2. ‫الرياضيات‬‫ملبحث‬
‫إشـراف‬

4. ١
_ ^ b ]_ ^ b ]_ ^ b ]_ ^ b ]
^ ]^ ]^ ]^ ]////^^^^
............. =
(1−(((1−
.............. =
((–((
٣,16−X25−.............. =
((((
.36−=
((+ ((6
.+=‫ه‬ ‫آـ‬
(((±(
.=3
((‫آ‬ ‫ا‬ ‫اد‬ ‫ا‬((
.+=+)(=
) (() (1() (() ((
.)(–)+........... = (
(((+(+
.–
((
((
.=++==.......
((((
.=3
(–+3(3(+3(3–
.=++..... =
((((
٤‫ن‬+٣

5. ٢
.=+......... =
(+(+
((
.
(+3
2 (+3
(+(+
3
2

............. =
(ω(ω(ω(ω
.
()+(()(
()+(()(
.=33........ =
(((+3(+3
.=..... =
((t((
(=+–+
(+++
(
+=+=
+==
١+ω
t
٣t
٣
t
٣
t
٣
t
٢
٣t
٢
١-٥‫ت‬+٣‫ت‬٢
-٣‫ت‬٣
٣
٥
٤
٢٥
٣
٥
٤
٥
٣
٢٥
٤
٥
٣
٢٥
١
٢
٤
٢٥
١
٢
٣
٢
١
٢
١
٢
t
٣
t
٣
t
٣t
٣
t
٣

6. ٣
(:
•++–=+
•+––=
•+)+= ()+(
•)++ ()(=+
(:
•)) + ((–)–(
•)2(–)3) + (2+(
•)) + ((–)+(–)–(
•)) ((
•)() ++(
•)) () ((
•)854−) (1824−(
•)(
•
•
() =+) (–(
(
(==
(J=
(++
(=
(
=3=+
٢-٥‫ت‬
٢-‫ت‬
)٢+‫ت‬) (٣+‫ت‬(
)٢–‫ت‬) (٣–‫ت‬(
٤-٥‫ت‬
٧‫ت‬
٧–‫ت‬
٢-‫ت‬
١٣-‫ت‬
٤+‫ت‬
١

7. ٤
==
2
5
(( )=
(:
===
=3=3=2+2
(
=3==3–
=
(:
=)+(=)+(
=+=3)+(
()(+–+=
(
=+=+=
(3
()+(=
(+( ) =1
(=
(:)ω+ω–ω()–ωω(
() =+ω(J
(+ω
١-١
١+٢ω١+٢ω٢
-٤
٣
١
-3+‫ت‬
١
-3-‫ت‬
٩-‫ت‬
١+‫ت‬
٢
٣
٢
٥t
٦
t
٣
t
٣
t
٢
t
٢
٥t
٦
١
٢
٣٦–٢‫ت‬
٣+٢‫ت‬
١+٤3
١-٤3

8. ٥
::
.144−....... =
((((
.. =............
((((
.=–.............
(+(–(+(
.–) =–(:
((
26
3
((
.=–:
(
4

(
3
4

(
7
4

(
5
4

................... =
((ω(ω(ω
.)–(–)+ (=.................
(–(+(+(–
.=+...................... =
(–(–(
2
5
+
1
5
(
2
5
1
5
.=J:
(}±{(}±{(}±±{(}{
٥–٣ω٢
٥ω-٣

9. ٦
.ω:
(±ω(±ω(±ω(ωω
:
(=+=–:
(+(÷
()(+–+=
:
(= +
(=–3
:
(
(=+.
:
(=)–(
(
++=
١
٤+٣ω+٢2
ω
١
٥+٣ω+٤2
ω
-١+3‫ت‬
٢
١
ω٢
+١
١
ω+١

10. ٧
١(‫م‬ ‫ا‬ ‫ا‬)‫ــ‬#،١‫ــ‬ ،٣،( ................‫ه‬:
‫أ‬(٤‫ــ‬ ‫ن‬٧‫ب‬(‫ــ‬)#(‫ن‬
‫ـ‬(‫ــ‬#)‫ــ‬٣(‫ــ‬ ‫ن‬١
‫د‬(‫ــ‬#+٣)‫ــ‬ ‫ن‬١(
٢(‫م‬ ‫ا‬ ‫ا‬)‫ــ‬٥‫ــ‬ ،١،٣،٧،( ..............‫ه‬:
‫أ‬(‫ــ‬)٤‫ن‬+٥(‫ب‬(٤‫ــ‬ ‫ن‬٩‫ـ‬(‫ــ‬ ‫ن‬٥‫د‬(٤‫ن‬
٣(‫ا‬ ‫ا‬)٨،١١،١٤،١٧،( ...........‫ه‬:
‫أ‬(٣‫ن‬+٥‫ب‬(٢‫ن‬+٧‫ـ‬(٦‫ن‬+٢‫د‬(٨‫ــ‬ ‫ن‬٥
٤(‫ــ‬ ‫م‬ ‫ا‬ ‫ا‬٢،٣،٨،١٣،...........‫ه‬
‫أ‬(‫ــ‬٢)+‫ن‬+١(×٥‫ب‬(‫ــ‬٢)+‫ــ‬ ‫ن‬١(×٥‫ـ‬(‫ــ‬٢+٥‫د‬ ‫ن‬(‫ــ‬٢‫ــ‬٥‫ن‬
٥(‫ا‬ ‫ع‬)‫ــ‬ ‫ر‬١(‫وي‬:
‫أ‬(١‫ب‬(٣‫ـ‬(١٠‫د‬(١١
٦(‫ا‬ ‫ع‬)٣‫ر‬+٢= (
‫أ‬(٢٥‫ب‬(٢٦‫ـ‬(١٢٠‫د‬(١٢٤
٧(‫ا‬ ‫ع‬)٢‫ــ‬ ‫ر‬١= (
‫أ‬(١٥‫ب‬(٢٥‫ـ‬(٣٥‫د‬(٤٥
٨($)‫ــ‬٢(‫ر‬+١
=
‫أ‬(٣‫ــ‬ ،٦،١٢‫ــ‬ ،٢٤،٤٨‫ب‬(‫ــ‬@+٣‫ــ‬@+٦‫ــ‬@
‫ـ‬(٣+٦+١٢+٢٤+٤٨‫د‬(٣‫ــ‬٦+١٢‫ــ‬٢٤+٤٨
٩(‫د‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ط‬ ‫و‬ ‫ا‬٧،٢٧‫ه‬:
‫أ‬(١٢،١٦،٢٠‫ب‬(١١،١٦،٢١‫ـ‬(١١،١٥،١٩‫د‬(١٢،١٧،٢٢
١٠(‫ا‬ ‫آ‬ ‫إذا‬)٦،٩،١٢،........( .......‫ح‬ ‫ن‬١٢=
‫أ‬(٣٦‫ب‬(٣٩‫ـ‬(٤٢‫د‬(٤٥
١١(‫أي‬:
‫أ‬(٨،٣‫ــ‬ ،٢‫ــ‬ ،٥،...................‫ب‬(٢،٤،٨،١٦،.................
‫ـ‬(‫ــ‬٢،٠،٢،٤،..................‫د‬(‫ــ‬١‫ــ‬ ،٥‫ــ‬ ،٩‫ــ‬ ،١٢،...........
٥
‫ر‬=١
٨
‫ر‬=١
٥
‫ر‬=١
٥
‫ر‬=١

11. ٨
١٢(‫ا‬)١٠٠،٩٨،٩٦،( ........‫ح‬ ‫ن‬ ‫آ‬ ‫إذا‬‫ن‬=١٠٢‫ــ‬٢‫أول‬ ‫ر‬ ‫ن‬ ‫ن‬
‫ه‬:
‫أ‬(٥٠‫ب‬(٥٢‫ـ‬(٥٣‫د‬(٥١
١٣(‫و‬٥‫ــ‬ ‫د‬ ‫ا‬ ‫ط‬ ‫أو‬١٢،١١٤‫ا‬ ‫ود‬ ‫د‬ ‫ن‬:
‫أ‬(٧‫ب‬(٦‫ـ‬(٥‫د‬(٨
١٤(‫ر‬ ‫ي‬ ‫ا‬ ‫آ‬ ‫ر‬ ‫أ‬٤٨٠٠‫ن‬ ‫وآ‬ ‫ر‬ ‫د‬‫ره‬ ‫وة‬
١٨٠‫ي‬ ‫ا‬ ‫را‬ ‫ن‬ ‫ر‬ ‫د‬١٥:
‫أ‬(٧٥٠٠‫ب‬ ‫ر‬ ‫د‬(٧٣٢٠‫ـ‬ ‫ر‬ ‫د‬(٧٣٠٠‫د‬ ‫ر‬ ‫د‬(٧٣٥٠‫ر‬ ‫د‬
١٥(‫ح‬ ‫ا‬ ‫ا‬‫ن‬‫ح‬ ‫ن‬ ‫ا‬٤+‫ح‬١٢}
‫أ‬(٢‫ح‬٨‫ب‬(‫ح‬٢+‫ح‬١٤‫ـ‬(‫ح‬٣+‫ح‬١٤‫د‬(‫ح‬١+‫ح‬١٥
١٦(‫د‬ ‫ا‬ ‫ط‬ ‫أو‬ ‫أر‬ ‫أد‬ ‫إذا‬٥،١٥‫ه‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ن‬:
‫أ‬(٥‫ب‬(٧‫ـ‬(٩‫د‬(١١
١٧(‫إذ‬‫ح‬ ‫ن‬ ‫آ‬ ‫ا‬١=٣‫ح‬ ،٧=١٥‫ح‬ ‫ن‬ ،٤=
‫أ‬(٩‫ب‬(١٢‫ـ‬(١٨‫د‬(٤٥
١٨(‫ح‬‫ن‬‫ح‬ ‫ن‬ ‫آ‬ ‫إذا‬‫ن‬‫ــ‬٤=‫ح‬‫ن‬+٢‫ن‬g+‫أ‬ ‫ن‬=
‫أ‬(‫ــ‬٤‫ب‬(‫ــ‬٢‫ـ‬(٢‫د‬(٤
١٩(‫ن‬ ‫ـ‬ ‫ن‬ ‫آ‬ ‫إذا‬=٢‫ن‬٢
‫ــ‬٧‫ا‬ ‫ر‬ ‫ن‬ ‫و‬ ‫ا‬ ً‫ا‬ ‫ن‬ ‫ع‬ ‫ن‬
‫ي‬ ‫ا‬١٩‫ه‬:
‫أ‬(٦٧‫ب‬(٨‫ـ‬(٧‫د‬(٦
٢٠(‫و‬ ‫ا‬ ‫ا‬ ‫وده‬ ‫ع‬٢٧‫ه‬ ‫ا‬ ‫ه‬ ‫ا‬ ‫ا‬ ‫ن‬ ،:
‫أ‬(٣‫ب‬(٦‫ـ‬(٩‫د‬(٢٧
٢١(‫و‬ ‫ا‬ ً‫ا‬ ‫ن‬ ‫ع‬ ‫ن‬ ‫آ‬ ‫إذا‬=‫ن‬٢
+٢‫ا‬ ‫ه‬ ‫ن‬ ، ‫ن‬=
‫أ‬(١١‫ب‬(٨‫ـ‬(٥‫د‬(٣
٢٢(‫ا‬)٣،١،#،( .........‫ه‬:
‫أ‬(‫ب‬(‫ـ‬ ‫ه‬(‫د‬ ‫ه‬ ‫و‬(
٢٣(‫ح‬٦‫ا‬) :١،٣،٩،( ...........‫ه‬
‫أ‬((& @‫ب‬(٣٤٢‫ـ‬(٢٤٣‫د‬(٧٢٩

12. ٩
٢٤(‫د‬ ‫ا‬ ‫ا‬ ‫ا‬٩،٢٥‫ه‬:
‫أ‬(١٧‫ب‬(١٥‫ـ‬(٣٤‫د‬(٢٢٥
٢٥(‫ا‬)‫ــ‬٣،١،٥،( .......
‫أ‬(‫ــ‬ ‫أ‬٢‫ب‬(‫أ‬٤
‫ـ‬(‫ــ‬ ‫أ‬ ‫ه‬#‫د‬(‫أ‬ ‫ه‬٥
٢٦(‫ح‬ ، ‫وده‬ ‫ه‬٢=٦‫ح‬ ،٤=٢٤‫ح‬ ‫ن‬ ،٦=
‫أ‬(٣٠‫ب‬(٦٤‫ـ‬(٩٦‫د‬(١٩٢
٢٧(‫ه‬.‫ح‬٣=١٢‫ح‬ ،٥=٤٨‫أ‬ ‫ن‬ ،=
‫أ‬(‫ــ‬١٢‫ب‬(٢‫ـ‬(٣‫د‬(١٢
٢٨(‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫أ‬ ‫أول‬ ‫ر‬
)١٠٢٤،٥١٢،٢٥٦،١٢٨،( ...‫ه‬
‫أ‬(١٠‫ب‬(١١‫ـ‬(١٢‫د‬(١٣
٢٩(‫ي‬ ‫ا‬ ‫أ‬ ‫إذا‬٣٦٠‫ا‬ ‫ه‬ ‫ا‬ ‫و‬ ‫ر‬ ‫د‬‫ل‬ ‫آ‬ ‫ا‬)@‫ن‬ ‫آ‬
‫ن‬ ‫ا‬ ‫ا‬١١:
‫أ‬(٢٨٦ ٥‫ب‬(٨٦٥ ٥‫ـ‬(٥٨٦ ٥‫د‬(٦٨٥ ٥
٣٠(‫آ‬ ‫إذا‬)٢٤،................،٦(‫وده‬ ‫د‬ ‫و‬ ‫أ‬ ‫ه‬‫دي‬
‫ه‬ ‫و‬ ‫ا‬ ‫ه‬ ‫ن‬:
‫أ‬(١٥‫ب‬(‫ــ‬١٥‫ـ‬(١٢‫د‬(‫ــ‬١٢
٣١(‫آ‬ ‫إذا‬$، ‫ص‬ ،١٢‫ص‬ ‫ن‬ ‫وده‬ ‫ه‬=
‫أ‬(٣‫ب‬(٤‫ـ‬(٦‫د‬(٩
٣٢(‫ود‬ ‫ا‬ ‫ع‬ ، ‫ا‬ ‫ا‬ ً‫ء‬‫ا‬ ‫ا‬:٢،٤،٨،١٦،.......‫وي‬
‫أ‬(٥١٠‫ب‬(٨١٦٠‫ـ‬(١٢٧٥‫د‬(٨١٩١
٣٣(‫ا‬ ً‫ا‬ ‫ن‬ ‫ع‬ ‫ن‬ ‫آ‬ ‫إذا‬‫ـ‬ ‫ه‬ ‫و‬‫ن‬=٢‫ن‬+٢
‫ــ‬٤‫ن‬
‫ح‬٥=
‫أ‬(٣٢‫ب‬(١٢٨‫ـ‬(١٦‫د‬(٦٤
٣٤(‫ح‬ ‫ن‬ ‫آ‬ ‫إذا‬ ‫ه‬٢=٢‫ح‬ ،٥=١٦‫ه‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ود‬ ‫ا‬ ‫ع‬ ‫ن‬ ،:
‫أ‬(٦٣‫ب‬(٦٤‫ـ‬(٣١‫د‬(٣٢

13. ١٠
٣٥(‫ا‬ ‫ع‬)#(‫ــ‬ ‫ن‬١
=
‫أ‬(١‫ب‬(٢‫ـ‬(٣‫د‬(
٣٦(‫ا‬ ‫ع‬)$(‫ن‬
=
‫أ‬(#‫ب‬(٧‫ـ‬(‫د‬ ‫ع‬(٣
.==.
.
.
=+=.
.
.
.=
.:
=
.:
==
.
.
.
.
.
.
.
‫ر‬=١
‫ر‬=١

14. ١١
.
.
.),(.......
:
.
١
٥
==
١
١٢٥
.
.:
)+) (+(12<
.
==
.
.
=
.+++ ..... +∞=
1
10
.
.
.
.=
.
.)
٣
٥(
.
.
.
.%
,,,

15. ١٢
.
١
٢
٣
٤
.
bbbb]]]]^^^^
‫ول‬ ‫ا‬ ‫ال‬ ‫ا‬:
.‫ا‬‫ا‬ ‫ا‬:
.+–=____________
((–((±
.‫م‬ ‫ا‬ ‫ا‬:١،........____________
((((
.++ .........+__________
((((
._________
((((
.___________
((((
............
٤٩١٦
٢‫ن‬
٢‫ن‬
‫ـــ‬
‫ن‬
٩٩٩٩٠١٩
‫ـ‬+٢‫ب‬-‫أ‬
‫ـ‬‫ـ‬
‫ـ‬ ‫أ‬
‫ن‬٢

16. ١٣
.
.
:
.)√()X(:
.( ).......
.( )
.( )
.( ))= (
.( )±
.
.
‫ا‬ ‫ال‬ ‫ا‬:
().(......
(
(‫ا‬ ‫اء‬ ‫ا‬ ‫ام‬ ‫ا‬ ‫رة‬ ‫ا‬ ‫أ‬"٤‫ن‬
–١‫ا‬٣"HHHHáááá****
‫ح‬ ‫وا‬ ‫ق‬ ‫ا‬ ‫وام‬،،،
٤٢
٢
٥‫ن‬+١
٧
‫ر‬=٥
٤

17. ١٤
::
.+++=____________
((((
.=+:__________
(ππππ(ππππ(ππππ(
.=____________
(ωωωω(ωωωω((
............___________
((((
.
××××××××××××××××= ...........≠≠≠≠=__________
((((
.==:__________
((((
‫ا‬ ‫ال‬ ‫ا‬:
(+=+
(+
()ωωωω+(=
٢ ٢
٤٢
١+ω
٢٤ ٣٥
‫ن‬+٢‫ن‬-١‫ن‬-٢‫ن‬+١
٢٢
ωωωω١+ωωωω
١
٢
١
٤
١
٨

18. ١٥
‫ا‬ ‫ال‬ ‫ا‬:
‫أ‬.++.........+
‫ب‬.=
‫ج‬.:
+++ ......... +=)+(*
‫ح‬ ‫وا‬ ‫ق‬ ‫ا‬ ‫وام‬،،،
٢

19. ١٦
/
(
:
(
(
(.
(
%
(
%
(
:

20. ١٧
(
:
(
:
(:
%
%
%

21. ١٨
(
=%
(
=%
%
%
%
(:
%%
%=,
=,=,
)(
%
%
%

22. ١٩
::
(
%
............................
(,(((.
(%
)(.....
(%(%((.
(
.........
(%(%(%(
(%
(%(%(%(
**
(...
(%(%(%(%
(..
(%(%(%(%

23. ٢٠
(
((
((.
(
...
((
((
::
:
(
(
(
(
:
%
%%
::

24. ٢١
:
%
%
%

25. ٢٢
:
::
(.
(:
(.
(.
(:
(
(.
(
.
(
.
(:)()(!!
(= !). (
()= ()+! (
(
!(1 k)
!(1 k)
+
−
=+.
()
1
2
= ! ()(
()= ()–()+! (
()(<)()(
.
()(
.

26. ٢٣
(:( )9
3( )8
0( )40
40( )100
99.
(( )5
0+( )5
1+( )5
2+( )5
3+( )5
4+( )5
5=.
(
.
(( )75
v4=( )75
5 v3+/.
(( )11
s3=( )2
11
7 s−
/.
(( )k
9=( )k
11( )k
18.
(( )k
3=k
()= (( )k
v=
(( )k
3:( )1 k
4
−
=
8
5
/
(( )16
5 v+=( )16
10 v2−/

27. ٢٤
::
()+(.
()
s
2
3
s
(.
(),()(
()–(
()+
1
s
(
()
2
s3
(
(++
6
1 2
7

+ ........... +=/.
()+
w
2
(
()+s2(
()
2
‫س‬
2
4
‫س‬
(
()+
2
s3
(
/
()+(
()+
1
s
(
()
s
3
3
s2
(
()
‫س‬
‫ص‬(
w s
( )
s w
+

28. ٢٥
(2
1
( s2)
s
−
(
9 33
( s2)
s
−
(
21 23
( s2)
s
−
)+
1
‫س‬
(
()
1
‫س‬
(
()+(:
/
::
(
.
(.(
(
:
:
(.
(.
(.
(.
(
.:
(
(

29. ٢٦
()= (
1
2
)= (
3
8
)Y= (
1
4
:
()(()(()(()Y.(
(.
.:
(
(
:
(.
(
::
(
(
(
()= (,)= (,)Y= (,:
()/(()/(()/(()/. (
()= (,)= (,)(
:(.().(
(:)= (,
)= (,.)–. (

30. ٢٧
(,
,:
((
(
()= (,)= (,
)= (,.
(
:
=.
:
١(‫ج‬ ‫أ‬ ‫اب‬ ‫أ‬ ‫ث‬ ‫وج‬ ‫وا‬ ‫ل‬ ‫ا‬ ‫ا‬ ‫ق‬ ‫ا‬ ‫د‬
‫ه‬ ‫د‬ ‫ي‬ ‫ا‬ ‫ب‬ ‫ا‬
‫أ‬(٣‫ب‬(٦‫ـ‬(٩‫د‬(١٢
٢(‫ا‬ ‫ام‬ ‫ر‬ ‫ن‬ ‫د‬
}١،٣،٤،٦{‫؟‬
‫أ‬(٤‫ب‬(٦‫ـ‬(١٢‫د‬(٣٤
٣(‫ا‬ ‫ا‬ ‫ر‬ ‫ا‬ ‫اد‬ ‫ا‬}٢،٤،٥،٧{‫إذا‬
‫ه‬ ‫ده‬ ، ‫ا‬ ‫ا‬ ‫د‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ار‬:
‫أ‬(٤‫ب‬(٩‫ـ‬(١٢‫د‬(١٦
٤(‫ل‬)‫ن‬،٩= (
‫أ‬(‫ب‬(‫ـ‬(‫د‬(
٥(٠!×٣= !
‫أ‬(‫ب‬(٣‫ـ‬(٦‫د‬(٩
٦(‫ل‬ ‫ن‬ ‫آ‬ ‫إذا‬)١٤‫ر‬ ،= (١٤×١٣×١٢‫ن‬‫ر‬=
‫أ‬(١٤‫ب‬(١٣‫ـ‬(١٢‫د‬(٣
٧(‫ل‬ ‫ن‬ ‫آ‬ ‫إذا‬)‫ن‬ ، ‫ن‬= (٦‫ن‬ ‫ن‬ ،=
!
!
!
!)‫ــ‬ ‫ن‬٩!(
!
)‫ــ‬ ‫ن‬٩!(
!
)‫ــ‬ ‫ن‬٩!(

31. ٢٨
‫أ‬(١‫ب‬(٢‫ـ‬(٣‫د‬(٦
٨(‫س‬‫وا‬ ‫ا‬ ‫آ‬ ‫ب‬
‫؟‬ ‫ة‬ ‫وا‬ ‫ا‬
‫أ‬(٢٠‫ب‬(٦٠‫ـ‬(٩٠‫د‬(١٢٠
٩(‫ن‬ ‫ن‬ ‫آ‬ ‫إذا‬= !٢٤‫ن‬ ‫ن‬=
‫أ‬(٦‫ب‬(٤‫ـ‬(١٢‫د‬(٨
١٠= (
‫أ‬(١٥‫ب‬(٢٠‫ـ‬(٢‫د‬(٦٠
١١(٥٦×٦= !
‫أ‬(٧!‫ب‬(٨!‫ـ‬(٩!‫د‬(١٠!
١٢(٦٠×٢= !
‫أ‬(٥!‫ب‬(٦!‫ـ‬(٧!‫د‬(٨!
١٣(‫آ‬ ‫إذا‬)٢‫ــ‬ ‫ن‬٣= ! (١‫ن‬ ‫ن‬ ،=
‫أ‬(‫ب‬(١‫ـ‬(٢‫د‬(٣
١٤(‫ل‬ ‫ن‬ ‫آ‬ ‫إذا‬)٧‫ر‬ ،(=‫ر‬ ‫ن‬ ،=
‫أ‬(١‫ب‬(٢‫ـ‬(٦‫د‬(٧
١٥(‫ن‬ ‫آ‬ ‫إذا‬=‫ر‬ ‫ن‬ ،=
‫أ‬(‫ب‬(٤‫ـ‬(٥‫د‬(٨
١٦(‫وي‬ ‫ب‬ ‫ب‬ ‫ث‬ ‫ر‬ ‫ا‬ ‫ق‬ ‫د‬:
‫أ‬(‫ب‬(‫ـ‬(‫د‬(
١٧(×٣= !
‫أ‬(‫ب‬(‫ل‬)٧،٣(‫ـ‬(×٣‫د‬(٧×٣!
+
!
!
!
!
!
×!
!
!
!
!×!
!
!

32. ٢٩
١٨(+‫ل‬)٥،٠= (
‫أ‬(٩‫ب‬(١٠‫ـ‬(٥‫د‬(١١
١٩(‫ن‬ ‫آ‬ ‫إذا‬:=‫ن‬ ‫ن‬=
‫أ‬(٢٠‫ب‬(٤‫ـ‬(١٢‫د‬(٦٤
٢٠(٥‫؟‬ ‫ب‬
‫أ‬(٥‫ب‬(٧‫ـ‬(٨‫د‬(١٠
٢١(‫ن‬ ‫آ‬ ‫إذا‬:=٣٥‫ن‬ ‫ن‬ ،=
‫أ‬(٥‫ب‬(٦‫ـ‬(٧‫د‬(٣٢
٢٢(‫آ‬ ‫إذا‬:=‫ر‬ ‫ن‬ ،=
‫أ‬(٣‫أو‬٤‫ب‬(٣‫أو‬٧‫ـ‬(٤‫أو‬٧‫د‬(٣‫أو‬١٠
٢٣(‫آ‬ ‫إذا‬:=١‫ر‬ ‫ن‬ ،=
‫أ‬(‫ب‬(١‫ـ‬(٥‫د‬(‫أو‬٥
٢٤(‫ك‬ ‫ا‬ ‫ا‬)٣‫ــ‬ ‫س‬٢‫ص‬(٧
‫ه‬:
‫أ‬(‫س‬٧
‫ب‬(‫ص‬٧
‫ـ‬) (‫ــ‬٣‫س‬(٧
‫د‬) (‫ــ‬٢‫ص‬(٧
٢٥(‫ار‬ ‫ا‬ ‫ك‬ ‫ود‬ ‫د‬)‫أ‬+٢‫ب‬(٦
‫ه‬:
‫أ‬(٥‫ب‬(٦‫ـ‬(٧‫د‬(٨
٢٦(‫ك‬ ‫ا‬ ‫ا‬)‫ب‬ ‫ــ‬ ‫أ‬(٤
‫ه‬:
‫أ‬(٦‫ب‬(٤‫ـ‬(‫ــ‬٤‫د‬(‫ــ‬٦
٢٧(‫ن‬ ‫آ‬ ‫إذا‬)١٢(٧
‫ك‬ ‫أ‬ ‫ه‬)١٢+‫ب‬(‫ن‬
‫وي‬ ‫ك‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ود‬ ‫د‬ ‫ن‬
‫أ‬(٩‫ب‬(٨‫ـ‬(٧‫د‬(٦
٢٨(‫ك‬ ‫ا‬ ‫ا‬ ‫ا‬)٢‫ــ‬ ‫س‬٣(٥
‫ه‬:
‫أ‬(٥‫ب‬(٧٢٠‫ـ‬(‫ــ‬٧٢٠‫د‬(‫ــ‬١٠٨٠
٢٩(‫ك‬ ‫و‬ ‫ا‬ ‫ا‬)٢+‫س‬(٦
‫ه‬:
‫أ‬(‫ح‬٥‫ب‬(‫ح‬٤‫ـ‬(‫ح‬٣‫د‬(‫ح‬٢

33. ٣٠
٣٠(‫ح‬ ‫ن‬ ‫آ‬ ‫إذا‬٨=‫ح‬٢٦‫ك‬)‫س‬+‫ص‬(‫ن‬
‫ن‬ ‫ن‬=
‫أ‬(٣٤‫ب‬(٣٣‫ـ‬(٣٢‫د‬(٣١
٣١(‫ح‬ ‫ن‬ ‫آ‬ ‫إذا‬١٣=‫ح‬١٤‫ك‬)١‫س‬ ‫ــ‬(٢٥
‫س‬ ‫ن‬=
‫أ‬(١‫ب‬(‫ــ‬١‫ـ‬(٢٥‫د‬(١٣
٣٢(‫ك‬ ‫ود‬ ‫أ‬ ‫ى‬ ‫ا‬ ‫إذا‬)‫أ‬+‫ب‬(٢‫ن‬
‫أ‬٨
‫ب‬١٢
‫ن‬ ‫ن‬=
‫أ‬(٢٠‫ب‬(١٠‫ـ‬(١٥‫د‬(١٢
٣٣(‫ك‬)‫س‬+‫ص‬(٨
‫ح‬ ‫ن‬٣+‫ح‬٨=
‫أ‬(٥٦‫ب‬(١١٣‫ـ‬(٣٦‫د‬(٨
٣٤(‫ح‬ ‫ن‬ ‫آ‬ ‫إذا‬١‫ح‬ ،٢‫اغ‬ ‫د‬Ω‫ل‬ ‫ن‬ ‫وآ‬)‫ح‬١= (٢‫ل‬)‫ح‬٢= (٠ ٥،
‫ل‬)‫ح‬١‫ح‬٢= (٠ ٦،‫ن‬‫ل‬)‫ح‬١= (
‫أ‬(٠ ٤‫ب‬(٠ ٣٥‫ـ‬(٠ ١٥‫د‬(٠ ١
٣٥(‫ح‬ ‫ن‬ ‫آ‬ ‫إذا‬١‫ح‬ ،٢‫اغ‬ ‫د‬Ω‫ل‬ ‫ن‬ ‫وآ‬)‫ح‬١= (٠ ٥‫ل‬ ،)‫ح‬٢= (٠ ٤،
‫ل‬)‫ح‬١‫ح‬٢= (٠ ٣‫ل‬ ‫ن‬)‫ح‬١= (
‫أ‬(٠ ٤‫ب‬(٠ ٦‫ـ‬(٠ ٥‫د‬(٠‫ذ‬
٣٦(‫ح‬ ‫ن‬ ‫آ‬ ‫إذا‬١‫ح‬ ،٢‫ل‬ ‫ن‬ ‫وآ‬ ‫د‬)‫ح‬١‫ح‬٢= (٠ ١٢‫ل‬ ،)‫ح‬١= (٣‫ل‬)‫ح‬٢(‫ن‬
‫ل‬)‫ح‬١= (
‫أ‬(٠ ٠٦‫ب‬(٠ ٠٤‫ـ‬(٠ ٢‫د‬(٠ ٦
٣٧(‫ر‬ ‫ر‬ ‫م‬‫ن‬ ‫ا‬ ‫ا‬ ‫ة‬ ‫إ‬ ‫ا‬ ‫أ‬ ‫د‬ ، ‫ة‬
‫ا‬ ‫أ‬ ‫إذا‬ ً‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ن‬ ‫أن‬ ‫ل‬ ‫ا‬ ‫ن‬ ، ً‫ا‬ ‫و‬=
‫أ‬($‫ب‬(@‫ـ‬(#‫د‬($
٣٨(‫أ‬‫ل‬ ‫ا‬ ‫ن‬ ‫رة‬ ‫ا‬ ‫ى‬ ‫ي‬ ‫ا‬ ‫ا‬ ‫ن‬ ‫آ‬ ‫ذا‬ ‫ة‬ ‫وا‬ ‫ة‬ ً
‫ه‬ ً ‫أ‬ ‫رة‬ ‫ى‬ ‫ا‬ ‫ي‬ ‫ا‬ ‫ا‬ ‫ن‬ ‫أن‬
‫أ‬(@‫ب‬(#‫ـ‬($‫د‬($
٣٩(‫ل‬ ‫ن‬ ‫آ‬ ‫إذا‬)‫ح‬١= (٠ ٣‫ل‬ ،)‫ح‬٢= (٠ ٥‫ل‬ ،)‫ح‬١‫ح‬٢= (٠ ٧‫ل‬ ‫ن‬ ،)‫ح‬١= ( /
‫أ‬(٠ ٢٥‫ب‬(٠ ٢‫ـ‬(٠ ٣‫د‬(١
‫ح‬٢
‫ح‬٢
‫ح‬٢

34. ٣١
٤٠(‫وق‬ ‫ي‬٦‫ات‬ ‫آ‬١،١،١،٢،٣،٣‫ن‬ ‫آ‬
‫ا‬ ‫ا‬ ‫ا‬‫ا‬ ‫ن‬ ‫ن‬ ‫ا‬ ‫ن‬ ‫ا‬ ‫ن‬ ‫أن‬ ‫ل‬ ‫ا‬ ، ‫ع‬ ‫ر‬٣‫؟‬
‫أ‬(#‫ب‬((‫ـ‬(! %‫د‬(# ^
٤١(‫ح‬ ‫ن‬ ‫آ‬ ‫إذا‬١‫ح‬ ،٢‫ل‬ ‫ن‬ ‫وآ‬ ‫ن‬ ‫ن‬ ‫د‬)‫ح‬١= (٠ ٤‫ل‬ ،)‫ح‬٢= (٠ ٥‫ن‬
‫ل‬)‫ح‬١‫ح‬٢= (
‫أ‬(٠ ٤‫ب‬(٠ ٥‫ـ‬(٠ ٢‫د‬(٠ ٩
٤٢(‫ت‬ ‫ا‬ ‫ا‬ ‫ر‬ ‫ل‬ ‫ا‬ ‫ن‬ ، ‫ات‬ ‫أ‬
‫وي‬ ‫ا‬
‫أ‬(# @‫ب‬(^!‫ـ‬(*‫د‬($
٤٣(‫ح‬ ‫ن‬ ‫آ‬ ‫إذا‬١‫ح‬ ،٢eΩ،‫ل‬)‫ح‬١= (٠ ٧،‫ل‬)‫ح‬٢= (٠ ٢٥،
‫ل‬)‫ح‬١‫ح‬ ‫ــ‬٢= (٠ ٥٥،‫ل‬ ‫ن‬)‫ح‬١/‫ح‬٢= (
‫أ‬(٠ ٤‫ب‬(٠ ٦‫ـ‬(٠ ٤٥‫د‬(٠ ٣

35. ٣٢
:
.
()= (
(= !
(
(
()= (,)(
()+(
()= (
()(
()(×!
(( )k
2=
:
(:( )25
3 v2−=( )25
2 v−
(( )k
7( )1 k
6
−
( )1 k
5
−
()
‫س‬3
1(≠
:
()
1
3
(.
()= (,)=(,)∩=(,
)(). (
()= (×
‫ن‬
‫ن‬−
 
 
 

36. ٣٣
:
(OΏ)=()= ()/=(
:)∩()/. (
(OΏ)= (
1
2
)C=(
2
3
)= (
1
3
.
(=)+(
:
(
.
:–
()+= ()–= ! (
.
٣(‫أن‬ ‫أ‬
3
0 ‫ر‬=

3
‫ر‬
 
 
 
×
5
3‫ر‬ −
 
 
 
=٥٦

37. ٣٤
)(
:)(
=–:
(
١٦٩
١٢٥+‫ت‬(
١٦٩
٥
١٦٩
١٢‫ت‬(
٥
١٦٩
١٢
١٦٩‫ت‬(
٥
١٦٩+
١٢
١٦٩‫ت‬
–=+)= (
) (() (() (() ((
,:
(
١٦
٩٩(
١٦
٩(
١٦
٩٠(
١٧
١٠٠
–.....
((((–
)–(=
((((
‫ا‬%
((%(%(%
") "(
((((
)+(
((((
) = !–(!=
(((,(
(,(,(,(,

38. ٣٥
:)(
(–
(==
.
(
)+= (( )3 w
3
−
=
:)(
(:
٦+١٢+١٨+ ....+٦‫ن‬=٣‫ن‬)‫ن‬+١(
‫ب‬(‫أن‬ ‫أ‬)٢+٥ωωωω+٢ωωωω٢
(٦
=٧٢٩
(‫ع‬ ‫د‬ ‫ا‬ ‫رة‬ ‫ا‬ ‫أ‬=
١
٢
)-١+٣‫ت‬(
:)(
(.
()=(,)=(,)∪=(,:
()(()(()/(
(
.
:)(
(,,
,:
((
(‫د‬ ‫آــ‬ ‫ا‬ ‫أ‬:+–=
:١٩٩٨٢٠٠٠
‫ا‬
‫ا‬‫ا‬‫ا‬‫ا‬ ١(‫ا‬‫ر‬ ‫ا‬ ‫ا‬ ‫ا‬
‫أ‬٦٠١٥٧٠٢٠
‫ب‬٨٥٢٥١٠٠٣٠ ٢(‫أوزا‬ ‫ت‬ ‫ا‬ ‫ذ‬ ‫ا‬ ‫ر‬
٨٠٠٨٥٠٠٦
‫س‬٢
٣
(‫س‬ ‫و‬ ‫س‬ ‫ا‬ ‫ا‬ ‫أ‬٤‫ك‬)
٢
+
‫س‬٢(٨