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1
Grade 8
/ Literal expressions: equalities, distributivity
79 exercises (100% corrected)
a
Calculation Using an Expression
(6 exercices)
Modeling by an expression
(3 exercices)
Simple discounts
(2 exercices)
Discounts
(12 exercices)
Factoring and calculation
(3 exercices)
Development and calculation
(4 exercices)
Distributivity: development
(8 exercices)
Distributivity: factoring
(10 exercices)
Modeling, development, reduction
(4 exercices)
Areas, development, reduction
(3 exercices)
Equality of expression
(9 exercices)
Modeling: equality of expressions
(1 exercice)
To the equations
(4 exercices)
image PNG : /home/_math/_exercice/d6/6359/metapost/a.png
A
B
C
D
3
2
x
Programme A
Choisir un nombre
Soustraire 2
Multiplier par
4
Elever au carré
Ajouter les deux nombres
Programme B
•
Choisir un nombre
•
Calculer son carré
•
Ajouter
6
au résultat
ChingQuizz
:
8
exercises
a
v
ailable
for
Quizz
assessmen
t
:
1.
Calculation
Using
an
Expr
ession
E.5655
Ev
aluate
the
follo
wing
literal
ex-
pressions
for
x
=
2
:
a
3
x
+
2
b
2
×
(3
x
−
1)
c
2
x
+
8
x
+
1
E.5656
Ev
aluate
the
follo
wing
literal
expres-
sions
for
x
=
−
1
:
a
4
x
+
1
b
3
×
(3
x
+
1)
c
9
−
3
x
9
+
x
E.8792
Ev
aluate
the
follo
wing
literal
expres-
sions
for
x
=
2
:
a
x
2
+
1
b
x
−
x
2
c
(
x
+
2)
2
E.8793
Ev
aluate
the
follo
wing
literal
expres-
sions
for
x
=
−
1
:
a
x
2
+
1
b
2
x
2
+
2
x
c
(
x
+
2)
2
E.4491
Using
men
tal
math,
complete
the
table
b
elo
w,
où
for
eac
h
ro
w
an
expression
is
ev
aluated
for
differen
t
v
alues
of
x
:
x
0
1
3
−
2
2
x
−
3
x
2
−
2
x
+3
2
x
2
−
4
2(
x
+4)
−
3
E.4520
Consider
the
expression
:
A
=
−
2
x
2
+4
x
+6
1
Ev
aluate
the
expression
A
for
the
v
alues
:
x
=
−
1
;
x
=
3
2
T
ell
whether
the
statemen
t
b
elo
w
is
true
or
false.
Justify
y
our
answ
er
:
ˇThe
expression
A
is
zero
for
an
y
v
alue
of
x
.ı
2.
Mo
deling
by
an
expr
ession
E.8795
Consider
the
rectangle
AB
C
D
sho
wn
b
elo
w
ha
ving
length
and
width
(
x
+2)
and
3
resp
ec-
tiv
ely
:
1
Determine
the
p
erimeter
and
area
of
the
rectangle
AB
C
D
when
x
=
1
?
x
=
4
?
2
a
Giv
e
an
expression,
in
terms
of
x
,
for
the
p
erimeter
of
the
rectangle
AB
C
D
.
b
Giv
e
an
expression,
as
a
function
of
x
,
for
the
area
of
the
rectangle
AB
C
D
.
E.8794
Here
are
t
w
o
calculation
programs
:
1
F
or
program
A
:
a
Giv
e
the
output
v
alue
of
program
A
when
the
input
v
alue
is
3
?
is
−
1
?
b
If
the
input
n
um
b
er
is
denoted
x
,
giv
e
an
expression
for
the
output
v
alue
of
program
A.
2
F
or
program
B
:
a
Giv
e
the
output
v
alue
of
program
B
when
the
input
v
alue
is
3
?
is
−
1
?
b
If
the
input
n
um
b
er
is
denoted
x
,
giv
e
an
expression
for
the
output
v
alue
of
program
B.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/5655
sacados/5655
chapExoCorrec/5656
sacados/5656
chapExoCorrec/8792
sacados/8792
chapExoCorrec/8793
sacados/8793
chapExoCorrec/4491
sacados/4491
chapExoCorrec/4520
sacados/4520
chapExoCorrec/8795
sacados/8795
A
B
C
D
3
2
x
chapExoCorrec/8794
sacados/8794
Programme A
Choisir un nombre
Soustraire 2
Multiplier par
4
Elever au carré
Ajouter les deux nombres
Programme B
•
Choisir un nombre
•
Calculer son carré
•
Ajouter
6
au résultat
H
A
B
C
D
E
F
I
G
7
cm
x
x
x
1
2
2
x
4
x
2
x
1
1
x
x
x
3
3
5
x
2
2
x
x
1
3
3.
Simple
disc
ounts
E.1908
Reduce,
if
p
ossible,
the
writing
of
the
follo
wing
expressions
:
a
3
×
x
×
2
b
5
+
x
c
4
x
+
x
+
x
d
3
x
+
2
+
x
e
5
×
x
+
x
f
4
x
+6+2+
x
−
3
x
E.8791
Consider
the
p
olygon
AB
C
D
E
F
sho
wn
shaded
b
elo
w
où
AB
GF
is
a
rectangle
and
C
D
E
G
is
a
square
:
1
Giv
e,
without
justification,
the
p
erimeter
of
p
olygon
AB
C
D
E
F
in
the
follo
wing
cases
:
a
D
C
=
1
b
D
C
=
4
2
Consider
the
expression
E
defined
b
y
:
E
=
14+4
x
a
Ev
aluate
the
expression
E
for
eac
h
of
the
v
alues
of
x
b
elo
w
:
x
=
1
;
x
=
4
b
Noting
x
the
length
of
segmen
t
[
D
C
]
,
justify
that
the
expression
E
still
yields
the
v
alue
of
the
p
erimeter
of
the
p
olygon
AB
C
E
F
.
4.
Disc
ounts
E.6305
Belo
w
are
sho
wn
6
rectangles
and
squares
o
where
the
letter
x
designates
the
same,
undeter-
mined
measuremen
t
of
some
of
the
sides
of
these
rectangles.
Justify
that
the
total
area
of
these
rectangles
can
b
e
expressed
using
the
follo
wing
literal
expression
:
3
x
2
+5
x
+5
E.6322
Belo
w
are
sho
wn
6
rectangles
and
squares
où
x
is
an
undetermined
length
but
expressing
the
side
length
of
some
of
these
triangles.
Giv
e
a
simplified
expression
represen
ting
the
total
area
of
these
six
rectangles.
E.8797
Definition
:
The
action
of
reducing
a
literal
expression
is
to
ˇ
coun
t
together
ı
similar
terms
in
order
to
a
v
oid
rep
etition.
(S.
Baruk)
Example
:
T
o
reduce
an
expression,
w
e
group
together
terms
of
the
same
t
yp
e
:
5
+
2
a
+
3
b
+
4
b
+
3
+
2
a
=
2
a
+
2
a
+
3
b
+
4
b
+
5
+
3
=
4
a
+
7
b
+
8
Often,
w
e
use
ˇ
simplify
ı
instead
of
reduce.
Reduce
the
follo
wing
expressions
:
a
−
2
x
+
5
−
4
x
+
3
b
−
5
x
+
4
x
+
3
E.1922
Consider
the
t
w
o
literal
expressions
b
elo
w
:
a
5
−
4
x
+
6
x
−
3
b
−
x
2
+
5
x
−
4
+
3
x
−
5
x
2
+
7
−
4
x
−
8
1
Cop
y
eac
h
of
these
expressions
and
then
:
underline
in
blac
k
the
terms
in
x
2
;
underline
in
red
the
terms
in
x
;
underline
in
blue
the
n
umeric
terms.
2
Reduce
these
t
w
o
expressions.
E.8799
Reduce
the
follo
wing
expressions
:
q
x
2
+
x
+
3
x
+
5
x
2
+
1
b
6
x
2
−
3+5
x
−
7
x
2
+4
−
2
x
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1908
sacados/1908
chapExoCorrec/8791
sacados/8791
H
A
B
C
D
E
F
I
G
7
cm
chapExoCorrec/6305
sacados/6305
x
x
x
1
2
2
x
4
x
2
x
1
1
chapExoCorrec/6322
sacados/6322
x
x
x
3
3
5
x
2
2
x
x
1
3
chapExoCorrec/8797
sacados/8797
chapExoCorrec/1922
sacados/1922
chapExoCorrec/8799
sacados/8799
A
B
C
D
3
2
x
E.6321
Reduce
the
follo
wing
expressions
:
a
3
x
+2
−
2
x
2
+5
x
+4
x
2
−
5
b
2
x
+
x
2
−
5
x
2
+3
x
−
2
E.8923
Simplify
the
follo
wing
expressions
:
a
5
x
×
2
x
−
3
x
×
2
−
x
×
2
x
+
5
×
2
x
b
3
×
2
−
x
×
3
+
2
x
×
x
−
5
x
2
E.8798
Reduce
the
follo
wing
expressions
:
a
2
x
×
3
x
−
2
×
4
x
+
5
×
2
−
3
×
3
x
2
−
3
2
b
5
×
2
x
−
3
×
4
+
3
x
×
2
−
2
x
×
3
x
E.1080
Reduce
the
follo
wing
expressions
:
a
−
2
x
×
3
x
+2
x
+3
x
2
−
4
x
b
2
×
(3
x
2
)
−
(4
x
)
×
x
+
x
2
E.1928
Reduce
the
follo
wing
expressions
:
a
3
x
+
5
x
×
(
−
2
x
)
+
x
×
2
b
2
+
3
×
4
−
x
−
x
c
−
3
×
2
+
(
x
×
5)
×
3
+
x
×
2
x
d
(
−
x
)
×
(
−
x
)
+
(
−
x
)
×
x
E.4519
Reduce
the
follo
wing
expressions
:
a
2
×
5
−
x
×
x
+
4
×
(
−
3)
+
3
×
(
−
2
x
)
b
x
×
(
−
3
x
)
+
7
×
3
−
2
x
×
(
−
2)
−
3
×
(
−
2
x
2
)
E.62
Expand
and
simplify
the
follo
wing
ex-
pressions
:
a
5
×
x
+
(
−
3)
×
2
x
+
x
×
2
x
b
2
x
×
(
−
2
x
)
+
(
−
x
2
)
×
(
−
2)
c
(
−
3)
×
x
+
(
−
2
x
)
×
(+2
x
)
+
x
2
×
3
5.
F
actoring
and
c
alculation
E.8954
Use
distributivit
y
to
calculate
the
follo
wing
expressions
:
a
13
×
7
+
13
×
3
b
12
×
5
+
8
×
5
a
3
×
7
+
3
×
3
E.5657
Using
a
men
tal
calculation,
giv
e
the
v
alue
of
the
follo
wing
calculations
:
a
12
×
17
+
12
×
3
b
15
×
19
−
5
×
19
c
23
×
81
−
3
×
81
E.8813
Use
distributivit
y
to
calculate
the
follo
wing
expressions
:
A
18.87
×
32.7
+
18.87
×
56.5
+
18.87
×
10.8
b
19.67
×
19.67
−
19.67
×
9.67
6.
Development
and
c
alculation
E.4492
Using
a
men
tal
calculation,
giv
e
the
v
alue
of
the
follo
wing
calculations
:
a
11
×
15
b
21
×
33
c
31
×
16
E.1253
P
erform
the
follo
wing
calculations,
lea
ving
the
steps
of
y
our
calculations
:
A
101
×
347
b
98
×
240
E.8955
Using
a
men
tal
calculation,
giv
e
the
v
alue
of
the
follo
wing
calculations
:
a
9
×
37
b
9
×
32
c
19
×
64
E.1226
Clev
er
calculation
:
A
101
×
347
b
98
×
240
7.
Distributivity
:
development
E.4512
Consider
the
rectangle
AB
C
D
sho
wn
b
elo
w
ha
ving
length
and
width
(
x
+2)
and
3
resp
ec-
tiv
ely
:
1
Determine
the
area
of
the
rectangle
AB
C
D
.
2
By
hatc
hing
the
represen
tation
of
AB
C
D
,
highligh
t
the
follo
wing
equalit
y
:
A
=
3
x
+
6
E.1910
Expand
and
reduce
the
follo
wing
expressions
:
a
3
×
(2
x
+
4)
b
x
×
(2
x
−
1)
c
(3
−
2
x
)
x
d
x
×
(3
+
x
)
h
ttps:/
/c
hingmath.fr
chapExoCorrec/6321
sacados/6321
chapExoCorrec/8923
sacados/8923
chapExoCorrec/8798
sacados/8798
chapExoCorrec/1080
sacados/1080
chapExoCorrec/1928
sacados/1928
chapExoCorrec/4519
sacados/4519
chapExoCorrec/62
sacados/62
chapExoCorrec/8954
sacados/8954
chapExoCorrec/5657
sacados/5657
chapExoCorrec/8813
sacados/8813
chapExoCorrec/4492
sacados/4492
chapExoCorrec/1253
sacados/1253
chapExoCorrec/8955
sacados/8955
chapExoCorrec/1226
sacados/1226
chapExoCorrec/4512
sacados/4512
A
B
C
D
3
2
x
chapExoCorrec/1910
sacados/1910
E.8810
Expand
and
reduce
the
follo
wing
expressions
:
a
3
×
(2
x
+
1)
b
x
+
(2
x
−
1)
×
2
E.1251
Consider
the
follo
wing
t
w
o
expres-
sions
:
The
pro
duct
of
3
b
y
the
sum
of
x
and
2
.
The
sum
of
the
pro
duct
of
3
b
y
x
and
6
.
Justify
that
these
t
w
o
expressions
are
equal.
E.1249
In
the
follo
wing
t
w
o
calculations,
use
distributivit
y
to
giv
e
the
follo
wing
expressions
in
their
dev
elop
ed
and
reduced
forms
:
a
7
×
(2
x
+
5)
+
4
b
3
×
(3
+
x
+
2
x
+
12
E.8925
Expand
and
reduce
the
follo
wing
expressions
:
a
x
+
2(2
x
−
1)
b
3
−
3
x
+
x
×
(3
x
+
1)
E.8812
Reduce
the
follo
wing
expressions
:
a
2(3
+
x
)
+
(2
+
x
)
×
4
b
2(3
+
x
)
+
5
+
2(
x
−
1)
E.8814
W
rite
the
literal
expressions
b
elo
w
in
their
expanded
and
reduced
forms
:
a
2
1
+
x
x
−
2
b
x
−
1
+
2
x
+
1
8.
Distributivity
:
factoring
E.8816
Using
distributivit
y
,
transform
the
writing
of
the
follo
wing
expressions
to
sho
w
their
factorized
forms
:
a
5
x
−
5
×
3
b
3
x
+
12
E.4548
F
actor
the
follo
wing
expressions
:
a
4
x
+
2
b
5
−
15
x
c
4
x
−
6
E.6344
F
actor
the
follo
wing
expressions
:
a
12
x
+
15
b
12
x
+
20
c
3
x
+
6
E.8815
Giv
e
the
factorized
form
of
the
fol-
lo
wing
expressions
:
a
2
×
x
+
2
×
4
b
25
x
+
15
E.1909
If
p
ossible,
factor
the
follo
wing
ex-
pressions
:
a
3
×
x
+
9
b
5
x
+
5
c
5
x
+
25
E.8811
F
actor
the
follo
wing
expressions
:
a
x
2
+
2
x
b
3
x
2
−
2
x
c
4
x
2
+
x
E.8821
F
actor
the
follo
wing
expressions
:
a
5
x
2
−
x
b
6
x
2
+
3
x
c
8
x
+
16
x
2
E.8927
F
actor
eac
h
of
the
follo
wing
expres-
sions
:
a
5
x
+
15
b
7
x
+
2
x
2
E.8822
F
actor,
if
p
ossible,
the
follo
wing
ex-
pressions
:
a
3
×
x
+
9
b
x
×
x
+
3
x
c
5
x
+
x
d
5
x
+
25
e
3
x
2
+
9
x
f
6
xy
+
12
x
E.4522
F
actor
the
follo
wing
expressions
:
a
3
×
x
+
6
b
4
x
2
−
3
x
c
15
x
2
+
5
d
5
x
2
+
4
x
e
6
x
2
+
9
x
f
12
x
2
−
4
x
9.
Mo
deling,
development,
r
e
duction
E.5659
The
follo
wing
calculation
program
is
considered
:
Cho
ose
a
n
um
b
er
;
Multiply
it
b
y
2
;
A
dd
3
;
Multiply
b
y
2
;
Subtract
6
1
Noting
x
as
the
starting
n
um
b
er,
giv
e
the
expression
con-
structed
b
y
this
calculation
program.
2
a
Without
justification,
complete
the
table
b
elo
w
:
Nom
bre
d’en
trée
1
0
4
−
2
Num
b
er
returned
b
Can
w
e
conjecture
a
new
expression
that
w
ould
repre-
sen
t
this
calculation
program?
c
Justify
y
our
previous
remark.
F
or
this
last
question,
an
y
trace
of
researc
h
will
b
e
considered.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/8810
sacados/8810
chapExoCorrec/1251
sacados/1251
chapExoCorrec/1249
sacados/1249
chapExoCorrec/8925
sacados/8925
chapExoCorrec/8812
sacados/8812
chapExoCorrec/8814
sacados/8814
chapExoCorrec/8816
sacados/8816
chapExoCorrec/4548
sacados/4548
chapExoCorrec/6344
sacados/6344
chapExoCorrec/8815
sacados/8815
chapExoCorrec/1909
sacados/1909
chapExoCorrec/8811
sacados/8811
chapExoCorrec/8821
sacados/8821
chapExoCorrec/8927
sacados/8927
chapExoCorrec/8822
sacados/8822
chapExoCorrec/4522
sacados/4522
chapExoCorrec/5659
sacados/5659
A
B
C
D
E
F
G
H
M
N
xcm
7
cm
x
2
2
x
3
x
A
B
C
D
N
M
P
E.1241
A
noteb
o
ok
costs
x
p
esos
and
a
binder
costs
5
p
esos
more
than
a
noteb
o
ok.
1
Giv
en
x
the
price
of
a
noteb
o
ok,
establish
a
literal
ex-
pression
as
a
function
of
x
represen
ting
the
follo
wing
pur-
c
hase
:
5
binders
and
4
noteb
o
oks
2
Reduce
the
expression
obtained
in
question
1
.
E.5700
All
calculations
and
an
y
record
of
researc
h,
no
matter
ho
w
incomplete,
will
b
e
con-
sidered
in
the
ev
aluation.
Marc
and
Sophie
are
c
hallenging
eac
h
other
with
math.
It’s
Marc’s
turn
;
he
prop
oses
a
calculation
program
to
his
class-
mate
:
Cho
ose
a
p
ositiv
e
in
teger
Square
this
n
um
b
er
A
dd
3
to
the
result
Then
m
ultiply
b
y
2
the
result
obtained
Subtract
6
from
the
previous
result
Finally
,
tak
e
half
of
the
last
result
W
rite
the
final
result
Sophie
announces
that
w
e
can
go
from
the
originally
c
hosen
n
um
b
er
to
the
final
n
um
b
er
in
one
step.
Is
she
righ
t?
E.6315
ˇ
I
tak
e
a
whole
n
um
b
er,
add
3
to
it,
and
m
ultiply
the
result
b
y
7
.
I
add
three
times
the
starting
n
um
b
er
to
the
result
and
remo
v
e
21
.
I
still
get
a
m
ultiple
of
10
.
ı
Is
this
true?
Justify
.
An
y
trace
of
researc
h,
ev
en
if
incomplete,
will
b
e
con-
sidered
in
the
assessmen
t.
10.
A
r
e
as,
development,
r
e
duction
E.1863
W
e
w
an
t
to
study
the
area
of
the
p
olygon
AB
C
D
E
F
GH
sho
wn
b
elo
w,
where
AB
M
N
is
a
rect-
angle
and
F
GH
N
and
C
D
E
M
are
squares
:
The
measuremen
t
F
E
=
7
cm
is
giv
en,
and
w
e
denote
the
mea-
suremen
t
of
segmen
t
[
C
D
]
b
y
x
.
1
Complete
the
table
b
elo
w
without
justification
:
V
alue
of
x
2
4
Area
A
of
p
olygon
AB
C
D
E
F
GH
2
a
Using
the
p
olygon
division
prop
osed
in
the
state-
men
t,
sho
w
that
the
area
A
can
b
e
expressed
as
:
A
=
7
+
2
x
×
x
+
2
x
2
b
Prop
ose
another
division
that
allo
ws
y
ou
to
justify
that
the
area
A
can
also
b
e
expressed
b
y
the
expression
:
A
=
4
x
2
+
7
x
Hin
t
:
y
ou
can
justify
this
last
question
either
b
y
reduction
or
b
y
a
differen
t
area
calculation
E.1252
Consider
the
shaded
AB
C
M
N
P
p
olygon
b
elo
w
:
où
the
quadrilaterals
AB
C
D
and
M
N
P
D
are
rectangles
and
x
is
the
length
of
the
segmen
t
[
AP
]
:
1
Giv
e
the
expression
for
the
p
erimeter
of
the
p
olygon
AB
C
M
N
P
in
terms
of
x
.
Giv
e
this
literal
expression
in
its
expanded
and
reduced
form.
2
Calculate
the
p
erimeter
of
the
figure
in
the
cases
où
x
=
5
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1241
sacados/1241
chapExoCorrec/5700
sacados/5700
chapExoCorrec/6315
sacados/6315
chapExoCorrec/1863
sacados/1863
A
B
C
D
E
F
G
H
M
N
xcm
7
cm
chapExoCorrec/1252
sacados/1252
x
2
2
x
3
x
A
B
C
D
N
M
P
3
cm
3
cm
5
cm
3
cm
3
cm
5
cm
x
cm
A
B
C
D
E
F
G
H
I
J
H
A
B
C
D
E
F
I
G
xcm
7
cm
E.1880
Consider
the
p
olygon
AB
E
F
GH
I
J
formed
from
the
rectangle
AB
C
D
from
whic
h
the
t
w
o
squares
D
H
I
J
and
C
E
F
G
of
side
x
cm
ha
v
e
b
een
remo
v
ed.
1
Repro
duce
this
figure
for
x
=
1.5
cm
.
2
a
Determine
as
a
function
of
x
the
p
erimeter
measure
of
this
p
olygon.
Giv
e
the
reduced
form
of
this
expres-
sion.
b
Deduce
the
measure
of
this
p
erimeter
for
x
=
1.5
cm
.
3
a
Giv
e
the
measure
of
the
area
of
the
p
olygon
AB
E
F
GH
I
J
for
x
=
1.5
cm
.
b
W
rite
a
literal
expression
represen
ting
the
area
of
this
p
olygon.
11.
Equality
of
expr
ession
E.1887
Consider
the
p
olygon
AB
C
D
E
F
sho
wn
shaded
b
elo
w
where
AB
GF
is
a
rectangle
and
C
D
E
G
is
a
square
:
1
Using
t
w
o
distinct
geometric
reasonings,
sho
w
that
the
area
A
admits
the
follo
wing
t
w
o
expressions
:
A
=
7
x
+
x
2
;
A
=
x
2
+
x
2
+
7
−
x
×
x
2
a
Complete
the
table
of
v
alues
b
elo
w
:
V
alue
of
x
1
3
P
olygon
area
AB
C
D
E
F
b
Chec
k
that
the
v
alues
obtained
are
v
alid
whatev
er
the
expression
used.
E.1240
1
Consider
the
follo
wing
t
w
o
expressions
:
A
=
5
x
+3
;
B
=
8
x
a
Complete
the
table
of
v
alues
b
elo
w
:
V
alue
of
x
1
−
2
V
alue
of
A
V
alue
of
B
b
Can
w
e
sa
y
that
the
expressions
A
and
B
are
equal?
2
Consider
the
follo
wing
t
w
o
expressions
:
C
=
8
x
+4
;
D
=
4
×
2
x
+1
a
Complete
the
table
of
v
alues
b
elo
w
:
V
alue
of
x
2
−
3
V
alue
of
C
V
alue
of
D
b
Can
w
e
sa
y
that
the
expressions
C
and
D
are
equal?
What
can
w
e
do
to
b
e
sure?
Note
:
T
o
sho
w
that
t
w
o
expressions
are
differen
t
,
w
e
lo
ok
for
a
v
alue
of
x
for
whic
h
these
t
w
o
expressions
ha
v
e
differen
t
results.
T
o
sho
w
that
t
w
o
expressions
are
equal
,
w
e
m
ust
sho
w
that
they
ha
v
e
the
same
expanded
and
simplified
forms.
E.1324
Indicate
whether
the
follo
wing
equa-
tions
are
true
or
false.
Explain
y
our
answ
er!
a
3
x
+
9
=
3
×
(
x
+
3)
b
3
×
(2
x
+
3)
=
6
x
+
5
E.8820
Sa
y
whether
the
follo
wing
equalities
are
true
or
false.
Justify!
a
5
x
+
3
=
8
x
c
8
x
+
4
=
4
×
(2
x
+
1)
E.1225
Explain
wh
y
these
equalities
in
v
olv-
ing
literal
expressions
are
false
:
a
3
×
(2
x
+
1)
+
3
=
5
x
+
6
b
2
x
+
2
×
(
x
+
2)
=
6
x
+
2
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1880
sacados/1880
3
cm
3
cm
5
cm
3
cm
3
cm
5
cm
x
cm
A
B
C
D
E
F
G
H
I
J
chapExoCorrec/1887
sacados/1887
H
A
B
C
D
E
F
I
G
xcm
7
cm
chapExoCorrec/1240
sacados/1240
chapExoCorrec/1324
sacados/1324
chapExoCorrec/8820
sacados/8820
chapExoCorrec/1225
sacados/1225
2
x
6
3
x
x
2
3
6
2
•
Choisir un nombre
•
Calculer son carré
•
Ajouter
6
au résultat
Choisir un nombre
Soustraire 2
Multiplier par
4
Elever au carré
Ajouter les deux nombres
E.1239
Whic
h
of
the
follo
wing
equalities
are
true
or
false?
Justify
:
a
false
equalit
y
b
y
a
coun
terexample
;
a
true
equalit
y
b
y
dev
elopmen
t
and
reduction
of
literal
expressions.
a
2
+
2
x
=
4
x
b
3
×
(
x
+
5)
=
3
×
x
+
15
c
2
×
(2
+
3)
=
2
x
+
6
d
5
a
+
35
=
5
×
(5
a
+
7)
e
3
×
(
x
+
2)
+
2
×
(5
x
−
1)
=
13
x
+
4
E.8817
Study
the
literal
expressions
b
elo
w.
Justify
:
a
3
×
(2
x
+
4)
=
6
x
+
12
b
5
x
+
13
=
5
×
(
x
+
2)
+
3
E.8818
T
ell
us
if
the
follo
wing
equations
are
true.
Justify
y
our
answ
er.
a
(2
x
+
1)
×
3
+
2
×
(3
x
+
2)
=
12
x
+
7
b
x
+
15
+
3
x
+
7
x
+
x
+
23
−
1
x
−
8
=
11
x
+
30
E.8819
T
ell
if
the
follo
wing
equalities
are
true
or
false.
Justify!
a
(2
x
+
1)
×
3
+
2
×
(3
x
+
2)
=
12
x
+
7
b
x
+
15
+
3
x
+
7
x
+
x
+
23
−
1
x
−
8
=
11
x
+
30
12.
Mo
deling
:
e
quality
of
expr
essions
E.6323
W
e
note
x
a
length
that
is
not
y
et
determined.
F
rom
this
length,
w
e
construct
the
t
w
o
figures
b
elo
w
:
Justify
that
these
t
w
o
figures
ha
v
e
the
same
area
regardless
of
the
v
alue
of
x
.
13.
T
o
the
e
quations
E.8695
W
e
consider
the
calculation
program
:
1
What
is
the
result
of
the
program
B
if
w
e
c
ho
ose
the
n
um
b
er
5
?
2
If
w
e
note
x
the
n
um
b
er
c
hosen
as
the
input
to
the
algo-
rithm,
justify
that
the
n
um
b
er
returned
b
y
is
expressed
as
x
2
+6
.
3
Determine
the
input
v
alue
so
that
this
calculation
pro-
gram
returns
as
an
output
v
alue
31
.
E.8796
Consider
the
calculation
program
sho
wn
in
the
diagram
b
elo
w
:
1
a
Noting
x
as
the
n
um
b
er
pro
vided
as
input
to
this
cal-
culation
program,
giv
e
an
expression
giving
the
n
um-
b
er
returned
b
y
this
calculation
program.
b
W
e
wish
to
ev
aluate
the
t
w
o
expressions
ˇ
x
2
+4
ı
and
ˇ
4
x
+
x
−
2
2
ı
for
certain
v
alues
of
x
:
x
−
2
0
3
4
x
+
x
−
2
2
x
−
2
0
3
x
2
+4
2
a
W
e
lo
ok
for
the
v
alue
of
x
suc
h
that
the
expression
has
the
v
alue
29
b
Chec
k
the
answ
ers
to
question
a
.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1239
sacados/1239
chapExoCorrec/8817
sacados/8817
chapExoCorrec/8818
sacados/8818
chapExoCorrec/8819
sacados/8819
chapExoCorrec/6323
sacados/6323
2
x
6
3
x
x
2
3
6
2
chapExoCorrec/8695
sacados/8695
Extrait Antilles-Guyanne Juin 2019
•
Choisir un nombre
•
Calculer son carré
•
Ajouter
6
au résultat
chapExoCorrec/8796
sacados/8796
Choisir un nombre
Soustraire 2
Multiplier par
4
Elever au carré
Ajouter les deux nombres
3
x
x
2
3
6
2
100
150
200
250
300
350
167
250
333
417
500
583
83
125
167
208
250
292
56
83
111
139
167
194
42
63
83
104
125
146
33
50
67
83
100
117
28
42
56
69
83
97
24
36
48
60
71
83
21
31
42
52
63
73
19
28
37
46
56
65
17
25
33
42
50
58
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
v
n
E.1881
Jacques
has
t
w
o
c
hildren,
P
aul
and
Marie.
P
aul
is
t
w
o
y
ears
older
than
Marie.
James
is
four
times
Mary’s
age.
1
If
P
aul
is
12
y
ears
old,
giv
e
the
ages
of
Mary
and
James.
2
W
e’ll
note
x
P
aul’s
age.
Giv
e
the
expression
for
James’
age
as
a
function
of
x
.
3
What
is
P
aul’s
age,
if
James
is
48?
E.8836
W
e
consider
the
figure
b
elo
w
com-
p
osed
of
three
rectangles
:
Determine
the
v
alue
of
x
so
that
the
area
of
this
figure
is
21
.
14.
Shar
e
E.4534
1
Reduce
the
follo
wing
expressions
:
a
3
x
2
−
5
+
6
x
−
8
x
2
+
4
x
+
4
b
3
×
2
x
−
5
×
2
+
x
×
(
−
3
x
)
−
(
−
5
x
)
×
(
−
2)
2
Expand
and
reduce
the
follo
wing
expressions
:
a
3(
x
+
4)
b
4(3
−
2
x
)
+
2(5
x
−
4)
3
F
actor
the
follo
wing
expressions
:
a
6
x
+
15
b
4
x
2
+
6
x
E.1925
1
Expand
and
reduce
the
follo
wing
expressions
:
a
3(
x
−
2)
b
2(6
x
+
3)
+
x
2
F
actor
the
follo
wing
expressions
:
a
3
x
+
9
b
x
2
+
2
x
E.1248
Using
distributivit
y
:
1
Giv
e
the
dev
elop
ed
and
reduced
form
of
the
follo
wing
literal
expressions
:
a
(3
x
+
2)
×
4
b
2.2
×
(3
−
5
x
)
2
Giv
e
the
factorized
form
of
the
follo
wing
literal
expres-
sions
:
a
3.1
×
5
x
−
2
×
3.1
b
3
×
x
+
12
15.
Unclassifie
d
exer
cises
E.6359
In
tra
v
enous
infusions
are
used
to
administer
flu-
ids
and
medications
to
patien
ts.
Nurses
need
to
calculate
the
flo
w
rate
D
of
an
infusion
in
drops
p
er
min
ute.
They
use
the
form
ula
D
=
d
×
v
60
×
n
où
:
d
:
is
the
flo
w
factor
in
drops
p
er
milliliter
(
m‘
)
;
v
:
is
the
v
olume
(in
m‘
)
of
the
infusion
;
n
:
is
the
n
um
b
er
of
hours
the
infusion
should
last.
1
A
n
urse
w
an
ts
to
double
the
duration
of
an
infusion.
Describ
e
precisely
ho
w
D
c
hanges
if
n
is
doubled
and
d
and
v
do
not
c
hange
2
Nurses
m
ust
also
calculate
the
v
olume
v
of
the
infusion
based
on
the
infusion
rate
D
.
An
infusion
with
a
flo
w
rate
of
50
drops
p
er
min
ute
should
b
e
administered
to
a
patien
t
for
3
hours.
F
or
this
infusion,
the
flo
w
factor
is
25
drops
p
er
milliliter.
What
is
the
v
olume
in
m‘
of
this
infusion?
3
A
n
urse
sets
the
flo
w
factor
to
10
drops
p
er
milliliter.
She
then
uses
the
table
adapted
to
this
setting
and
giv-
ing
the
v
alue
of
the
parameter
D
of
the
n
um
b
er
of
drops
p
er
min
uutes.
Here’s
the
table
:
Kno
wing
that
she
has
to
infuse
a
patien
t
for
a
maxim
um
of
1
=
2
h
and
that
the
rate
D
of
drops
p
er
min
ute
m
ust
not
exceed
60
and
giv
en
the
v
alues
giv
en
in
the
table,
what
c
hoice
can
she
mak
e
for
the
v
olume
(
v
)
of
the
infusion
and
the
n
um
b
er
of
hours
(
n
)
that
the
infusion
will
last?
Justify
y
our
approac
h.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1881
sacados/1881
chapExoCorrec/8836
sacados/8836
3
x
x
2
3
6
2
chapExoCorrec/4534
sacados/4534
chapExoCorrec/1925
sacados/1925
chapExoCorrec/1248
sacados/1248
chapExoCorrec/6359
sacados/6359
extrait de Pisa
100
150
200
250
300
350
167
250
333
417
500
583
83
125
167
208
250
292
56
83
111
139
167
194
42
63
83
104
125
146
33
50
67
83
100
117
28
42
56
69
83
97
24
36
48
60
71
83
21
31
42
52
63
73
19
28
37
46
56
65
17
25
33
42
50
58
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
v
n
4
x
1
4
x
1
;
5
2
x
de∏nir
script
1
demander
donner
une
v
aleur
et
atteindre
st
ylo
en
p
osition
d’écriture
a
v
ancer
de
4
*rép
onse+
1,5
tourner
de
B
degrés
a
v
ancer
de
2
*rép
onse
tourner
de
90
degrés
rép
éter
A
fois
relev
er
le
st
ylo
de∏nir
script
2
demander
donner
une
v
aleur
et
atteindre
st
ylo
en
p
osition
d’écriture
a
v
ancer
de
4
*rép
onse+
1
tourner
de
D
degrés
rép
éter
C
fois
relev
er
le
st
ylo
quand
est
cliqué
demander
à
Choisissez
un
nom
bre?
et
attendre
en
v
o
y
er
à
tous
le
nom
bre
a
été
saisi
mettre
Nom
bre
à
rép
onse
mettre
Résultat
1
à
2*
nom
bre
+3
mettre
Résultat
1
à
Résultat
1
*
Résultat
1
dire
regroup
e
le
résultat
est
Résultat
1
p
endan
t
2
secondes
Quand
je
reçois
le
nom
bre
a
été
saisi
mettre
à
Résultat
2
à
Nom
bre
*
Nom
bre
mettre
à
Résultat
2
à
Résultat
2
*
4
mettre
à
Résultat
2
à
Résultat
2
+12*
Nom
bre
mettre
à
Résultat
2
à
Résultat
2
+
9
attendre
3
secondes
dire
regroup
e
le
résultat
2
est
Résultat
2
E.1362
Let
A
=
3
2
×
1
4
+
1
4
:
1
Calculate
A
b
y
first
calculating
the
paren
theses.
2
Calculate
A
b
y
first
using
distributivit
y
.
Giv
e
the
results
in
simplified
form.
E.8899
P
art
1
In
this
part,
all
lengths
are
expressed
in
cen
timeters.
Consider
the
t
w
o
figures
b
elo
w,
an
equilateral
triangle
and
a
rectangle,
where
x
represen
ts
an
y
p
ositiv
e
n
um
b
er.
1
Construct
the
equilateral
triangle
for
x
=
2
2
a
Sho
w
that
the
p
erimeter
of
the
rectangle
as
a
func-
tion
of
x
can
b
e
written
12
x
+3
.
b
F
or
what
v
alue
of
x
is
the
p
erimeter
of
the
rectangle
equal
to
18
cm
?
3
Is
it
true
that
the
t
w
o
figures
ha
v
e
the
same
p
erimeter
for
all
v
alues
of
x
?
Justify
.
P
art
I
I
W
e
created
the
scripts
(opp
osite)
on
Scratc
h
that,
after
asking
the
user
for
the
v
alue
of
x
,
construct
the
t
w
o
figures
in
P
art
I
.
In
these
t
w
o
scripts,
the
letters
A
,
B
,
C
,
and
D
replace
n
um-
b
ers.
Giv
e
v
alues
to
A
,
B
,
C
,
and
D
so
that
these
t
w
o
scripts
construct
the
figures
in
part
I
and
then
sp
ecify
the
figure
asso
ciated
with
eac
h
of
the
scripts.
E.8942
Here
is
a
script
en
tered
b
y
Alice
in
an
algorithmic
soft
w
are.
1
Alice
c
hose
3
as
her
n
um
b
er,
calculate
the
v
alues
of
Result
1
and
Result
2
?
Justify
b
y
sho
wing
the
calculations
p
erformed.
2
Generalization.
a
Calling
x
the
n
um
b
er
c
hosen
in
the
algorithm,
giv
e
a
literal
expression
translating
the
first
part
of
the
algo-
rithm
corresp
onding
to
Result
1
.
b
Calling
x
the
n
um
b
er
c
hosen
in
the
algorithm,
giv
e
a
literal
expression
translating
the
second
part
of
the
algorithm
corresp
onds
to
Result
2
.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/1362
sacados/1362
chapExoCorrec/8899
sacados/8899
4
x
1
4
x
1
;
5
2
x
de∏nir
script
1
demander
donner
une
v
aleur
et
atteindre
st
ylo
en
p
osition
d’écriture
a
v
ancer
de
4
*rép
onse+
1,5
tourner
de
B
degrés
a
v
ancer
de
2
*rép
onse
tourner
de
90
degrés
rép
éter
A
fois
relev
er
le
st
ylo
de∏nir
script
2
demander
donner
une
v
aleur
et
atteindre
st
ylo
en
p
osition
d’écriture
a
v
ancer
de
4
*rép
onse+
1
tourner
de
D
degrés
rép
éter
C
fois
relev
er
le
st
ylo
chapExoCorrec/8942
sacados/8942
quand
est
cliqué
demander
à
Choisissez
un
nom
bre?
et
attendre
en
v
o
y
er
à
tous
le
nom
bre
a
été
saisi
mettre
Nom
bre
à
rép
onse
mettre
Résultat
1
à
2*
nom
bre
+3
mettre
Résultat
1
à
Résultat
1
*
Résultat
1
dire
regroup
e
le
résultat
est
Résultat
1
p
endan
t
2
secondes
Quand
je
reçois
le
nom
bre
a
été
saisi
mettre
à
Résultat
2
à
Nom
bre
*
Nom
bre
mettre
à
Résultat
2
à
Résultat
2
*
4
mettre
à
Résultat
2
à
Résultat
2
+12*
Nom
bre
mettre
à
Résultat
2
à
Résultat
2
+
9
attendre
3
secondes
dire
regroup
e
le
résultat
2
est
Résultat
2
1
2
3
4
5
6
7
8
A
B
C
D
Nom
bre
c
hoisi
Résultat
a
v
ec
le
programme
1
Résultat
a
v
ec
le
programme
2
0
-20
-20
1
-16
-16
2
-12
-12
3
-8
-8
4
5
6
E.8944
Here
are
t
w
o
calculation
pro-
grams
:
Calculation
program
1
:
Subtract
5
Multiply
b
y
4
Calculation
program
2
:
Multiply
b
y
6
Subtract
20
Subtract
double
the
start-
ing
n
um
b
er
1
a
What
result
do
w
e
get
when
w
e
apply
the
calculation
program
1
to
the
n
um
b
er
3
?
b
What
result
do
w
e
get
when
w
e
apply
the
computation
program
2
to
the
n
um
b
er
3
?
2
Demonstrate
that
b
y
c
ho
osing
the
n
um
b
er
−
2
,
b
oth
pro-
grams
giv
e
the
same
result.
3
W
e
decide
to
run
more
trials.
T
o
do
this,
a
spreadsheet
is
used
and
the
follo
wing
screenshot
is
obtained
:
What
form
ula
could
ha
v
e
b
een
en
tered
in
cell
B2
b
efore
cop
ying
it
do
wn
to
cell
B5
?
4
The
results
sho
wn
in
the
columns
B
and
C
are
equal.
Lucy
then
thinks
that,
for
an
y
n
um
b
er
c
hosen
at
the
b
eginning,
b
oth
programs
alw
a
ys
giv
e
the
same
result.
Sho
w
that
Lucie
is
correct.
E.5084
The
follo
wing
calculation
program
is
prop
osed
:
Choisir
a
n
um
b
er.
Subtract
6
.
Calculate
the
square
of
the
result.
1
a
W
e
c
ho
ose
the
n
um
b
er
−
4
at
the
start,
sho
w
that
the
result
obtained
is
100
.
b
W
e
c
ho
ose
15
as
the
starting
n
um
b
er,
what
is
the
result
obtained?
2
Noting
x
as
a
n
um
b
er,
what
expression
giv
es
the
result
obtained?
E.5085
W
e
consider
the
follo
wing
t
w
o
calcula-
tion
programs
:
Cho
ose
a
n
um
b
er.
A
dd
3
to
that
n
um
b
er.
Multiply
the
result
b
y
2
.
View
pro
duct.
Cho
ose
a
n
um
b
er.
Multiply
b
y
3
this
n
um
b
er.
A
dd
2
to
the
result.
Displa
y
the
sum.
1
a
Quel
(s)
résultat
(s)
do
y
ou
get
with
these
t
w
o
calcu-
lation
programs
when
the
c
hosen
n
um
b
er
is
4
?
b
Can
w
e
sa
y
that
these
t
w
o
calculation
programs
are
equiv
alen
t?
2
a
What
n
um
b
er
m
ust
b
e
c
hosen
to
obtain
the
n
um
b
er
18
b
y
the
first
calculation
program?
b
What
n
um
b
er
should
b
e
c
hosen
to
get
the
n
um
b
er
8
b
y
the
second
calculation
program?
E.4612
F
actor
the
follo
wing
expressions
:
a
3
x
+
6
b
2
x
−
8
c
27
x
+
18
h
ttps:/
/c
hingmath.fr
chapExoCorrec/8944
sacados/8944
1
2
3
4
5
6
7
8
A
B
C
D
Nom
bre
c
hoisi
Résultat
a
v
ec
le
programme
1
Résultat
a
v
ec
le
programme
2
0
-20
-20
1
-16
-16
2
-12
-12
3
-8
-8
4
5
6
chapExoCorrec/5084
sacados/5084
chapExoCorrec/5085
sacados/5085
chapExoCorrec/4612
sacados/4612
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