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/ Proportionality
62 exercises (100% corrected)
a
Equality of fractions (equations)
(4 exercices)
Duration and speed
(14 exercices)
Reminders: proportionality and percentage
(5 exercices)
Evolutions : introduction
(4 exercices)
Evolution and proportionality coefficient
(6 exercices)
Evolution: search for future value
(5 exercices)
Evolution: search for the initial value
(7 exercices)
Developments: rate search
(5 exercices)
Evolution: initial value, future value and evolution rate
(2 exercices)
Successive evolutions
(3 exercices)
Evolution and affine functions
(1 exercice)
image PNG : /home/_math/_exercice/d0/893/metapost/05_1.png
ChingQuizz
:
1
exercise
a
v
ailable
for
Quizz
assessmen
t
:
1.
Equality
of
fr
actions
(e
quations)
E.1856
1
Cop
y
and
complete
the
follo
wing
equations
correctly
:
a
3
×
=
4
b
3
2
×
=
4
5
c
1
2
×
=
7
5
2
Using
the
cross
pro
duct,
find
the
differen
t
v
alues
of
x
making
the
follo
wing
equalities
true.
Giv
e
the
v
alues
in
simplified
forms
:
a
2
3
=
x
5
b
7
x
=
8
9
c
1
x
=
3
E.1845
T
est
eac
h
of
the
equalities
for
the
indicated
v
alue
:
a
5
7
=
3
x
p
our
x
=
21
5
b
x
3
=
5
2
p
our
x
=
15
2
c
3
2
=
x
5
p
our
x
=
15
2
d
−
2
x
=
3
4
p
our
x
=
−
8
3
E.1844
Using
the
cross
pro
duct,
determine
the
v
alue
of
ˇ
x
ı
v
erifying
the
equalit
y
:
a
3
5
=
2
x
b
x
6
=
7
8
c
7
4
=
2
x
d
−
2
x
=
4
10
e
3
7
=
x
4
f
5
4
=
1
x
E.1052
Using
the
cross
pro
duct,
solv
e
the
follo
wing
equations
:
a
−
2
3
=
5
x
b
x
−
3
=
7
2
c
−
2
3
=
−
3
x
2.
Dur
ation
and
sp
e
e
d
E.11514
Note
:
The
n
um
b
er
60
has
12
divisors,
whic
h
allo
ws
for
the
follo
wing
con
v
ersions
:
12
min
=
0
;
2
h
;
15
min
=
0
;
25
h
30
min
=
0
;
5
h
;
45
min
=
0
;
75
h
1
A
t
a
normal,
constan
t
pace,
a
w
alk
er
co
v
ers
1
k
m
in
15
min
.
Giv
e
its
sp
eed
in
k
m
=
h
.
2
A
car
tra
v
eling
at
a
constan
t
sp
eed
co
v
ers
56
k
m
in
30
min
utes.
Giv
e
its
sp
eed
in
k
m
=
h
.
3
An
airliner
flying
at
a
constan
t
sp
eed
co
v
ers
170
k
m
in
12
min
utes.
Giv
e
its
sp
eed
in
k
m
=
h
.
E.11515
A
man
is
w
alking
and
co
v
ers
the
13.65
km
of
the
cit
y’s
circumference
in
3
h
15
min.
Calculate
the
w
alking
sp
eed
of
this
man
in
miles
p
er
hour.
E.11516
Prop
osition
:
A
v
erage
sp
eed
connects
distance
and
dura-
tion
of
uniform
motion
through
three
equiv
alen
t
iden
tities
:
v
=
d
t
d
=
v
×
t
t
=
d
v
A
commercial
airliner
flew
from
P
aris
to
Mexico
Cit
y
in
11
h
50
min
.
W
e
assume
that
its
cruising
sp
eed
of
238
m
=
s
w
as
main
tained
throughout
the
journey
.
Determine
the
distance
tra
v
eled
b
y
this
aircraft
in
k
m
.
E.11517
The
marathon
is
a
sp
orting
ev
en
t
in
whic
h
participan
ts
m
ust
run
42
195
m
.
The
w
orld
record
w
as
set
in
2003
at
the
Berlin
Marathon
in
2
h
05
min
.
Giv
e
its
a
v
erage
sp
eed
expressed
in
k
m
=
h
rounded
to
the
near-
est
unit.
E.11518
In
3
h
33
min
,
a
driv
er
tra
v
eled
291
;
1
k
m
.
What
w
as
his
a
v
er-
age
sp
eed
in
k
m
=
h
?
E.11519
A
runner
co
v
ers
23
;
4
k
m
in
1
h
12
min
.
What
w
as
his
a
v
erage
sp
eed
in
k
m
=
h
?
E.11520
A
driv
er
tra
v
els
212
;
8
k
m
in
1
h
54
min
.
What
w
as
his
a
v
erage
sp
eed
in
k
m
=
h
?
E.11521
A
driv
er
tra
v
els
64
;
4
k
m
in
48
min
utes.
What
w
as
his
sp
eed
in
k
m
=
h
?
E.11522
During
a
comp
etition,
a
cyclist
starts
the
race
at
10
h
45
and
finishes
at
12
h
36
.
The
distance
tra
v
eled
is
51
;
8
k
m
.
What
w
as
the
a
v
erage
sp
eed
expressed
in
k
m
=
h
?
E.11523
A
cyclist
tra
v
els
11
;
4
k
m
in
45
min
.
What
w
as
his
a
v
erage
sp
eed
in
k
m
=
h
?
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1856
sacados/1856
chapExoCorrec/1845
sacados/1845
chapExoCorrec/1844
sacados/1844
chapExoCorrec/1052
sacados/1052
chapExoCorrec/11514
sacados/11514
chapExoCorrec/11515
sacados/11515
chapExoCorrec/11516
sacados/11516
chapExoCorrec/11517
sacados/11517
chapExoCorrec/11518
sacados/11518
chapExoCorrec/11519
sacados/11519
chapExoCorrec/11520
sacados/11520
chapExoCorrec/11521
sacados/11521
chapExoCorrec/11522
sacados/11522
chapExoCorrec/11523
sacados/11523
E.11524
A
driv
er
driv
es
at
a
constan
t
sp
eed
of
111
k
m
=
h
for
42
min
.
What
distance
did
they
tra
v
el?
E.11525
A
cyclist
rides
at
a
constan
t
sp
eed
of
19
;
5
k
m
=
h
on
a
route
of
35
;
1
k
m
.
Ho
w
long
did
the
trip
tak
e?
E.11526
A
driv
er
tra
v
els
a
distance
of
141
;
9
k
m
.
He
lea
v
es
at
9
h
47
and
arriv
es
at
11
h
26
.
Determine
the
a
v
erage
sp
eed
in
k
m
=
h
for
this
journey
.
E.11527
A
cyclist
sets
off
at
14
h
22
on
a
journey
of
75
;
4
k
m
and
rides
at
a
sp
eed
of
39
k
m
=
h
.
What
time
will
he
finish
his
journey?
3.
R
eminders
:
pr
op
ortionality
and
p
er
c
entage
E.874
Emilie
and
An
toine
eac
h
mak
e
a
c
ho
colate
cak
e.
An
toine
uses
100g
c
ho
colate,
20g
flour
and
30g
milk
p
o
w-
der.
Emilie
uses
220g
c
ho
colate,
45g
flour
and
58g
p
o
wdered
milk
Calculate
for
the
t
w
o
cak
es,
the
p
ercen
tage
of
c
ho
colate
they
con
tain
resp
ectiv
ely
.
Of
Emilie
and
An
toine,
who
has
the
cak
e
ric
her
in
c
ho
colate?
E.9236
A
ccording
to
the
2000
census,
Mex-
ico
w
ould
ha
v
e
102
million
p
eople,
of
whom
34
million
w
ould
b
e
under
the
age
of
14
.
What
p
ercen
tage
do
es
this
age
group
represen
t
of
the
total
p
opulation?
(value
defaulte
d
to
the
unit)
E.898
1
What
sums
are
3.85
%
of
150
000
e
,
378
000
e
,
500
000
e
,
then
1
000
000
e
?
2
What
p
ercen
tage,
rounded
to
the
nearest
h
undredth,
of
500
000
e
représen
te
14
553
e
?
3
What
p
ercen
tage,
rounded
to
the
nearest
h
undredth,
of
1
000
000
e
représen
te
14
553
e
?
E.887
A
miniature
glob
e
has
a
circumference
of
40
cm
,
while
the
circumference
of
the
earth
is
40
000
k
m
1
Complete
the
follo
wing
table
:
Circonférence
Ec
helle
A
ctual
size
(m)
Reduced
size
(m)
2
Complete
the
dotted
lines
with
the
correct
v
alue
:
ˇ
The
scale
of
this
th
um
bnail
is
1
:
:
:
:
:
:
ı
Definition
:
scale
of
a
reduction
is
the
co
efficien
t
of
pro-
p
ortionalit
y
to
go
from
ˇactual
sizeı
to
ˇtaille
réduiteı.
E.893
The
car
b
elo
w
is
a
reduction
of
the
F
errari
F40.
In
realit
y
,
its
length
is
4.44
meters.
1
a
Giv
e
the
scale
of
this
represen
tation
b
Kno
wing
that
the
car
(the
r
e
al
one)
is
1.98
meters
wide,
giv
e
the
width
of
this
reduction
to
the
nearest
millime-
ter.
2
Another
reduction
of
this
car
is
offered
to
scale
1
37
.
Giv
e
the
length
of
this
new
reduction.
4.
Evolutions
:
intr
o
duction
E.9228
In
one
y
ear,
the
price
of
an
ob
ject
increased
from
130
e
to
149.5
e
.
W
e
wish
to
determine
the
p
ercen
tage
increase
exp
erienced
b
y
the
price
of
this
ob
ject
in
1
y
ear.
1
By
what
amoun
t
did
the
price
of
this
item
increase?
2
Complete
the
table
b
elo
w
:
Référence
Augmen
tation
Prix
P
ourcen
tage
100
%
3
Complete
the
op
erations
b
elo
w
to
obtain
the
p
ercen
tage
increase
exp
erienced
b
y
the
price
of
this
ob
ject
:
F
rom
the
cross
pro
duct
:
x
×
:
:
:
=
:
:
:
×
:
:
:
W
e
deriv
e
:
x
=
:
:
:
×
:
:
:
:
:
:
=
:
:
:
%
h
ttps:/
/c
hingmath.fr
chapExoCorrec/11524
sacados/11524
chapExoCorrec/11525
sacados/11525
chapExoCorrec/11526
sacados/11526
chapExoCorrec/11527
sacados/11527
chapExoCorrec/874
sacados/874
chapExoCorrec/9236
sacados/9236
chapExoCorrec/898
sacados/898
chapExoCorrec/887
sacados/887
chapExoCorrec/893
sacados/893
chapExoCorrec/9228
sacados/9228
Valeur initiale
Augmentation
Valeur ∏nale
300
50
25
12
150
20
%
%
Valeur initiale
Réduction
Valeur ∏nale
200
50
120
440
55
12
%
−
12
%
E.894
In
one
y
ear,
the
n
um
b
er
of
studen
ts
at
a
sc
ho
ol
has
decreased
from
1025
studen
ts
to
943
studen
ts.
W
e
wish
to
determine
the
p
ercen
tage
reduction
in
enrollmen
t
for
this
facilit
y
:
1
By
ho
w
man
y
studen
ts
has
the
sc
ho
ol’s
enrollmen
t
de-
creased?
2
Complete
the
table
b
elo
w
:
Référence
Réduction
Effectif
P
ourcen
tage
100
%
3
Complete
the
op
erations
b
elo
w
to
obtain
the
p
ercen
tage
reduction
exp
erienced
b
y
the
facilit
y’s
w
orkforce
:
F
rom
the
cross
pro
duct
:
x
×
:
:
:
=
:
:
:
×
:
:
:
W
e
deriv
e
:
x
=
:
:
:
×
:
:
:
:
:
:
=
:
:
:
%
E.7919
1
In
order
to
p
erform
an
augmen
tation
of
20
%
on
a
set
of
v
alues,
w
e
use
the
table
b
elo
w
to
complete
:
2
Justify
that
the
ro
ws
ˇ
Initial
v
alue
ı
and
ˇ
Final
V
alue
ı
represen
t
a
prop
ortionalit
y
situation
for
whic
h
the
pro-
p
ortionalit
y
co
efficien
t
will
b
e
sp
ecified.
E.7918
1
In
order
to
p
erform
a
reduction
of
12
%
on
a
set
of
v
alues,
w
e
use
the
table
b
elo
w
to
complete
:
2
Justify
that
the
ro
ws
ˇ
Initial
v
alue
ı
and
ˇ
Final
V
alue
ı
represen
t
a
prop
ortionalit
y
situation
for
whic
h
the
pro-
p
ortionalit
y
co
efficien
t
will
b
e
sp
ecified.
5.
Evolution
and
pr
op
ortionality
c
o
efficient
E.872
Prop
osal
:
When
a
quan
tit
y
increases
b
y
a
%
,
the
m
ultiplier
co
ef-
ficien
t
that
reflects
this
c
hange
has
a
v
alue
of
1+
a
100
.
When
a
quan
tit
y
decreases
b
y
a
%
,
the
m
ultiplier
co
ef-
ficien
t
that
reflects
this
c
hange
has
a
v
alue
of
1
−
a
100
.
Matc
h
eac
h
of
the
follo
wing
c
hanges
with
the
appropriate
m
ul-
tiplier
co
efficien
t
:
a
10
%
b
12
%
c
2
%
d
112
%
e
10
%
f
25
%
E.9232
Prop
osal
:
Consider
a
c
hange
with
a
m
ultiplier
co
efficien
t
of
k
:
If
k
>
1
,
then
this
c
hange
is
an
increase
with
a
p
ercen
t-
age
increase
of
a
,
whic
h
has
a
v
alue
of
:
a
=
k
−
1
×
100
If
k
<
1
,
then
this
c
hange
is
a
decrease,
the
p
ercen
tage
a
of
whic
h
is
:
a
=
1
−
k
×
100
Asso
ciate
eac
h
of
the
follo
wing
m
ultiplier
co
efficien
ts
with
the
nature
of
the
corresp
onding
c
hange
and
its
asso
ciated
p
ercen
t-
age
:
a
1
;
05
b
0
;
8
c
1
;
2
d
0
;
95
e
1
;
4
f
0
;
6
E.10918
1
Asso
ciate
the
appropriate
m
ultiplying
factor
with
eac
h
of
the
follo
wing
c
hanges
:
a
20
%
b
3
%
c
7.5
%
2
Asso
ciate
with
eac
h
of
the
follo
wing
m
ultiplier
co
effi-
cien
ts,
the
nature
of
the
corresp
onding
ev
olution
and
its
asso
ciated
p
ercen
tage
:
a
1.3
b
0.9
c
1.88
h
ttps:/
/c
hingmath.fr
chapExoCorrec/894
sacados/894
chapExoCorrec/7919
sacados/7919
Valeur initiale
Augmentation
Valeur ∏nale
300
50
25
12
150
20
%
%
chapExoCorrec/7918
sacados/7918
Valeur initiale
Réduction
Valeur ∏nale
200
50
120
440
55
12
%
−
12
%
chapExoCorrec/872
sacados/872
chapExoCorrec/9232
sacados/9232
chapExoCorrec/10918
sacados/10918
E.10946
1
Asso
ciate
the
appropriate
m
ultiplying
factor
with
eac
h
of
the
follo
wing
c
hanges
:
a
13
%
b
18
%
c
1.2
%
2
Asso
ciate
with
eac
h
of
the
follo
wing
m
ultiplier
co
effi-
cien
ts,
the
nature
of
the
corresp
onding
ev
olution
and
its
asso
ciated
p
ercen
tage
:
a
1.1
b
0.73
c
1.31
E.1126
1
T
o
mak
e
an
increase
of
12
%
,
m
ultiply
b
y
.
.
.
.
.
.
.
.
.
the
old
price.
2
T
o
mak
e
an
increase
of
.
.
.
.
.
.
.
.
.
%,
m
ultiply
b
y
1.45
the
old
price.
3
T
o
mak
e
a
decrease
of
12
%
,
m
ultiply
b
y
.
.
.
.
.
.
.
.
.
the
old
price.
4
T
o
mak
e
a
decrease
of
.
.
.
.
.
.
.
.
.
%,
m
ultiply
b
y
0.23
the
old
price.
E.5573
1
What
is
the
m
ultiplier
asso
ciated
with
an
increase
of
5
%
?
2
What
is
the
m
ultiplier
asso
ciated
with
a
reduction
of
5
%
?
6.
Evolution
:
se
ar
ch
for
futur
e
value
E.9233
A
merc
han
t
increases
in
Jan
uary
2002
the
prices
of
all
its
items
from
12%
.
1
Giv
e
the
m
ultiplier
co
efficien
t
asso
ciated
with
this
c
hange.
2
A
D
VD
pla
y
er
costs,
b
efore
increase,
372
euros.
Ho
w
m
uc
h
will
it
cost
afterw
ards?
E.9234
A
merc
han
t
increases
the
prices
of
all
his
items
b
y
8
%
.
1
Giv
e
the
m
ultiplier
co
efficien
t
asso
ciated
with
this
ev
o-
lutino.
2
A
D
VD
pla
y
er
costs,
b
efore
increase,
329
euros.
Ho
w
m
uc
h
will
it
coùt
after?
E.885
The
selling
price,
excluding
tax,
of
a
surfb
oard
is
23
000
F
.
One
m
ust
pa
y
a
T
V
A
(value
adde
d
tax)
of
18
%
.
Calculate
the
selling
price,
to
the
public,
of
this
surfb
oard.
E.899
1
Giv
e
the
m
ultiplier
co
efficien
t
asso
ciated
with
a
reduc-
tion
of
7.5
%
.
2
An
ob
ject
costs
132
e
and
undergo
es
a
reduction
of
7.5
%
.
What
is
its
new
price
after
the
discoun
t
is
applied?
E.892
A
store
sp
ecializing
in
the
sale
of
automobile
accessories
sells
a
mo
del
of
tire
at
120
e
unit.
During
a
promotion,
he
decides
to
offer
a
discoun
t
of
25
%
on
the
purc
hase
of
eac
h
tire.
Its
adv
ertising
p
oster
states
:
ˇLe
4
e
tire
is
gratuitı.
Is
this
correct?
Justify
.
7.
Evolution
:
se
ar
ch
for
the
initial
value
E.884
In
Jan
uary
2002
,
a
retailer
increases
the
prices
of
all
its
items
at
12%
.
1
Giv
e
the
m
ultiplier
co
efficien
t
asso
ciated
with
this
ev
olu-
tion.
2
A
television
set
costs,
after
increase,
476
euros.
Ho
w
m
uc
h
did
it
cost
b
efore?
E.891
A
retailer
increases
the
prices
of
all
its
pro
ducts
at
8
%
.
1
Giv
e
the
m
ultiplier
co
efficien
t
asso
ciated
with
this
ev
olu-
tion.
2
A
television
set
costs,
after
increase,
540
euros.
Ho
w
m
uc
h
did
it
cost
b
efore?
E.9238
An
ob
ject,
after
undergoing
a
reduc-
tion
of
12
%
,
costs
48.4
e
.
What
w
as
the
price
of
this
ob
ject
b
efore
the
reduction?
E.900
A
shopk
eep
er
increases
the
prices
of
all
his
items
b
y
8%
.
1
A
D
VD
pla
y
er
costs,
b
efore
increase,
329
euros.
Ho
w
m
uc
h
will
it
cost
afterw
ards?
2
A
television
costs,
after
increase,
540
euros.
Ho
w
m
uc
h
did
it
cost
b
efore?
E.1424
An
appliance
store
is
offering
a
dis-
coun
t
of
12
%
on
all
its
items.
1
A
television
set
cost
245
e
.
What
will
its
new
price
b
e?
2
The
price
of
a
dry
er
after
this
discoun
t
is
435.6
e
.
Deter-
mine
the
initial
price
of
this
dry
er
E.1457
In
one
store,
the
o
wner
raises
all
his
prices
b
y
12
%
.
1
A
video
recorder
cost
215
e
b
efore
increase.
Giv
e
the
price
of
this
ob
ject
after
undergoing
the
increase.
2
And
a
D
VD
pla
y
er
has
undergone
an
increase
of
36
e
.
De-
termine
the
price
of
this
D
VD
pla
y
er
b
efore
the
increase
and
its
price
after
the
increase.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/10946
sacados/10946
chapExoCorrec/1126
sacados/1126
chapExoCorrec/5573
sacados/5573
chapExoCorrec/9233
sacados/9233
chapExoCorrec/9234
sacados/9234
Groupe Ouest - Juin 2003
chapExoCorrec/885
sacados/885
chapExoCorrec/899
sacados/899
chapExoCorrec/892
sacados/892
chapExoCorrec/884
sacados/884
chapExoCorrec/891
sacados/891
Groupe Ouest - Juin 2003
chapExoCorrec/9238
sacados/9238
chapExoCorrec/900
sacados/900
Groupe Ouest - Juin 2003 - 2 points
chapExoCorrec/1424
sacados/1424
chapExoCorrec/1457
sacados/1457
E.1421
1
a
Aline
go
es
shopping
in
a
store
running
promotions.
She
buys
an
item
originally
w
orth
36
e
and
discoun
ted
b
y
25
%
.
Calculate
its
new
price.
b
Another
item
cost
20.4
e
after
a
discoun
t
of
15
%
.
De-
termine
the
initial
price
of
this
ob
ject.
2
Giv
e
the
purc
hase
price
of
these
t
w
o
items
b
efore
their
reduction,
then
after
their
reduction.
Deduct
the
total
p
ercen
tage
discoun
t
on
his
t
w
o
pur-
c
hases.
8.
Developments
:
r
ate
se
ar
ch
E.2116
Answ
er
the
follo
wing
questions.
No
justification
is
required
:
1
The
price
of
an
ob
ject
has
b
een
m
ultiplied
b
y
1.56
.
What
is
the
asso
ciated
p
ercen
tage
increase?
2
The
n
um
b
er
of
pupils
in
a
sc
ho
ol
has
fallen.
This
n
um-
b
er
has
b
een
m
ultiplied
b
y
0.86
.
What
is
the
asso
ciated
p
ercen
tage
reduction?
E.886
In
a
store,
a
video
recorder
costs
34
000
F
and
is
sold
at
a
price
of
25
500
F
.
What
is
the
p
ercen
tage
reduction
from
the
original
price?
E.9230
During
the
sale
p
erio
d,
the
listed
price
of
a
dress
is
4
500
F
.
After
discoun
t,
the
sale
price
of
this
dress
is
3
825
F
.
What
is
the
p
ercen
tage
of
this
discoun
t?
E.9235
Answ
er
the
follo
wing
questions.
No
justification
is
required
:
1
An
ob
ject
increased
from
112
e
à
156.8
e
.
What
w
as
the
p
ercen
tage
increase?
2
A
sale
item
costing
4
000
F
C
F
A
sho
ws
a
discoun
t
of
1
500
F
C
A
.
What
is
the
p
ercen
tage
discoun
t
giv
en?
E.9237
Arriv
ed
the
mon
th
of
July
,
the
sales
b
egin
in
F
rance.
A
store
displa
ys
−
15
%
on
all
items
in
its
store.
A
sw
eater
w
en
t
from
:
40
e
à
34.4
e
.
Explain
wh
y
the
o
wner
has
b
een
falsely
adv
ertising.
9.
Evolution
:
initial
value,
futur
e
value
and
evolution
r
ate
E.1127
In
its
1995
census,
Mexico
had
91.15
million
inhabitan
ts.
Whereas
in
2000
,
there
w
ere
97.48
mil-
lion
inhabitan
ts.
1
What
is
the
p
ercen
tage
increase
in
p
opulation
b
et
w
een
these
t
w
o
dates?
Round
to
the
nearest
ten
th.
2
Whereas
b
et
w
een
1980
and
2000
,
the
p
opulation
grew
b
y
43.1%
.
Giv
e
the
p
opulation
of
Mexico
in
1980
?
Round
the
result
to
the
nearest
ten
thousand
inhabitan
ts.
E.3377
Heimriri
and
her
brother
T
eh
ui
w
an
t
to
sp
oil
their
mom
for
Mother’s
Da
y
.
They
ha
v
e
18
000
F
and
tak
e
adv
an
tage
of
the
sales.
1
In
the
windo
w
of
a
jew
elry
store,
they
see
b
eautiful
12
000
F
earrings.
Calculate
the
price
of
the
earrings
after
a
discoun
t
of
25
%
?
2
In
the
same
jew
elry
store,
they
see
a
b
eautiful
ring.
After
a
discoun
t
of
20
%
,
the
price
of
the
ring
is
7
840
F
.
What
w
as
its
original
price?
3
As
Heimriri
prepares
to
lea
v
e
the
jew
elry
store,
she
is
c
harmed
b
y
a
mother-of-p
earl
p
endan
t.
Here’s
what
the
tag
sa
ys
:
P
endan
t
2
800
F
2
100
F
Determine
the
p
ercen
tage
discoun
t
tak
en
on
the
price
of
this
p
endan
t.
10.
Suc
c
essive
evolutions
E.9229
A
to
y
costs
100
e
.
It
is
first
reduced
b
y
10
%
,
then
b
y
a
second
reduction
of
10
%
:
1
What
is
the
selling
price
of
this
to
y
after
these
t
w
o
dis-
coun
ts?
2
What
is
the
total
ˇ
p
ercen
tage
ı
of
the
discoun
t
allo
cated
to
this
to
y?
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1421
sacados/1421
chapExoCorrec/2116
sacados/2116
chapExoCorrec/886
sacados/886
chapExoCorrec/9230
sacados/9230
chapExoCorrec/9235
sacados/9235
chapExoCorrec/9237
sacados/9237
chapExoCorrec/1127
sacados/1127
chapExoCorrec/3377
sacados/3377
chapExoCorrec/9229
sacados/9229
Réduction de
10%
Réduction de
32%
Augmentation de
5%
Augmentation de
1%
p
x
↦−
1
;
05
×
x
p
x
↦−
0
;
68
×
x
p
x
↦−
0
;
9
×
x
p
x
↦−
1
;
01
×
x
E.7971
The
manager
of
the
largest
m
ulti-sp
ort
club
in
the
region
noted
that
b
et
w
een
2010
Jan-
uary
1
er
and
2012
Decem
b
er
31
,
the
total
n
um
b
er
of
mem
b
ers
increased
b
y
10
%
,
and
then
increased
again
b
y
5
%
b
et
w
een
2013
Jan
uary
1
er
and
2015
Decem
b
er
31
.
The
total
n
um
b
er
of
mem
b
ers
in
2010
w
as
1
000
.
1
Calculate
and
justify
the
total
n
um
b
er
of
mem
b
ers
on
31
Decem
b
er
2012
.
2
Calculate
and
justify
the
total
n
um
b
er
of
mem
b
ers
on
Decem
b
er
31
2015
.
3
Martine
thinks
that
on
Decem
b
er
31
2015
,
there
should
b
e
1
150
mem
b
ers,
b
ecause
she
sa
ys
:
ˇ
an
increase
of
10
%
follo
w
ed
b
y
another
increase
of
5
%
,
whic
h
mak
es
a
total
increase
of
15
%
ı.
What
do
y
ou
think?
Explain
y
our
answ
er.
E.9231
Note
:
All
attempts,
ideas,
and
approac
hes,
ev
en
if
unsuc-
cessful
or
p
o
orly
form
ulated,
will
b
e
tak
en
in
to
accoun
t
for
ev
aluation
purp
oses.
An
item
undergo
es
a
successiv
e
increase
of
5
%
follo
w
ed
b
y
a
reduction
of
5
%
.
Will
the
price
of
the
item
c
hange?
Please
sp
ecify
y
our
answ
er.
11.
Evolution
and
affine
functions
E.7924
Eac
h
ev
olution
is
asso
ciated
with
a
linear
function.
F
or
eac
h
of
the
prop
osed
ev
olutions,
asso
ciate
the
corresp
onding
linear
function
:
12.
Shar
e
E.4921
1
A
dictionary
costs
25
e
.
An
increase
of
16
%
is
applied
to
the
price
of
this
item.
Giv
e
the
new
price
of
the
dictionary
.
2
A
television
has
its
price
increased
from
375
e
à
270
e
during
a
sale.
Giv
e
the
p
ercen
tage
discoun
t
applied
to
the
price
of
this
item.
Justify
y
our
answ
er.
E.10947
1
A
television
costs
191
e
.
A
reduction
of
11
%
is
applied
to
the
price
of
this
item.
Giv
e
the
new
price
of
the
television.
2
A
cell
phone
has
its
price
increased
from
424
e
à
477
e
.
Giv
e
the
p
ercen
tage
increase
applied
to
the
price
of
this
item.
Justify
y
our
answ
er.
13.
Unclassifie
d
exer
cises
E.1131
A
store
mak
es
a
discoun
t
of
15
%
on
its
en
tire
store
during
the
sale
p
erio
d.
1
Help
him
b
y
telling
him
ho
w
m
uc
h
to
m
ultiply
the
old
prices
b
y
to
mak
e
the
lab
el
c
hange.
2
A
television
set
costs,
b
efore
discoun
ting,
599
e
.
What
is
its
price
after
discoun
ting?
3
After
reduction,
a
D
VD
pla
y
er/writer
costs
248.2
e
.
What
w
as
its
price
b
efore
discoun
t?
h
ttps:/
/c
hingmath.fr
chapExoCorrec/7971
sacados/7971
chapExoCorrec/9231
sacados/9231
chapExoCorrec/7924
sacados/7924
Réduction de
10%
Réduction de
32%
Augmentation de
5%
Augmentation de
1%
p
x
↦−
1
;
05
×
x
p
x
↦−
0
;
68
×
x
p
x
↦−
0
;
9
×
x
p
x
↦−
1
;
01
×
x
chapExoCorrec/4921
sacados/4921
chapExoCorrec/10947
sacados/10947
chapExoCorrec/1131
sacados/1131
1
2
3
4
5
A
B
C
D
E
F
G
x
75
80
85
90
95
100
1
2
3
4
5
A
B
C
D
E
F
G
x
75
80
85
90
95
100
90
95
100
105
110
115
420
445
470
495
520
545
405
430
455
480
505
530
120
m
60
m
30
m
90
m
A
B
C
D
(départ)
E
F
G
H
I
J
K
L
E.6281
P
auline’s
uncle
regularly
partic-
ipates
in
a
(sailb
o
at
r
ac
e)
organized
ev
ery
y
ear
on
the
same
stretc
h
of
w
ater.
In
2012
,
he
completed
the
course
consisting
of
t
w
o
short
and
three
long
lo
ops
in
8
hours
and
40
min
utes.
When
she
participated
in
2013
,
it
to
ok
her
8
hours
and
25
min
utes
to
complete
the
course
consisting
of
three
short
and
t
w
o
long
lo
ops
that
y
ear.
He
remem
b
ers
that
he
did
not
complete
an
y
lo
op
in
less
than
75
min
utes.
He
also
kno
ws
that
it
to
ok
him
15
min
utes
longer
to
run
the
long
lo
op
than
it
did
to
run
the
short
lo
op.
Ho
w
ev
er,
he
w
an
ts
to
kno
w
ho
w
long
it
to
ok
him
to
sail
the
short
lo
op
and
the
long
lo
op
on
his
sailb
oat.
1
Con
v
ert
the
times
ac
hiev
ed
for
these
2012
and
2013
runs
to
min
utes.
2
P
auline
decided,
using
a
spreadsheet,
to
help
her
uncle
determine
the
times
for
the
short
lo
op
as
w
ell
as
for
the
long
lo
op.
A
cop
y
of
the
resulting
screen
is
giv
en
b
elo
w
:
She
noted
x
the
duration
in
min
utes
for
the
short
lo
op.
a
What
form
ula
for
obtaining
the
time
in
min
utes
needed
to
run
the
long
lo
op
will
she
en
ter
in
cell
B2
?
b
She
will
en
ter
in
cell
B3
the
form
ula
ˇ
=2*B1+3*B2
ı.
What
do
es
this
form
ula
calculate?
c
What
form
ula
will
she
en
ter
in
cell
B4
to
calculate
the
tra
v
el
time
when
she
attends
2013
?
She
then
copied
the
form
ulas
en
tered
in
B2
,
B3
,
and
B4
to
the
righ
t
and
got
the
follo
wing
screen
:
3
If
she
en
ters
the
n
um
b
er
105
in
cell
H1
,
what
v
alues
will
she
get
in
cells
H2
,
H3
,
and
H4
?
4
Using
the
cop
y
of
the
screen
obtained
with
the
spread-
sheet,
sp
ecify
the
times
needed
for
his
uncle
to
w
alk
the
short
lo
op
as
w
ell
as
to
w
alk
the
long
lo
op.
E.10836
A
professional
and
an
amateur
are
going
to
do
a
k
arting
session
on
the
trac
k
b
elo
w
(shown
in
solid
lines)
.
This
trac
k
is
made
up
of
segmen
ts,
half
circles
and
quarter
circles.
The
professional
mak
es
a
lap
in
60
seconds.
The
amateur
mak
es
a
lap
in
72
seconds.
1
Sho
w
that
the
length
of
the
run
w
a
y
is
1
045
m
,
rounded
to
the
nearest
unit.
An
y
trace
of
researc
h
will
b
e
v
alued.
2
Calculate
the
a
v
erage
sp
eed
of
the
professional
in
m
=
s
.
W
e’ll
round
to
the
nearest
h
undredth.
3
F
or
safet
y
reasons
on
this
circuit,
amateurs
m
ust
not
ex-
ceed
60
k
m
=
h
a
v
erage
sp
eed.
Do
es
this
amateur
resp
ect
the
safet
y
rules?
4
The
professional
and
the
amateur
start
at
the
same
time
from
the
starting
line
and
complete
sev
eral
laps
of
the
circuit.
Recall
that
the
professional
completes
one
lap
in
60
s
and
the
amateur
in
72
s
.
a
Decomp
ose
60
and
72
in
to
a
pro
duct
of
prime
factors.
b
After
ho
w
long
do
they
find
themselv
es
on
the
starting
line
together
for
the
first
time?
c
Ho
w
man
y
laps
will
they
eac
h
ha
v
e
completed
b
y
then?
E.1130
In
metrop
olitan
F
rance,
in
2001
the
p
op-
ulation
w
as
60.9
million
while
in
1950
there
w
ere
42
million
inhabitan
ts
.
What
w
as
the
p
ercen
tage
increase
in
p
opulation
b
et
w
een
these
t
w
o
dates?
(round
to
the
nearest
ten
th)
h
ttps:/
/c
hingmath.fr
chapExoCorrec/6281
sacados/6281
1
2
3
4
5
A
B
C
D
E
F
G
x
75
80
85
90
95
100
1
2
3
4
5
A
B
C
D
E
F
G
x
75
80
85
90
95
100
90
95
100
105
110
115
420
445
470
495
520
545
405
430
455
480
505
530
chapExoCorrec/10836
sacados/10836
ex 5 polynesie juin 2023
120
m
60
m
30
m
90
m
A
B
C
D
(départ)
E
F
G
H
I
J
K
L
chapExoCorrec/1130
sacados/1130
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