الجدع مشترك علمي - المغرب -

1. http://ad2math.voila.net/ adnanemath@gmail.com ‫ط‬ ‫أآ‬ ‫ن‬ .‫ذ‬ Page 1
‫ا‬IN‫ت‬ ‫ا‬ ‫دئ‬ ‫و‬
‫ا‬ ‫ر‬ ‫ا‬ ‫آ‬n‫د‬:
‫ا‬1:
1(‫د‬ ‫ا‬ ‫ت‬ ‫د‬14‫ا‬80.
2(‫د‬ ‫ا‬ ‫ت‬ ‫د‬35‫د‬ ‫ا‬ ‫رة‬ ‫ا‬50‫و‬170.
3(‫د‬‫ا‬‫د‬ ‫آ‬‫اد‬ ‫ا‬8‫و‬36‫و‬24‫و‬30‫و‬2‫و‬5.
4(‫ا‬ ‫و‬ ‫ا‬ ‫اد‬ ‫ا‬ ‫د‬60.
5(‫ه‬13‫د‬ ‫ا‬704‫؟‬ ‫ا‬ ‫؟‬
6(‫د‬ ‫ا‬ ‫ه‬2352‫د‬ ‫ا‬ ‫ت‬21‫؟‬ ‫ا‬ ‫؟‬
‫ا‬2:
‫ا‬ ‫اد‬ ‫ا‬ ‫أو‬ ‫ا‬ ‫ى‬ ‫اء‬ ‫إ‬:
161 §§ 144 §§ 10000 §§ 23000 §§ 1080 §§ 1400ൈ49.
‫ا‬3:
‫ا‬ ‫ر‬ ‫ا‬ ‫ا‬ ‫ل‬:
48 64 235 161 5175 48 150
§§ §§ §§ §§ §§
75 144 300 46 12375 56 140
×
×
‫ا‬4:
‫ا‬ ‫ر‬ ‫ا‬ ‫ت‬ ‫ا‬ ‫ا‬ ‫ل‬:
75 §§ 164 §§ 738 §§ 1690 §§ 1044 §§ 34 80 51× ×
‫ا‬5:
‫د‬ ‫آ‬ ‫ا‬ ‫ك‬ ‫ا‬ ‫ا‬ ‫د‬x‫و‬y‫ا‬ ‫ت‬ ‫ا‬ ‫آ‬:
1(x=75‫و‬y= 325.
2(x=330‫و‬y= 420.
3(x=214‫و‬y= 816.
4(x=575‫و‬y= 1275.
5(x=132‫و‬y= 666.
‫ا‬6:
‫ا‬ ‫د‬‫ا‬ ‫ك‬ ‫ا‬‫د‬x‫و‬y‫ا‬ ‫ت‬ ‫ا‬ ‫آ‬:
1(x=75‫و‬y= 325.
2(x=330‫و‬y= 420.
3(x=214‫و‬y= 816.
4(x=575‫و‬y= 1275.
5(x=132‫و‬y= 666
‫ا‬7:
1(‫د‬ ‫ا‬ ‫ه‬111111‫؟‬ ‫ا‬ ‫؟‬ ‫أو‬
2(‫اد‬ ‫ا‬ ‫أن‬1000000001‫و‬320
െ 1‫و‬1234563
‫أو‬ ‫اد‬ ‫أ‬.
3(‫د‬ ‫ا‬ ‫د‬(1310
+ 3)2
‫د‬ ‫ا‬13.
4(‫د‬ ‫ا‬ ‫أن‬(499999)2
+999999‫ا‬25.
‫ا‬8:
‫ا‬ ‫ا‬ ‫د‬ ‫ا‬X12‫ه‬6،‫د‬ ‫ا‬ ‫ه‬X‫اد‬ ‫ا‬ ‫آ‬4‫و‬3‫و‬2.
‫ا‬9:
‫اد‬ ‫ا‬ ‫د‬ ‫ا‬ ‫اد‬ ‫ا‬ ‫و‬ ‫و‬ ‫ا‬ ‫اد‬ ‫ا‬ ‫د‬‫ا‬:
( )
( ) ( )
73 32² 1 ;; 15² 9² ;; 15² 13² ;; ;; 642 97681 ;; 41² 765²15 12
3 22176543 34569820 ;; ;; 2n 8 ;; 4n² 1 ;; n (n 1)97 97
3n² n ;; n n 1 n 2 ;; 5n² 5n 1 ;; 8n² 8n 1
(n 1)(n 2)(n
+ × − + × +
× × + + +
+ + + + + + + + +
+ + ( )( )
( ) ( ) ( )
3) ;; 2n² 4n 7 ;; 2012²n² 2009² ;; 2n 5 2n 6
n n 3 ;; 1 n 1 ² n 2 ² ;; n² 3n 4 ;; n² 3n 4
+ + + + + +
+ + + + + − + + +

2. http://ad2math.voila.net/ adnanemath@gmail.com ‫ط‬ ‫أآ‬ ‫ن‬ .‫ذ‬ Page 2
‫ا‬10:
a‫و‬b،‫ن‬ ‫ن‬ ‫دان‬:ab = 2880‫و‬pgcd(a;b) = 24.
‫د‬ ‫ا‬ ‫د‬a‫و‬b.
‫ا‬11:
x‫و‬y، ‫د‬a = x + y – 1‫و‬b = x – y + 2
1(‫أ‬a + b‫أن‬ ‫ا‬ ‫م‬a‫و‬b‫و‬ ‫ا‬.
2(‫أن‬:(x + y -1)(x – y + 2) = x² - y² + x + 3y – 2
3(‫زواج‬ ‫ا‬ ‫د‬(x;y)‫ا‬:x² - y² + x + 3y – 2 = 0.
‫ا‬12:
‫د‬ ‫اد‬ ‫أ‬ ‫ا‬ ‫اد‬ ‫ا‬ ‫أن‬:( ) ( )3n² 13n 17 ;;; n 1 ;;; 2n 2 ² 2n 1 ²n+ + − + + − +
‫ا‬13:
‫أن‬:( )( )n² 11n 30 n 5 n 6+ + = + +‫د‬ ‫ا‬ ‫زو‬ ‫ا‬n² 11n 30+ +.
‫ا‬14:
1(‫د‬ ‫ا‬ ‫أن‬4 2 2n n 4− +‫ا‬4.
2(n‫أن‬ ،‫م‬ ‫د‬:n(n4
– 1)‫ا‬5.
3(n‫أن‬ ،‫م‬ ‫د‬:n3
– n‫ا‬3.
‫ا‬15:
‫أن‬n‫دي‬ ‫د‬:
1(‫أن‬:n² 2n 1+ +‫ا‬4.
2(‫أن‬:n² 1−‫ا‬8.
3(‫ا‬‫أن‬:4 1n −‫ا‬16.
‫ا‬16:
n‫وي‬ ‫أو‬ ‫أآ‬ ‫د‬2.
1(‫د‬ ‫ا‬ ‫آ‬ ‫أن‬n4
+4‫آ‬ ‫ق‬.
2(‫د‬ ‫ا‬ ‫أن‬ ‫ا‬n4
+4‫أو‬.
‫ا‬17:
‫آ‬ ‫ا‬ ‫اد‬ ‫ا‬ ‫أآ‬:
1(A = (n3
+3n²+n)(n3
+3n²+n+2)+1
2(B = n(n+1)(n+2)(n+3)+1
‫ا‬18:
n‫و‬m‫ن‬ ‫د‬ ‫دان‬:
1(‫د‬ ‫ا‬ ‫أن‬m²+n²+6‫ا‬8.
2(‫د‬ ‫ا‬ ‫أن‬m²+n²–2‫ا‬8.
‫ا‬19:
‫أن‬:
n(n 1)(n 2)
IN
3
+ +
∈.
‫ا‬20:‫ا‬ ‫ا‬ ‫ه‬X‫و‬Y‫و‬Z‫م‬ ‫أر‬0‫إ‬9‫و‬ ،XY 10X Y= +‫و‬XYZ 100X 10Y Z= + +.
1(‫أن‬:XY YX+‫ا‬11.
2(‫أن‬ ‫ض‬:X Y>‫أن‬ ،:XY YX−‫ا‬9.
3(‫أن‬ ‫ض‬:X Z Y+ =‫أن‬ ،:XYZ‫ا‬11.
4(‫أن‬ ‫ض‬:X Y Z+ +‫ت‬9‫أن‬ ،:XYZ‫ت‬9.
5(‫ن‬ ‫آ‬ ‫إذا‬X Z>‫أن‬XYZ ZYX−‫ا‬99.