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4
3
2
1
Grade 12 - Comp.
/ Algorithms
12 exercises (100% corrected)
a
Repetitive structure
(3 exercices)
Repetitive structure: study of the stop condition
(1 exercice)
Repetitive structure: studying the threshold of a sequence
(4 exercices)
Repetitive structure: finding the stopping condition
(4 exercices)
Fonction
terme(n)
Pour
i
de
1
à
n
U
×
U
120
Fin
Pour
Renvoyer
U
Fonction
terme(n)
Pour
i
de
1
à
n
U
115
U
×
U
120
Fin
Pour
Renvoyer
U
Fonction
terme(n)
U
115
Pour
i
de
1
à
n
U
×
U
120
Fin
Pour
Renvoyer
U
Algorithme
1
Algorithme
2
Algorithme
3
Fonction
terme1(A)
n
0
U
50
000
Tant
que
U
A
n
U
·
U
3
000
Fin
Tant
que
Renvoyer
n
Fonction
terme2(n)
U
50
000
Pour
i
allant
de
1
à
n
U
·
U
3
000
Fin
Tant
que
Renvoyer
U
Fonction
terme3(n)
U
50
000
Pour
i
allant
de
0
à
n
U
·
U
3
000
Fin
Tant
que
Renvoyer
U
Fonction
suite(n)
U
5
Pour
i
de
0
à
n
U
1
2
×
Fin
Pour
Renvoyer
U
Fonction
suite(n)
Pour
i
de
0
à
n
U
5
U
1
2
×
Fin
Pour
Renvoyer
U
Fonction
suite(n)
U
5
Pour
i
de
0
à
n
U
1
2
×
Renvoyer
U
Fin
Pour
Algorithme
1
Algorithme
2
Algorithme
3
1.
R
ep
etitive
structur
e
E.6145
Consider
the
sequence
u
n
defined
for
an
y
natural
n
um
b
er
:
u
0
=
115
;
u
n
+1
=
0.4
·
u
n
+
120
Consider
the
three
algorithm
parts
b
elo
w,
eac
h
presen
ting
a
function
terme()
taking
an
in
teger
n
greater
than
or
equal
to
1
for
argumen
t
:
Explain
wh
y
the
functions
term()
of
the
first
t
w
o
algorithms,
called
with
the
in
teger
n
,
do
not
return
the
term
of
the
se-
quence
u
n
of
rank
n
.
E.6147
Consider
the
sequence
u
n
de-
fined
for
an
y
natural
n
um
b
er
:
u
0
=
50000
;
u
n
+1
=
0.95
·
u
n
+
3000
for
an
y
n
∈
N
Consider
the
three
parts
of
algorithms
eac
h
presen
ting
a
func-
tion
f
:
Whic
h
of
the
ab
o
v
e
functions,
b
y
executing
step
b
y
step
and
observing
the
successiv
e
v
alues
tak
en
b
y
the
v
ariable
U
,
to
ob-
tain
all
the
v
alues
of
the
terms
in
the
sequence
u
n
for
ranks
from
0
to
n
.
E.6148
Consider
the
sequence
u
n
de-
fined
for
all
natural
n
um
b
ers
:
u
0
=
5
;
u
n
+1
=
1
2
·
u
n
+
1
for
all
n
∈
N
1
W
e
w
an
t
to
write
a
function
in
an
algorithm
that
tak
es
a
non-zero
natural
n
um
b
er
n
as
an
argumen
t
and
returns
the
v
alue
of
the
term
of
rank
n
of
the
sequence
u
n
Only
one
of
the
follo
wing
three
functions
is
suitable.
Indicate
whic
h
one
and
justify
wh
y
the
other
t
w
o
cannot
giv
e
the
exp
ected
result.
2
By
calling
the
function
f
with
the
argumen
t
9
,
the
v
ari-
able
U
is
successiv
ely
assigned
the
follo
wing
v
alues
:
5
3.5
2.75
2.375
2.185
2.0938
2.0469
2.0234
2.0117
2.0059
What
conjecture
can
b
e
made
ab
out
the
direction
of
v
ari-
ation
of
this
sequence?
2.
R
ep
etitive
structur
e
:
study
of
the
stop
c
ondition
E.6150
W
e
study
the
ev
olution
of
the
p
opulation
of
a
to
wn,
since
1
er
Jan
uary
2008
.
The
p
opulation
of
this
to
wn
from
1
er
Jan
uary
2008
is
consid-
ered
b
y
the
function
f
defined
on
0
;
+
∞
b
y
:
f
(
x
)
=
3
1
+
2e
−
0.05
x
where
x
denotes
the
n
um
b
er
of
y
ears
since
1
er
Jan
uary
2008
and
f
(
x
)
the
n
um
b
er
of
inhabitan
ts
in
h
undreds
of
thousands.
It
is
assumed
that
f
is
increasing
on
0
;
+
∞
Consider
the
follo
wing
algorithm
:
X
←
0
As
long
as
f(X)
2
X
←
X+1
End
As
long
as
If
w
e
run
this
algorithm,
then
at
the
end
of
execution
the
v
ariable
X
will
ha
v
e
the
v
alue
28
.
In
terpret
this
result
in
the
con
text
of
this
problem.
3.
R
ep
etitive
structur
e
:
studying
the
thr
eshold
of
a
se
quenc
e
E.6146
Consider
the
sequence
a
n
de-
fined
b
y
:
a
0
=
2500
;
a
n
+1
=
0.8
·
a
n
+
400
1
Assume
that
the
general
term
of
the
sequence
a
n
can
b
e
expressed
as
:
a
n
=
500
×
0.8
n
+
2000
Deduce
the
limit
of
the
sequence
a
n
.
2
W
e
prop
ose
the
follo
wing
algorithm
:
N
←
0
A
←
2500
As
long
as
A
−
2000
>
50
A
←
A
×
0.8+400
h
ttps:/
/c
hingmath.fr
chapExoCorrec/6145
sacados/6145
Fonction
terme(n)
Pour
i
de
1
à
n
U
×
U
120
Fin
Pour
Renvoyer
U
Fonction
terme(n)
Pour
i
de
1
à
n
U
115
U
×
U
120
Fin
Pour
Renvoyer
U
Fonction
terme(n)
U
115
Pour
i
de
1
à
n
U
×
U
120
Fin
Pour
Renvoyer
U
Algorithme
1
Algorithme
2
Algorithme
3
chapExoCorrec/6147
sacados/6147
Fonction
terme1(A)
n
0
U
50
000
Tant
que
U
A
n
U
·
U
3
000
Fin
Tant
que
Renvoyer
n
Fonction
terme2(n)
U
50
000
Pour
i
allant
de
1
à
n
U
·
U
3
000
Fin
Tant
que
Renvoyer
U
Fonction
terme3(n)
U
50
000
Pour
i
allant
de
0
à
n
U
·
U
3
000
Fin
Tant
que
Renvoyer
U
chapExoCorrec/6148
sacados/6148
Fonction
suite(n)
U
5
Pour
i
de
0
à
n
U
1
2
×
Fin
Pour
Renvoyer
U
Fonction
suite(n)
Pour
i
de
0
à
n
U
5
U
1
2
×
Fin
Pour
Renvoyer
U
Fonction
suite(n)
U
5
Pour
i
de
0
à
n
U
1
2
×
Renvoyer
U
Fin
Pour
Algorithme
1
Algorithme
2
Algorithme
3
chapExoCorrec/6150
sacados/6150
Extrait d'Asie Juin 2015
chapExoCorrec/6146
sacados/6146
Extrait du bac du Liban Juin 2014
Valeur de
u
Valeur de
n
u>
4500
(vrai/faux)
5700
0
vrai
vrai
faux
N
←
N+1
End
As
long
as
a
Explain
what
the
v
alue
of
v
ariable
N
represen
ts
at
the
end
of
this
algorithm.
b
Using
the
calculator,
determine
the
v
alue
of
v
ariable
N
at
the
end
of
this
algorithm
and
in
terpret
the
result.
E.7007
Consider
the
sequence
u
n
is
defined
b
y
u
0
=
5700
and
for
an
y
natural
n
um
b
er
n
b
y
:
u
n
+1
=
1.015
·
u
n
−
300
Consider
the
follo
wing
algorithm
:
u
←
5
700
n
←
0
As
long
as
u
>
4500
u
←
1;
015
×
u
−
300
n
←
n+1
End
As
long
as
1
Cop
y
and
complete
the
table
b
elo
w,
adding
as
man
y
columns
as
necessary
b
et
w
een
the
second
and
last
columns.
2
A
t
the
end
of
the
algorithm’s
execution,
what
is
the
v
alue
of
the
v
ariable
n
?
In
terpret
this
v
alue
in
the
con
text
of
the
exercise.
E.7017
Consider
the
follo
wing
algorithm
:
U
←
4
N
←
0
As
long
as
U
<
40
U
←
0;
92
×
U+8
N
←
N+1
End
As
long
as
1
Cop
y
the
follo
wing
table
and
complete
it,
adding
as
man
y
columns
as
necessary
.
The
v
alues
of
U
will
b
e
rounded
to
the
ten
th.
V
alue
of
U
4
.
.
.
.
.
.
V
alue
of
N
0
.
.
.
.
.
.
Condition
U
<
40
vraie
.
.
.
.
.
.
2
Giv
e
the
v
alue
of
the
v
ariable
N
at
the
end
of
the
execu-
tion
of
this
algorithm.
E.7855
Ma
y
a
has
20
e
in
her
piggy
bank
on
June
1
er
2018
.
F
rom
that
date
on
w
ards,
eac
h
mon
th
she
sp
ends
a
quarter
of
the
con
ten
ts
of
her
piggy
bank
and
then
puts
20
e
more
in
to
it.
F
or
an
y
natural
n
um
b
er
n
,
let
u
n
b
e
the
amoun
t
of
money
in
Ma
y
a’s
piggy
bank
at
the
end
of
the
n
th
mon
th.
W
e
ha
v
e
:
u
0
=
20
.
W
e
assume
that
for
an
y
natural
n
um
b
er
n
:
u
n
+1
=
0.75
·
u
n
+20
W
e
consider
the
follo
wing
algorithm
:
U
←
20
N
←
0
As
long
as
U
<
70
U
←
0.75
×
U+20
N
←
N+1
End
While
Display
N
1
Cop
y
and
complete
the
table
b
elo
w,
whic
h
outlines
the
differen
t
steps
in
v
olv
ed
in
executing
the
algorithm.
A
dd
as
man
y
columns
as
necessary
in
place
of
the
dotted
one.
Round
the
results
to
t
w
o
decimal
places.
.
.
.
.
.
.
.
.
.
V
alue
of
U
20
.
.
.
.
.
.
.
.
.
V
alue
of
N
0
.
.
.
.
.
.
.
.
.
Condition
U
<
70
true
true
false
.
.
.
.
.
.
.
.
.
2
What
v
alue
is
displa
y
ed
at
the
end
of
the
execution
of
this
algorithm?
In
terpret
this
v
alue
in
the
con
text
of
the
exercise.
4.
R
ep
etitive
structur
e
:
finding
the
stopping
c
ondition
E.6149
W
e
consider
the
sequence
u
n
defined
b
y
:
u
0
=
20
;
u
n
+1
=
0.92
·
u
n
+
3
1
On
admits
that
the
general
term
of
the
sequence
u
n
admits
for
expression
:
u
n
=
−
17.5
×
0.92
n
+
37.5
Deduce
the
limit
of
the
sequence
u
n
.
2
a
Recop
y
and
complete
the
follo
wing
algorithm
so
that
at
the
end
of
its
execution
the
v
ariable
N
represen
ts
the
rank
from
whic
h
the
terms
of
the
sequence
will
ha
v
e
a
v
alue
greater
than
or
equal
to
25
.
U
←
20
N
←
0
As
long
as
...
U
←
0.92
×
U
+
3
N
←
N
+
1
End
As
long
as
que
b
Using
the
calculator,
determine
the
rank
from
whic
h
the
terms
of
the
sequence
u
n
will
for
the
first
time
b
e
greater
than
or
equal
to
25
.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/7007
sacados/7007
Valeur de
u
Valeur de
n
u>
4500
(vrai/faux)
5700
0
vrai
vrai
faux
chapExoCorrec/7017
sacados/7017
chapExoCorrec/7855
sacados/7855
Extrait Liban Mai 2018
chapExoCorrec/6149
sacados/6149
E.6151
1
Determine
b
y
calculation
the
smallest
v
alue
of
the
natu-
ral
n
um
b
er
n
suc
h
that
:
250
+
1250
×
0.8
n
<
500
2
W
e
consider
the
sequence
u
n
defined
b
y
:
u
0
=
1500
;
u
n
+1
=
0.8
·
u
n
+
50
for
all
n
∈
N
Complete
the
algorithm
b
elo
w
so
that
at
the
end
of
its
execution,
the
v
ariable
u
has
the
v
alue
obtained
in
the
previous
question
:
u
←
1500
n
←
0
While
......
do
u
←
......
n
←
......
End
While
E.7856
Consider
the
sequence
u
n
de-
fined
b
y
u
0
=
65
and
for
an
y
natural
n
um
b
er
n
:
u
n
+1
=
0.8
·
u
n
+18
W
e
admit
that
:
u
n
=
90
−
25
×
0.8
n
Consider
the
algorithm
b
elo
w
:
line
1
u
←
65
line
2
n
←
0
que
......
line
4
n
←
n+1
line
5
u
←
0;
8
×
u+18
line
6
Fin
As
long
as
1
Cop
y
and
complete
the
line
3
of
this
algorithm
so
that
it
determines
the
smallest
natural
n
um
b
er
n
suc
h
that
:
u
n
85
.
2
What
is
the
v
alue
of
the
v
ariable
n
at
the
end
of
the
algorithm’s
execution?
3
Calculate
the
result
of
the
previous
question
b
y
solving
the
inequation
u
n
85
E.7854
A
compan
y
offers
ann
ual
photo-
copier
main
tenance
con
tracts.
The
director
of
this
compan
y
notes
that,
eac
h
y
ear,
14
%
additional
con
tracts
are
signed
and
7
are
terminated.
In
2017
,
the
compan
y
had
120
con
tracts.
W
e
mo
del
the
situation
with
a
sequence
u
n
where
u
n
is
the
n
um
b
er
of
con
tracts
signed
in
y
ear
2017+
n
.
Th
us,
w
e
ha
v
e
:
u
0
=
120
1
Justify
that,
for
an
y
natural
n
um
b
er
n
,
w
e
ha
v
e
:
u
n
+1
=
1.14
·
u
n
−
7
2
Giv
en
its
curren
t
structural
capacit
y
,
the
compan
y
can
only
tak
e
on
190
con
tracts.
Bey
ond
that,
the
compan
y
will
ha
v
e
to
hire
more
staff.
W
e
therefore
w
an
t
to
kno
w
in
whic
h
y
ear
the
compan
y
will
need
to
hire.
T
o
do
this,
w
e
use
the
follo
wing
algorithm
:
n
←
0
u
←
120
As
long
as
......
n
←
n+1
.........
End
As
long
as
Display
2017+n
a
Cop
y
and
complete
the
algorithm
ab
o
v
e.
b
What
is
the
y
ear
displa
y
ed
at
the
end
of
the
algorithm?
In
terpret
this
v
alue
in
the
con
text
of
the
exercise.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/6151
sacados/6151
chapExoCorrec/7856
sacados/7856
chapExoCorrec/7854
sacados/7854
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