الامتحان-الوطني-في-الرياضيات-2017-الدورة-الاستدراكية-شعبة-العلوم-التجريبية

3 1
P a g e
3
2017
  - 
RS 22
- 
- 
- . 
-  
2.5
8.5

3 2
3
 2017
-
RS22
, , ,O i j k
()S
2 2 2 2 2 2 1 0x y z x y z      
()P
0yz
0.51
()S
1 , 1 , 1
2
0.5
,dP
()P
()S
C
0.5
C
2
()
1 , 2 , 2A
()P
0.25
0 , 1 , 1u
()
0.75
2A u u  
()
()S
0.5
()
()S
10
1.51
A
B
8
() 15 pA
19
() 70 pB
2
X
0.5
2
( 2) 15 pX
1  
X
EX
4
5
0.751
24 8 0zz  
2
,,O u v
A
B
C
a
b
c
22ai  
44bi
48ci
0.5
z
M
z
M
M
R
A
2
4z iz
0.75 
B
C
R
ABC
3
BC
0.5
6c
0.5
M
z
6z
ABC
R
V
B
R
R
B
V
B
B
B

3 3
3
 2017
-
RS22
2-1-2-3-4
-1
-2
0 1
1
x
y
2-1-2-3-4
-1
-2
0 1
1
x
y
n
u
017u
1112
4
nn
uu
n
IN
0.51
16
n
u
n
IN
0.5
n
u
n
u
2
n
v
16
nn
vu
n
IN
0.5
n
v
0.5
1
16 4
n
n
u
n
IN
n
u
0.5
n
16,0001
n
u
I
g
IR
2
( ) 1 ( 1) x g x x e  
0.251
( 0 ) 0g
12
g
C
g
( ) 0gx
x
,0
( ) 0gx
x
0,
II
f
IR
2
( ) 1 1 x f x x x e   
f
C
f
,,O i j
(
2cm
)
0.751
2
2
( ) 1 4 2
xx
x
f x x e e
x
IR
lim ( )
xfx
0.5
lim ( ) 1
xf x x
D
1yx
f
C
0.25
f
C
D
0.5 2
lim ( )
xfx
(
()fx
11
1x x x e
xx
)
0.25 
f
C
0.753
( ) ( )f x g x
x
IR
0.75
f
,0
0,
f
IR
0.75
f
C
3
1
14
,,O i j
D
f
C
(
3 2,5f  
1 0,75f  
)
505
:1
x
H x x e
:x h x xe
IR
0
1
21
x
xe dx e
0.75
02
1
2
1 3 1
x
x e dx e
0.5
2
cm
f
C
D
1x
g
C

 م ا
طا نا ارا 2017
5/17
ﺢﻴﺤﺼﺘلوﻷا نﻴرﻤﺘﻝا
1( أ- : ﺎﻨﻴدﻝ
( ) ( )
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
2 2 2
2 2 2
2 2 2 2 2 2
2 2 2
2 2 2
2 2 2 2
, , 2 2 2 1 0
2 2 2 1
2 1 1 2 1 1 2 1 1 1 1 1 1
1 1 1 4
1 1 1 2
M x y z S x y z x y z
x x y y z z
x x y y z z
x y z
x y z
∈ ⇔ + + − − − − =
⇔ − + − + − =
⇔ − + + − + + − + = + + +
⇔ − + − + − =
⇔ − + − + − =
نذإ
( )
S ﺎﻫزﻜرﻤ ﻲﺘﻝا ﺔﻜﻠﻔﻝا ﻲﻫ
( )
1,1,1Ω ﺎﻬﻋﺎﻌﺸ و
2R=
ب-
( )
( )
( ) ( )
( ) ( ) ( )
222
1 1
, 0
0 1 1
d P − Ω = =
+ +
 نأ ﺎﻤﺒ
( )
( )
,d P RΩ < نﺈﻓ
( )
P ﺔﻜﻠﻔﻝا ﻊطﻘﻴ
( )
S ةرﺌاد قﻓو
( )
C
ج - نأ ﺎﻤﺒ
( )
( )
, 0d PΩ = نﺈﻓ
( )
P
ﺔﻜﻠﻔﻝا ﻊطﻘﻴ
( )
S
ةرﺌاد قﻓو
( )
C
( ىرﺒﻜﻝا ةرﺌادﻝا )
ةرﺌادﻝا زﻜرﻤ ﻪﻨﻤ و
( )
C
ﺔطﻘﻨﻝا وﻫ
( )
1,1,1Ω
وﻫ ﺎﻬﻋﺎﻌﺸ و2.
ىوﺘﺴﻤﻝا ﻰﻠﻋ ﺔﻜﻠﻔﻝا زﻜرﻤﻝ يدوﻤﻌﻝا طﻘﺴﻤﻝا وﻫ ةرﺌادﻝا زﻜرﻤ )
( )
P ﺎﺤﻝا ﻩذﻫ ﻲﻓ يأ ﺔطﻘﻨﻝا وﻫ ﺔﻝ
Ω
ﺎﻬﻋﺎﻌﺸ و
( )
( )
2 2 2 2
, 2 0 2r R d P= − Ω = − =(
2( أ- ﺎﻨﻴدﻝ0y z− = ىوﺘﺴﻤﻠﻝ ﺔﻴﺘرﺎﻜﻴد ﺔﻝدﺎﻌﻤ ﻲﻫ
( )
P نذإ
( )
0,1, 1u− ىوﺘﺴﻤﻠﻝ ﺔﻴﻤظﻨﻤ ﺔﻬﺠﺘﻤ ﻲﻫ
( )
P
نأ ﺎﻤﺒ و
( ) ( )
P∆ ⊥ نﺈﻓ
( )
0,1, 1u− مﻴﻘﺘﺴﻤﻠﻝ ﺔﻬﺠوﻤ ﺔﻬﺠﺘﻤ
( )
∆
ب-
 : ﺎﻨﻴدﻝ
( )
0,1, 1u− و
( )
0, 3,1AΩ −
نذإ
3 1 0 0 0 0 2.
1 1 1 1 3 1
A u i j k i
−
Ω ∧ = − + =
− − −
ﻪﻨﻤ و
2A uΩ ∧ =

 م ا
طا نا ارا 2017
6/17
: ﺎﻨﻴدﻝ و
( ) ( ) ( )
2 2 2
0 1 1 2u= + + − =
: ﻲﻝﺎﺘﻝﺎﺒ و
2A u uΩ ∧ =
 : ﺎﻨﻴدﻝ
( )
( )
, 2
A u
du
Ω ∧
Ω ∆ = =
نأ ﺎﻤﺒ نذإ
( )
( )
,d RΩ ∆ < مﻴﻘﺘﺴﻤﻝا نﺈﻓ
( )
∆ ﺔﻜﻠﻔﻝا ﻊطﻘﻴ
( )
S نﻴﺘطﻘﻨ ﻲﻓ
ج - مﻴﻘﺘﺴﻤﻠﻝ يرﺘﻤرﺎﺒ لﻴﺜﻤﺘ
( )
∆ : وﻫ
( )
1
2
2
x
y t t
z t
=
= − + ∈
= −
ℝ
مﻴﻘﺘﺴﻤﻝا ﻊطﺎﻘﺘ ﻲﺘطﻘﻨ نﻤ ﺔطﻘﻨ لﻜ تﺎﻴﺜادﺤإ ثوﻠﺜﻤ ددﺤﻨﻝ
( )
∆ ﺔﻜﻠﻔﻝا و
( )
S
( ) ( ) ( ) ( )
( ) ( ) ( )
2 2 2 2
1
2
, , 2
1 1 1 2
x
y t t
M x y z S z t
x y z
=
= − + ∈
∈ ∆ ∩ ⇔ = −
− + − + − =
ℝ
ﺔﻝدﺎﻌﻤﻝا ﻰﻠﻋ لﺼﺤﻨ ضﻴوﻌﺘﻝا دﻌﺒ
2
4 3 0t t− + =
: ﺎﻨﻴدﻝ
4∆ =
: نذإ 3t= وأ 1t=
1t= :
1
2 1 1
2 1 1
x
y
z
=
= − + = −
= − =
3t= :
1
2 3 1
2 3 1
x
y
z
=
= − + =
= − = −