.
The
values
in
the
c
olumn
B
have
b
e
en
r
ounde
d
to
the
thou-
sandth.
1
Justify
the
con
ten
ts
of
cell
B2
.
2
The
form
ula
in
cell
B3
has
b
een
copied
do
wn.
What
is
this
form
ula?
3
Is
the
journalist’s
sen
tence
recalled
at
the
b
eginning
of
this
part
correct?
P
art
C
-
Using
a
sequence
In
this
part,
w
e’re
in
terested
in
the
follo
wing
extract
from
the
article
:
Betwe
en
1990
and
2000,
this
r
ate
plunges
to
0.7%
.
F
r
om
now
on,
a
c
entury
wil
l
b
ar
ely
suffic
e
to
achieve
such
a
r
esult.
W
e
note
C
1
the
m
ultiplier
co
efficien
t
that
m
ust
b
e
applied
to
the
purc
hasing
p
o
w
er
of
the
y
ear
1990
to
obtain
that
of
the
y
ear
1991.
Similarly
,
w
e
define
C
2
the
m
ultiplier
co
efficien
t
that
m
ust
b
e
applied
to
the
purc
hasing
p
o
w
er
of
the
y
ear
1990
to
obtain
that
of
the
y
ear
1992,
C
3
the
m
ultiplier
co
efficien
t
that
m
ust
b
e
applied
to
the
purc
hasing
p
o
w
er
of
the
y
ear
to
obtain
that
of
1993,
.
.
.
,
C
n
the
m
ultiplier
co
efficien
t
that
m
ust
b
e
ap-
plied
to
the
purc
hasing
p
o
w
er
of
the
y
ear
1990
to
obtain
that
of
the
y
ear
1990+
n
.
1
What
is
the
nature
of
the
sequence
(
C
n
)
th
us
con-
structed?
Sp
ecify
its
first
term
and
its
reason.
2
Using
y
our
calculator,
deduce
whether
the
duration
of
one
cen
tury
giv
en
ab
o
v
e
is
correct.
The
pro
cedure
will
b
e
explained.
E.185
The
main
source
of
natural
radioac-
tivit
y
to
whic
h
h
umans
are
exp
osed
is
a
radioactiv
e
gas
called
radon.
It
escap
es
from
v
olcanic
and
granite
subsoils,
as
w
ell
as
from
certain
building
materials,
and
stagnates
in
p
o
orly
v
en
tilated
areas.
Indo
or
radon
concen
tration
is
expressed
in
Becquerels
p
er
cu-
bic
meter
(
B
q
·
m
−
3
)
.
P
art
A
In
an
exp
erimen
t,
the
radon
concen
tration
w
as
read
at
the
end
of
eac
h
da
y
.
The
graph
b
elo
w
sho
ws
the
readings
for
one
w
eek.
F
or
example,
at
the
end
of
the
second
da
y
,
the
radon
concen-
tration
is
appro
ximately
1
000
B
q
·
m
−
3
1
Using
graphical
represen
tation
:
a
Explain
wh
y
,
in
this
situation,
the
deca
y
is
not
linear.
b
Determine
the
da
y
on
whic
h
the
radon
concen
tration
b
ecomes
less
than
half
of
the
first
da
y
.
2
The
follo
wing
table
sho
ws
the
n
umerical
data
measured
during
the
exp
erimen
t.
In
one
table,
data
concerning
radon
gas
concen
tration
w
ere
en
tered.
The
m
ultiplication
co
efficien
t
b
et
w
een
t
w
o
consecutiv
e
v
alues
w
as
calculated.
h
ttps:/
/c
hingmath.fr
0
1
2
3
4
5
6
7
8
9
1011121314151617181920
1
2
3
4
5
6
7
8
9
10
11
12
13
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
A
B
Année
Co
e`cien
t
m
ultiplicateur
1
1,020
2
1,040
3
1,061
4
1,082
5
1,104
6
1,126
7
1,149
8
1,172
9
1,195
10
1,219
11
1,243
12
1,268
13
1,294
14
1,319
15
1,346
16
1,373
17
1,400
18
1,428
19
1,457
20
1,486
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
A
B
21
1,516
22
1,546
23
1,577
24
1,608
25
1,641
26
1,673
27
1,707
28
1,741
29
1,776
30
1,811
31
1,848
32
1,885
33
1,922
34
1,961
35
2,000
36
2,040
37
2,081
38
2,122
39
2,165
40
2,208
sacados/185
Asie - Juin 2004 - 11 points
Jours
0
1
2
3
4
5
6
7
Concentration de radon
0
200
400
600
800
1000
1200
D
e
e
c
r
o
i
s
s
a
n
c
e
r
a
d
i
o
a
c
t
i
v
e
1
2
A
B
C
D
E
F
G
H
I
n
0
1
2
3
4
5
6
u
n
408
Jour
Concen
tration
de
radon
(en
B
q
·
m
−
3
)
Co
efficien
t
m
ultiplicateur
1
1200
2
996
0.83
3
840
0.84
4
696
0.83
5
576
0.83
6
480
0.83
7
408
0.85
a
What
is
the
p
ercen
tage
c
hange
in
radon
concen
tration
b
et
w
een
da
y
1
and
da
y
2?
b
The
n
umerical
data
allo
w
us
to
c
ho
ose
an
exp
onen
tial
deca
y
mo
del.
Justify
this
c
hoice.
c
What
is
the
p
ercen
tage
decrease
in
radon
concen
tra-
tion
during
the
first
w
eek?
P
art
B
1
F
rom
da
y
7,
it
is
assumed
that
deca
y
con
tin
ues
with
0.84
as
the
v
alue
of
the
m
ultiplier
co
efficien
t.
a
What
w
ould
b
e
the
radon
concen
tration
on
da
y
8?
Round
to
the
nearest
in
teger.
b
W
e
mo
del
this
deca
y
b
y
a
sequence
(
u
n
)
where
u
n
rep-
resen
ts
the
radon
concen
tration
on
da
y
n
+7
.
W
e
then
ha
v
e
u
0
=
408
.
What
t
yp
e
of
sequence
is
this?
Justify
that
:
u
n
=
408
×
(
0.84)
n
.
2
The
table
b
elo
w
is
extracted
from
a
spreadsheet
:
Columns
are
mark
ed
with
the
letters
A
,
B
,
C
,.
.
.
and
the
ro
ws
are
mark
ed
with
n
um
b
ers
1
,
2
,
3
.
.
.
W
e
w
an
t
to
write
in
cell
C2
a
form
ula
that
will
allo
w
us
to
obtain
b
y
recop
ying
to
the
righ
t
the
terms
of
the
sequence
up
to
u
6
.
a
Among
the
follo
wing
form
ulas,
cop
y
celle
(s)
that
fits
(or
fits)
:
=$B$2
×
0.84
=408
×
(0.84)^C1
=408
×
0.84
=B2
×
(0.84)^C1
b
Suggest
a
form
ula
to
b
e
en
tered
in
C2
in
suc
h
a
w
a
y
that
it
remains
v
alid
if
the
v
alue
of
cell
B2
is
c
hanged.
c
Complete
the
table
in
App
endix
(to
b
e
r
eturne
d
with
the
c
opy)
using
a
calculator
(r
esults
wil
l
b
e
r
ounde
d
to
the
ne
ar
est
inte
ger)
.
3
The
Conseil
Sup
érieur
d’Hygiène
Publique
has
issued
an
opinion
on
the
harmfulness
of
this
gas
in
dw
ellings
:
b
e-
lo
w
200
B
q
·
m
−
3
,
it
is
considered
harmless.
Determine
the
da
y
from
whic
h
the
radon
concen
tration
is
less
than
200
B
q
·
m
−
3
E.183
F
or
all
calculations
in
this
exercise,
w
e
will
round
up
to
the
euro
cen
t
Pierre,
a
new
graduate,
has
t
w
o
job
offers
from
t
w
o
differ-
en
t
companies.
Before
accepting
either
offer,
he
studies
the
salaries
offered
b
y
eac
h
compan
y
.
P
artie
A
En
treprise
Boss
The
Boss
compan
y
offers
him
the
follo
wing
con
tract
for
em-
plo
ymen
t
starting
1
er
Jan
uary
2005
:
the
initial
mon
thly
salary
is
1
180
e
and
increases
eac
h
1
er
Jan
uary
b
y
12
e
.
W
e
note
u
0
this
initial
salary
,
u
1
the
salary
at
1
er
Jan
uary
2006,
u
2
the
salary
at
1
er
Jan
uary
2007.
.
.
,
u
n
the
salary
at
1
er
Jan
uary
of
the
y
ear
(2005+
n
)
.
1
Calculate
u
1
and
u
2
.
2
What
is
the
nature
of
the
sequence
(
u
n
)
?
Justify
y
our
answ
er.
3
a
Express
u
n
as
a
function
of
n
for
an
y
natural
n
um
b
er
n
.
b
What
w
ould
his
mon
thly
salary
b
e
in
2010?
Compan
y
Rapido
The
Rapido
compan
y
offers
him,
for
the
same
job
starting
1
er
Jan
uary
2005,
the
follo
wing
emplo
ymen
t
con
tract
:
the
initial
mon
thly
salary
is
1027.50
e
and
increases
eac
h
1
er
Jan
uary
b
y
3.5%
.
W
e
note
v
0
this
initial
salary
,
v
1
the
salary
at
1
er
Jan
uary
2006,
v
2
the
salary
at
1
er
Jan
uary
2007,.
.
.
,
v
n
the
salary
at
1
er
Jan
uary
of
the
y
ear
(2005+
n
)
.
4
Calculate
v
1
and
v
2
.
5
What
is
the
nature
of
the
sequence
(
v
n
)
?
Justify
y
our
answ
er.
6
a
Express
v
n
as
a
function
of
n
for
an
y
natural
n
um
b
er
n
.
b
What
w
ould
his
mon
thly
salary
b
e
in
2010?
P
art
B
Before
making
his
c
hoice
for
one
or
other
of
the
companies,
Pierre
w
an
ts
to
compare
the
successiv
e
amoun
ts
of
the
salaries
prop
osed.
T
o
do
this,
he
creates
a
table
using
a
spreadsheet
program
1
Explain
ho
w
Pierre
w
as
able
to
complete
the
column
A
(c
el
ls
going
fr
om
A2
to
A14
)
without
ha
ving
to
t
yp
e
all
the
v
alues
con
tained
in
these
cells.
2
What
form
ulas
m
ust
he
write
in
cells
B2
and
B3
to
obtain,
b
y
cop
ying
it
do
wn,
the
terms
of
the
sequence
(
u
n
)
in
the
column
B
?
3
What
form
ulas
m
ust
he
write
in
cells
E2
and
E3
to
obtain,
b
y
cop
ying
it
do
wn,
the
terms
of
the
sequence
(
v
n
)
in
the
column
E
?
4
T
able
2
records
the
results
obtained.
Complete
all
the
empt
y
cells
in
this
table
in
the
app
endix
to
b
e
returned
with
the
cop
y
P
art
C
1
Compare
the
ev
olution
of
mon
thly
w
ages
in
eac
h
com-
pan
y
.
2
a
In
whic
h
y
ear,
for
the
first
time,
will
the
Rapido
com-
h
ttps:/
/c
hingmath.fr
1
2
A
B
C
D
E
F
G
H
I
n
0
1
2
3
4
5
6
u
n
408
sacados/183
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A
B
C
D
E
F
G
Année
Salaire
mensuel
a
v
ec
Boss
Salaire
ann
uel
a
v
ec
Boss
Cum
ul
des
salaires
a
v
ec
Boss
Salaire
mensuel
a
v
ec
Rapido
Salaire
ann
uel
a
v
ec
Rapido
Cum
ul
des
salaires
a
v
ec
Rapido
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A
B
C
D
E
F
G
Année
Salaire
mensuel
a
v
ec
Boss
Salaire
ann
uel
a
v
ec
Boss
Cum
ul
des
salaires
a
v
ec
Boss
Salaire
mensuel
a
v
ec
Rapido
Salaire
ann
uel
a
v
ec
Rapido
Cum
ul
des
salaires
a
v
ec
Rapido
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
1180,00
14160,00
14160,00
1027,50
12330,00
12330,00
1192,00
14301,00
28464,00
1063,46
12761,55
25091,55
1204,00
14448,00
42912,00
1100,68
13208,20
38299,75
1216,00
14592,00
57504,00
1139,21
13670,49
51970,25
1228,00
14736,00
72240,00
1179,08
12330,00
66119,20
1240,00
14880,00
87120,00
1220,35
14644,17
80763,38
1252,00
15024,00
102144,00
1263,06
15156,72
95920,09
1264,00
15168,00
117312,00
1307,27
15687,20
111607,20
1276,00
15312,00
132624,00
1353,02
16236,26
127843,55
1288,00
15456,00
148080,00
1400,38
16804,52
144648,08
1300,00
15600,00
163680,00
1449,39
17392,68
162040,76
1312,00
15744,00
179424,00
1500,12
18001,43
180042,19
1324,00
15888,00
195312,00
1552,62
18631,48
198673,66
pan
y’s
cum
ulativ
e
earnings
exceed
the
Boss
compan
y’s
cum
ulativ
e
earnings?
b
Compare
with
the
results
obtained
in
question
C
1
and
commen
t.
T
able
1.
Mon
thly
w
ages
and
cum
ulativ
e
w
ages
T
able
2.
Affic
hage
mon
thly
salaries
and
cum
ulativ
e
des
salaries
E.181
The
follo
wing
table
giv
es
the
n
um
b
er
of
In
ternet
users
w
orldwide
(in
mil
lions)
for
the
y
ears
1995
to
2000.
Année
1995
1996
1997
1998
1999
2000
Nom
bre
d’utilisateurs
(en
mil
lions)
34
56
92
145
243
414
W
e
w
an
t
to
use
a
spreadsheet
to
analyze
this
data.
The
table
pro
vided
in
annex
(to
b
e
returned
with
the
cop
y)
has
b
een
dra
wn
up
P
art
A
1
Explain
ho
w
it
is
p
ossible
to
complete
the
column
A
with-
out
ha
ving
to
en
ter
all
the
v
alues
con
tained
in
the
cells.
2
In
cell
C3
,
w
e
ha
v
e
calculated
the
quotien
t
of
the
n
um
b
er
of
In
ternet
users
in
1996
b
y
the
n
um
b
er
of
In
ternet
users
in
1995.
What
do
es
this
quotien
t
represen
t?
What
form
ula
should
b
e
en
tered
in
cell
C3
to
p
erform
this
calculation
and
obtain
the
n
um
b
ers
in
column
C
?
3
a
What
is
the
p
ercen
tage
increase
in
the
n
um
b
er
of
In
ternet
users
b
et
w
een
1995
and
1996?
Bet
w
een
1996
and
1997?
(Per
c
entages
r
ounde
d
to
the
ne
ar
est
whole
numb
er
wil
l
b
e
given.)
b
What
form
ula
m
ust
b
e
en
tered
in
cell
D3
to
obtain,
b
y
cop
ying
do
wn,
the
p
ercen
tages
of
v
ariation
in
the
n
um
b
er
of
In
ternet
users
o
v
er
the
y
ears?
c
Complete
column
D
of
table
in
app
endix
(to
b
e
returned
with
cop
y)
d
Is
the
gro
wth
in
the
n
um
b
er
of
In
ternet
users
b
et
w
een
1995
and
2000
exp
onen
tial?
Justify
y
our
answ
er.
P
artie
B
1
T
o
study
the
gro
wth
in
the
n
um
b
er
of
In
ternet
users
w
orldwide,
w
e
c
ho
ose
to
mo
del
it
b
y
a
geometric
sequence
(
u
n
)
of
first
term
u
0
=
34
.
The
task
is
to
find
a
v
alue
for
the
reason
of
this
geometric
sequence,
whic
h
allo
ws
this
mo
deling.
This
v
alue
will
b
e
en
tered
in
the
cell
I1
.
What
form
ula
should
b
e
en
tered
in
cell
F3
to
calculate
u
1
,
using
the
con
ten
ts
of
cell
I1
,
so
as
to
obtain,
b
y
cop
ying
do
wn,
the
terms
u
2
,
u
3
,
u
4
and
u
5
?
In
this
w
a
y
,
v
alues
can
b
e
automatically
up
dated
if
the
n
um
b
er
con
tained
in
cell
I1
is
c
hanged.
In
the
r
est
of
the
exer
cise,
we
wil
l
take
1.645
as
the
value
of
the
r
e
ason
for
the
se
quenc
e
(
u
n
)
.
2
Calculate
u
1
,
u
2
,
u
3
,
u
4
and
u
5
,
then
complete
the
col-
umn
F
of
the
table
in
the
app
endix
to
b
e
returned
with
the
cop
y
(results
rounded
to
the
nearest
unit
will
b
e
giv
en)
3
Assuming
that,
un
til
2004,
this
mo
del
remains
reliable,
giv
e
an
estimate
of
the
n
um
b
er
of
In
ternet
users
w
orld-
wide
in
2004.
h
ttps:/
/c
hingmath.fr
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A
B
C
D
E
F
G
Année
Salaire
mensuel
a
v
ec
Boss
Salaire
ann
uel
a
v
ec
Boss
Cum
ul
des
salaires
a
v
ec
Boss
Salaire
mensuel
a
v
ec
Rapido
Salaire
ann
uel
a
v
ec
Rapido
Cum
ul
des
salaires
a
v
ec
Rapido
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A
B
C
D
E
F
G
Année
Salaire
mensuel
a
v
ec
Boss
Salaire
ann
uel
a
v
ec
Boss
Cum
ul
des
salaires
a
v
ec
Boss
Salaire
mensuel
a
v
ec
Rapido
Salaire
ann
uel
a
v
ec
Rapido
Cum
ul
des
salaires
a
v
ec
Rapido
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
1180,00
14160,00
14160,00
1027,50
12330,00
12330,00
1192,00
14301,00
28464,00
1063,46
12761,55
25091,55
1204,00
14448,00
42912,00
1100,68
13208,20
38299,75
1216,00
14592,00
57504,00
1139,21
13670,49
51970,25
1228,00
14736,00
72240,00
1179,08
12330,00
66119,20
1240,00
14880,00
87120,00
1220,35
14644,17
80763,38
1252,00
15024,00
102144,00
1263,06
15156,72
95920,09
1264,00
15168,00
117312,00
1307,27
15687,20
111607,20
1276,00
15312,00
132624,00
1353,02
16236,26
127843,55
1288,00
15456,00
148080,00
1400,38
16804,52
144648,08
1300,00
15600,00
163680,00
1449,39
17392,68
162040,76
1312,00
15744,00
179424,00
1500,12
18001,43
180042,19
1324,00
15888,00
195312,00
1552,62
18631,48
198673,66
sacados/181
1
2
3
4
5
6
7
A
B
C
D
E
F
G
H
I
Année
Nom
bre
d’utilisateurs
Quotien
t
P
ourcen
tage
d’augmen
tation
n
u
n
Raison
1995
34
0
1996
56
1,6471
1
1997
92
1,6429
2
1998
145
1,5761
3
1999
243
1,6759
4
2000
414
1,7037
5
1
2
3
A
B
C
D
E
F
G
H
I
J
n
1
2
3
4
5
6
7
8
9
coût
du
n
e
mètre
135
139,05
coût
total
de
n
mètres
forés
135
274,05
E.178
south
America
ffl
No
v
2004
ffl
12
p
oin
ts
In
the
summer
of
2003,
F
rance
w
as
hit
b
y
an
excep-
tional
heat
w
a
v
e.
Monsieur
Dup
on
t
w
an
ts
to
dig
a
w
ell
at
the
b
ottom
of
his
garden.
A
natural
underground
w
ater
reserv
e
lies
at
9
meters.
He
requests
quotes
for
drilling
the
w
ell.
Quote
n
◦
1
Fixed
price
for
taking
c
harge,
visit
on
terrain
:
40
e
V
A
T
included.
Fixed
price
p
er
meter
foré
:
150
e
incl.
V
A
T
Quote
n
◦
2
No
fixed
price
for
pic
k-up,
but
the
price
p
er
meter
dep
ends
on
the
depth
reac
hed
:
the
first
meter
costs
135
e
incl.
V
A
T,
eac
h
subsequen
t
meter
costs
3%
more
than
the
previous
one.
W
e’ll
study
these
t
w
o
quotes
to
estimate
the
cost
of
drilling
a
9-meter
w
ell.
P
art
A
Quote
study
n
◦
1
1
W
e
note
u
0
the
tak
eo
v
er
fee
of
40
e
and
u
n
(for
n
1
)
the
total
cost
of
n
meter
drilled.
Th
us
:
u
0
=
40
and
u
1
=
190
.
Calculate
u
2
and
u
3
2
a
What
t
yp
e
of
gro
wth
do
es
the
drilling
exp
ense
cor-
resp
ond
to?
b
Justify
that
:
u
n
=
40+150
n
3
Then
calculate
the
cost
of
a
9-meter
b
orehole.
P
art
B
Quotation
study
n
◦
2
1
W
e
note
v
1
the
cost
of
the
first
meter
drilled
and
v
n
the
cost
of
the
n-th
meter
drilled.
Th
us
v
1
=
135
.
Sho
w
that
:
v
2
=
139.05
.
2
a
What
t
yp
e
of
gro
wth
do
es
the
drilling
exp
ense
cor-
resp
ond
to?
b
Justify
that
:
v
n
=
135
×
(1.03)
n
−
1
3
Then
calculate
the
total
cost
of
drilling,
w
e
use
the
spreadsheet
b
elo
w
:
a
What
form
ula
m
ust
b
e
en
tered
in
cell
D3
to
obtain
in
eac
h
cell,
after
automatic
cop
ying
to
J3
,
the
cost
of
the
n
-th
meter
drilled?
b
What
form
ula
m
ust
b
e
en
tered
in
cell
D4
to
obtain
in
eac
h
cell,
after
automatic
cop
ying
to
J4
,
the
total
cost
of
n
meters
drilled?
c
Complete
this
table.
Amoun
ts
will
b
e
rounded
to
the
nearest
cen
t.
d
What
is
the
cost
of
a
9-meter
b
orehole?
E.174
In
an
imaginary
coun
try
noted
I
,
there
is
a
capital
P
and
a
collection
of
villages
V
.
As
of
1
er
Jan
uary
2002,
P
and
V
had
200
000
and
300
000
inhabitan
ts
resp
ectiv
ely
.
Eac
h
y
ear,
the
p
opulation
of
P
in-
creases
b
y
10
%
,
while
that
of
V
decreases
b
y
20
000
inhabi-
tan
ts.
1
a
As
of
1
er
Jan
uary
2002,
what
p
ercen
tage
do
es
the
p
opulation
of
P
represen
t
compared
to
that
of
I
?
b
Calculate
the
p
opulation
of
P
,
that
of
V
,
then
that
of
I
at
1
er
2003.
What
p
ercen
tage
then
do
es
the
p
opulation
of
P
repre-
sen
t
in
relation
to
that
of
I
?
2
Let
n
b
e
a
natural
n
um
b
er.
Let
p
n
b
e
the
p
opulation
of
P
at
1
er
Jan
uary
(2002+
n
)
;
th
us
p
0
=
200
000
.
a
Express
p
n
+1
as
a
function
of
p
n
and
deduce
the
nature
of
the
sequence
(
p
n
)
.
b
Express
p
n
as
a
function
of
n
.
Calculate
p
5
.
What
do
es
this
v
alue
represen
t?
3
Let
n
b
e
a
natural
n
um
b
er.
Let
v
n
b
e
the
p
opulation
of
V
at
1
er
Jan
uary
(2002+
n
)
;
th
us
v
0
=
300
000
.
a
Express
v
n
+1
as
a
function
of
v
n
and
deduce
the
nature
of
the
sequence
(
v
n
)
.
b
Express
v
n
as
a
function
of
n
.
Calculate
v
5
.
What
do
es
this
v
alue
represen
t?
4
This
question
in
v
olv
es
the
table
giv
en
b
elo
w.
A
spreadsheet
giv
es
in
the
column
A
the
y
ears
from
2002
to
2007,
in
the
column
B
the
p
opulation
of
the
capital
P
,
in
column
C
the
p
opulation
of
all
villages
V
and
in
column
D
the
total
p
opulation
of
the
coun
try
I
at
1
er
Jan
uary
of
the
corresp
onding
y
ear.
a
Indicate
the
form
ulas
that
should
b
e
written
in
the
cells
D2
,
A3
,
B3
and
C3
in
order
to
obtain
automati-
cally
,
b
y
cop
ying
do
wn
the
y
ears
in
the
column
A
and
the
p
opulations
in
the
columns
B
,
C
and
D
.
b
Complete
the
table
b
elo
w.
5
a
Graphically
represen
t
the
ev
olution
of
the
p
opula-
tion
of
P
and
that
of
V
b
y
placing
the
p
oin
ts
of
co-
ordinates
(
n
;
p
n
)
and
(
n
;
v
n
)
when
the
in
teger
v
aries
from
0
to
5.
the
graphical
units
will
b
e
2
cm
for
one
y
ear
on
the
x-axis
and
1
cm
for
10
000
inhabitan
ts
on
the
y-axis,
whic
h
will
b
e
graduated
from
200
000
in-
habitan
ts
b
Giv
e
the
y
ear
x
in
whic
h
the
p
opulation
of
P
will
ex-
ceed
that
of
V
.
c
Assuming
linear
ev
olution
of
the
p
opulations
of
P
and
V
qu
during
the
y
ear
x
,
graphically
determine
the
quar-
ter
qu
in
whic
h
the
p
opulation
of
P
will
exceed
that
of
V
,
sho
wing
all
useful
plots.
h
ttps:/
/c
hingmath.fr
1
2
3
4
5
6
7
A
B
C
D
E
F
G
H
I
Année
Nom
bre
d’utilisateurs
Quotien
t
P
ourcen
tage
d’augmen
tation
n
u
n
Raison
1995
34
0
1996
56
1,6471
1
1997
92
1,6429
2
1998
145
1,5761
3
1999
243
1,6759
4
2000
414
1,7037
5
sacados/178
1
2
3
A
B
C
D
E
F
G
H
I
J
n
1
2
3
4
5
6
7
8
9
coût
du
n
e
mètre
135
139,05
coût
total
de
n
mètres
forés
135
274,05
sacados/174
Liban - juin 2005 - 12 points
1
2
3
4
5
6
7
A
B
C
D
Année
P
opulation
de
P
au
1
jan
vier
P
opulation
de
V
au
1
jan
vier
P
opulation
de
I
au
1
jan
vier
2002
200
000
300
000
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
A
B
C
D
Programmme
d’en
traînemen
t
d’Aline
Programmme
d’en
traînemen
t
de
Blandine
Programmme
d’en
traînemen
t
de
Caroline
P
ourcen
tage
d’augmen
tation
4
13
;
50%
5%
Distance
U
(
n
parcourue
par
Aline
n
(en
k
m
)
Distance
V
(
n
parcourue
par
Blandine
la
semaine
n
(en
k
m
,
arr
ondie
à
0,001)
Distance
W
(
n
par-
courue
par
Car-
oline
la
semaine
n
(en
k
m
,
ar-
r
ondie
à
0,001)
semaine
1
20
20
20
semaine
2
27
22,7
semaine
3
30,250
semaine
4
semaine
5
48
33,190
41,551
semaine
6
37,671
47,628
semaine
7
62
42,757
54,010
semaine
8
69
48,529
60,710
semaine
9
55,080
67,746
semaine
10
semaine
11
82,889
semaine
12
97
80,535
semaine
13
99,586
semaine
14
111
103,747
108,565
semaine
15
118
117,753
117,993
Distance
totale
parcourue
1035
841,849
957,856
Distance
mo
y
enne
69
56,123
Distance
(en
km
)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Semaine
20
40
60
80
100
120
E.184
Aline,
Blandine
and
Caroline
de-
cided
to
resume
cycling
training
ev
ery
Saturda
y
for
15
w
eeks.
Using
a
c
hart,
eac
h
has
dra
wn
up
her
training
program.
They
ride
20
k
m
in
the
first
w
eek
and
w
an
t
to
do
an
outing
together
in
the
fifteen
th
w
eek.
The
app
endix
repro
duces
the
final
state
of
the
spreadsheet
used.
The
v
alues
of
some
cells
ha
v
e
b
een
hidden.
P
art
A
Aline’s
training
program
The
distance
co
v
ered
b
y
Aline
eac
h
w
eek
is
plotted
on
the
graph
in
the
app
endix,
and
some
distances
app
ear
in
the
col-
umn
B
of
the
table.
W
e
note
U
(
n
)
the
distance
co
v
ered
in
the
n
-th
w
eek.
Th
us
:
U
(1)
=
20
;
U
(15)
=
118
.
1
Using
column
v
alues
B
and
graph
:
a
Conjecture
the
nature
of
the
sequence
of
n
um
b
ers
U
(
n
)
.
(Justify
the
answer
given.]
b
Then
express
U
(
n
)
as
a
function
of
n
for
an
y
in
teger
n
b
et
w
een
1
and
15.
2
Calculate
the
distance
co
v
ered
b
y
Aline
in
the
ten
th
w
eek.
3
What
form
ula,
copied
to
the
righ
t,
has
she
en
tered
in
to
cell
B23
to
calculate
the
a
v
erage
distance
eac
h
tra
v
eled
during
the
w
ork
outs?
P
artie
B
Blandine’s
training
program
Blandine
runs
20
k
m
the
first
w
eek.
She
w
an
ts
to
increase
the
distance
co
v
ered
eac
h
w
eek
b
y
the
same
p
ercen
tage
so
that
the
distance
co
v
ered
in
the
fifteen
th
w
eek
is,
to
the
near-
est
unit,
118
k
m
.
T
o
do
this,
she
tested
differen
t
p
ercen
tages
written
in
the
cell
C3
.
1
What
form
ula
did
she
en
ter
in
cell
C7
and
then
cop
y
do
wn
from
C8
to
C20
,
kno
wing
that
the
results
up
dated
automatically
when
she
c
hanged
the
w
eekly
p
ercen
tage
increase?
2
T
esting
allo
w
ed
her
to
find
that
a
w
eekly
increase
of
13.5%
is
suitable.
W
e
note
V
(
n
)
the
distance
Blandine
tra
v
eled
on
the
n
-th
w
eek.
a
What
is
the
nature
of
the
sequence
of
n
um
b
ers
V
(
n
)
?
(Justify
the
answer
given)
b
Express
V
(
n
)
as
a
function
of
n
,
for
an
y
in
teger
n
b
e-
t
w
een
1
and
15.
c
Ho
w
far
do
es
Blandine
tra
v
el
in
the
ten
th
w
eek?
3
Calculate
the
p
ercen
tage
increase
in
distance
tra
v
eled
b
e-
t
w
een
the
first
and
fifteen
th
w
eek.
P
art
C
Caroline
training
program
Caroline
runs
20
k
m
in
the
first
w
eek.
T
o
calculate
the
dis-
tances
co
v
ered
in
subsequen
t
w
eeks,
she
has
en
tered
the
for-
m
ula
:
in
cell
D7
=D6
×
(1+$D$3)+$D$2
and
copied
it
do
wn
from
D8
to
D20
.
1
The
v
alue
in
cell
D7
has
b
een
hidden.
What
is
this
v
alue?
2
What
is
the
form
ula
con
tained
b
y
the
cell
D8
?
3
Note
W
(
n
)
the
distance
tra
v
elled
b
y
Caroline
on
the
n
-
th
w
eek.
Is
the
sequence
of
n
um
b
ers
W
(
n
)
arithmetic?
Is
it
geo-
metric?
Justify
answ
ers.
4
Calculate
the
a
v
erage
distance
co
v
ered
b
y
Caroline
dur-
ing
her
training
sessions.
h
ttps:/
/c
hingmath.fr
1
2
3
4
5
6
7
A
B
C
D
Année
P
opulation
de
P
au
1
jan
vier
P
opulation
de
V
au
1
jan
vier
P
opulation
de
I
au
1
jan
vier
2002
200
000
300
000
sacados/184
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
A
B
C
D
Programmme
d’en
traînemen
t
d’Aline
Programmme
d’en
traînemen
t
de
Blandine
Programmme
d’en
traînemen
t
de
Caroline
P
ourcen
tage
d’augmen
tation
4
13
;
50%
5%
Distance
U
(
n
parcourue
par
Aline
n
(en
k
m
)
Distance
V
(
n
parcourue
par
Blandine
la
semaine
n
(en
k
m
,
arr
ondie
à
0,001)
Distance
W
(
n
par-
courue
par
Car-
oline
la
semaine
n
(en
k
m
,
ar-
r
ondie
à
0,001)
semaine
1
20
20
20
semaine
2
27
22,7
semaine
3
30,250
semaine
4
semaine
5
48
33,190
41,551
semaine
6
37,671
47,628
semaine
7
62
42,757
54,010
semaine
8
69
48,529
60,710
semaine
9
55,080
67,746
semaine
10
semaine
11
82,889
semaine
12
97
80,535
semaine
13
99,586
semaine
14
111
103,747
108,565
semaine
15
118
117,753
117,993
Distance
totale
parcourue
1035
841,849
957,856
Distance
mo
y
enne
69
56,123
Distance
(en
km
)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Semaine
20
40
60
80
100
120
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
A
B
C
D
E
F
G
H
I
Etude
comparativ
e
des
deux
prop
ositions
de
bail
Prop
osition
1
Prop
osition
2
Années
n
u
n
Lo
y
er
ann
uel
Cum
ul
des
lo
y
ers
ann
uels
v
n
Lo
y
er
ann
uel
Cum
ul
des
lo
y
ers
ann
uels
2007
0
400
4800
4800
400
4800
4800
2008
1
9816
4992
9792
2009
2
15048
5192
14984
2010
3
454
5448
20496
450
5399
20383
2011
4
472
5664
26160
468
5615
25998
2012
5
490
5880
32040
487
5840
31838
2013
6
508
6096
38136
506
6074
37912
2014
7
526
6312
44448
526
6316
44228
2015
8
544
6528
50976
547
6569
50797
2016
9
562
6744
57720
569
6832
57629
2017
10
580
6960
64680
592
7105
64734
2018
11
598
7176
71856
616
7389
72124
2019
12
616
7392
79248
640
7685
79809
2020
13
86856
7992
87801
E.1967
Mr
and
Mrs
X
are
planning
to
ren
t
an
apartmen
t
for
a
few
y
ears.
The
landlord
is
offering
them
t
w
o
t
yp
es
of
lease
from
1
er
Jan-
uary
2007.
Prop
osal
1
:
to
1
er
Jan
uary
2007,
the
mon
thly
ren
t
is
400.
This
mon
thly
ren
t
remains
un-
c
hanged
during
2007
and
will
b
e
sub
ject
to
an
increase
of
18
on
the
first
of
Jan
uary
of
eac
h
subsequen
t
y
ear.
Prop
osal
2
:
to
1
er
Jan
uary
2007,
the
mon
thly
ren
t
is
400.
This
mon
thly
ren
t
remains
un-
c
hanged
during
2007
and
will
b
e
sub
ject
to
an
increase
of
4
%
on
the
first
of
Jan
uary
of
eac
h
of
the
follo
wing
y
ears.
Mr
and
Mrs
X
study
and
compare
the
t
w
o
prop
osals
using
an
automated
spreadsheet
giv
en
in
App
endix
1.
The
format
of
the
cells
is
suc
h
that
the
v
alues
displa
y
ed
are
rounded
to
the
unit.
1
Study
of
the
prop
osal
1
Mr.
and
Mrs.
X
decide
to
note
u
n
the
amoun
t
in
eu-
ros
of
the
mon
thly
ren
t
they
will
b
e
c
harged
during
the
y
ear
(2007+
n
)
,
where
n
denotes
a
natural
n
um
b
er,
if
they
c
ho
ose
prop
osition
1.
Th
us
:
u
0
=
400
a
Calculate
u
1
and
u
2
.
b
What
is
the
nature
of
the
sequence
(
u
n
)
?
c
Express
u
n
as
a
function
of
n
,
for
an
y
natural
n
um
b
er
n
.
d
Ho
w
m
uc
h
will
the
mon
thly
ren
t
b
e
in
2020
with
pro-
p
osal
1?
e
What
form
ula
did
Mr.
and
Mrs.
X
write
in
cellcould
they
write
in
cell
C5
and
automatically
cop
y
do
wn
to
calculate
in
column
C
the
first
terms
of
the
sequence
(
u
n
)
?
Complete
the
cells
C5
,
C6
,
C17
of
the
table
in
ap-
p
endix
1
.
2
Prop
osal
study
2
Mr.
and
Mrs.
X
decide
to
note
v
n
the
amoun
t
in
euros
of
the
mon
thly
ren
t
they
will
b
e
c
harged
during
the
y
ear
(2007+
n
)
,
where
n
denotes
a
natural
n
um
b
er,
if
they
c
ho
ose
prop
osition
2.
Th
us
:
v
0
=
400
.
a
Calculate
v
1
and
v
2
.
Round
to
the
nearest
whole
n
um-
b
er.
b
Justify
that
the
sequence
(
v
n
)
is
a
geometric
sequence
whose
reason
will
b
e
sp
ecified.
c
Justify
that
for
an
y
natural
n
um
b
er
n
,
w
e
ha
v
e
:
v
n
=
400
×
1.04
n
.
d
What
will
the
mon
thly
ren
t
b
e
in
2020
with
prop
osal
2?
Round
to
the
nearest
whole
n
um
b
er.
e
Complete
the
cells
G5
,
G6
,
G17
of
the
table
in
ap-
p
endix
1
.
3
Ann
ual
ren
ts
p
er
prop
osal
1
a
In
column
D
,
Mr
and
Mrs
X
ha
v
e
calculated
the
amoun
t
of
ann
ual
ren
t
due,
if
they
c
ho
ose
prop
osal
1,
for
eac
h
of
the
y
ears
sho
wn
in
column
A
.
What
form
ula
could
they
ha
v
e
written
in
cell
D4
and
automatically
copied
do
wn
for
it?
Complete
the
cells
D5
,
D6
,
D17
of
the
table
in
the
app
endix.
Mr
and
Mrs
X
ha
v
e
similarly
calculated,
in
the
columns
H
and
I
of
the
table
in
the
app
endix,
ann
ual
ren
ts
and
cum
ulativ
e
ann
ual
ren
ts
corresp
onding
to
prop
osal
2.
4
a
Mr
and
Mrs
X
plan
to
ren
t
the
apartmen
t
for
5
y
ears
from
Jan
uary
1,
2007.
Whic
h
lease
prop
osal
should
they
c
ho
ose?
Justify
.
b
After
ho
w
man
y
full
y
ears
of
ren
tal
(starting
1
er
Jan-
uary
2007)
is
prop
osal
1
more
adv
an
tageous
than
pro-
p
osal
2?est-elle
plus
a
v
an
tageuse
que
la
prop
osition
2?
h
ttps:/
/c
hingmath.fr
sacados/1967
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
A
B
C
D
E
F
G
H
I
Etude
comparativ
e
des
deux
prop
ositions
de
bail
Prop
osition
1
Prop
osition
2
Années
n
u
n
Lo
y
er
ann
uel
Cum
ul
des
lo
y
ers
ann
uels
v
n
Lo
y
er
ann
uel
Cum
ul
des
lo
y
ers
ann
uels
2007
0
400
4800
4800
400
4800
4800
2008
1
9816
4992
9792
2009
2
15048
5192
14984
2010
3
454
5448
20496
450
5399
20383
2011
4
472
5664
26160
468
5615
25998
2012
5
490
5880
32040
487
5840
31838
2013
6
508
6096
38136
506
6074
37912
2014
7
526
6312
44448
526
6316
44228
2015
8
544
6528
50976
547
6569
50797
2016
9
562
6744
57720
569
6832
57629
2017
10
580
6960
64680
592
7105
64734
2018
11
598
7176
71856
616
7389
72124
2019
12
616
7392
79248
640
7685
79809
2020
13
86856
7992
87801
1
2
3
4
5
6
7
8
9
10
A
B
C
D
Année
n
u
n
2000
0
210
15
2001
1
225
2002
2
2003
3
2004
4
2005
5
2006
6
300
2007
7
2008
8
0
1
2
3
4
5
6
7
150
200
250
300
350
1
2
3
4
5
6
7
8
A
B
C
Année
n
v
n
2006
0
310
2007
1
2008
2
2009
3
2010
4
2011
5
2012
6
402
E.1906
Both
parts
are
indep
enden
t
In
a
media
library
,
the
managemen
t
wishes
to
renew
the
sto
c
k
a
v
ailable
for
loan
(notament
en
c
e
dér
oms,
D
VDs)
and
increase
the
n
um
b
er
of
computers
(with
Internet
ac
c
ess)
a
v
ail-
able
to
the
public.
One
of
the
solutions
b
eing
explored
to
find
the
financial
means
to
meet
this
demand
is
to
increase
mem-
b
ership.
P
art
1
:
Study
of
the
ev
olution
of
the
n
um
b
er
of
mem-
b
ers
First,
w
e
study
the
ev
olution
of
the
n
um
b
er
of
mem
b
ers
as
a
func-
tion
of
time.
W
e
call
u
0
the
n
um-
b
er
of
mem
b
ers
for
the
y
ear
2000
and
u
n
the
n
um
b
er
of
mem
b
ers
for
the
y
ear
(2000+n)
.
The
table
and
graph
b
elo
w
represen
t
the
ev
olution
of
the
n
um
b
er
of
mem-
b
ers
b
et
w
een
2000
and
2006.
1
A
ccording
to
the
graph,
what
t
yp
e
of
gro
wth
do
es
the
se-
quence
(
u
n
)
corresp
ond
to?
Note
that
the
sequence
(
u
n
)
is
an
arithmetic
sequence
of
reason
15
and
first
term
u
0
=
210
.
2
a
Calculate
u
2
.
b
Express
u
n
+1
as
a
function
of
u
n
.
c
Express
u
n
as
a
function
of
n
and
u
0
.
3
In
cell
D2
,
w
e
ha
v
e
placed
the
reason
for
the
sequence.
a
What
form
ula
could
b
e
written
in
cell
C4
,
using
cell
D2
,
then
cop
y
do
wn
to
C10
,
to
calculate
the
terms
of
the
sequence?
b
If
this
gro
wth
mo
del
holds
un
til
2008,
what
will
b
e
the
n
um
b
er
of
mem
b
ers
in
2008?
P
art
2
:
Planning
a
mark
eting
study
Managemen
t
decides
to
sligh
tly
reduce
mem
b
ership
fees
to
further
encourage
mem
b
ership
gro
wth.
A
mark
eting
study
estimates
that
with
these
new
rates,
mem
b
ership
will
increase
b
y
5
%
p
er
y
ear
after
2006.
W
e
call
v
0
,
the
n
um
b
er
of
mem
b
ers
in
2006
and
v
n
,
the
n
um
b
er
of
mem
b
ers
in
(2006+
n
)
.
1
a
Calculate
v
1
,
v
2
.
Giv
e
the
rounding
to
unit
y
of
these
v
alues.
b
T
o
what
t
yp
e
of
gro
wth
do
es
the
sequence
(
v
n
)
corre-
sp
ond?
c
Sp
ecify
the
nature
and
reason
of
the
sequence
(
v
n
)
.
d
Sho
w
that,
for
an
y
natural
n
um
b
er
n
:
v
n
=
300
·
1.05
n
.
2
What
form
ula
can
b
e
used
in
cell
C3
,
then
copied
do
wn
to
C8
to
calculate
the
forecast
n
um
b
er
of
mem
b
ers?
3
Calculate
the
p
ercen
tage
increase
in
mem
b
ership
b
e-
t
w
een
2006
and
2012.
2.
Unclassifie
d
financial
ye
ars
E.1828
the
four
p
arts
of
this
exer
cise
c
an
b
e
tr
e
ate
d
indep
endently
of
e
ach
other.
P
art
A
:
The
differen
t
t
yp
es
of
family
with
at
least
one
c
hild
under
5
in
1990
and
1999
(do
cument
1
in
app
endix
1)
1
In
terpret
with
a
sen
tence
eac
h
of
the
t
w
o
v
alues
en
tered
in
cells
E7
and
F4
of
the
do
cumen
t
in
App
endix
1.
2
Wh
y
is
the
sum
of
the
fiv
e
p
ercen
tages
en
tered
in
cells
E4
to
E8
on
do
cumen
t
1
not
equal
to
100?
3
Calculate
the
three
missing
v
alues
a
,
b
and
c
from
Do
c-
umen
t
1.
(numb
ers
of
families
wil
l
b
e
r
ounde
d
to
the
thousand
and
p
er
c
entages
to
0.1
%
)
P
art
B
:
Num
b
er
of
c
hildren
and
family
t
yp
es
in
1999
(Do
c-
ument
2
in
App
endix
1)
1
A
ccording
to
Do
cumen
t
2
in
App
endix
1,
what
share
do
families
with
t
w
o
or
more
c
hildren
represen
t
among
ˇtra-
ditionalı
families,
in
1999?
2
a
By
reading
do
cumen
ts
1
and
2,
giv
e
:
the
p
ercen
tage
of
ˇtraditionalı
families
among
all
families
in
1999,
the
p
ercen
tage
of
one-c
hild
families
among
ˇtradi-
tionalı
families
in
1999.
b
Deduct
the
p
ercen
tage
share
represen
ted
b
y
ˇtradi-
tionalı
families
with
one
c
hild
among
all
families
in
1999.
P
art
C
:
Spreadsheet
w
ork
In
App
endix
1,
Do
cumen
t
1
is
an
automated
spreadsheet.
The
n
um
b
ers
of
families
ha
v
e
b
een
previously
en
tered
on
this
spreadsheet
and
form
ulas
ha
v
e
b
een
used
to
calculate
the
p
er-
cen
tages
of
columns
C
,
E
and
F
(some
of
the
p
er
c
entages
ob-
taine
d
ar
e
given)
.
1
Giv
e
the
form
ula
to
b
e
en
tered
in
cell
C4
and
whic
h,
when
copied
do
wn,
to
C8
,
will
giv
e
all
the
column
p
ercen
tages
C
.
h
ttps:/
/c
hingmath.fr
sacados/1906
1
2
3
4
5
6
7
8
9
10
A
B
C
D
Année
n
u
n
2000
0
210
15
2001
1
225
2002
2
2003
3
2004
4
2005
5
2006
6
300
2007
7
2008
8
0
1
2
3
4
5
6
7
150
200
250
300
350
1
2
3
4
5
6
7
8
A
B
C
Année
n
v
n
2006
0
310
2007
1
2008
2
2009
3
2010
4
2011
5
2012
6
402
chapExoCorrec/1828
sacados/1828
1
2
3
4
5
6
7
8
A
B
C
D
E
F
1990
1999
Ev
olution
de
1990
à
1999
(en
%)
Nom
bre
en
%
Nom
bre
en
%
Ensem
ble
total
des
familles
9
126
000
100,0
8
822
000
100,0
-3,3
F
amilles
ˇtraditionnellesı
7
083
000
a
6
474
000
73,4
-8,6
F
amilles
monoparen
tales
1
397
000
15,3
1
640
000
18,6
b
F
amilles
recomp
osées
646
000
7,1
708
000
8,0
9,6
-
don
t
aucun
enfan
t
n’est
du
couple
actuel
c
d
328
000
3,7
5,8
-
don
t
au
moins
un
enfan
t
est
du
couple
actuel
e
f
380
000
4,3
13,1
10
20
30
40
50
60
1
enfan
t
2
enfan
t
3
enfan
t
4
enfan
ts
ou
plus
1
enfan
t
2
enfan
t
3
enfan
t
4
enfan
ts
ou
plus
1
enfan
t
2
enfan
t
3
enfan
t
4
enfan
ts
ou
plus
40
40
15
5
56
28
10
5
28
37
24
1
Famille
"traditionnelles"
Familles
monoparentales
Familles
recomposées
1
2
3
4
5
6
7
8
9
10
11
A
B
C
D
E
Année
Population
Taux d’évolution
arrondi à
0
;
1%
n
u
n
1950
2500
×
0
2500
1960
3014
20
;
6%
1
1970
3683
22
;
2%
2
1980
4453
20
;
9%
3
1990
5201
4
2000
6080
5
6
7
8
9
2
Similarly
,
giv
e
the
form
ula
to
b
e
en
tered
in
cell
F4
and
whic
h
when
copied
do
wn
to
F8
,
will
giv
e
all
the
p
ercen
t-
ages
in
column
F
.
P
art
D
:
Changes
in
the
n
um
b
er
of
blended
families
1
Bet
w
een
1990
and
1999,
the
ann
ual
increase
in
the
n
um-
b
er
of
blended
families
w
as
1.02
%
.
V
erify
that
o
v
er
this
p
erio
d
this
n
um
b
er
of
families
has
increased
b
y
appro
xi-
mately
9.6
%
.
It
is
no
w
assumed
that
the
ann
ual
ev
olution
of
1.02
%
con
tin
ues
b
ey
ond
this
p
erio
d.
2
W
e
note
u
0
the
n
um
b
er
of
blended
families
in
1990
(
u
0
=
646
000
)
,
and
u
n
their
n
um
b
er,
n
y
ears
later,
in
1990+
n
.
a
What
is
the
nature
of
the
sequence
(
u
n
)
?
Justify
the
answ
er
and
sp
ecify
its
reason.
b
Express
u
n
as
a
function
of
n
.
3
Ho
w
man
y
stepfamilies
can
w
e
estimate
in
2005?
Do
cumen
t
1
Source
:
Surv
eys
ˇF
amily
history
studyı
1990
and
1999,
Insee
Do
cumen
t
2
:
Nom
bres
c
hildren
b
y
family
t
yp
e
in
1999
Reading
example
:
11
%
of
blended
families
ha
v
e
4
or
more
c
hildren
;
this
is
the
case
for
5
%
traditional
families
and
5
%
single-paren
t
families.
Source
:
Enquête
ˇÉtude
de
l’histoire
familialeı
1999,
Insee
E.548
The
parts
A
et
B
are
indep
enden
t.
P
art
A
In
Alb
ert
Jacquard’s
b
o
ok
ˇ
The
Time
of
the
Finite
W
orld
Has
Come
ı
,
the
follo
wing
statemen
t
app
ears
:
A
p
opulation
increase
of
2
%
p
er
y
ear
ma
y
seem
v
ery
small,
y
et
it
corresp
onds
to
a
doubling
in
35
y
ears,
th
us
a
quadru-
pling
in
70
y
ears,
and
a
m
ultiplication
b
y
7
in
less
than
a
cen
tury
.
Are
the
author’s
statemen
ts
correct?
Justify
y
our
answ
er.
P
art
B
1
The
follo
wing
w
orksheet,
tak
en
from
a
spreadsheet,
sho
ws
the
w
orld
p
opulation
in
millions
:
What
form
ula
should
b
e
en
tered
in
C3
to
complete
col-
umn
C
b
y
cop
ying
this
form
ula
do
wn?
2
a
Calculate
the
o
v
erall
gro
wth
rate
of
the
w
orld
p
op-
ulation
b
et
w
een
y
ears
1950
and
2000
.
b
Sho
w
that
the
a
v
erage
rate
of
c
hange
p
er
decade
b
et
w
een
the
y
ears
1950
and
2000
is
appro
ximately
19
;
45
%
.
3
Consider
the
geometric
sequence
u
with
first
term
u
0
=
2500
and
common
ratio
q
=
1
;
195
.
a
What
form
ula,
to
b
e
copied
do
wn,
can
b
e
written
in
E3
to
calculate
the
terms
of
the
sequence
u
?
b
If
w
e
assume
that
the
w
orld
p
opulation
will
gro
w
at
the
same
rate
b
ey
ond
the
y
ear
2000
,
w
e
can
estimate
that
the
w
orld
p
opulation
in
the
y
ear
(1950+
10
n
)
will
b
e
appro
ximately
equal
to
the
term
u
n
of
this
sequence
What
p
opulation
can
w
e
therefore
predict
for
the
y
ear
2010
?
F
or
the
y
ear
2050
?
c
By
ho
w
m
uc
h
w
ould
the
w
orld
p
opulation
th
us
increase
in
a
cen
tury?
h
ttps:/
/c
hingmath.fr
1
2
3
4
5
6
7
8
A
B
C
D
E
F
1990
1999
Ev
olution
de
1990
à
1999
(en
%)
Nom
bre
en
%
Nom
bre
en
%
Ensem
ble
total
des
familles
9
126
000
100,0
8
822
000
100,0
-3,3
F
amilles
ˇtraditionnellesı
7
083
000
a
6
474
000
73,4
-8,6
F
amilles
monoparen
tales
1
397
000
15,3
1
640
000
18,6
b
F
amilles
recomp
osées
646
000
7,1
708
000
8,0
9,6
-
don
t
aucun
enfan
t
n’est
du
couple
actuel
c
d
328
000
3,7
5,8
-
don
t
au
moins
un
enfan
t
est
du
couple
actuel
e
f
380
000
4,3
13,1
10
20
30
40
50
60
1
enfan
t
2
enfan
t
3
enfan
t
4
enfan
ts
ou
plus
1
enfan
t
2
enfan
t
3
enfan
t
4
enfan
ts
ou
plus
1
enfan
t
2
enfan
t
3
enfan
t
4
enfan
ts
ou
plus
40
40
15
5
56
28
10
5
28
37
24
1
Famille
"traditionnelles"
Familles
monoparentales
Familles
recomposées
chapExoCorrec/548
sacados/548
1
2
3
4
5
6
7
8
9
10
11
A
B
C
D
E
Année
Population
Taux d’évolution
arrondi à
0
;
1%
n
u
n
1950
2500
×
0
2500
1960
3014
20
;
6%
1
1970
3683
22
;
2%
2
1980
4453
20
;
9%
3
1990
5201
4
2000
6080
5
6
7
8
9
Année
1989
1990
1991
1992
1993
1994
1995
Nom
bre
de
p
oissons
en
milliers
0
1
2
3
4
5
6
E.177
Scien
tists
w
an
t
to
study
the
long-term
ev
olution
of
a
fish
p
opulation
in
a
small
riv
er.
T
o
do
this,
they
ha
v
e
the
results
of
coun
ts
carried
out
in
a
p
ortion
of
this
riv
er
b
et
w
een
1990
and
1994.
The
table
and
graph
b
elo
w
giv
e
the
n
um
b
ers
found
p
er
y
ear
from
1990
to
1994.
Y
ear
Num
b
er
of
fish
1990
5150
1991
4840
1992
4570
1993
4250
1994
3960
1
A
first
scien
tist
suggests
mo
deling
the
ev
olution
of
fish
n
um
b
ers
b
y
an
arithmetic
sequence.
Wh
y
do
es
the
graph
suggest
that
an
arithmetic
sequence
migh
t
b
e
suitable?
2
This
first
scien
tist
c
ho
oses
to
mo
del
the
ev
olution
of
the
n
um
b
er
of
fish
b
y
the
arithmetic
sequence
(
u
n
)
of
reason
r
=
−
300
and
first
term
u
0
=
5150
.
Th
us,
u
n
represen
ts
the
n
um
b
er
of
fish
in
the
y
ear
(1990+
n
)
.
a
What
in
terpretation
can
b
e
giv
en
to
the
reason
for
this
sequence
for
the
fish
p
opulation?
b
Express
u
n
as
a
function
of
n
.
c
Calculate
the
p
opulation
size
predicted
b
y
this
mo
del
in
2004.
3
A
second
scien
tist
is
not
con
vinced
b
y
this
mo
del
and
prop
oses
for
this
p
opulation
an
exp
onen
tial
ev
olution.
Indeed,
he
notes
that
:
4840
5150
∼
4570
4840
∼
4250
4570
∼
3960
4250
∼
0.935.
He
then
c
ho
oses
to
mo
del
the
ev
olution
of
the
n
um
b
er
of
fish
b
y
the
geometric
sequence
(
v
n
)
,
of
reason
q
=
0.935
and
of
first
term
v
0
=
5150
.
Th
us,
v
n
represen
ts
the
n
um
b
er
of
fish
in
the
y
ear
(1990+
n
)
.
a
What
is
the
p
ercen
tage
ann
ual
decline
in
fish
n
um
b
ers
according
to
this
mo
del?
b
Express
v
n
as
a
function
of
n
.
c
Calculate
v
14
.
The
result
will
b
e
rounded
to
the
unit.
4
In
2004,
a
coun
t
w
as
carried
out
and
1980
fish
w
ere
recorded
in
the
section
of
riv
er
studied.
a
Whic
h
of
the
t
w
o
mo
dels
prop
osed
ab
o
v
e
is
the
more
relev
an
t?
Justify
y
our
answ
er.
b
W
e
c
ho
ose
to
use
the
mo
del
prop
osed
b
y
the
second
scien
tist.
Calculate
v
30
and
v
40
(r
esults
wil
l
b
e
r
ounde
d
to
unity)
.
Determine
the
y
ear
from
whic
h
the
fish
p
opulation
will
fall
b
elo
w
500
individuals.
E.1897
Mr
and
Mrs
Dup
ond
wish
to
b
or-
ro
w
200
000
e
to
buy
a
house.
They
are
studying
prop
osals
from
t
w
o
banks
for
15-y
ear
loans
starting
1
er
Jan
uary
2007.
The
mon
thly
repa
ymen
ts
on
the
loan
offered
b
y
Crédit
du
Soleil
bank
are
1
500
e
for
the
en
tire
duration
of
the
loan.
The
mon
thly
repa
ymen
ts
on
the
loan
offered
b
y
Caisse
Azur
bank
are
1
230
e
in
the
first
y
ear
and
increase
b
y
3
%
eac
h
y
ear.
1
In
this
question,
w
e’re
in
terested
in
the
loan
offered
b
y
the
bank
Crédit
du
Soleil.
a
What
is
the
total
amoun
t
that
Mr
and
Mrs
Dup
ond
will
ha
v
e
to
pa
y
to
the
bank
Crédit
du
Soleil
in
2007
if
they
tak
e
out
this
loan?
b
After
15
y
ears,
ho
w
m
uc
h
will
Monsieur
and
Madame
Dup
ond
ha
v
e
repaid
if
they
tak
e
out
this
loan?
This
sum
is
called
real
v
alue
of
the
loan
.
2
In
this
question,
w
e
are
in
terested
in
the
loan
offered
b
y
the
Caisse
d’Azur
bank.
R
esults
wil
l
b
e
r
ounde
d
if
ne
c
essary
to
the
eur
o
c
ent.
a
Calculate
the
mon
thly
repa
ymen
ts
that
Mr
and
Mrs
Dup
ond
will
ha
v
e
to
mak
e
in
2008
if
they
tak
e
out
this
loan.
W
e
note
u
0
the
amoun
t
in
euros
of
the
mon
thly
pa
ymen
ts
in
2007,
u
1
the
amoun
t
in
euros
of
the
mon
thly
pa
ymen
ts
in
2008
and,
more
generally
,
u
n
the
amoun
t
in
euros
of
mon
thly
installmen
ts
in
2007+
n
,
n
b
eing
an
in
teger
b
e-
t
w
een
0
and
14.
Th
us
:
u
0
=
1
230
.
b
Giv
e
u
1
.
Calculate
u
2
.
c
What
is
the
nature
of
the
sequence
(
u
n
)
?
Justify
y
our
answ
er.
d
Express
u
n
as
a
function
of
n
for
in
tegers
n
b
et
w
een
0
and
14.
Ho
w
m
uc
h
will
Monsieur
and
Madame
Dup
ond’s
mon
thly
pa
ymen
ts
b
e
in
2016
if
they
tak
e
out
the
loan
offered
b
y
Caisse
Azur
bank?
e
A
graphical
represen
tation
of
the
sequence
(
u
n
)
,
for
in
tegers
b
et
w
een
0
and
14,
is
giv
en
in
annexe
.
Determine
graphically
,
from
whic
h
y
ear
on
w
ards
the
mon
thly
repa
ymen
ts
requested
from
Mr
and
Mrs
Dup
ond
b
y
the
Caisse
Azur
bank
will
b
e
higher
than
those
requested
b
y
the
Crédit
du
Soleil
bank.
3
Before
making
their
c
hoice
for
either
of
the
t
w
o
banks,
Monsieur
and
Madame
Dup
ond
also
w
an
t
to
kno
w
the
real
v
alue
of
the
loan
prop
osed
b
y
the
Caisse
Azur
bank.
to
do
this,
they
use
a
table.
W
e
giv
e
in
app
endix
1
their
spreadsheet,
in
whic
h
the
con
ten
ts
of
some
b
o
xes
ha
v
e
b
een
hidden.
a
Complete
b
o
xes
C3
,
C4
,
D2
,
D3
and
D4
of
the
table
giv
en
in
annexe
.
No
justification
is
required.
b
Whic
h
form
ula
ma
y
ha
v
e
b
een
written
in
cell
C3
to
ob-
tain,
after
cop
ying
do
wn
to
cell
C16
,
the
terms
of
the
h
ttps:/
/c
hingmath.fr
chapExoCorrec/177
sacados/177
Année
1989
1990
1991
1992
1993
1994
1995
Nom
bre
de
p
oissons
en
milliers
0
1
2
3
4
5
6
sacados/1897
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1300
1400
1500
1600
1700
1800
1900
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
A
B
C
D
Rang
n
Année
n
Mensualité
u
n
v
ersés
à
la
banque
Caisse
Azur
Mon
tan
t
ann
uel
v
ersé
à
la
banque
Caisse
Azur
0
2007
1
230,00
1
2008
2
2009
3
2010
1
344,05
16
128,65
4
2011
1
384,38
16
612,51
5
2012
1
425,91
17
110,89
6
2013
1
468,68
17
624,21
7
2014
1
512,74
18
152,94
8
2015
1
558,13
19
697,53
9
2016
19
258,45
10
2017
1
653,02
19
836,21
11
2018
1
702,61
20
431,29
12
2019
1
753,69
21
044,23
13
2020
1
806,30
21
675,56
14
2021
1
860,49
22
325,82
15
2022
V
aleur
du
prêt
274
519,97
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
A
B
C
D
Année
Rang
du
terme
de
c
haque
suite
Compte
d’Urbain
Suite
u
n
:
Tirelire
de
Victor
Suite
v
n
2000
0
3000,0
1000,00
2001
1
3082,50
1240,00
2002
2
3167,27
1480,00
2003
3
3254,37
1720,00
2004
4
3343,86
1960,00
2005
5
3435,82
2200,00
2006
6
3530,31
2440,00
2007
7
3627,39
2680,00
2008
8
3727,14
2920,00
2009
9
3829,64
3160,00
2010
10
3934,95
3400,00
2011
11
4043,16
3640,00
2012
12
2013
13
2014
14
2015
15
2016
16
2017
17
2018
18
sequence
(
u
n
)
in
column
C
?
c
Whic
h
form
ula
ma
y
ha
v
e
b
een
written
in
cell
D2
to
obtain,
after
cop
ying
do
wn
to
cell
D16
,
the
amoun
t
of
money
paid
in
to
column
D
?
d
Mr
and
Mrs
Dup
ond
ha
v
e
calculated
in
cell
D17
the
real
v
alue
of
the
loan
offered
to
them
b
y
the
bank
Caisse
Azur.
What
form
ula
could
they
write
in
cell
D17
for
this?
E.1886
On
Jan
uary
1,
2000,
t
w
o
babies
w
ere
b
orn
:
Urbain
and
Victor.
Their
resp
ectiv
e
families
de-
cide
to
sa
v
e
for
their
c
hild.
Urbain’s
family
pa
ys
3
000
euros
on
the
da
y
their
sons
are
b
orn,
in
to
an
accoun
t
where
the
ann
ual
in
terest
rate
is
2.75
%
.
No
withdra
w
als
or
dep
osits
are
made
in
subsequen
t
y
ears.
The
in
terest
rate
remains
fixed.
Victor’s
family
places
1
000
euros
in
a
piggy
bank
on
01
=
01
=
2000
and
then
pa
ys
in,
ev
ery
first
Jan
uary
thereafter,
240
euros
without
ev
er
making
a
withdra
w
al.
1
Calculate
the
money
a
v
ailable
in
eac
h
c
hild’s
accoun
t
on
their
first
birthda
y
.
W
e
call
u
n
the
amoun
t
in
euros
in
Urbain’s
accoun
t
on
the
first
of
Jan
uary
in
the
y
ear
2000+
n
.
W
e
call
v
n
the
amoun
t
in
euros
in
Victor’s
piggy
bank
on
the
first
of
Jan
uary
in
the
y
ear
2000+
n
.
In
the
table
b
elo
w,
the
situation
has
b
een
represen
ted
in
a
spreadsheet.
2
a
What
form
ula
can
w
e
write
in
cell
C3
if
w
e
w
an
t
to
obtain
b
y
cop
ying
do
wn
the
v
alues
of
the
sequence
(
u
n
)
?
b
Whic
h
form
ula
then
con
tains
the
cell
C7
?
3
a
What
form
ula
can
w
e
write
in
cell
D3
if
w
e
w
an
t
to
obtain
b
y
cop
ying
do
wn
the
v
alues
of
the
sequence
(
v
n
)
?
b
Whic
h
form
ula
then
con
tains
the
cell
D8
?
4
a
What
is
the
nature
of
the
sequence
(
u
n
)
and
its
c
har-
acteristic
elemen
ts?
b
Express
u
n
as
a
function
of
n
.
c
What
is
the
nature
of
the
sequence
(
v
n
)
and
its
c
har-
acteristic
elemen
ts?
d
Express
v
n
as
a
function
of
n
.
5
Complete
the
table
in
App
endix
2.
6
On
what
anniv
ersary
date
will
Victor
ha
v
e
more
money
in
his
piggy
bank
than
Urbain
has
in
his
accoun
t?
7
Victor
can
disp
ose
of
all
the
money
in
his
piggy
bank
af-
ter
his
eigh
teen
th
birthda
y
.
His
family
con
tin
ues
to
mak
e
ann
ual
pa
ymen
ts.
a
With
the
sum
a
v
ailable
in
his
piggy
bank,
will
he
b
e
able
to
buy
a
car
w
orth
6
000
euros
from
Jan
uary
2,
2018?
b
Determine
the
minim
um
n
um
b
er
of
y
ears
required
for
his
piggy
bank
to
ha
v
e
a
sufficien
t
balance
to
buy
the
car?
h
ttps:/
/c
hingmath.fr
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1300
1400
1500
1600
1700
1800
1900
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
A
B
C
D
Rang
n
Année
n
Mensualité
u
n
v
ersés
à
la
banque
Caisse
Azur
Mon
tan
t
ann
uel
v
ersé
à
la
banque
Caisse
Azur
0
2007
1
230,00
1
2008
2
2009
3
2010
1
344,05
16
128,65
4
2011
1
384,38
16
612,51
5
2012
1
425,91
17
110,89
6
2013
1
468,68
17
624,21
7
2014
1
512,74
18
152,94
8
2015
1
558,13
19
697,53
9
2016
19
258,45
10
2017
1
653,02
19
836,21
11
2018
1
702,61
20
431,29
12
2019
1
753,69
21
044,23
13
2020
1
806,30
21
675,56
14
2021
1
860,49
22
325,82
15
2022
V
aleur
du
prêt
274
519,97
sacados/1886
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
A
B
C
D
Année
Rang
du
terme
de
c
haque
suite
Compte
d’Urbain
Suite
u
n
:
Tirelire
de
Victor
Suite
v
n
2000
0
3000,0
1000,00
2001
1
3082,50
1240,00
2002
2
3167,27
1480,00
2003
3
3254,37
1720,00
2004
4
3343,86
1960,00
2005
5
3435,82
2200,00
2006
6
3530,31
2440,00
2007
7
3627,39
2680,00
2008
8
3727,14
2920,00
2009
9
3829,64
3160,00
2010
10
3934,95
3400,00
2011
11
4043,16
3640,00
2012
12
2013
13
2014
14
2015
15
2016
16
2017
17
2018
18
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