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I
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2252
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8
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2
2
C
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Fo
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1
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]
s
tu
d
ied
th
e
m
at
h
em
atica
l
u
n
d
er
s
tan
d
in
g
o
f
f
r
ac
tio
n
s
am
o
n
g
p
r
e
-
s
er
v
ice
teac
h
er
s
.
I
n
th
is
ca
s
e,
o
u
r
in
ter
est
lie
s
in
d
iag
n
o
s
in
g
an
d
ass
es
s
in
g
th
e
co
m
p
r
eh
e
n
s
io
n
o
f
s
y
s
tem
s
o
f
t
wo
lin
ea
r
e
q
u
atio
n
s
with
two
u
n
k
n
o
wn
s
.
T
h
is
e
x
am
in
atio
n
i
s
b
ased
o
n
a
m
o
d
el
ass
o
ciate
d
with
th
e
ep
is
tem
o
lo
g
y
an
d
p
h
e
n
o
m
e
n
o
lo
g
y
o
f
th
e
s
e
s
y
s
tem
s
.
Ma
n
y
s
tu
d
ies
in
m
ath
em
atics
ed
u
ca
tio
n
h
a
v
e
f
o
c
u
s
ed
o
n
th
e
teac
h
in
g
an
d
lear
n
in
g
o
f
al
g
eb
r
a
f
r
o
m
v
ar
io
u
s
p
e
r
s
p
ec
tiv
es.
Fo
r
ex
a
m
p
le,
Ma
d
r
id
et
a
l
.
[
1
1
]
s
tu
d
y
th
e
in
tr
o
d
u
ctio
n
o
f
alg
eb
r
aic
th
o
u
g
h
t
in
Sp
ain
th
r
o
u
g
h
Sp
an
is
h
m
at
h
em
atics
b
o
o
k
s
f
r
o
m
t
h
e
1
6
th
,
1
7
th
,
a
n
d
1
8
th
ce
n
tu
r
ies,
in
p
ar
ticu
lar
,
th
ey
f
o
cu
s
o
n
th
e
d
if
f
er
en
t m
eth
o
d
s
f
o
r
s
o
l
v
in
g
q
u
ad
r
atics e
q
u
atio
n
s
p
r
esen
ted
in
th
ese
b
o
o
k
s
; D
u
r
u
a
n
d
Ko
k
lu
[
1
2
]
a
n
aly
ze
th
e
r
ea
d
in
g
c
o
m
p
r
e
h
en
s
io
n
o
f
m
ath
em
atica
l
tex
ts
an
d
alg
e
b
r
a
ic
eq
u
atio
n
s
o
f
m
id
d
le
s
ch
o
o
l
s
tu
d
en
ts
;
Ay
ala
-
Altam
ir
an
o
et
a
l
.
[
1
3
]
e
x
am
in
e
th
e
d
ev
elo
p
m
en
t
o
f
alg
e
b
r
ai
c
th
in
k
in
g
in
a
g
r
o
u
p
o
f
2
5
s
tu
d
en
ts
ag
e
9
-
10.
Sp
an
is
h
R
ea
l
Dec
r
eto
2
1
7
/2
0
2
2
[
1
4
]
estab
lis
h
es
th
e
o
r
g
an
izatio
n
an
d
m
i
n
im
u
m
cu
r
r
icu
lu
m
f
o
r
co
m
p
u
ls
o
r
y
s
ec
o
n
d
ar
y
ed
u
ca
t
io
n
.
I
t
s
tr
u
ctu
r
es
m
ath
em
atica
l
k
n
o
wled
g
e
ar
o
u
n
d
th
e
co
n
ce
p
t
o
f
m
ath
em
atica
l
s
en
s
e,
wh
ich
in
clu
d
es
th
e
al
g
eb
r
aic
s
en
s
e.
T
h
is
o
n
e
p
r
o
v
i
d
es
th
e
lan
g
u
a
g
e
th
r
o
u
g
h
wh
ich
m
ath
em
atics
is
co
m
m
u
n
icate
d
,
a
n
d
its
f
u
n
d
am
en
tal
ch
ar
ac
te
r
is
tics
ar
e
s
ee
in
g
th
e
g
e
n
er
al
i
n
th
e
p
a
r
ticu
lar
,
r
ec
o
g
n
izin
g
p
atter
n
s
an
d
r
elatio
n
s
h
ip
s
b
et
wee
n
v
ar
iab
les,
an
d
ex
p
r
ess
in
g
th
em
th
r
o
u
g
h
d
if
f
er
en
t
r
ep
r
esen
tatio
n
s
,
as
well
as
m
o
d
ellin
g
m
ath
em
atica
l
o
r
r
ea
l
-
wo
r
ld
s
itu
atio
n
s
u
s
in
g
s
y
m
b
o
lic
e
x
p
r
ess
io
n
s
.
W
ith
in
th
e
b
asic
co
n
ce
p
ts
in
clu
d
ed
in
th
is
alg
eb
r
aic
s
en
s
e
ar
e
s
y
s
tem
s
o
f
two
lin
ea
r
e
q
u
atio
n
s
with
two
u
n
k
n
o
wn
s
.
A
s
y
s
tem
o
f
lin
ea
r
eq
u
atio
n
s
with
two
u
n
k
n
o
wn
s
co
n
s
is
ts
o
f
two
o
r
m
o
r
e
eq
u
atio
n
s
,
ea
c
h
with
two
u
n
k
n
o
wn
s
.
W
h
en
th
e
v
ar
iab
l
es
in
th
e
s
y
s
tem
h
av
e
an
e
x
p
o
n
en
t
o
f
o
n
e,
th
e
s
y
s
tem
is
r
ef
er
r
ed
to
as
lin
ea
r
.
So
lv
in
g
s
u
ch
a
s
y
s
tem
m
ea
n
s
f
in
d
in
g
th
e
v
alu
es
o
f
ea
c
h
v
ar
iab
le
th
at
s
atis
f
y
th
e
e
q
u
a
tio
n
s
.
T
h
er
e
f
o
r
e,
a
s
o
lu
tio
n
to
a
s
y
s
tem
o
f
e
q
u
ati
o
n
s
with
two
u
n
k
n
o
wn
s
co
n
s
is
ts
o
f
an
o
r
d
er
ed
p
air
o
f
n
u
m
b
er
s
th
at
s
atis
f
ies
th
e
s
y
s
tem
.
A
lin
ea
r
eq
u
atio
n
wi
th
two
u
n
k
n
o
wn
s
will
h
av
e
i
n
f
in
itely
m
an
y
s
o
lu
tio
n
s
f
o
r
m
in
g
a
lin
e
(
wh
e
n
g
r
ap
h
ically
r
ep
r
esen
ted
)
,
h
en
c
e
th
e
ter
m
“
lin
ea
r
e
q
u
atio
n
”
[
1
5
]
.
As
s
tated
b
y
I
s
tú
r
iz
et
a
l.
[
1
6
]
,
eq
u
atio
n
s
p
lay
a
f
u
n
d
am
en
ta
l
r
o
le
i
n
v
ar
io
u
s
m
ath
em
atica
l
co
n
ce
p
ts
th
r
o
u
g
h
o
u
t
co
m
p
u
ls
o
r
y
s
ec
o
n
d
ar
y
ed
u
ca
tio
n
.
C
o
n
s
eq
u
en
tly
,
p
r
o
b
lem
s
an
d
s
itu
atio
n
s
th
at
ar
e
s
o
lv
ed
u
s
in
g
s
y
s
tem
s
o
f
two
l
in
ea
r
eq
u
atio
n
s
with
two
u
n
k
n
o
wn
s
ar
e
f
r
eq
u
en
t
an
d
co
m
m
o
n
in
th
e
e
d
u
ca
tio
n
al
s
y
s
tem
,
p
r
o
v
id
i
n
g
a
v
alu
a
b
le
o
p
p
o
r
t
u
n
ity
to
lear
n
b
asic
alg
eb
r
aic
c
o
n
ce
p
ts
an
d
f
o
s
ter
p
r
o
b
lem
-
s
o
lv
in
g
a
b
ilit
ies
[
1
7
]
.
T
o
s
o
lv
e
a
s
y
s
tem
o
f
two
l
in
ea
r
eq
u
atio
n
s
with
two
u
n
k
n
o
wn
s
,
s
ec
o
n
d
ar
y
ed
u
ca
tio
n
s
tu
d
en
ts
ca
n
u
s
e
alg
eb
r
aic
o
r
g
e
o
m
etr
ic
m
eth
o
d
s
.
Acc
o
r
d
in
g
to
r
esear
ch
,
s
tu
d
en
ts
en
co
u
n
ter
v
a
r
io
u
s
c
o
g
n
itiv
e
d
if
f
ic
u
lties
,
s
o
m
e
o
f
wh
ich
ca
n
b
e
attr
ib
u
t
ed
to
th
eir
co
n
ce
p
tio
n
s
[
1
8
]
;
th
e
ep
is
tem
o
lo
g
ical
o
b
s
tacle
o
f
tr
an
s
itio
n
in
g
f
r
o
m
ar
ith
m
etic
to
alg
eb
r
a
[
1
9
]
;
c
o
n
ce
p
tu
al
d
ef
icien
cies
in
m
at
h
em
atics
[
2
0
]
.
Ad
d
itio
n
ally
,
M
an
za
n
er
o
[
2
1
]
r
elies
o
n
APOE
th
e
o
r
y
to
id
en
tify
d
if
f
icu
lties
th
at
s
tu
d
e
n
ts
f
ac
e
wh
en
s
tu
d
y
in
g
th
e
co
n
ce
p
t
o
f
th
e
s
o
lu
tio
n
o
f
a
s
y
s
tem
o
f
lin
ea
r
eq
u
atio
n
s
.
Mo
r
eo
v
er
,
s
o
m
e
s
tu
d
ies
h
av
e
ex
p
lo
r
e
d
th
e
r
elatio
n
s
h
i
p
th
at
s
tu
d
en
ts
estab
lis
h
b
etwe
en
p
o
in
ts
o
n
a
lin
e
an
d
th
e
co
r
r
esp
o
n
d
i
n
g
s
o
lu
tio
n
s
o
f
th
e
eq
u
atio
n
,
f
in
d
in
g
t
h
at
m
an
y
s
tu
d
en
ts
s
tr
u
g
g
l
e
to
m
ak
e
th
is
co
n
n
ec
tio
n
[
2
2
]
.
T
h
e
r
esear
ch
p
r
o
b
lem
m
o
tiv
a
tin
g
th
is
s
tu
d
y
r
ev
o
l
v
es
ar
o
u
n
d
d
iag
n
o
s
in
g
an
d
ev
alu
atin
g
s
tu
d
en
ts
'
co
m
p
r
eh
e
n
s
io
n
o
f
s
y
s
tem
s
o
f
two
lin
ea
r
eq
u
atio
n
s
as
th
ey
l
ea
r
n
alg
eb
r
a
in
s
ch
o
o
l.
T
h
e
r
ef
o
r
e,
th
e
aim
o
f
th
is
s
tu
d
y
is
to
a
n
aly
ze
th
e
u
n
d
e
r
s
tan
d
in
g
o
f
m
at
h
em
atica
l
k
n
o
wled
g
e,
s
p
ec
if
ically
o
f
s
y
s
tem
s
o
f
two
lin
ea
r
eq
u
atio
n
s
with
two
u
n
k
n
o
w
n
s
,
am
o
n
g
Sp
an
is
h
4
th
s
ec
o
n
d
ar
y
ed
u
ca
tio
n
(
E
SO)
y
ea
r
s
tu
d
en
ts
.
Fo
r
th
is
p
u
r
p
o
s
e,
we
h
av
e
ch
o
s
en
an
ep
is
tem
o
lo
g
ical
an
d
p
h
en
o
m
en
o
lo
g
ical
an
aly
s
is
o
f
s
y
s
tem
s
o
f
two
lin
ea
r
eq
u
atio
n
s
with
two
u
n
k
n
o
wn
s
,
b
ased
o
n
t
h
e
s
tu
d
ies b
y
Gallar
d
o
et
a
l.
[
2
3
]
.
2.
M
E
T
H
O
D
T
h
e
r
esear
ch
co
n
d
u
cte
d
is
d
escr
ip
tiv
e,
ex
p
l
o
r
ato
r
y
,
a
n
d
q
u
an
titativ
e
in
n
at
u
r
e,
u
s
in
g
a
wr
itten
q
u
esti
o
n
n
air
e
with
m
ath
em
ati
ca
l
task
s
.
T
h
e
s
tu
d
y
was
ca
r
r
i
ed
o
u
t
d
u
r
i
n
g
th
e
th
ir
d
tr
im
ester
o
f
th
e
ac
ad
em
ic
y
ea
r
at
a
p
r
iv
ate
s
ch
o
o
l
in
th
e
p
r
o
v
in
ce
o
f
Má
lag
a
(
Sp
ain
)
.
An
in
ten
tio
n
al
s
am
p
le
o
f
two
g
r
o
u
p
s
f
r
o
m
th
e
4
th
E
SO y
ea
r
was c
h
o
s
en
:
-
Gr
o
u
p
A:
co
m
p
r
is
ed
of
24
s
tu
d
en
ts
in
th
eir
4
th
y
ea
r
of
E
SO.
T
h
ey
h
av
e
ch
o
s
en
th
e
s
cien
tific
b
r
an
ch
,
in
ten
d
to
p
u
r
s
u
e
f
u
r
th
e
r
s
tu
d
ies
an
d
,
in
g
e
n
er
al,
h
av
e
a
g
o
o
d
ac
a
d
em
ic
p
er
f
o
r
m
a
n
ce
.
T
h
ey
h
a
v
e
h
a
d
ex
p
o
s
u
r
e
to
s
y
s
tem
s
of
two
li
n
ea
r
e
q
u
atio
n
s
with
two
u
n
k
n
o
wn
s
twice
(
d
u
r
in
g
th
eir
3
rd
y
ea
r
of
E
SO
an
d
in
th
e
1
s
t
tr
im
ester
of
th
ei
r
4
th
y
ea
r
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t J E
v
al
&
R
es E
d
u
c
,
Vo
l
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
9
1
4
-
3
9
2
2
3916
-
Gr
o
u
p
B:
co
m
p
r
is
ed
of
13
s
tu
d
en
ts
in
th
eir
4
th
y
ea
r
of
E
SO.
T
h
ey
h
av
e
ch
o
s
en
th
e
b
r
an
ch
o
r
ie
n
ted
to
war
d
s
s
o
cial
s
cien
ce
s
an
d
h
u
m
an
ities
an
d
th
eir
ac
ad
em
ic
p
er
f
o
r
m
an
ce
is
in
g
en
er
al
av
e
r
ag
e.
T
h
ey
h
a
v
e
h
ad
ex
p
o
s
u
r
e
to
s
y
s
tem
s
of
tw
o
lin
ea
r
eq
u
atio
n
s
with
two
u
n
k
n
o
wn
s
o
n
ce
(
in
th
ei
r
3
rd
E
S
O
y
ea
r
)
.
T
h
e
q
u
esti
o
n
n
ai
r
e
was
d
esig
n
ed
with
an
in
itial
s
et
o
f
ta
s
k
s
o
r
g
an
ized
b
y
lev
els,
f
o
ll
o
win
g
th
e
ca
teg
o
r
ies
p
r
o
p
o
s
ed
i
n
th
e
m
o
d
el
o
f
Ma
r
tín
[
2
4
]
.
A
s
et
o
f
v
ar
iab
les,
co
llectiv
ely
r
e
f
er
r
ed
to
as
task
v
ar
iab
les,
wer
e
d
eter
m
in
ed
.
T
h
e
ty
p
e
o
f
task
v
ar
iab
le
is
a
q
u
alitativ
e
in
d
ep
en
d
en
t
v
a
r
iab
le
with
th
r
ee
ca
teg
o
r
ies
r
ep
r
esen
tin
g
th
r
ee
lev
els
o
f
d
i
f
f
icu
lty
b
ased
o
n
o
u
r
e
p
is
tem
o
lo
g
ical
class
if
icatio
n
:
tech
n
ical,
an
aly
tical
,
an
d
f
o
r
m
al.
T
h
e
y
d
escr
ib
e
th
e
n
ec
ess
ar
y
elem
en
ts
f
o
r
d
iag
n
o
s
in
g
an
d
ev
alu
atin
g
s
tu
d
en
ts
'
co
m
p
r
eh
e
n
s
io
n
in
r
elatio
n
to
th
e
an
aly
ze
d
m
ath
e
m
atica
l
k
n
o
wled
g
e.
T
ab
le
1
il
lu
s
tr
ates
th
e
ca
teg
o
r
ies
an
d
s
u
b
ca
teg
o
r
ies
with
in
th
e
co
m
p
r
eh
e
n
s
io
n
/co
g
n
itiv
e
d
o
m
ain
(
tech
n
ical,
an
aly
tical,
an
d
f
o
r
m
al
)
,
th
e
alg
eb
r
aic
k
n
o
wled
g
e
(
co
n
ce
p
t,
s
o
lu
tio
n
,
eq
u
iv
alen
ce
,
t
y
p
es
,
an
d
r
eso
lu
tio
n
o
f
s
y
s
tem
s
o
f
two
lin
ea
r
eq
u
atio
n
s
with
t
wo
u
n
k
n
o
wn
s
)
,
t
h
e
d
if
f
er
en
t
s
y
s
tem
s
o
f
r
ep
r
esen
t
atio
n
(
a
lg
e
b
r
aic
=
A
,
g
eo
m
etr
ic
al
=
G
,
n
u
m
er
ical
=
N
,
an
d
v
e
r
b
a
l
=
V
)
,
as
well
as
th
e
s
itu
atio
n
s
in
wh
ich
p
air
s
o
f
r
el
atio
n
s
h
ip
s
o
f
lin
ea
r
d
ep
en
d
en
c
e
o
cc
u
r
s
im
u
ltan
e
o
u
s
ly
.
T
ab
le
1.
C
ateg
o
r
ies
an
d
s
u
b
ca
teg
o
r
ies
of
th
e
m
o
d
el
u
s
ed
C
a
t
e
g
o
r
i
e
s
A
l
g
e
b
r
a
i
c
k
n
o
w
l
e
d
g
e
C
o
n
c
e
p
t
o
f
s
y
st
e
m
o
f
t
w
o
l
i
n
e
a
r
e
q
u
a
t
i
o
n
s
w
i
t
h
t
w
o
u
n
k
n
o
w
n
s
S
o
l
u
t
i
o
n
o
f
s
y
st
e
ms
o
f
t
w
o
l
i
n
e
a
r
e
q
u
a
t
i
o
n
s
w
i
t
h
t
w
o
u
n
k
n
o
w
n
s
Ty
p
e
s
o
f
s
y
st
e
ms
o
f
t
w
o
l
i
n
e
a
r
e
q
u
a
t
i
o
n
s
w
i
t
h
t
w
o
u
n
k
n
o
w
n
s
Eq
u
i
v
a
l
e
n
t
s
sy
s
t
e
ms
o
f
t
w
o
l
i
n
e
a
r
e
q
u
a
t
i
o
n
s
w
i
t
h
t
w
o
u
n
k
n
o
w
n
s
R
e
s
o
l
u
t
i
o
n
o
f
sy
st
e
ms
o
f
t
w
o
l
i
n
e
a
r
e
q
u
a
t
i
o
n
s
w
i
t
h
t
w
o
u
n
k
n
o
w
n
s
A
G
N
V
A
G
N
V
A
G
N
V
A
G
N
V
A
G
N
Te
c
h
n
i
c
a
l
TC
A
TC
G
TC
N
TC
V
TSA
TSG
TSN
TSV
TTA
TTG
TTN
TTV
TEA
TEG
TEN
TEV
TR
A
TR
G
TR
N
A
n
a
l
y
t
i
c
a
l
A
C
A
A
C
G
A
C
N
A
C
V
A
S
A
A
S
G
A
S
N
A
S
V
A
TA
A
TG
A
TN
A
TV
A
EA
A
EG
A
EN
A
EV
A
R
A
A
R
G
A
R
N
F
o
r
mal
F
C
A
F
C
G
F
C
N
F
C
V
FSA
FSG
FSN
FSV
F
TA
F
TG
F
TN
F
TV
F
EA
F
EG
F
EN
F
EV
F
R
A
F
R
G
F
R
N
2
.
1
.
T
ec
hn
ica
l
ca
t
eg
o
ry
I
n
th
ese
task
s
,
s
tu
d
en
ts
s
h
o
u
ld
d
em
o
n
s
tr
ate
a
m
ec
h
an
ical,
te
ch
n
ical,
o
r
r
o
u
tin
e
u
s
e
o
f
alg
o
r
ith
m
s
f
o
r
s
o
lv
in
g
s
y
s
tem
s
an
d
r
ec
o
g
n
iz
e
an
d
id
e
n
tify
co
n
ce
p
ts
in
its
v
ar
io
u
s
s
y
s
tem
s
o
f
r
ep
r
esen
tatio
n
.
W
ith
th
is
,
we
aim
to
estab
lis
h
d
if
f
er
en
ce
s
b
e
twee
n
s
u
b
jects a
n
d
o
b
tain
in
te
r
p
r
etab
le
in
f
o
r
m
atio
n
in
ter
m
s
o
f
co
m
p
r
eh
en
s
io
n
.
Sp
ec
if
ically
,
in
Fig
u
r
e
1
,
we
p
r
o
v
id
e
ex
am
p
les
o
f
tech
n
ic
al
task
s
wh
er
e
s
tu
d
en
ts
ar
e
ask
ed
to
cir
cle
th
e
co
r
r
ec
t
an
s
wer
.
T
h
ese
task
s
ar
e
r
elativ
ely
ea
s
y
to
ev
alu
a
te,
u
s
u
ally
ad
m
itti
n
g
o
n
ly
c
o
r
r
ec
t
o
r
in
c
o
r
r
ec
t
ass
es
s
m
en
ts
with
o
u
t f
u
r
th
er
o
p
tio
n
s
.
2
.
2
.
Ana
ly
t
ica
l
ca
t
e
g
o
ry
N
on
-
r
o
u
tin
e
ac
tiv
ities
th
at
r
e
q
u
ir
e
a
r
ef
lectiv
e
u
s
e
o
f
k
n
o
wl
ed
g
e
b
y
s
tu
d
e
n
ts
.
T
h
ey
in
v
o
lv
e
an
aly
s
is
an
d
r
ef
lectio
n
o
n
th
e
s
tr
u
ctu
r
e
an
d
ex
te
r
n
al
f
u
n
ctio
n
in
g
o
f
t
h
e
alg
o
r
ith
m
an
d
co
n
ce
p
ts
in
its
v
ar
io
u
s
s
y
s
tem
s
o
f
r
e
p
r
esen
tatio
n
.
I
n
p
ar
ticu
l
ar
,
we
h
a
v
e
s
elec
ted
v
ar
io
u
s
in
co
m
p
lete
task
s
an
d
t
h
e
s
t
u
d
en
ts
ar
e
ask
ed
to
co
m
p
lete
th
em
as sh
o
wn
in
Fig
u
r
e
2
.
2
.
3
.
F
o
rma
l
ca
t
e
g
o
ry
A
ctiv
ities
th
at
r
eq
u
ir
e
a
co
m
p
l
ete
k
n
o
wled
g
e
o
f
s
y
s
tem
s
o
f
t
wo
lin
ea
r
eq
u
atio
n
s
with
two
u
n
k
n
o
wn
s
in
its
d
if
f
er
en
t
r
ep
r
esen
tatio
n
s
y
s
tem
s
(
d
ef
in
itio
n
,
p
r
o
p
e
r
ties
,
an
d
co
n
n
ec
tio
n
s
)
.
I
n
th
is
ty
p
e
o
f
ac
tiv
ity
,
n
o
t
o
n
ly
th
e
f
in
al
an
s
wer
is
ev
alu
ated
,
b
u
t
also
th
e
d
if
f
er
e
n
t
r
es
o
lu
tio
n
p
r
o
ce
s
s
es,
s
tr
ateg
ies
u
s
ed
,
an
d
ar
g
u
m
en
ts
p
r
esen
ted
b
y
ea
ch
ev
al
u
ated
s
tu
d
en
t.
I
n
th
ese
task
s
s
tu
d
en
ts
ar
e
ask
ed
to
ex
p
lain
as
in
d
icate
d
in
th
e
f
o
llo
win
g
ex
am
p
le
as sh
o
wn
in
T
ab
le
2
.
T
o
cr
ea
te
th
e
wr
itten
q
u
esti
o
n
n
air
e,
n
in
etee
n
task
s
wer
e
s
elec
ted
f
o
r
ea
ch
ca
te
g
o
r
y
(
tech
n
ical,
an
aly
tical,
an
d
f
o
r
m
al
)
.
T
h
ey
wer
e
ch
o
s
en
b
ec
au
s
e
th
ey
p
r
esen
ted
f
av
o
r
a
b
le
co
n
d
itio
n
s
f
o
r
o
b
s
er
v
in
g
th
e
f
u
n
d
am
e
n
tal
u
n
d
e
r
s
tan
d
in
g
o
f
s
y
s
tem
s
o
f
two
lin
ea
r
eq
u
atio
n
s
with
two
u
n
k
n
o
wn
s
,
as
th
ey
ex
clu
s
iv
ely
f
o
cu
s
ed
o
n
t
h
e
s
tu
d
ied
m
ath
e
m
atica
l
k
n
o
wled
g
e,
b
u
t
th
e
y
ar
e
n
o
t
th
e
o
n
ly
q
u
esti
o
n
s
th
a
t
ca
n
b
e
p
o
s
ed
.
Fo
r
th
e
v
alid
atio
n
o
f
th
e
q
u
esti
o
n
n
air
e,
tr
ian
g
u
latio
n
was
u
s
ed
with
ex
p
er
ts
in
m
ath
em
atics
ed
u
ca
tio
n
f
r
o
m
th
e
u
n
iv
er
s
ities
o
f
C
ó
r
d
o
b
a,
Po
n
ti
f
icia
d
e
Salam
an
ca
an
d
Má
lag
a.
T
h
e
an
s
wer
s
g
iv
en
b
y
th
e
s
tu
d
en
ts
wer
e
co
n
s
id
er
ed
an
o
b
s
er
v
ab
le
m
an
if
estatio
n
o
f
th
eir
u
n
d
er
s
tan
d
i
n
g
o
f
s
y
s
tem
s
o
f
two
lin
ea
r
eq
u
atio
n
s
with
two
u
n
k
n
o
wn
s
,
d
esp
ite
th
e
lim
itatio
n
s
in
v
o
lv
ed
.
T
h
e
d
if
f
er
en
t
r
esp
o
n
s
es
g
iv
en
b
y
th
e
s
u
b
jects
wer
e
an
aly
ze
d
a
n
d
ev
alu
ated
in
ter
m
s
o
f
co
m
p
r
eh
en
s
io
n
o
f
th
e
s
tu
d
ied
m
ath
em
atica
l
k
n
o
wle
d
g
e.
I
t
was
ag
r
ee
d
to
s
co
r
e
th
e
task
s
f
r
o
m
0
to
3
,
f
o
llo
win
g
th
ese
cr
iter
ia:
i)
th
e
s
tu
d
en
t
d
o
es
n
o
t
d
o
th
e
ac
ti
v
ity
o
r
d
o
es
it
to
tally
in
c
o
r
r
ec
tly
(
0
p
o
in
ts
);
ii)
th
e
s
tu
d
en
t
an
s
wer
s
with
r
ea
s
o
n
ab
le
in
d
icatio
n
s
o
f
c
o
r
r
ec
tn
ess
an
d
h
is
an
s
wer
s
ar
e
in
th
e
r
ig
h
t
d
ir
ec
tio
n
(
1
p
o
in
t
);
i
ii)
th
e
s
tu
d
e
n
t
g
iv
es
in
co
m
p
lete
o
r
p
ar
tially
co
r
r
ec
t
an
s
wer
s
(
2
p
o
in
ts
);
an
d
iv
)
t
h
e
s
tu
d
en
t
g
iv
es
a
c
o
r
r
ec
t
an
s
wer
o
r
with
m
in
o
r
m
is
tak
es
(
3
p
o
in
ts
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
C
o
mp
r
eh
en
s
io
n
o
f lin
ea
r
s
ystems
w
ith
t
w
o
u
n
kn
o
w
n
s
in
s
ec
o
n
d
a
r
y
ed
u
c
a
tio
n
(
Ju
a
n
C
a
r
lo
s
Ma
r
tín
Mo
lin
a
)
3917
Circ
le
t
he
o
nes
t
ha
t
co
rr
esp
o
nd
to
s
y
s
t
em
s
of
t
wo
lin
ea
r
equa
t
io
ns
wit
h
t
wo
un
k
no
wns
:
a)
2
+
=
12
4
+
3
=
11
}
b)
2
+
2
=
2
5
2
+
=
2
}
c)
=
30
+
3
=
2
1
}
d)
2
−
1
=
3
2
−
=
0
}
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o
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r
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r
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u
r
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1
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x
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p
les
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tech
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plet
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Th
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Fig
u
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2
.
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x
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p
les
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task
s
f
r
o
m
th
e
an
al
y
tical
ca
teg
o
r
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T
ab
le
2
.
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x
am
p
les
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task
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f
r
o
m
th
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f
o
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m
al
ca
teg
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
8
2
2
I
n
t J E
v
al
&
R
es E
d
u
c
,
Vo
l
.
13
,
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.
6
,
Dec
em
b
er
2
0
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4
:
3
9
1
4
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3
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2
2
3918
3.
RE
SU
L
T
S
T
ab
le
1
s
h
o
ws
th
e
a
v
er
ag
e
p
e
r
ce
n
tag
es
o
f
co
r
r
ec
t
an
s
wer
s
o
b
tain
ed
f
o
r
ea
ch
o
f
th
e
s
tu
d
en
t
g
r
o
u
p
s
co
n
s
id
er
in
g
t
h
e
d
if
f
er
en
t
ca
te
g
o
r
ies.
R
eg
ar
d
in
g
th
e
tec
h
n
ic
al
ca
teg
o
r
y
,
as
s
h
o
wn
in
Fig
u
r
e
3
,
ass
o
ciate
d
with
alg
o
r
ith
m
ic
asp
ec
ts
,
it is
g
en
er
ally
o
b
s
er
v
ed
th
at
s
u
b
jects f
r
o
m
b
o
th
g
r
o
u
p
s
h
av
e
g
o
o
d
tech
n
ical
k
n
o
wled
g
e
in
g
eo
m
etr
ic
-
ty
p
e
s
y
s
tem
s
(
T
C
G)
as
well
as
th
eir
s
o
lu
tio
n
s
(
T
SG)
.
Ho
wev
er
,
s
ig
n
if
ican
t
d
if
f
er
en
ce
s
wer
e
f
o
u
n
d
b
etwe
en
g
r
o
u
p
s
A
an
d
B
in
t
h
e
co
n
ce
p
t
o
f
eq
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iv
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t
g
e
o
m
etr
ic
-
ty
p
e
(
T
E
G)
,
as
well
as
in
th
e
r
eso
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tio
n
o
f
alg
eb
r
aic
-
ty
p
e
(
T
R
A)
an
d
n
u
m
er
ical
-
ty
p
e
(
T
R
N)
s
y
s
tem
s
.
Fig
u
r
e
3
.
Av
e
r
ag
e
p
e
r
ce
n
tag
es
o
f
r
ig
h
t a
n
s
wer
s
in
ea
ch
g
r
o
u
p
f
o
r
t
h
e
tech
n
ical
ca
teg
o
r
y
W
h
en
an
aly
zin
g
th
e
a
n
aly
tic
al
ca
teg
o
r
y
as
s
h
o
wn
in
Fig
u
r
e
4
,
a
h
ig
h
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ce
n
tag
e
o
f
co
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r
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ed
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p
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g
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p
s
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h
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it
a
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atter
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g
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th
er
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d
if
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tag
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ter
m
s
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h
e
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ig
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est
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m
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p
s
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ce
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t
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eb
r
aic
-
t
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p
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s
o
l
u
tio
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(
ASA)
.
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tab
le
d
if
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er
e
n
ce
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wer
e
f
o
u
n
d
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th
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t
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ty
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e
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AC
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n
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m
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ical
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t
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e
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C
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s
y
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tem
s
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d
th
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o
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al
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ty
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m
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ical
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ty
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e
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ASN)
,
an
d
g
eo
m
etr
ic
-
ty
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e
(
ASG)
.
G
r
o
u
p
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o
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tain
e
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n
o
c
o
r
r
ec
t
a
n
s
wer
s
f
o
r
AC
A,
AC
N,
A
C
V
,
ASG,
ASV,
A
SN,
AT
N,
AE
N,
AE
V,
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A,
an
d
AR
G,
s
o
th
ey
d
id
n
o
t
g
iv
e
a
c
o
r
r
ec
t a
n
s
wer
f
o
r
6
3
% o
f
th
e
q
u
esti
o
n
s
.
Fig
u
r
e
4
.
Av
e
r
ag
e
p
e
r
ce
n
tag
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o
f
r
ig
h
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n
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wer
s
in
ea
ch
g
r
o
u
p
f
o
r
t
h
e
an
aly
tical
ca
teg
o
r
y
C
o
n
s
id
er
in
g
th
e
f
o
r
m
al
ca
teg
o
r
y
as
s
h
o
wn
in
Fig
u
r
e
5
,
it
was
f
o
u
n
d
th
at
b
o
th
g
r
o
u
p
s
h
ad
th
e
h
ig
h
est
p
er
ce
n
tag
e
o
f
av
er
a
g
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co
r
r
ec
t
an
s
wer
s
in
th
e
c
o
n
ce
p
t
o
f
eq
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iv
alen
t
v
er
b
al
-
ty
p
e,
with
g
r
o
u
p
A
b
ei
n
g
t
h
e
o
n
l
y
o
n
e
th
at
e
x
ce
ed
ed
5
0
%
o
f
c
o
r
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t
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s
wer
s
.
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ly
2
1
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0
5
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f
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r
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t
a
n
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wer
s
wer
e
o
b
t
ain
ed
in
g
r
o
u
p
B
.
R
eg
ar
d
in
g
th
e
d
if
f
er
e
n
t
ca
teg
o
r
ies,
it
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s
h
o
wn
th
at
s
tu
d
en
ts
h
av
e
a
p
r
ed
o
m
in
an
tly
tech
n
ical,
b
y
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te
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d
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m
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tal
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o
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er
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eq
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o
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e
ar
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ilar
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elate
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t
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lev
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g
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p
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ay
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e
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s
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s
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th
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ath
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atics.
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n
e
q
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d
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tio
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eq
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with
two
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n
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wn
s
,
th
e
d
if
f
er
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ce
s
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r
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s
ig
n
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ica
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t
m
ay
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e
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e
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d
if
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e
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en
t
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tu
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ts
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r
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h
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at
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h
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v
e
ch
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s
en
.
0
25
50
75
100
T
C
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S
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N
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%
Techni
cal
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t
e
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ori
e
s
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r
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p
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r
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p
B
0
10
20
30
40
50
AC
A
AC
G
AC
N
AC
V
AS
A
AS
G
AS
N
AS
V
AT
A
AT
G
A
T
N
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V
AE
A
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N
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V
AR
A
AR
G
AR
N
%
A
nal
y
t
i
cal
ca
t
e
g
ori
e
s
G
r
o
u
p
A
G
r
o
u
p
B
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
v
al
&
R
es E
d
u
c
I
SS
N:
2252
-
8
8
2
2
C
o
mp
r
eh
en
s
io
n
o
f lin
ea
r
s
ystems
w
ith
t
w
o
u
n
kn
o
w
n
s
in
s
ec
o
n
d
a
r
y
ed
u
c
a
tio
n
(
Ju
a
n
C
a
r
lo
s
Ma
r
tín
Mo
lin
a
)
3919
Fig
u
r
e
5
.
Av
e
r
ag
e
p
e
r
ce
n
tag
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o
f
r
ig
h
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wer
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r
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p
f
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r
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Fig
u
r
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6
s
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ly
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th
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1
9
task
s
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r
d
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g
t
o
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h
e
ca
teg
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ies
o
f
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n
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o
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ep
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h
e
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o
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ate
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at
th
e
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r
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t
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els
o
f
u
n
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e
r
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h
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elate
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o
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ic
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o
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e
h
ig
h
est
p
er
ce
n
ta
g
e
o
f
c
o
r
r
ec
t
an
s
wer
s
.
T
h
e
h
ig
h
p
e
r
ce
n
tag
e
o
f
co
r
r
ec
t
an
s
wer
s
f
o
r
th
e
s
o
lu
tio
n
s
m
ay
b
e
b
ec
au
s
e
s
tu
d
en
ts
ar
e
m
o
r
e
f
a
m
iliar
with
it
d
u
e
t
o
lear
n
in
g
it
ea
r
lier
wh
en
s
o
lv
i
n
g
e
q
u
atio
n
s
,
wh
ile
f
o
r
th
e
g
eo
m
etr
ic
task
s
,
th
e
v
is
u
al
co
m
p
o
n
e
n
t
m
ay
h
el
p
co
m
p
r
eh
e
n
s
io
n
an
d
m
ak
e
th
e
m
m
o
r
e
in
t
u
itiv
e.
Fig
u
r
e
6
.
Av
e
r
ag
e
p
e
r
ce
n
tag
es
o
f
r
ig
h
t a
n
s
wer
s
in
ea
ch
g
r
o
u
p
f
o
r
all
task
s
B
y
co
m
p
ar
in
g
th
e
f
r
e
q
u
en
cies
o
f
av
er
a
g
e
p
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ce
n
tag
es
o
f
c
o
r
r
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t
r
esp
o
n
s
es
in
ea
ch
g
r
o
u
p
in
th
e
1
9
task
s
ac
co
r
d
in
g
to
th
e
tech
n
ic
al,
an
aly
tical,
an
d
f
o
r
m
al
ca
te
g
o
r
ies,
it
is
s
h
o
wn
th
at
in
th
e
tech
n
ical
task
s
th
e
s
tu
d
en
ts
h
av
e
m
o
r
e
r
ig
h
t
an
s
wer
s
,
with
s
im
ilar
tr
en
d
s
o
f
a
cc
u
r
ac
y
i
n
b
o
th
g
r
o
u
p
s
.
I
n
th
e
tech
n
ical
ca
teg
o
r
y
,
th
e
av
er
a
g
e
p
e
r
ce
n
tag
e
o
f
co
r
r
ec
t
r
esp
o
n
s
es
f
o
r
g
r
o
u
p
A
is
4
9
%,
wh
ile
in
th
e
a
n
aly
tical
ca
teg
o
r
y
it
is
2
5
%,
an
d
in
th
e
f
o
r
m
al
ca
teg
o
r
y
it
i
s
2
3
%.
I
n
co
n
tr
ast,
f
o
r
g
r
o
u
p
B
,
th
e
av
er
a
g
e
p
e
r
ce
n
tag
e
o
f
co
r
r
ec
t
r
esp
o
n
s
es
is
2
4
%,
in
th
e
tech
n
ical
ca
teg
o
r
y
,
3
.
1
%
in
t
h
e
an
aly
tical
ca
te
g
o
r
y
,
an
d
2
.
8
%
in
th
e
f
o
r
m
al
ca
teg
o
r
y
.
Fin
ally
,
wh
en
co
m
p
ar
in
g
t
h
e
av
er
a
g
e
o
f
co
r
r
ec
t
r
esp
o
n
s
es
ac
h
iev
ed
b
y
b
o
th
g
r
o
u
p
s
(
A
an
d
B
)
in
th
e
co
m
p
lete
q
u
esti
o
n
n
air
e,
g
r
o
u
p
A
o
b
tain
ed
b
etter
r
esu
lts
,
b
ec
au
s
e
th
e
y
ac
h
iev
ed
an
av
e
r
ag
e
o
f
3
2
%
co
r
r
ec
t
r
esp
o
n
s
es
f
o
r
th
e
c
o
m
p
lete
q
u
esti
o
n
n
air
e
,
wh
ile
g
r
o
u
p
B
o
b
tain
e
d
an
a
v
er
ag
e
o
f
1
0
% c
o
r
r
ec
t r
esp
o
n
s
es f
o
r
it.
4.
DIS
CU
SS
I
O
N
T
h
e
r
esu
lts
o
b
tain
ed
i
n
d
icate
th
at
s
tu
d
en
ts
’
co
m
p
r
eh
en
s
io
n
o
f
s
y
s
tem
s
o
f
lin
ea
r
e
q
u
atio
n
s
with
two
u
n
k
n
o
wn
s
is
in
g
en
e
r
al
lo
w
an
d
in
s
u
f
f
icien
t
.
E
s
s
en
tially
,
th
ey
h
av
e
a
lim
ited
u
n
d
er
s
ta
n
d
in
g
o
f
c
o
n
ce
p
tu
al
asp
ec
ts
,
an
d
t
h
ey
m
o
s
tly
r
el
y
o
n
in
s
tr
u
m
en
tal,
tec
h
n
ical,
an
d
r
o
te
-
b
ased
asp
ec
ts
.
T
h
i
s
s
itu
atio
n
m
ay
b
e
ass
o
ciate
d
with
a
p
r
ag
m
atic
t
ea
ch
in
g
s
ty
le
em
p
lo
y
ed
b
y
th
e
teac
h
er
s
.
I
n
lin
e
with
th
is
,
J
o
n
s
s
o
n
et
a
l.
[
2
5
]
s
tate
d
th
at
alg
o
r
ith
m
ic
lear
n
i
n
g
in
v
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lv
es
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p
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with
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F
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%
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
5
2
-
8
8
2
2
I
n
t J E
v
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&
R
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u
c
,
Vo
l
.
13
,
No
.
6
,
Dec
em
b
er
2
0
2
4
:
3
9
1
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3920
r
ef
lectio
n
o
n
th
e
m
ea
n
in
g
.
L
ik
ewise,
E
d
m
o
n
d
s
[
2
6
]
p
o
in
ts
o
u
t
th
at
s
tu
d
en
ts
ten
d
t
o
h
av
e
d
if
f
icu
lties
th
in
k
in
g
ab
s
tr
ac
tly
ab
o
u
t
alg
o
r
ith
m
s
.
T
h
e
s
tu
d
en
ts
in
th
e
s
am
p
le
ex
h
ib
it
a
ten
d
e
n
cy
o
f
u
s
in
g
an
d
u
n
d
er
s
tan
d
in
g
alg
eb
r
aic
asp
ec
ts
m
ai
n
ly
f
r
o
m
a
p
r
o
ce
d
u
r
al
p
er
s
p
ec
tiv
e.
Ho
wev
er
,
c
o
n
ce
r
n
i
n
g
f
o
r
m
al
asp
ec
ts
,
th
er
e
is
a
h
ig
h
p
er
ce
n
tag
e
o
f
p
o
s
itiv
e
r
esp
o
n
s
es
r
elate
d
to
alg
eb
r
aic
k
n
o
w
led
g
e
ass
o
ciate
d
with
v
er
b
al
r
ep
r
esen
tatio
n
s
o
f
eq
u
iv
alen
t sy
s
tem
s
o
f
eq
u
atio
n
s
(
FEV)
.
I
n
ter
m
s
o
f
tech
n
ical
th
in
k
in
g
,
p
ar
ticu
lar
ly
with
r
e
g
ar
d
t
o
al
g
eb
r
aic
co
n
ce
p
ts
,
s
tu
d
en
ts
s
h
o
w
a
g
o
o
d
tech
n
ical
k
n
o
wled
g
e
in
g
eo
m
etr
ic
-
ty
p
e
s
y
s
tem
s
(
T
C
G)
,
an
d
th
is
s
im
ilar
ity
ca
n
b
e
o
b
s
er
v
e
d
in
b
o
t
h
a
n
aly
ze
d
g
r
o
u
p
s
.
T
h
e
s
itu
atio
n
is
s
im
ila
r
f
o
r
s
o
lv
in
g
s
y
s
tem
s
o
f
two
lin
ea
r
eq
u
atio
n
s
with
two
u
n
k
n
o
wn
s
(
T
SG)
.
T
h
ese
f
in
d
in
g
s
a
r
e
c
o
n
s
is
ten
t
with
s
tu
d
ies
in
d
icatin
g
th
at
g
eo
m
etr
ic
r
ep
r
esen
tatio
n
p
lay
s
an
im
p
o
r
tan
t
r
o
le
i
n
s
tu
d
en
ts
'
tr
an
s
itio
n
f
r
o
m
r
ec
u
r
s
iv
e
ca
lcu
latio
n
s
to
ex
p
r
ess
in
g
g
en
er
al
f
o
r
m
u
las
[
2
7
]
.
Fu
r
th
er
m
o
r
e,
in
r
ec
en
t
y
ea
r
s
,
th
e
p
r
o
m
o
tio
n
an
d
in
te
g
r
atio
n
o
f
Geo
Ge
b
r
a
s
o
f
twar
e
in
m
ath
em
atics
class
r
o
o
m
s
h
av
e
h
elp
ed
s
tu
d
en
ts
in
ter
n
alize
g
eo
m
etr
ic
r
e
p
r
esen
tatio
n
s
m
o
r
e
f
r
eq
u
en
tly
an
d
as
th
eir
p
r
ef
er
r
e
d
m
o
d
e,
co
m
p
a
r
ed
to
o
th
er
ty
p
es o
f
r
ep
r
esen
tatio
n
s
(
alg
eb
r
aic,
n
u
m
er
ic,
tab
u
lar
,
an
d
v
er
b
al)
[
2
8
]
,
[
2
9
]
.
T
h
e
co
n
ce
p
ts
o
f
alg
eb
r
aic
-
ty
p
e
(
AC
A)
,
n
u
m
er
ical
-
ty
p
e
(
AC
N)
s
y
s
tem
s
,
an
d
t
h
e
s
o
lu
tio
n
s
f
o
r
v
er
b
al
-
ty
p
e
(
ASV)
,
n
u
m
er
ical
-
ty
p
e
(
ASN)
,
an
d
g
e
o
m
etr
ic
-
ty
p
e
(
A
SG)
p
r
esen
t
clea
r
d
i
f
f
er
en
ce
s
b
o
th
am
o
n
g
s
tu
d
en
ts
an
d
b
etwe
en
g
r
o
u
p
s
.
T
h
e
ex
i
s
ten
ce
o
f
s
u
c
h
d
if
f
er
en
ce
s
h
a
s
p
r
ev
io
u
s
ly
b
ee
n
f
o
u
n
d
an
d
h
ig
h
lig
h
ted
in
th
e
s
tu
d
y
b
y
B
ar
b
ier
i
et
a
l.
[
3
0
]
r
eg
ar
d
in
g
th
e
p
r
ed
ictio
n
o
f
p
er
f
o
r
m
a
n
ce
p
r
o
f
iles
in
alg
eb
r
a
am
o
n
g
s
ec
o
n
d
ar
y
ed
u
ca
tio
n
s
tu
d
en
ts
.
W
h
ile
th
e
v
ar
io
u
s
ty
p
es
o
f
er
r
o
r
s
ex
h
ib
ited
b
y
th
e
s
tu
d
en
ts
ar
e
co
n
ce
r
n
in
g
,
th
ey
also
p
r
esen
t
a
g
o
o
d
o
p
p
o
r
tu
n
ity
f
o
r
teac
h
e
r
s
to
attem
p
t
to
d
elv
e
d
ee
p
i
n
to
b
o
th
c
o
n
ce
p
t
u
al
an
d
p
r
o
ce
d
u
r
al
u
n
d
er
s
tan
d
i
n
g
.
Fo
r
in
s
tan
ce
,
Hu
et
a
l.
[
3
1
]
attem
p
ted
t
o
co
n
s
id
er
th
ese
er
r
o
r
s
wh
e
n
s
o
lv
in
g
q
u
ad
r
atic
eq
u
atio
n
s
.
I
n
th
is
r
esp
ec
t,
th
er
e
ar
e
m
a
n
y
p
o
s
s
ib
ilit
ies
th
an
ca
n
b
e
co
n
s
id
er
e
d
wh
en
teac
h
in
g
alg
eb
r
a
d
u
r
in
g
s
ec
o
n
d
ar
y
e
d
u
ca
tio
n
.
Fo
r
ex
a
m
p
le,
J
im
én
ez
et
a
l.
[
3
2
]
p
r
o
p
o
s
e
d
th
e
ap
p
licatio
n
o
f
th
e
ed
u
ca
tio
n
al
escap
e
r
o
o
m
an
d
b
r
ea
k
o
u
t
f
o
r
lear
n
i
n
g
alg
eb
r
a
in
t
h
e
th
ir
d
co
u
r
s
e
o
f
s
ec
o
n
d
ar
y
ed
u
ca
tio
n
;
wh
ile
B
o
k
h
o
v
e
an
d
Dr
ijv
er
s
[
3
3
]
ev
al
u
ate
d
th
e
d
i
g
ital
to
o
ls
,
wh
ich
ar
e
u
s
ef
u
l
f
o
r
alg
eb
r
a
e
d
u
ca
tio
n
.
L
astl
y
,
Ho
u
g
h
et
a
l.
[
3
4
]
co
n
s
id
er
ed
th
e
p
o
s
s
ib
ilit
ies o
f
u
s
in
g
co
n
ce
p
t m
ap
s
to
ass
ess
t
ea
ch
er
s
’
g
r
o
wth
in
u
n
d
er
s
tan
d
in
g
o
f
al
g
eb
r
a.
5.
CO
NCLU
SI
O
N
R
esu
lts
o
b
tain
ed
f
r
o
m
o
u
r
s
a
m
p
le
s
h
o
w
th
at
th
e
m
at
h
em
at
ical
k
n
o
wled
g
e
o
f
s
y
s
tem
s
o
f
two
lin
ea
r
eq
u
atio
n
s
with
two
u
n
k
n
o
w
n
s
f
o
r
th
ese
4
th
y
ea
r
s
ec
o
n
d
a
r
y
s
ch
o
o
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1
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m
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c
a
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tac
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m
a
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:
m
a
riab
a
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t6
1
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m
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c
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.
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