أنشطة داعمة في مادة الرياضيات التقويم السنوي العام للمستوى السادس ابتدائي

1. 2
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
.ِ‫ة‬َ‫ب‬ ِ‫ناس‬ُ‫الْم‬ ‫ِد‬‫ع‬‫َوا‬‫ق‬ْ‫ال‬ ِ‫ال‬َ‫م‬ْ‫ع‬ِ‫ت‬ ْ‫ابس‬ ِ‫ة‬َّ‫ِي‬‫د‬‫تيا‬ْ‫ع‬ِْ‫ل‬‫ا‬ ِ‫َّعات‬‫ل‬َ‫ض‬ُ‫الْم‬ ِ‫ِساحات‬‫م‬ ُ‫اب‬ َ‫س‬ِ‫ح‬ ♦
ِ‫ــة‬َّ‫ي‬ِ‫ـاد‬َّ‫ــي‬ِ‫ت‬ْ‫ع‬ِْ‫ال‬ ِ‫ـــات‬َ‫ع‬َّ‫ـل‬ َ‫ض‬ُ‫م‬ْ‫ل‬‫ا‬ ُ‫ــســاحـــات‬ِ‫م‬
‫لَى‬َ‫ع‬ ٍّ‫ري‬ َ‫ش‬َ‫ع‬ ٍ‫د‬َ‫د‬َ‫ع‬ ِ‫ة‬َ‫م‬ ْ‫ِس‬‫ق‬ِ‫ل‬
َ‫ل‬ِ‫إ‬ َ‫ة‬َ‫ِل‬‫ص‬‫الفا‬ ُ‫ل‬ِّ‫و‬َ‫ح‬ُ‫أ‬ 0,1
ٍ‫د‬ِ‫ح‬‫وا‬ ٍ‫م‬ْ‫ق‬َ‫ر‬ِ‫ب‬ ِ‫مين‬َ‫الي‬
‫لَى‬َ‫ع‬ ٍّ‫ري‬ َ‫ش‬َ‫ع‬ ٍ‫د‬َ‫د‬َ‫ع‬ ِ‫ة‬َ‫م‬ ْ‫ِس‬‫ق‬ِ‫ل‬
َ‫ل‬ِ‫إ‬ َ‫ة‬َ‫ِل‬‫ص‬‫الفا‬ ُ‫ل‬ِّ‫و‬َ‫ح‬ُ‫أ‬ 0,01
.ِ‫ن‬ْ‫ي‬َ‫ْم‬‫ق‬َ‫ر‬ِ‫ب‬ ِ‫مين‬َ‫الي‬
41,32 : 0,1 = 413,2
78,541 : 0,01 = 7854,1
h
b
l
L
D
d
a
b
h
b
h
B
l
b x h
S =
2
S = L x
D x d
S =
2(B + b) x h
S =
2
:
َ
‫ي‬ِ‫ه‬ ٍ‫ث‬َّ‫ل‬َ‫ث‬ُ‫م‬ ُ‫ة‬َ‫اح‬ َ‫س‬ِ‫م‬ ●
ُ‫ة‬َ‫ساح‬ِ‫م‬ ●
‫ي‬ِ‫ه‬ ‫يل‬ ِ‫ط‬َ‫ت‬ ْ‫س‬ُ‫م‬
ِ‫ول‬ُّ‫الط‬ ُ‫داء‬ُ‫ج‬
. ِ‫ض‬ْ‫ر‬َ‫ع‬ْ‫ل‬‫ا‬َ‫و‬
ِ‫ع‬ َ‫ل‬ ْ‫�ض‬ َ‫أ‬ ْ‫ال‬ ‫ي‬ ِ‫از‬َ‫و‬َ‫ت‬ُ‫م‬ ُ‫ة‬ َ‫اح‬ َ‫�ض‬ِ‫م‬ •
: َ‫ي‬ ِ‫ه‬
: َ‫ي‬ ِ‫ه‬ ٍ ِّ‫ي‬َ‫ع‬ُ‫م‬ ‫ة‬ َ‫اح‬ َ‫�ض‬ِ‫م‬ •ُ‫ف‬ ِ‫ر‬ َ‫ح‬ْ‫ن‬ُ‫م‬ ِ‫ه‬ْ‫ب‬ ِ‫�ض‬ ُ‫ة‬ َ‫اح‬ َ‫�ض‬ِ‫م‬ •
: َ‫ي‬ ِ‫ه‬
:
َ
‫ي‬ِ‫ه‬ ٍ‫َّع‬‫ب‬َ‫ر‬ُ‫م‬ ُ‫ة‬َ‫ساح‬ِ‫م‬ ●
.ِ‫ه‬ ِ‫س‬ْ‫ف‬َ‫ن‬ ‫ي‬ِ‫ف‬ ِ‫ع‬ْ‫ل‬ ِ‫ض‬ ُ‫اء‬َ‫د‬ُ‫ج‬
ِ‫اع‬َ‫ف‬ِ‫ت‬ ْ‫ْر‬ ْ‫ال‬ ِ‫ف‬ ِ‫ة‬َ‫د‬ ِ‫اع‬َ‫ق‬ ُ‫اء‬َ‫د‬ ُ‫ج‬
.‫ا‬َ‫َه‬‫ل‬ ِ‫ق‬ِ‫ف‬‫ا‬َ‫ُو‬ ْ‫ال‬
. ِ‫ن‬ْ‫ي‬ َ‫ر‬ ْ‫ط‬ُ‫ق‬ْ‫ل‬‫ا‬ ِ‫اء‬َ‫د‬ ُ‫ج‬ ‫ف‬ ْ‫�ص‬ِ‫ن‬ِ‫موع‬ ْ َ‫م‬ ِ‫داء‬ ُ‫ج‬ ُ‫ف‬ ْ‫�ص‬ِ‫ن‬
. ِ‫فاع‬ِ‫ت‬ ْ‫ر‬ ْ‫ال‬ ِ‫ف‬ ِ ْ‫ي‬َ‫ت‬َ‫د‬ ِ‫ْقاع‬‫ل‬‫ا‬
‫ة‬َ‫د‬ِ‫اع‬َ‫ق‬‫ال‬ ِ‫اء‬َ‫د‬ُ‫ج‬ ُ‫ف‬ ْ‫ص‬ِ‫ن‬
‫ا‬َ‫ه‬َ‫ل‬ ِ‫ق‬ِ‫اف‬َ‫و‬ُ‫م‬ْ‫ل‬‫ا‬ ِ‫اع‬َ‫ف‬ِ‫ت‬ِْ‫ر‬ ْ‫ال‬َ‫و‬
S = a x a = a2
S = b x h
Aire du trapèze Aire du losange Aire du
parallélogramme
Aire du rectangle
Aire du carré
Aire du triangle
ُ‫س‬ْ‫ر‬ َّ‫الد‬
37
ُ‫َّر‬‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬َ‫و‬ ُ‫م‬َ‫ه‬ْ‫ف‬َ‫أ‬
Aires de polygones usuels
ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬
23,41 : 0,1 = ...........
45,89 : 0,1 = ...........
35,47 : 0,01 = ...........
125,04 : 0,01 = ...........
65,2 : 0,01 = ...........
78 : 0,01 = ...........
ِ‫ف‬ َ‫ة‬َ‫م‬ِ‫ز‬ّ‫الل‬َ‫ار‬َ‫ف‬ْ‫األَص‬ ُ‫ضيف‬ُ‫أ‬
: ِ‫الت‬َ‫الح‬ ِ‫ض‬ْ‫ع‬َ‫ب‬
41,3 : 0,01 = 4130
42 : 0,01 = 4 200

2. 3
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬ُ‫ن‬َّ‫ر‬‫رن‬‫ن‬ َ‫م‬‫مر‬‫ر‬ َ‫ت‬‫تم‬‫م‬ َ‫أ‬َ‫و‬ ُ‫ق‬ِّ‫ب‬‫بق‬‫ق‬ َ‫ط‬‫طب‬‫ب‬ ُُ‫أ‬ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
‫مثلث‬‫األضلع‬ ‫متوازي‬‫معين‬‫منحرف‬ ‫شبه‬
: ٍ‫ث‬َّ‫ل‬َ‫ث‬ُ‫م‬ ِ
ّ‫ل‬ُ‫ك‬ َ‫ة‬َ‫اح‬ َ‫س‬ِ‫م‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
: ٍ‫ع‬َ‫ال‬ ْ‫َض‬‫أ‬ ‫ِي‬‫از‬َ‫و‬َ‫ت‬ُ‫م‬ ِ
ّ‫ل‬ُ‫ك‬ َ‫ة‬َ‫اح‬ َ‫س‬ِ‫م‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
: ٍ‫ن‬ِّ‫ي‬َ‫ع‬ُ‫م‬ ِ
ّ‫ل‬ُ‫ك‬ َ‫ة‬َ‫اح‬ َ‫س‬ِ‫م‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
: ٍ‫ف‬ِ‫ر‬َ‫ح‬ْ‫ن‬ُ‫م‬ ‫به‬ ِ‫ش‬ ِ
ّ‫ل‬ُ‫ك‬ ‫ة‬َ‫اح‬ َ‫س‬ِ‫م‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
: ٍ‫ل‬ْ‫ك‬ َ‫ش‬ ِ
ّ‫ل‬ُ‫ك‬ َ‫ة‬َ‫اح‬ َ‫س‬ِ‫م‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
: ِ‫يل‬ِ‫ط‬َ‫ت‬ ْ‫س‬ُ‫م‬ْ‫ل‬‫ا‬ َ‫ة‬َ‫اح‬ َ‫س‬ِ‫م‬َ‫و‬ ِ‫ع‬َّ‫ب‬َ‫ر‬ُ‫م‬ْ‫ل‬‫ا‬ َ‫ة‬َ‫اح‬ َ‫س‬ِ‫م‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
1
2
3
4
6
5
‫القيا�س‬ ‫وحدة‬
‫القيا�س‬‫وحدة‬
‫قياس‬ ‫وحدة‬
9m
11cm
4cm
4m
4m
B
B
B = . . . . . . h = . . . . . .
b = . . . . . .
A = . . . . . .
b
b
h = 3cm
hh
7cm
3,5cm
5cm
3cm
b = 4
h = 3
A =
A =
b = 5
h = 3
. . . . . . .
. . . . . . .
b = 5
h = 3
A = 5 x 3 = 15 (‫القيا�س‬ ‫وحدة‬)
. . . . . .
. . . . . .
. . . . . .
. . . . . . .
. . . . . .. . . . . . . . . . . . . . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . . .
. . . . . .
. . . . . .
. . . . . .
. . . . . . .
b
b
b
L
l
b
b
b
b
h
h h
h h
h h
4 x 3
2
12
2
(‫القيا�س‬ ‫)وحدة‬
D = 7cm
d = 4cm
d
D

3. 4
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
.ِ‫ِل‬‫ئ‬‫ا‬ َ‫س‬َ‫الم‬ ِّ‫ل‬َ‫ح‬ ِ‫ف‬ ِ‫ة‬َّ‫ي‬ِ‫ب‬ ُ‫اس‬َ‫ن‬َّ‫ت‬‫ال‬ ِ‫ل‬ِ‫و‬‫ا‬َ‫د‬َ‫ج‬َ‫و‬ ‫ي‬ِ‫ب‬ ُ‫ناس‬َّ‫ت‬‫ال‬ ِ‫ِل‬‫م‬‫ا‬َ‫ع‬ُ‫م‬ ُ‫ِال‬‫م‬ْ‫ع‬َ‫ت‬ ْ‫اس‬ ♦
ُ‫ة‬َّ‫ي‬ِ‫ب‬ ُ‫اس‬َ‫ن‬َّ‫ٱلت‬
ُ‫س‬ْ‫ر‬ َّ‫الد‬
38
Proportionnalité
ِ ِ ِ ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬
16 : 10 = 1,6
‫بيعي‬َ‫ط‬ ٍ‫ح‬‫حي‬َ‫ص‬ ٍِ‫د‬َ‫د‬َ‫ع‬ ِ‫ب‬ْ‫ر‬َ‫ض‬ِ‫ل‬
:ِ‫ِين‬‫م‬َ‫الْي‬ ‫لى‬َ‫ع‬ 0 ُ‫ضيف‬ُ‫ن‬ 10 ِ‫ف‬
ِ‫ف‬ ‫بيعي‬َ‫ط‬ ٍ‫ح‬‫حي‬َ‫ص‬ ٍِ‫د‬َ‫د‬َ‫ع‬ ِ‫ب‬ْ‫ر‬َ‫ض‬ِ‫ل‬
:ِ‫ِين‬‫م‬َ‫الْي‬ ‫لى‬َ‫ع‬ ِ‫ن‬ْ‫ي‬َ‫ر‬ْ‫ف‬ِ‫ص‬ ُ‫ضيف‬ُ‫ن‬ 100
7 x 10 = 70
8 x 100 = 800
10 15 25 7 ‫يات‬ِ‫َو‬‫ل‬َ‫احل‬ ُ‫د‬َ‫د‬ َ‫ع‬
16 24 40 11,2 ‫بالدرهم‬ ‫َّمن‬‫ث‬‫ال‬
3 6 9 15 18
2 4 6 10 12
2
3
2
3
:x
ُ‫ل‬ َ‫و‬ْ‫د‬َ ْ‫ٱل‬� �َ‫ذ‬ َ‫ه‬ ‫ى‬َّ‫م‬ َ‫�س‬ُ‫ي‬ •
ِ‫ل‬ ْ‫و‬َ‫أ‬ ْ‫ال‬ ِ‫ر‬ ْ‫��ط‬ َّ‫ٱل�ص‬‫ا‬ َ‫اد‬َ‫د‬�� ْ‫ع‬َ‫أ‬‫ا‬ َّ‫ن‬َ‫أ‬ ِ‫ل‬ ِ‫ة‬َّ‫ِي‬‫ب‬�� ُ‫ا�ص‬َ‫ن‬َّ‫ت‬‫ٱل‬‫ا‬ َ‫ل‬ َ‫و‬ْ‫د‬�� َ‫ج‬
ْ‫ي‬َ‫أ‬‫ا‬ ، ِ‫َّ��ان‬‫ث‬‫ال‬ ِ‫ر‬ ْ‫��ط‬ َّ‫ٱل�ص‬‫ا‬ ِ‫��داد‬ ْ‫ع‬َ‫أ‬‫ا‬ َ‫��ع‬َ‫م‬ ٌ‫ة‬َ‫��ب‬ ِ‫ا�ص‬َ‫ن‬َ‫ت‬ُ‫م‬
َ‫ِل‬‫إ‬‫ا‬ ‫ل‬ ْ‫و‬َ‫أ‬ ْ‫ال‬ ِ‫ر‬ ْ‫��ط‬ َّ‫ٱل�ص‬‫ا‬ ِ ‫اد‬َ‫د‬�� ْ‫ع‬َ‫أ‬‫ا‬ ْ‫��ن‬ِ‫م‬ ُ‫��ل‬ِ‫ق‬َ‫ت‬ْ‫ن‬َ‫ن‬ ‫��ا‬َ‫ن‬َّ‫ن‬َ‫أ‬‫ا‬
ِ‫ف‬ ٍ‫د‬َ‫د‬�� َ‫ع‬ ِّ‫ل‬ُ‫ك‬ ِ‫ب‬ْ َ‫ِ���ر‬‫ب‬ ِ‫َّ��ان‬‫ث‬‫ٱل‬‫ا‬ ِ‫ر‬ ْ‫��ط‬ َّ‫ٱل�ص‬‫ا‬ ِ‫اد‬َ‫د‬�� ْ‫ع‬َ‫أ‬‫ا‬
‫��ل‬ ِ‫ام‬َ‫ع‬ ُ‫م‬ ‫ى‬َّ‫��م‬ َ‫�ص‬ُ‫ي‬ ُ‫د‬َ‫د‬��َ‫ْع‬‫ل‬‫ٱ‬‫ا‬ ‫��ذا‬َ‫ه‬ .ِ‫د‬َ‫د‬��َ‫ْع‬‫ل‬‫ٱ‬‫ا‬ ِ‫���س‬ْ‫ف‬َ‫ن‬
.‫��ب‬ ُ‫َا�س‬‫ن‬َّ‫ت‬‫�ٱل‬
، ْ‫َ��ن‬‫ت‬َ‫ق‬‫ي‬ِ‫ر‬ َ‫ط‬ ‫ىل‬ِ‫إ‬� ُ‫أ‬‫ا‬�� َ‫ْج‬‫ل‬َ‫ن‬ ‫ة‬ِّ‫ِي‬‫ب‬�� ُ‫َنا�س‬‫ت‬ ‫��ة‬َ‫ي‬ِ‫ع‬ ْ‫�س‬ َ‫و‬ ِّ‫��ل‬َ ِ‫ل‬ •
،16DH ‫��ات‬ّ‫ي‬ِ‫َو‬‫ل‬ َ‫ح‬ 10 ُ‫��ن‬َ‫َم‬‫ث‬ ‫َ��غ‬‫ل‬ْ‫ب‬َ‫ي‬ : ً‫ا‬��َ‫ث‬ َ‫م‬
7 ،‫ْ��وى‬‫ل‬ َ‫ح‬ 25 ،‫ْ��وى‬‫ل‬ َ‫ح‬ 15 ُ‫��ن‬َ‫َم‬‫ث‬ َ‫��و‬ ُ‫ماه‬
. ‫ت‬ ‫��ا‬ّ‫ي‬ ِ‫َو‬‫ل‬ َ‫ح‬
َ‫و‬ ُ‫ه‬ ‫ب‬ ُ‫ا�ض‬َ‫ن‬َّ‫ت‬‫ٱل‬‫ا‬ ‫ل‬ِ‫عام‬ُ‫م‬
1,6 ِ‫ف‬ ِ‫ل‬ َّ‫و‬ َ‫أ‬‫ل‬‫ا‬ ِ‫ر‬ ْ‫��ط‬ َّ‫ٱل�ص‬‫ا‬ ْ‫��ن‬ِ‫م‬ ٍ‫د‬َ‫د‬�� َ‫ع‬ ّ‫ل‬ُ‫ك‬ ُ‫ب‬ُِ ْ‫���ر‬َ‫ن‬
. ِ‫ّ��ان‬َ‫ث‬‫ال‬ ِ‫ر‬ ْ‫��ط‬ َّ‫ٱل�ص‬‫ا‬ َ‫��داد‬ ْ‫ع‬َ‫أ‬‫ا‬ ُ‫د‬��ِ َ‫ن‬ َ‫و‬
ِ‫د‬َ‫د‬�� َ‫ع‬ ِ‫ف‬ ُ‫ب‬ِ ْ‫���ر‬َ‫ن‬ َ‫و‬ ٍ‫ة‬َ‫د‬�� ِ‫واح‬ ‫ْ��وى‬‫ل‬ َ‫ح‬ َ‫��ن‬َ‫َم‬‫ث‬ ُ‫��ب‬ ُ‫�ص‬ ْ‫ح‬َ‫ن‬
. ِ‫��ات‬ّ‫َوي‬‫ل‬َ ْ‫ٱحل‬‫ا‬
1 ُ‫َة‬‫ق‬‫ي‬ِ‫ر‬ َّ‫ٱلط‬�
2 ُ‫َة‬‫ق‬‫ي‬ِ‫ر‬ َّ‫ٱلط‬�
ُ‫ق‬ِّ‫ب‬َ‫ط‬ُ‫أ‬َ‫و‬ ُ‫م‬َ‫ه‬ْ‫ف‬َ‫أ‬
89 x 10 = 890
27 x 100 = 2700
x1,6
7 x 10 = ...........
59 x 10 = ...........
785 x 10 = ...........
3651 x 10 = ...........
9 x 100 = ...........
72 x 100 = ...........
846 x 100 = ...........
7319 x 100 = ...........

4. 5
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
: ِ‫ل‬ َ‫و‬ْ‫د‬َ ْ‫ٱل‬� َ‫ء‬ ْ‫ل‬ َ‫م‬ ُ‫ل‬ِ‫م‬ ْ‫ك‬ُ‫أ‬� 7,50dh ِ‫د‬ ِ‫�لو�ح‬ ِ ْ‫ّت‬ِ‫ل‬‫ٱل‬� ُ‫ن‬َ‫م‬َ‫ث‬ ُ‫ُغ‬‫ل‬ْ‫ب‬َ‫ي‬ ، ِ‫ْزين‬‫ن‬َ‫ْب‬‫ل‬‫ٱ‬� ِ‫ة‬ ََََََّ‫ط‬ َ َ‫م‬ ِ‫ف‬
: ِ‫ة‬َّ‫ِي‬‫ب‬ ُ‫َا�س‬‫ن‬َّ‫ت‬‫ٱل‬� ِ‫ل‬ َ‫و‬ْ‫د‬ َ‫ج‬ َ‫ء‬ ْ‫ل‬ َ‫م‬ ُ‫ل‬ِ‫م‬ ْ‫ك‬ُ‫أ‬�
ْ‫ن‬ ِ‫م‬ ‫ا‬ً‫اق‬ ِ‫ط‬ْ‫�ن‬ ‫ا‬َ‫ه‬ْ‫َي‬‫ل‬ َ‫ع‬ ُ‫ل‬ َّ‫�س‬ َ‫ح‬ُ ْ‫ٱل‬� ِ‫ة‬َّ‫ي‬ َ‫�س‬َ‫ك‬ْ‫ل‬‫ٱ‬� ِ‫ات‬َ‫َاب‬‫ت‬ِ‫ْك‬‫ل‬‫ٱ‬� ُ‫ل‬ِ‫م‬ ْ‫ك‬ُ‫أ‬�
: ِ‫ل‬ َ‫و‬ْ‫د‬َ ْ‫ٱل‬�
.............. : ‫لى‬ َ‫ع‬ ُ‫ل‬ ُ‫�ص‬ ْ‫ح‬َ‫أ‬‫ا‬ َ‫و‬ 16 ‫ف‬ 0,750 : ُ‫ب‬ِ ْ‫�ر‬َ‫أ‬‫ا‬
: 1,5 ‫لى‬ َ‫ع‬ ( 16 x 0,75) َ‫ج‬ ِ‫خار‬ ُ‫ب‬ ُ‫�ض‬ ْ‫ح‬َ‫أ‬‫ا‬ •
. ِ‫ل‬ َ‫و‬ْ‫د‬َ ْ‫ل‬‫ٱ‬‫ا‬ ‫ف‬ ِ‫ة‬ َ‫غ‬ ِ‫ْفار‬‫ل‬‫ٱ‬‫ا‬ ِ‫ة‬َ‫ن‬‫ا‬ ْ‫ل‬‫ٱ‬‫ا‬ ‫ف‬ َ‫ة‬ َ‫تيج‬َّ‫ن‬‫ل‬‫ٱ‬‫ا‬ ِ‫ه‬ِ‫ذ‬َ‫ه‬ ُ‫ب‬ُ‫ت‬ْ‫ك‬َ‫أ‬‫ا‬ َ‫و‬
. ِ‫ن‬ْ‫ي‬َ‫داء‬ُ ْ‫ل‬‫ٱ‬‫ا‬ ُ‫ن‬ ِ‫قار‬ُ‫أ‬‫ا‬ •
. ) ُ‫ن‬َ‫َّم‬َ‫ث‬‫ال‬ ( ِ‫ّان‬َ‫ث‬‫ال‬ ِِ‫ر‬ ْ‫ط‬ ََّ‫َل�ص‬‫ا‬ِ‫ب‬ ‫ا‬َ‫َه‬‫ل‬ ِ‫ة‬َ‫ق‬َ‫ف‬‫وا‬ُ‫ْ�م‬‫ل‬‫ٱ‬‫ا‬ ِ‫داد‬ ْ‫ع‬َ‫أ‬‫ل‬‫ٱ‬‫ا‬ َ‫ِل‬‫إ‬‫ا‬ ) ِ‫ات‬ ْ‫ّت‬ِ‫ل‬‫ال‬ ُ‫د‬َ‫د‬ َ‫ع‬ ( ِ‫ل‬ َّ‫و‬َ‫أ‬ ْ‫ل‬‫ٱ‬‫ا‬ ِ‫ر‬ ْ‫ط‬ ََّ‫ل�ض‬‫ٱ‬‫ا‬ ِ‫داد‬ ْ‫ع‬َ‫أ‬‫ا‬ ْ‫ن‬ِ‫م‬ ُ‫ل‬ِ‫ق‬َ‫ت‬ْ‫ن‬َ‫ن‬ َ‫ف‬ْ‫ي‬َ‫ك‬ •
ِ‫�س‬ْ‫ف‬َ‫ن‬ ‫ف‬ ُ‫ب‬ُ ْ‫�ر‬َ‫ن‬ ِ‫ن‬َ‫ّم‬َ‫ث‬‫ل‬‫ٱ‬‫ا‬ َ‫ِل‬‫إ‬‫ا‬ ِ‫ات‬ ْ‫ّت‬ِ‫ل‬‫ل‬‫ٱ‬‫ا‬ ِ‫د‬َ‫د‬ َ‫ع‬ ْ‫ن‬ِ‫م‬ ُ‫ل‬ِ‫ق‬َ‫ت‬ْ‫ن‬َ‫ن‬ ‫ا‬َ‫م‬َ‫د‬ْ‫ن‬ ِ‫ع‬ ُ‫ه‬َّ‫ن‬ ِ‫إ‬ ِ‫ل‬ ِ‫ات‬ ْ‫ّت‬ِ‫ل‬‫ل‬‫ٱ‬‫ا‬ ِ‫د‬َ‫د‬ َ‫ع‬ َ‫ع‬َ‫م‬ ٌ‫ب‬ ِ‫ا�ص‬َ‫ن‬َ‫ت‬ُ‫م‬ ‫ى‬ََّ‫د‬َ‫ؤ‬‫و‬ُ‫ل‬‫ٱ‬‫ا‬ َ‫ن‬َ‫ّم‬َ‫ث‬‫ل‬‫ٱ‬‫ا‬ َّ‫ِن‬‫إ‬‫ا‬ ُ‫قول‬َ‫ن‬ •
. ِِ‫ب‬ ُ‫ا�ص‬َ‫ن‬َّ‫ت‬‫ال‬ َ‫ل‬ِ‫ام‬َ‫ع‬ُ‫م‬ ‫ى‬َّ‫م‬ َ‫�ص‬ُ‫ي‬ ............... . . . ُ‫ل‬ِ‫ام‬َ‫ع‬ُ‫ل�م‬‫ٱ‬‫ا‬ .ِ‫د‬َ‫د‬َ‫ْع‬‫ل‬َ‫ا‬
: ِ‫ة‬َّ‫ِي‬‫ب‬ ُ‫َا�س‬‫ن‬َّ‫ت‬‫ٱل‬� ِ‫ل‬ َ‫و‬ْ‫د‬ َ‫ج‬ َ‫ء‬ ْ‫ل‬ َ‫م‬ ُ‫ل‬ِ‫م‬ ْ‫ك‬ُ‫أ‬�
: ِِ‫ل‬ َ‫و‬ْ‫د‬َ ْ‫ٱل‬� َ‫ء‬ ْ‫ل‬ َ‫م‬ ُ‫ل‬ِ‫م‬ ْ‫ك‬ُ‫أ‬�‫و‬ ٍ‫َة‬‫ل‬‫حا‬ ِ‫ل‬ُ‫ك‬ ‫ف‬ ِِ‫ب‬ ُ‫َا�س‬‫ن‬َّ‫ت‬‫�ل‬ َ‫ل‬ ِ‫عام‬ ُ‫م‬ ُ‫ب‬ ُ‫�س‬ ْ‫ح‬ُ‫أ‬�
1
23
4
5
10 6 5 4 2 ...
ِ‫ات‬‫ر‬ّ‫ت‬ِّ‫ل‬‫ٱل‬‫ا‬ ُ‫د‬َ‫د‬َ‫ع‬
... ... ... ... ... 7,5 ِ‫م‬َ‫ه‬ْ‫ر‬ِّ‫ٱلد‬ِ‫ب‬ ُ‫ن‬َ‫م‬َّ‫ٱلث‬‫ا‬
...
......
8 20 30 4 ...
... ... ... 10 12
20
8
= ....
20
= ....
30
= 10
....
= ....
12
•
8
20
=
20
....
= 30
....
= ....
10
= ....
12
•
0,750 1,5 kg‫ب‬ ‫التفاح‬ ‫كمية‬
... 16 DH‫ب‬ ‫الثمن‬
... 16
54 12
......
63 ... 13,5
35 105
...
12 2,5 ...
84 ... 38,5
21 15
7 ...
... 56
28 49
ُ‫��ب‬ ُ‫�ص‬ ْ‫ح‬َ‫أ‬‫ا‬ 16DH َ‫��و‬ ُ‫ه‬ ِ‫ف��اح‬ُْ‫ت‬‫ل‬‫ٱ‬‫ا‬ َ‫��ن‬ِ‫م‬ 1,5kg ُ‫��ن‬َ‫َم‬‫ث‬
. ِ‫ف��اح‬ُْ‫ت‬‫ل‬‫ٱ‬‫ا‬ َ‫��ن‬ِ‫م‬ 750g َ‫��ن‬َ‫َم‬‫ث‬
. ِ‫ة‬َّ‫بي‬ ُ‫نا�ص‬َّ‫ت‬‫ل‬‫ٱ‬‫ا‬ ِ‫ل‬ َ‫و‬ْ‫د‬ َ‫ج‬ ِ‫ف‬ ِ‫َة‬‫ل‬ َ‫أ‬‫ا‬ ْ‫َ�ص‬‫ل‬‫ٱ‬‫ا‬ ِ‫يات‬ َ‫ط‬ْ‫ع‬ُ‫م‬ ُ‫ِّل‬‫ث‬َ‫م‬ُ‫أ‬‫ا‬
. ‫اه‬ُ‫ع‬ْ‫ي‬َ‫ب‬ ََّ‫م‬َ‫ت‬ ‫َّتي‬‫ل‬َ‫ا‬ ِ‫ح‬‫فا‬ُّّ‫ت‬‫ال‬ ِ‫ة‬َّ‫ي‬ّ‫َم‬‫ك‬َ‫ع‬َ‫م‬ ٌ‫ب‬ِ‫اس‬َ‫ن‬َ‫ت‬ُ‫م‬ ُ‫ن‬َ‫ّم‬َ‫ث‬‫ال‬
ِ‫ل‬َ‫و‬ْ‫د‬َ‫الْج‬ َ‫ن‬ِ‫م‬ ِ‫ة‬َ‫غ‬ِ‫ر‬‫َلْفا‬‫ا‬ ِ‫ة‬َ‫ن‬‫َلْخا‬‫ا‬ ‫ف‬ ُ‫ه‬َ‫ت‬ْ‫ب‬َ‫ت‬َ‫ك‬ ‫ما‬
16 x 0,75 1,5 x ..............َ‫و‬
‫؟‬ ُ‫ج‬ِ‫ت‬ْ‫ن‬َ‫ت‬ ْ‫�ض‬َ‫أ‬‫ا‬ ‫ماذا‬
( 16 x 0,75) ‫ج‬ ِ
َ ْ ‫ٱ‬ ْ ‫ٱ‬ ْ ‫ٱ‬ َّ ‫ٱ‬
( 16 x 0,75) : 1,5 = ..............

5. 6
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
. ِ‫ة‬َ‫ب‬ ِ‫ناس‬ُ‫الم‬ ِ‫د‬ِ‫ع‬‫َوا‬‫ق‬‫ال‬ ِ‫ال‬َ‫م‬ْ‫ع‬ِ‫ت‬ ْ‫س‬ِ‫اب‬ ٍ‫ص‬ْ‫ُر‬‫ق‬ ِ‫ة‬َ‫ِساح‬‫م‬َ‫و‬ ٍ‫ة‬َ‫ِر‬‫ئ‬‫دا‬ ِ‫ط‬‫حي‬ُ‫م‬ ُ‫ساب‬ِ‫ح‬ ♦
ِ‫ص‬ْ‫ر‬ُ‫ق‬ْ‫ل‬‫ٱ‬ ُ‫ة‬َ‫ساح‬ِ‫م‬َ‫و‬ ِ‫ة‬َ‫ر‬ِ‫ائ‬ّ‫ٱلد‬ ُ‫ط‬‫حي‬ُ‫م‬
ُ‫س‬ْ‫ر‬ َّ‫الد‬
39
ُ‫َّر‬‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬َ‫و‬ ُ‫م‬َ‫ه‬ْ‫ف‬َ‫أ‬
Périmètre du cercle et aire du disque
ِ ٍ ٍ ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬
ُ‫ل‬ِّ‫و‬َ‫ح‬ُ‫ن‬ 100 ِ‫ف‬ ٍّ‫ري‬ َ‫ش‬َ‫ع‬ ٍ‫د‬َ‫د‬َ‫ع‬ ِ‫ب‬ْ‫ر‬َ‫ض‬ِ‫ل‬
‫ا‬ً‫ْر‬‫ف‬ِ‫ص‬ ُ‫ضيف‬ُ‫ن‬َ‫و‬ ِ‫مين‬َ‫الي‬ َ‫ل‬ِ‫إ‬ َ‫ة‬َ‫ِل‬‫ص‬‫الفا‬
: َ‫ِك‬‫ل‬َ‫ذ‬ ُ‫ر‬ْ‫األَم‬ َ‫ّب‬َ‫ل‬َ‫ط‬َ‫ت‬ ‫ا‬َ‫ذ‬ِ‫إ‬ ِ‫ن‬ْ‫ي‬َ‫ْر‬‫ف‬ِ‫ص‬ ْ‫و‬َ‫أ‬
ِ‫ة‬َ‫ِر‬‫ئ‬‫ا‬ّ‫اَلد‬ َ‫ل‬ِ‫إ‬ ‫ِي‬‫م‬َ‫ت‬ْ‫ن‬َ‫ت‬ َ‫ل‬ ٌ‫ة‬َ‫ْط‬‫ق‬ُ‫ن‬ E
ِ‫ة‬َ‫ِر‬‫ئ‬‫ا‬ّ‫اَلد‬ َ‫ل‬ِ‫إ‬ ‫ِي‬‫م‬َ‫ت‬ْ‫ن‬َ‫ت‬ َ‫ل‬ ٌ‫ة‬َ‫ْط‬‫ق‬ُ‫ن‬ C
ِ‫ة‬َ‫ِر‬‫ئ‬‫ا‬ّ‫اَلد‬ َ‫ل‬ِ‫إ‬ ‫ِي‬‫م‬َ‫ت‬ْ‫ن‬َ‫ت‬ َ‫ل‬ ٌ‫ة‬َ‫ْط‬‫ق‬ُ‫ن‬ O
ِ‫ة‬َ‫ِر‬‫ئ‬‫ا‬ّ‫اَلد‬ َ‫ل‬ِ‫إ‬ ‫ِي‬‫م‬َ‫ت‬ْ‫ن‬َ‫ت‬ ٌ‫ة‬َ‫ْط‬‫ق‬ُ‫ن‬ B ‫ما‬َ‫ن‬ْ‫ي‬َ‫ب‬
ِ‫ص‬ْ‫ُر‬‫ق‬ْ‫اَل‬ َ‫ل‬ِ‫إ‬ ‫ِي‬‫م‬َ‫ت‬ْ‫ن‬َ‫ت‬ َ‫ل‬ ٌ‫ة‬َ‫ْط‬‫ق‬ُ‫ن‬ C
ِ‫ص‬ْ‫ُر‬‫ق‬ْ‫اَل‬ َ‫ل‬ِ‫إ‬ ‫ِي‬‫م‬َ‫ت‬ْ‫ن‬َ‫ت‬ ٌ‫ة‬َ‫ْط‬‫ق‬ُ‫ن‬ B
ِ‫ص‬ْ‫ُر‬‫ق‬ْ‫اَل‬ َ‫ل‬ِ‫إ‬ ‫ِي‬‫م‬َ‫ت‬ْ‫ن‬َ‫ت‬ ٌ‫ة‬َ‫ْط‬‫ق‬ُ‫ن‬ E
ِ‫ص‬ْ‫ُر‬‫ق‬ْ‫اَل‬ َ‫ل‬ِ‫إ‬ ‫ِي‬‫م‬َ‫ت‬ْ‫ن‬َ‫ت‬ ٌ‫ة‬َ‫ْط‬‫ق‬ُ‫ن‬ O
37,546 x 100 = 3754,6
5,2 x 100 = 520
0,03 x 100 = 3
‫قر�ص‬
: َ‫و‬ ُ‫ه‬ d ‫ها‬ُ‫ر‬ ْ‫ط‬ُ‫ق‬ ٍ‫ة‬َ‫ِر‬‫ئ‬�‫د‬ ُ‫يط‬ ُ‫م‬
: َ‫ي‬ ِ‫ه‬ ِ‫�ص‬ ْ‫ُر‬‫ق‬ْ‫ل‬‫ٱ‬� ُ‫ة‬ َ‫�ساح‬ ِ‫م‬
: ٌ‫ة‬ َ‫ظ‬ َ‫اح‬ ُ‫م‬
O
E
B
C
D
r
x
x
x
O
E
B
C
D
r
x
x
x
: ‫ها‬ُ‫ر‬ ْ‫ط‬ُ‫ق‬ ‫و‬ r ‫ها‬ ُ‫اع‬َ‫ع‬ ُ‫�س‬ ‫و‬ O ‫ها‬ُ‫ز‬َ‫ك‬ ْ‫ر‬ َ‫م‬ ٌ‫ة‬َ‫ِر‬‫ئ‬�‫د‬
D = 2 x r
P = π x d
P = π x 2r
A = r x r x π
A = r2
x π
ْ‫ي‬َ‫أ‬�
ْ‫ي‬َ‫أ‬�
A =
1
2
P x r π = 3,14 ً‫ا‬‫ِب‬‫ل‬‫غا‬ ُ‫ذ‬ ُ‫خ‬ْ‫أ‬‫ا‬َ‫ن‬
ُ‫ل‬ِّ‫و‬َ‫ح‬ُ‫ن‬ 10 ِ‫ف‬ ٍّ‫ري‬ َ‫ش‬َ‫ع‬ ٍِ‫د‬َ‫د‬َ‫ع‬ ِ‫ب‬ْ‫ر‬َ‫ض‬ِ‫ل‬
ْ‫و‬َ‫أ‬ ِ‫د‬ِ‫ح‬‫ا‬َ‫و‬ ِ‫م‬ْ‫ق‬َ‫ر‬ِ‫ب‬ ِ‫ِين‬‫م‬َ‫الْي‬ َ‫ل‬ِ‫إ‬ َ‫ة‬َ‫ِل‬‫ص‬‫َا‬‫ف‬ْ‫ال‬
:َ‫ِك‬‫ل‬َ‫ذ‬ ُ‫ر‬ْ‫األَم‬ َ‫َّب‬‫ل‬َ‫ـط‬َ‫ت‬ ‫ذا‬ِ‫إ‬ 0 ُ‫ضيف‬ُ‫ن‬
79,45 x 10 = 794,5
3,8 x 10 = 38
38,51 x 10 = ...........
5,93 x 10 = ...........
0,7 x 10 = ...........
536,2 x 10 = ...........
45,328 x 100 = ..........
9,8 x 100 = .............
0,3 x 100 = ..............
0,07 x 100 = ............

6. 7
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
: َ‫ل‬ َ‫و‬ْ‫د‬َ‫ٱل‬� ُ‫أ‬ َ‫ا‬ ْ‫م‬َ‫أ‬� َ‫و‬ ٍ‫�ص‬ ْ‫ر‬ُ‫ق‬ َ‫و‬ ٍ‫ة‬َ‫ِر‬‫ئ‬�‫د‬ َُّ‫ل‬ُ‫ك‬ ُ‫ظ‬ ِ‫الح‬ُ‫أ‬�
: ٍ‫َة‬‫ل‬‫حا‬ ِّ‫ل‬ُ‫ك‬ ِ‫ف‬ َ‫ة‬ َ‫ِ�ساح‬ ْ‫ٱل‬� ْ‫و‬ َ‫أ‬� َ‫حيط‬ُ ْ‫ٱل‬� ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬�
.S4 ‫و‬ S3, S2, S1 ‫ِها‬‫ت‬‫�ساحا‬ ِ‫م‬ ُ‫ن‬ َ‫قار‬ُ‫أ‬� َ‫و‬ ِ‫ة‬َ‫ن‬َّ‫َو‬‫ل‬ُ‫ٱل‬� ِ‫ة‬َ‫ّالي‬‫ت‬‫ٱل‬� ِ‫ال‬َ‫ك‬ ْ‫�س‬ َ‫أ‬ ْ‫ِا‬‫ل‬ P4 ‫و‬ P3, P2, P1 ِ‫يطات‬ ِ‫ح‬ُ‫ٱل‬� ُ‫ن‬ ِ‫قار‬ُ‫أ‬�
‫؟‬ ُ‫ظ‬ ِ‫ُاح‬‫ت‬ �‫ماذ‬
: ِ‫ل‬ َ‫و‬ْ‫د‬َ ْ‫ٱل‬� َ‫ء‬ ْ‫ل‬ َ‫م‬ ُ‫ل‬ِ‫م‬ ْ‫ك‬ُ‫أ‬�
.9cm ‫ها‬ ُ‫عاع‬ ُ‫�ص‬ ٍ‫ة‬ َ‫ر‬ِ‫ئ‬‫دا‬ ُ‫يط‬ ُ‫م‬ •
.5cm ُ‫ه‬ ُ‫ر‬ ْ‫ط‬ُ‫ق‬ ٍ‫�س‬ ْ‫ر‬ُ‫ق‬ ُ‫يط‬ ُ‫م‬ •
. ِ‫ل‬ْ‫ك‬ َّ‫ٱل�ص‬‫ا‬ ُ‫ة‬ َ‫�صاح‬ِ‫م‬ •
. ِ‫ل‬ْ‫ك‬ َّ‫ٱل�ص‬‫ا‬ ُ‫ة‬ َ‫�صاح‬ِ‫م‬ •
1
2
4
cm2 ِ‫ب‬ ُ‫ة‬ َ‫ِ�ساح‬ ْ‫ٱل‬� cm ِ‫ب‬ ُ‫حيط‬ُ ْ‫ٱل‬� ُ‫ر‬ْ‫ط‬ُ‫ق‬ْ‫ل‬‫ٱ‬� ُ‫عاع‬ ُّ‫ٱلش‬�
... ... ... ... (1)
... ... ... ... (2)
... ... ... ... (3)
... ... ... ... (4)
ُ‫ة‬ َ‫ِ�ساح‬ ْ‫ٱل‬� ُ‫حيط‬ُ ْ‫ٱل‬� ُ‫ر‬ْ‫ط‬ُ‫ق‬ْ‫ل‬‫ٱ‬� ُ‫عاع‬ ُّ‫ٱلش‬�
... ... ... 7 1 ُ‫�ص‬ْ‫ر‬ُ‫ق‬‫�ل‬
... ... 34 ... 2 ُ‫�ص‬ْ‫ر‬ُ‫ق‬‫�ل‬
... 56,52 ... ... 3 ُ‫�ص‬ْ‫ر‬ُ‫ق‬‫�ل‬
78,5 ... ... ... 4 ُ‫�ص‬ْ‫ر‬ُ‫ق‬‫�ل‬
4cm
3,5cm
5,5cm
6cm
3 cm
8,4 cm
S1 S2 S3 S4
P1
P2 P3
P4
3
)1(
)3(
)2(
)4(

7. 8
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
. ِ‫طيلت‬َ‫ت‬ ْ‫س‬ُ‫اَلْم‬ ‫وازي‬َ‫ت‬ُ‫م‬َ‫و‬ ِ‫ب‬ََّ‫ع‬َ‫ك‬ُ‫ِلْم‬‫ل‬ ِ‫ة‬َ‫ِّي‬‫ل‬ُ‫ك‬ْ‫اَل‬َ‫و‬ ِ‫ة‬َّ‫ي‬ِ‫ب‬ِ‫ن‬‫اَلْجا‬ ِ‫ة‬َ‫ِساح‬‫م‬ْ‫اَل‬ ُ‫ساب‬ِ‫ح‬ ♦
ُ‫ة‬َّ‫ي‬ّ‫ل‬ُ‫ك‬ْ‫ل‬‫ٱ‬‫و‬ ُ‫ة‬َّ‫بي‬ِ‫ٱلجان‬ ُ‫ساحات‬ِ‫ٱلم‬ : ِ‫طيالت‬ ْ‫س‬ُ‫م‬ْ‫ل‬‫ٱ‬ ‫ي‬‫از‬‫و‬َ‫ت‬ُ‫م‬َ‫و‬ ُ‫ب‬َّ‫ع‬َ‫ك‬ُ‫م‬ْ‫ل‬‫ٱ‬
ُ‫س‬ْ‫ر‬ َّ‫الد‬
40
ُ‫َّر‬‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬َ‫و‬ ُ‫م‬َ‫ه‬ْ‫ف‬َ‫أ‬
Le cube et le parallélépipède : aires latérales et totales
ِ ِ ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬
45,328 x 1000 = ..........
14,31 x 1000 = ..........
5,2 x 1000 = ..........
1000 ِ‫ف‬ ٍّ‫ري‬ َ‫ش‬َ‫ع‬ ٍ‫د‬َ‫د‬َ‫ع‬ ِ‫ب‬ْ‫ر‬َ‫ض‬ِ‫ل‬
ِ‫مين‬َ‫الي‬ َ‫ل‬ِ‫إ‬ ٍ‫م‬‫قا‬ْ‫ر‬َ‫أ‬ ِ‫ة‬َ‫ث‬‫َل‬‫ث‬ِ‫ب‬ َ‫ة‬َ‫ِل‬‫ص‬‫الفا‬ ُ‫ل‬ِّ‫و‬َ‫ح‬ُ‫أ‬
:َ‫ِك‬‫ل‬َ‫ذ‬ ُ‫ر‬ْ‫األَم‬ َ‫ّب‬َ‫ل‬َ‫ط‬َ‫ت‬ ‫ا‬َ‫ّم‬َ‫كُل‬ ‫ا‬ً‫فار‬ْ‫ص‬َ‫أ‬ َ‫يف‬ِ‫ض‬ُ‫أ‬َ‫و‬
45,32 x 1000 = 45320
21,9 x 1000 = 21900
: َ‫ي‬ ِ‫ه‬ ِ‫ب‬َّ‫ع‬َ‫ك‬ُ‫ْم‬‫ل‬ِ‫ل‬ ُ‫ة‬َّ‫ِبي‬‫ن‬‫ا‬ ْ‫ٱل‬� ُ‫ة‬ َ‫ِ�ساح‬ ْ‫ل‬َ� •: َ‫ي‬ ِ‫ه‬ ِ‫َطيات‬‫ت‬ ْ‫�س‬ُ ْْ‫ٱل‬� ‫َو�زي‬‫ت‬ُ ِ‫ل‬ ُ‫ة‬َّ‫ي‬‫ِب‬‫ن‬‫ا‬ ْ‫ٱل‬� ُ‫ة‬ َ‫ِ�ساح‬ ْ‫ل‬َ� •
ُ‫داء‬ َ‫ج‬ ْ‫ي‬َ‫أ‬‫ا‬ ِ‫ة‬َّ‫بي‬ِ‫ن‬‫ا‬ ْ‫ٱل‬‫ا‬ ِ‫جوه‬ُ‫ْو‬‫ل‬‫ٱ‬‫ا‬ ِ‫�صاحات‬ِ‫م‬ ُ‫موع‬ ْ َ‫م‬
: ِ‫فاع‬ِ‫ت‬ ْ‫ر‬ ْ‫ٱل‬‫ا‬ ِ‫ف‬ ِ‫ة‬َ‫د‬ ِ‫ْقاع‬‫ل‬‫ٱ‬‫ا‬ ِ‫يط‬ ُ‫م‬
: َ‫ي‬ ِ‫ه‬ ِ‫ت‬ َ‫يا‬ ِ‫ط‬َ‫ت‬ ْ‫�س‬ُ ْْ‫ٱل‬� ‫َو�زي‬‫ت‬ُ ِ‫ل‬ ُ‫ة‬َّ‫ّي‬‫ل‬ُ‫ك‬ْ‫ل‬‫ٱ‬� ُ‫ة‬ َ‫ِ�ساح‬ ْ‫ل‬َ� •
ِ‫ة‬ َ‫�صاح‬ِ‫م‬ َ‫و‬ ِ‫ة‬َّ‫بي‬ِ‫ن‬‫ا‬ ْ‫ٱل‬‫ا‬ ِ‫جوه‬ُ‫ْو‬‫ل‬‫ٱ‬‫ا‬ ِ‫ة‬ َ‫�صاح‬ِ‫م‬ ُ‫موع‬ ْ َ‫م‬
.ِ ْ‫ي‬َ‫ت‬َ‫د‬ ِ‫ْقاع‬‫ل‬‫ٱ‬‫ا‬
: َ‫ي‬ ِ‫ه‬ ِ‫ب‬َّ‫ع‬َ‫ك‬ُ‫ْم‬‫ل‬ِ‫ل‬ ُ‫ة‬َّ‫ّي‬‫ل‬ُ‫ك‬ْ‫ل‬‫ٱ‬� ُ‫ة‬ َ‫ِ�ساح‬ ْ‫ل‬َ� •
. ٍ‫ه‬ ْ‫ج‬ َ‫و‬ َ‫ة‬ َ‫�صاح‬ِ‫م‬ ٍ‫ات‬ َّ‫ر‬َ‫م‬ 4
.ٍ‫ه‬ ْ‫ج‬ َ‫و‬ ٌ‫ة‬ َ‫�صاح‬ِ‫م‬ ٍ‫ات‬ َّ‫ر‬َ‫م‬ 6
2 x ( a + b ) x h
4 x a x a
6 x a x a
‫تان‬َ‫د‬ ِ‫ْقاع‬‫ل‬َ�
ُ‫ة‬َّ‫ِبي‬‫ن‬‫ا‬ ْ‫ٱل‬� ُ‫جوه‬ ُ‫ْو‬‫ل‬َ�
a
a
h
b

8. 9
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
: ٍ‫م‬ َّ‫�س‬ َ ُ‫م‬ ِّ‫ل‬ُ‫ك‬ِ‫ل‬ َ‫ة‬َّ‫ّي‬‫ل‬ُ‫ك‬ْ‫ل‬‫ٱ‬� َ‫ِ�ساحة‬ ْ‫ٱل‬�‫و‬ َ‫ة‬َّ‫ِبي‬‫ن‬‫ا‬ ْ‫ٱل‬� َ‫ة‬ َ‫ِ�ساح‬ ْ‫ٱل‬� ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬�
: ِ‫َطيات‬‫ت‬ ْ‫�س‬ُ ْ‫ٱل‬� ‫َو�زي‬‫ت‬ُ ِ‫ل‬ َ‫ة‬َّ‫ِبي‬‫ن‬‫ا‬ ْ‫ٱل‬� َ‫ة‬ َ‫ِ�ساح‬ ْ‫ٱل‬� ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬�
َ‫ن‬ ِ‫م‬ ٍّ‫ل‬ُ‫ك‬ِ‫ل‬ َ‫ة‬َّ‫ّي‬‫ل‬ُ‫ك‬ْ‫ل‬‫ٱ‬� َ‫ة‬ َ‫ِ�ساح‬ ْ‫ٱل‬�‫و‬ َ‫ة‬َّ‫ِبي‬‫ن‬‫ا‬ ْ‫ٱل‬� َ‫ة‬ َ‫�ساح‬ِ ْ‫ٱل‬� ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬� َّ‫م‬ُ‫ث‬ ِ‫َطيات‬‫ت‬ ْ‫�س‬ُ ْ‫ٱل‬� ‫َو�زي‬‫ت‬ ُ‫م‬ َ ْ‫َ�س‬‫ن‬ َ‫و‬ ِ‫ب‬َّ‫ع‬َ‫ك‬ُ ْ‫ٱل‬� َ ْ‫َ�س‬‫ن‬ ُ‫ظ‬ ِ‫الح‬ُ‫أ‬�
: ِ‫َطيات‬‫ت‬ ْ‫�س‬ُ ْ‫ٱل‬� ‫َو�زي‬‫ت‬ ُ‫م‬ َ‫و‬ ِ‫ب‬ََّ‫ع‬َ‫ك‬ُ ْ‫ٱل‬�
‫مكعب‬
‫متو�زي‬
‫�ل�ستطيات‬
1
2
3
ً‫ل‬َّ‫و‬َ‫أ‬ ُ‫ل‬ِّ‫و‬َ‫ح‬ُ‫أ‬
240cm َ‫ل‬ِ‫إ‬ 24dm
: َ‫ة‬َ‫ِد‬‫ع‬‫القا‬ ُ‫ق‬ِّ‫ب‬َ‫ط‬ُ‫أ‬َ‫و‬
ٌ‫روب‬ْ‫ض‬َ‫م‬ ِ‫ة‬َ‫ِد‬‫ع‬‫القا‬ َ‫حيط‬ُ‫م‬
ِ‫ع‬‫ِفا‬‫ت‬ْ‫ر‬ ِ‫ال‬ ِ‫ف‬
4 cm
5 cm
3 cm
3 cm
5 cm
6 cm
: َ‫ة‬َ‫د‬ ِ‫ْقاع‬‫ل‬‫ٱ‬� ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُ‫أ‬� ِ‫ة‬َّ‫ِبي‬‫ن‬‫ا‬ ْ‫ٱل‬� ِ‫ة‬ َ‫ِ�ساح‬ ْ‫ٱل‬� ِ‫اب‬ َ‫�س‬ِ ِ‫ل‬ •
: َ‫ة‬َ‫د‬ ِ‫ْقاع‬‫ل‬‫ٱ‬� ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُ‫أ‬� ِ‫ة‬َّ‫ِبي‬‫ن‬‫ا‬ ْ‫ٱل‬� ِ‫ة‬ َ‫�ساح‬ِ ْ‫ٱل‬� ِ‫اب‬ َ‫�س‬ِ ِ‫ل‬ •
: َ‫ة‬َ‫د‬ ِ‫ْقاع‬‫ل‬‫ٱ‬� ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُ‫أ‬� ِ‫ة‬َّ‫ّي‬‫ل‬ُ‫ك‬ْ‫ل‬‫ٱ‬� ِ‫ة‬ َ‫ِ�ساح‬ ْ‫ٱل‬� ِ‫اب‬ َ‫�س‬ِ ِ‫ل‬ •
24dm :َ‫و‬ ُ‫ه‬ ِ‫ة‬َ‫د‬ ِ‫ْقاع‬‫ل‬‫ٱ‬� ِ‫يط‬ ُ‫م‬
: ِ ْ‫َن‬‫ت‬َ‫د‬ ِ‫قاع‬ْ‫ل‬‫ٱ‬� ُ‫ة‬ َ‫�ساح‬ ِ‫م‬ ُ‫ب‬ َ‫�س‬ ْ‫ح‬َ‫أ‬� ِ‫ة‬َّ‫ي‬ّ‫ل‬ُ‫ك‬ْ‫ل‬‫ٱ‬� ِ‫ة‬ َ‫ِ�ساح‬ ْ‫ٱل‬� ِ‫اب‬ َ‫�س‬ِ ِ‫ل‬ •
ِ‫ة‬َّ‫ِبي‬‫ن‬‫ا‬ ْ‫ٱل‬� ِ‫ة‬ َ‫اح‬ َ‫�س‬ِ‫ْم‬‫ل‬ِ‫ل‬ ‫َها‬‫ف‬‫�سي‬ُ‫أ‬� َ‫و‬
‫حيث‬ 2 x ( a + b ) x h
6 x a x a5 x 6 + 5 x 6
‫حيث‬ 4 x a x aa = 4 cm
a = 6 cm
b = 5 cmh = 3 cm ‫و‬‫و‬
5 cm
3,5 cm
2 cm

9. 10
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
.ِ‫م‬ْ‫ج‬َ‫الح‬ ُ‫هوم‬ْ‫ف‬َ‫م‬ ♦
. ِ‫م‬ْ‫ج‬َ‫الح‬ ِ‫اس‬َ‫ِي‬‫ق‬ ِ‫دات‬َ‫ح‬َ‫و‬ ُ‫مال‬ْ‫ع‬ِ‫ت‬ ْ‫اس‬ ♦
ِ‫اس‬َ‫ي‬ِ‫ق‬ْ‫ل‬‫ا‬ ُ‫دات‬َ‫ح‬َ‫و‬ : ُ‫م‬ْ‫ج‬َ‫ح‬ْ‫ل‬َ‫ا‬
ُ‫س‬ْ‫ر‬ َّ‫الد‬
41
ُ‫َّر‬‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬َ‫و‬ ُ‫م‬َ‫ه‬ْ‫ف‬َ‫أ‬
Le volume : unités de mesure
. ِ‫م‬ِ‫م‬ِ ‫ج‬‫جم‬‫م‬ ‫الح‬‫الحج‬‫ج‬ ِ‫ياس‬‫ياس‬‫اس‬ ‫ق‬ ِ‫دات‬‫قي‬ ِ‫دات‬‫ِي‬‫ق‬ ِ‫دات‬ِ‫ِي‬‫قي‬ ِ‫دات‬‫ِي‬‫ي‬ ‫ح‬‫ق‬ ِ‫حدات‬‫ق‬ ِ‫دات‬ ‫و‬ ُ‫عمال‬‫و‬ ُ‫عمال‬‫و‬ ُ‫مال‬ ِ‫ت‬‫تع‬‫ع‬ ‫اس‬‫است‬‫ت‬ ♦ ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬
5 x 3 = .......
5 x 7 = .......
5 x 11 = .......
5 x 2 = .......
5 x 6 = .......
5 x 10 = .......
5 x 1 = .......
5 x 5 = .......
5 x 9 = .......
5 x 0 = .......
5 x 4 = .......
5 x 8 = .......
ْ‫��ن‬ِ‫م‬ ٍ‫وي��ات‬ْ َ‫ت‬ َ‫��راء‬ ْ‫ِج‬‫إ‬‫ا‬ ِ‫��ال‬َّ‫ت‬‫ٱل‬‫ا‬ ُِ‫ل‬َ‫و‬ْ‫د‬��َ ِ‫ٱل‬‫ا‬ ُ‫ي��ح‬ِ‫ت‬ُ‫ي‬ •
ِ‫��دات‬ َ‫ح‬َ‫و‬ ‫َ��ى‬‫ل‬ َ‫ع‬ ُ‫ل‬ِ‫م‬َ‫ت‬�� ْ‫�ص‬َ‫ي‬َ‫و‬ ‫ى‬َ‫��ر‬ ْ‫خ‬ ُ‫أ‬‫ا‬ َ‫ل‬ِ‫إ‬‫ا‬ ٍ‫ة‬َ‫د‬�� ْ‫ح‬َ‫و‬
. ً‫مال‬ْ‫ع‬ِ‫ت‬�� ْ‫ا�ص‬ ِ َ‫��ر‬ْ‫ك‬َ‫أ‬‫ل‬‫ٱ‬‫ا‬ ِ‫ج��وم‬ُ‫ٱحل‬‫ا‬ ِ‫ا���س‬َ‫ي‬ِ‫ق‬
:َ‫هو‬ ِ‫اع‬ ْ‫�ص‬َ‫أ‬‫ل‬‫ٱ‬‫ا‬ ‫وازي‬َ‫ت‬ُ‫م‬ ُ‫م‬ ْ‫ج‬ َ‫ح‬ •
َ‫ل‬َ‫و‬ْ‫د‬َ‫ج‬ َُ‫َّر‬َ‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬
ِ‫ف‬ ِ‫ب‬ْ‫ر‬َّ‫ض‬‫ال‬
5
‫�لكعب‬ ‫�لت‬
m3
‫�لكعب‬ ‫�لدي�سمت‬
dm3
‫�لكعب‬ ‫�ل�سنتيمت‬
cm3
‫�لكعب‬ ‫�ليليمت‬
mm3
5
5
5
3
3
3
9
9
9
0
0 0 0 0
V = L x lx h
5,39 m3 = 5390 dm3
= 5390 000 cm3
‫وازي‬َ‫ت‬ُ‫م‬ َ‫و‬ُ‫ه‬ ‫ِي‬‫ذ‬َّ‫اَل‬ ِ‫م‬ َّ‫س‬َ‫ج‬ُ‫الم‬ ‫ا‬ََ‫ه‬ ُ‫م‬ْ‫ج‬َ‫ح‬
ِ‫بات‬َّ‫ع‬َ‫ك‬ُ‫اَلْم‬ ُ‫د‬َ‫د‬َ‫ع‬ َ‫و‬‫ه‬ ، ٍ‫ت‬َ‫ِيل‬‫ط‬َ‫ت‬ ْ‫س‬ُ‫م‬
ُ‫ن‬َّ‫و‬َ‫ك‬َ‫ت‬َ‫ي‬ ‫ِي‬‫ت‬َّ‫اَل‬ ِ‫ع‬ْ‫و‬َّ‫الن‬ َ‫ِن‬‫م‬ ِ‫ة‬َ‫غير‬َّ‫الص‬
ِ‫يق‬ِ‫ب‬ْ‫ط‬َ‫ت‬ِ‫ب‬ ٍٍ‫د‬َ‫د‬َ‫ع‬‫ال‬ ‫ا‬ََ‫َه‬‫لَى‬َ‫ع‬ ُ‫ل‬ُ‫ص‬ْ‫ح‬َ‫أ‬ ، َ‫اه‬ْ‫ِن‬‫م‬
V = L x lx h ِ‫ة‬َ‫ِد‬‫ع‬‫القا‬ ِ‫ه‬َِ‫ه‬
1dm
1dm
1dm
1cm3
1dm3

10. 11
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
ْ‫ن‬ ِ‫م‬ ِ‫بات‬َّ‫ع‬َ‫ك‬ُ ْ‫ٱل‬� َُُّ‫د‬ ُ‫ع‬َ‫أ‬�
ِّ‫ل‬ُ‫ك‬ ‫ف‬ ِ‫ع‬ ْ‫ّو‬َ‫ن‬‫ٱل‬�
: ٍ‫م‬ َّ‫�س‬ َ ُ‫م‬
: cm3 ‫ب‬ ٍ‫م‬ َّ‫�س‬ َ ُ‫م‬ ِّ‫ل‬ُ‫ك‬ َ‫م‬ ْ‫ج‬ َ‫ح‬ ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬�
: ‫ّايل‬َ‫ت‬‫ٱل‬� ِ‫م‬ َََّ‫�س‬ َ‫ج‬ُ‫ٱل‬� َ‫م‬ ْ‫ج‬ َ‫ح‬ ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬�
ِ‫بات‬ََّ‫ع‬َ‫ك‬ُ ْ‫ٱل‬� ِ‫د‬َ‫د‬ َ‫ع‬ ِ‫َفْ�ص‬‫ن‬ ْ‫ن‬ ِ‫م‬ ُ‫ن‬َّ‫و‬َ‫َك‬‫ت‬َ‫ي‬ ‫ا‬ً‫م‬ َّ‫�س‬ َ ُ‫م‬ ُ‫م‬ َ‫�س‬ ْ‫ر‬َ‫أ‬�
: ُ‫ل‬ٍّ‫و‬ َ‫ح‬ُ‫أ‬�
ُّ‫ل‬ُ‫ك‬ ‫ا‬َ‫ْه‬‫ن‬ ِ‫م‬ ُ‫ن‬َّ‫و‬َ‫َك‬‫ت‬َ‫ي‬ ‫َّتي‬َ‫ل‬‫ٱ‬� َ‫ة‬َ‫غري‬ َّ‫ٱل�س‬� ِ‫بات‬َّ‫ع‬َ‫ك‬ُ ْ‫ٱل‬� َُُّ‫د‬ ُ‫ع‬َ‫أ‬�
: cm3 ِ‫ب‬ ُ‫ه‬َ‫م‬ ْ‫ج‬ َ‫ح‬ ُ‫ُب‬‫ت‬ ْ‫ك‬َ‫أ‬� َ‫و‬ ٍ‫م‬ َََّ‫�س‬ َ ُ‫م‬
: ُ‫ل‬ِ‫م‬ْ‫ك‬ ُ‫أ‬‫ا‬ َ‫و‬ 1dm3 ‫ها‬ْ‫ن‬ِ‫م‬ ُ‫ن‬َّ‫كَو‬َ‫ت‬َ‫ي‬ ‫َّتي‬َََ‫ل‬‫ٱ‬‫ا‬ َ‫و‬ 1cm3 ‫ها‬ُ‫م‬ ْ‫ج‬ َ‫ح‬ ‫َّتي‬َََ‫ل‬‫ٱ‬‫ا‬ ِ‫بات‬ََّ‫ُكَع‬ ْ‫ل‬‫ٱ‬‫ا‬ َ‫د‬َ‫د‬ َ‫ع‬ ُ‫ب‬ ُ‫�ص‬ ْ‫ح‬َ‫أ‬‫ا‬ •
1
4
5
6
319m3 = ......... dm3
10mm3 = ......... dm3
1500cm3 = ......... dm3
0,75m3 = ......... dm3
50225mm3 = ......... cm3
25,8cm3 = ......... mm3
1dm3 = ......... cm3
1m3 = ......... dm3
1m3 = ......... cm3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1cm
1cm
1cm
. . . . . . . .................
1cm ُ‫ُه‬‫ف‬ْ‫ر‬َ‫ح‬ ٌ‫ب‬َّ‫ع‬َ‫ك‬ُ‫م‬
َ‫هي‬ ٍ‫ه‬ْ‫ج‬َ‫و‬ ُ‫ة‬َ‫ِساح‬‫م‬
ُ‫ه‬ُ‫م‬ْ‫ج‬َ‫ح‬َ‫و‬ 1cm2
1cm3
َ‫و‬‫ه‬
: ُ‫ل‬ِ‫م‬ْ‫ك‬ ُ‫أ‬‫ا‬ َ‫و‬ 1m3 ‫ها‬ْ‫ن‬ِ‫م‬ ُ‫ن‬َّ‫كَو‬َ‫ت‬َ‫ي‬ ‫َّتي‬َََ‫ل‬‫ٱ‬‫ا‬ َ‫و‬ 1dm3
ٍ‫م‬ ْ‫َج‬ ْ‫حل‬‫ٱ‬‫ا‬ ِ‫ذات‬ ِ‫بات‬ََّ‫ُكَع‬ ْ‫ل‬‫ٱ‬‫ا‬ َ‫د‬َ‫د‬ َ‫ع‬ ُ‫ب‬ ُ‫�ص‬ ْ‫ح‬َ‫أ‬‫ا‬ •
: ُ‫ل‬ِ‫م‬ْ‫ك‬ ُ‫أ‬‫ا‬ َ‫و‬ 1m3 ‫ها‬ْ‫ن‬ِ‫م‬ ُ‫ن‬َّ‫كَو‬َ‫ت‬َ‫ي‬ ‫َّتي‬َََ‫ل‬‫ٱ‬‫ا‬‫و‬ 1cm3
ٍ‫م‬ ْ‫َج‬ ْ‫حل‬‫ٱ‬‫ا‬ ِ‫ذات‬ ِ‫بات‬ََََّ‫ُكَع‬ ْ‫ل‬َ‫ٱ‬‫ا‬ َ‫د‬َ‫د‬ َ‫ع‬ ُ‫ب‬ ُ‫�ص‬ ْ‫ح‬َ‫أ‬‫ا‬ •
ٌ‫َراغات‬‫ف‬ َ‫ك‬‫ا‬َ‫ن‬ُ‫ه‬ َ‫س‬ْ‫لَي‬
ٍ‫ة‬َّ‫ئي‬ْ‫ر‬َ‫م‬ ُ‫ر‬ْ‫َي‬‫غ‬
2
1cm3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10cm
6cm
5cm

11. 1212
ُ‫ناء‬ْ‫غ‬ِ‫إل‬‫ا‬َ‫و‬ ُ‫م‬ْ‫ع‬َّ‫الد‬َ‫و‬ ُ‫بيت‬ْ‫ث‬َّ‫ت‬‫ال‬َ‫و‬ ُ‫ويم‬ْ‫ق‬َّ‫ت‬‫ال‬
ِ‫ن‬ْ‫ي‬َ‫د‬َ‫د‬َ‫ع‬ ِ
ّ‫ل‬ُ‫ك‬ ِ‫ع‬‫مو‬ْ‫ج‬َ‫م‬ ِ‫ساب‬ِ‫ح‬ِ‫ل‬ ِ‫يالت‬ِ‫ث‬ْ‫م‬َّ‫ٱلت‬ِ‫ب‬ ُ‫عين‬َ‫ت‬ ْ‫َس‬‫أ‬
: ِ‫ـن‬ْ‫ي‬َ‫ي‬ِ‫ـر‬ ْ‫س‬َ‫ك‬
: ُ‫ـب‬ ُ‫ـس‬ْ‫َح‬‫أ‬‫و‬ ُ‫ظ‬ِ‫ُلح‬‫أ‬
: ٍ‫ر‬ ْ‫س‬َ‫ك‬ ُّ‫ل‬ُ‫ك‬ ُ‫ه‬ُ‫ل‬ِّ‫ث‬َ‫م‬ُ‫ي‬ ‫ذي‬َّ‫َل‬‫ٱ‬� َ‫ء‬ْ‫ز‬ُ‫ج‬ْ‫ل‬َ‫ٱ‬� ُ‫ن‬ ِّ‫و‬َ‫ل‬ُ‫أ‬
: ُ‫ـب‬ ُ‫ـس‬ْ‫َح‬‫أ‬
ُ‫س‬ْ‫ف‬َ‫ن‬ ُ‫ه‬َ‫ل‬ ً‫طيال‬َ‫ت‬ ْ‫س‬ُ‫م‬ ٍ‫ل‬ْ‫ك‬ َ‫ش‬ ّ
ِ‫ل‬ُ‫ك‬ َ‫ت‬ْ‫ح‬َ‫ت‬ ُ‫م‬ ُ‫س‬ْ‫َر‬‫أ‬
: َ‫ة‬َ‫ساح‬ِ‫م‬ْ‫ل‬‫ٱ‬� ِ‫ه‬ِ‫ذ‬َ‫ه‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬ َّ‫م‬ُ‫ث‬ ِ‫ه‬ِ‫ت‬َ‫ساح‬ِ‫م‬
. ِ‫طيالت‬َ‫ت‬ ْ‫س‬َ‫م‬ ْ‫ن‬َ‫ع‬ ٍ‫ات‬ِ‫م‬‫لو‬ْ‫ع‬َ‫م‬ ‫الي‬ّ‫ت‬‫ٱل‬� ُ‫ل‬ َ‫و‬ْ‫د‬َ‫ج‬ْ‫ل‬‫ٱ‬� ُ‫ل‬ِّ‫ث‬َ‫م‬ُ‫ي‬
.ِ‫ة‬َ‫غ‬ِ‫فار‬ْ‫ل‬‫ٱ‬� ِ‫خانات‬ْ‫ل‬‫ٱ‬� َ‫ء‬ْ‫ل‬َ‫م‬ ُ‫ل‬ِ‫م‬ْ‫ك‬ُ‫أ‬
. ِ‫ب‬ ْ‫و‬َْ‫ث‬‫ٱل‬ َ‫ن‬ِ‫م‬ 16m ‫ع‬ْ‫ي‬َ‫ب‬ ‫ي‬ِ‫ف‬ 8dh ٌ‫تاجر‬ َ‫ح‬ِ‫ب‬َ‫ر‬
. ِ‫ب‬ ْ‫و‬َْ‫ث‬‫ٱل‬ ِ‫س‬ّ‫ف‬َ‫ن‬ َ‫ن‬ِ‫م‬ 24m ‫ــ‬ِ‫ل‬ ِ‫ه‬ِ‫ع‬ْ‫ي‬َ‫ب‬ َ‫د‬ْ‫ن‬ِ‫ع‬ ُ‫ح‬َ‫ب‬ْ‫ر‬َ‫ي‬ َ‫س‬ ْ‫م‬َ‫ك‬
2
4
1
3
56
7
+ =
=
+ =
=
1
6
1
4
......
......
4
8
2
6
......
......
7
12
2
3
......
......
......
......
+ = =
......
......
=
......
......
5
6
5
12
......
......
......
......+ = =
......
...... =
......
......
3
8
5
7
......
......
......
......+ = =
......
...... =
......
......
4
5
1
9
......
......
......
......+ = =
......
...... =
......
......
105m 1,7m 25m 85m
................. 1,2m ................. 17m
................. ................. ................. .................
420m2
................. 80m2
.................
ُ‫ول‬ُّ‫لط‬َ‫ا‬
ُ‫ض‬ْ‫ر‬َ‫ع‬ْ‫ل‬َ‫ا‬
ُ‫ط‬‫حي‬ُ‫م‬ْ‫ل‬َ‫ا‬
‫المساحة‬
3
8
3
8
2
9
2
8
4
9
2
9
2
8
4
9= =+ +
.
.
.
.
ِ‫ر‬َ‫م‬ْ‫َح‬ْ‫ال‬ِ‫ب‬ ِ‫ر‬َ‫َصف‬ْ‫ال‬ِ‫ب‬
ِ‫ق‬َ‫ر‬ ْ‫َز‬ْ‫ال‬ِ‫ب‬ ‫الخضر‬ِ‫ب‬
8
10
8
12
3
10
3
12= =– –
.
.
.
.

12. 13
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
13
َ‫د‬َ‫د‬َ‫ع‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
‫ي‬ِ‫ف‬ ِ‫ات‬ِ‫ب‬َّ‫ع‬َ‫ك‬ُ‫م‬ْ‫ل‬‫ٱ‬
.ٍ‫م‬ َّ‫س‬َ‫ج‬ُ‫م‬ ِ
ّ‫ل‬ُ‫ك‬
. ِ‫طيالت‬َ‫ت‬ ْ‫س‬ُ‫م‬ْ‫ل‬‫ٱ‬ ‫ي‬‫از‬‫و‬َ‫ت‬ُ‫م‬ِ‫ل‬َ‫و‬ ِ‫ب‬َّ‫ع‬َ‫ك‬ُ‫م‬ْ‫ل‬ِ‫ل‬ َ‫ة‬َّ‫ي‬ِ‫ل‬ُ‫ك‬ْ‫ل‬‫ٱ‬ َ‫ة‬َ‫ساح‬ِ‫م‬ْ‫ل‬‫ٱ‬‫و‬ َ‫ة‬َّ‫ي‬ِ‫ب‬ِ‫ان‬َ‫ج‬ْ‫ل‬‫ٱ‬ َ‫ة‬َ‫ساح‬ِ‫م‬ْ‫ل‬‫ٱ‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
: ٍ‫ة‬َ‫ل‬‫حا‬ ِ
ّ‫ل‬ُ‫ك‬ ‫ي‬ِ‫ف‬ َِ‫ة‬َ‫ن‬َّ‫و‬َ‫ل‬ُ‫م‬ْ‫ل‬‫ٱ‬ َ‫ة‬َ‫اح‬ َ‫س‬ِ‫م‬ْ‫ل‬‫ٱ‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
.‫ما‬ُ‫ه‬ْ‫ن‬ِ‫م‬ ٍ‫د‬ِ‫اح‬‫و‬ ِ
ّ‫ل‬ُ‫ك‬ِ‫ل‬ َ‫ة‬َّ‫ي‬ِ‫ل‬ُ‫ك‬ْ‫ل‬‫ٱ‬َ‫و‬ َ‫ة‬َّ‫ي‬ِ‫ب‬ِ‫جان‬ْ‫ل‬‫ٱ‬ َ‫ة‬َ‫ساح‬ِ‫م‬ْ‫ل‬‫ٱ‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬َ‫و‬ ِ‫طيالت‬َ‫ت‬ ْ‫س‬ُ‫م‬ْ‫ل‬‫ٱ‬ ‫ي‬‫از‬َ‫و‬َ‫ت‬ُ‫م‬ َ‫ر‬ ْ‫ش‬َ‫ن‬َ‫و‬ ِ‫ب‬َّ‫ع‬َ‫ك‬ُ‫م‬ْ‫ل‬‫ٱ‬ َ‫ر‬ ْ‫ش‬َ‫ن‬ ُ‫ظ‬ِ‫ُلح‬‫أ‬
: ٍ‫ة‬َ‫ب‬ ِ‫ناس‬َ‫ت‬ُ‫م‬ ٍ‫داد‬ْ‫َع‬‫أ‬ ِ‫ل‬ ِ‫داو‬َ‫ج‬ َ‫ء‬ْ‫ل‬َ‫م‬ ُ‫ل‬ِ‫م‬ْ‫ك‬ُ‫أ‬
8
9
10
11
12
13
7 mm 2 cm
3 cm
4 cm
28 19
21 ...........
7,3 2
........... 6,5
3,6 ...........
2,4 1,5
........... 8
4,5 2,5
. . . . . . . . . . . . . . . . . . . . .
‫لَى‬َ‫ع‬ ٌ‫م‬ َّ‫س‬َ‫ج‬ُ‫م‬ ُّ‫ي‬َ‫أ‬ ‫ي‬ِ‫و‬َ‫ت‬ْ‫ح‬َ‫ي‬َ‫ل‬
ٍ‫ة‬َّ‫ٍي‬‫ئ‬ْ‫ر‬َ‫م‬ ِ‫ر‬‫َي‬‫غ‬ ٍ‫َات‬‫غ‬‫ا‬َ‫َر‬‫ف‬
3 cm
5 cm
3 cm
2 cm
AB = 5 cm
AC = 3 cm IJ = 4 cm
6 cm
6cm
A
B
C
J
I

13. 14
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
ِ‫م‬ِ‫ئ‬‫القا‬ِ‫ر‬‫شو‬ْ‫و‬َ‫الم‬ ْ‫ِن‬‫م‬ ٍّ‫ل‬ُ‫ك‬ِ‫ل‬ ِ‫ة‬َّ‫لّي‬ُ‫ك‬‫ال‬ ِ‫ة‬َ‫ِساح‬‫م‬ْ‫وال‬ ِ‫ة‬َّ‫ِبي‬‫ن‬‫الجا‬ ِ‫ة‬َ‫ِساح‬‫م‬‫ال‬ ُ‫ساب‬ِ‫ح‬ ♦
.ِ‫ة‬َ‫ِم‬‫ئ‬‫القا‬ ِ‫ة‬َ‫ن‬‫طوا‬ ْ‫واألُس‬
ُ‫ة‬َََّ‫ي‬ِّ‫ل‬ُ‫ك‬ْ‫ل‬‫ٱ‬َ‫و‬ ُ‫ة‬َّ‫بي‬ِ‫جان‬ْ‫ل‬‫ٱ‬ ُ‫ساحات‬ِ‫م‬ْ‫ل‬‫ٱ‬ : ُ‫ة‬َ‫م‬ِ‫قائ‬ْ‫ل‬‫ٱ‬ ُِ‫ة‬َ‫ن‬‫ا‬‫و‬‫ط‬ ْ‫ُس‬‫أل‬‫ٱ‬‫و‬ ُ‫م‬ِ‫قائ‬ْ‫ل‬‫ٱ‬ ُ‫وشور‬َ‫م‬ْ‫ل‬‫ٱ‬
ُ‫س‬ْ‫ر‬ َّ‫الد‬
42
ُ‫َّر‬‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬َ‫و‬ ُ‫م‬َ‫ه‬ْ‫ف‬َ‫أ‬
Le prisme droit et le cylindre droit : Les aires latérales
et les aires totales
.ِ‫ة‬‫م‬‫مة‬‫ة‬ ِ‫ئ‬‫القا‬‫القائم‬‫م‬ ِ‫ة‬‫طوان‬‫طوانة‬‫ة‬ ‫س‬‫سطوان‬‫طوان‬ ‫واأل‬ ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬
7 x 3 = .......
7 x 7 = .......
7 x 11 = .......
7 x 2 = .......
7 x 6 = .......
7 x 10 = .......
7 x 1 = .......
7 x 5 = .......
7 x 9 = .......
7 x 0 = .......
7 x 4 = .......
7 x 8 = .......
ِ‫يط‬ ُ‫م‬ ُ‫داء‬ ُ‫ج‬: َ‫ي‬ِ‫ه‬ ِ‫م‬ِ‫ئ‬‫ٱلقا‬‫ا‬ ِ‫ور‬ ُ‫�ص‬ْ‫و‬َ‫ْم‬‫ل‬ِ‫ل‬ ُ‫ة‬َّ‫بي‬ِ‫ن‬‫ٱلا‬‫ا‬ ُ‫ة‬ َ‫�صاح‬ِ‫ل‬َ‫ا‬ •
h ِ‫َاع‬‫ف‬ِ‫ت‬ ْ‫ر‬ ِ‫ٱل‬‫ا‬َ‫و‬ p ِ‫ة‬َ‫د‬ ِ‫ٱلقاع‬‫ا‬
p ٌ‫داء‬ ُ‫ج‬: َ‫ي‬ِ‫ه‬ ٍ‫ة‬َ‫م‬ِ‫ئ‬‫قا‬ ٍ‫ة‬َ‫ن‬‫طوا‬ ْ‫�ص‬ُ‫أ‬ ِ‫ل‬ ُ‫ة‬َّ‫بي‬ِ‫ن‬‫ٱلا‬‫ا‬ ُ‫ة‬ َ‫�صاح‬ِ‫ل‬َ‫ا‬ •
‫أ�صطوانة‬‫ل‬‫ٱ‬‫ا‬ ِ‫َاع‬‫ف‬ِ‫ت‬ ْ‫ِر‬‫إ‬‫ا‬ h ‫ف‬ ِ‫ة‬َ‫د‬ ِ‫ٱلقاع‬‫ا‬ ِ‫يط‬ ُ‫م‬
: َ‫ي‬ِ‫ه‬ ِ‫م‬ِ‫ئ‬‫ٱلقا‬‫ا‬ ِِ‫ور‬ ُ‫�ص‬ْ‫و‬َ‫ْم‬‫ل‬ِ‫ل‬ ُ‫ة‬َّ‫ّي‬‫ل‬ُ‫ٱلك‬‫ا‬ ُ‫ة‬ َ‫�صاح‬ِ‫ل‬َ‫ا‬ •
.ِ ْ‫ي‬َ‫ت‬َ‫د‬ ِ‫ْقاع‬‫ل‬َ‫ٱ‬‫ا‬ ْ‫ي‬َ‫ت‬ َ‫�صاح‬ِ‫وم‬ ِ‫ة‬َّ‫بي‬ِ‫ن‬‫ا‬ ْ‫ٱل‬‫ا‬ ِ‫ة‬ َ‫�صاح‬ِ‫ل‬‫ٱ‬‫ا‬ ُ‫موع‬ْ َ‫م‬
ُ‫موع‬ْ َ‫م‬: َ‫ي‬ِ‫ه‬ ٍ‫ة‬َ‫م‬ِ‫ئ‬‫قا‬ ٍ‫ة‬َ‫ن‬‫طوا‬ ْ‫�ص‬ ُ‫أ‬ ِ‫ل‬ ُ‫ة‬َّ‫ّي‬‫ل‬ُ‫ٱلك‬‫ا‬ ُ‫ة‬ َ‫�صاح‬ِ‫ل‬َ‫ا‬ •
.ِ ْ‫ي‬َ‫ت‬َ‫د‬ ِ‫ْقاع‬‫ل‬‫ٱ‬‫ا‬ ْ‫ي‬َ‫ت‬ َ‫�صاح‬ِ‫وم‬ ِ‫ة‬َّ‫بي‬ِ‫ن‬‫ٱلا‬‫ا‬ ِ‫ة‬ َ‫�صاح‬ِ‫ل‬‫ٱ‬‫ا‬
َ‫ل‬َ‫و‬ْ‫د‬َ‫ج‬ ُ‫َّر‬َ‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬
ِ‫ف‬ ِ‫ب‬ْ‫ر‬َّ‫ض‬‫ال‬
7
p x hp x h = 2 x π x r x h
p x h + 2 x π x r2
‫ة‬َ‫د‬ ِ‫ٱلقاع‬‫ا‬‫ة‬َ‫د‬ ِ‫ٱلقاع‬‫ا‬

14. 15
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
ُ‫َه‬‫ت‬ َ‫�ساح‬ ِ‫م‬ ُ‫ب‬ َ‫�س‬ ْ‫ح‬َ‫أ‬� . 41,23cm2
‫ُها‬‫ت‬ َ‫�ساح‬ ِ‫م‬ ِ ْ‫َي‬‫ت‬َ‫د‬ ِ‫َاع‬‫ق‬‫ٱل‬� ْ‫ن‬ ِ‫م‬ ٍ‫ة‬َ‫د‬ ِ‫قاع‬ ُّ‫ل‬ُ‫ك‬ .ُ‫ه‬َ ْ‫َ�ش‬‫ن‬ َ‫و‬ َ‫ِم‬‫ئ‬‫ٱلقا‬� َ‫�سور‬ ْ‫ٱملو‬� ُ‫ظ‬ ِ‫الح‬ُ‫أ‬�
. ُ‫ة‬َّ‫ّي‬‫ل‬ُ‫ٱلك‬� ُ‫َه‬‫ت‬ َ‫�ساح‬ ِ‫م‬ َ‫و‬ ُِ‫ة‬َّ‫ِبي‬‫ن‬‫ٱجلا‬�
َ‫ة‬َّ‫ِبي‬‫ن‬‫ٱجلا‬� َ‫ة‬ َ‫ِ�ساح‬ ْ‫مل‬َ� ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬� . 2cm َ‫هو‬ ِ ْ‫َي‬‫ت‬َ‫د‬ ِ‫َاع‬‫ق‬‫ٱل‬� ْ‫ن‬ ِ‫م‬ ٍ‫ة‬َ‫د‬ ِ‫قاع‬ ُ‫عاع‬ ُ‫�س‬ .‫ها‬َ ْ‫َ�ش‬‫ن‬ َ‫و‬ َ‫ة‬َ‫ِم‬‫ئ‬‫ٱلقا‬� َ‫َة‬‫ن‬�‫طو‬ ْ‫ُ�س‬‫ال‬‫ٱ‬� ُ‫ظ‬ ِ‫الح‬ُ‫أ‬�
. ِ‫ة‬َ‫ن‬�َ‫و‬ ِ‫ط‬ ْ‫�س‬ ُ‫أ‬ ْ‫ِل‬‫ل‬ َ‫ة‬َّ‫ّي‬‫ل‬ُ‫ٱلك‬� َ‫ة‬ َ‫ِ�ساح‬ ْ‫مل‬َ� َ‫و‬
َ‫ة‬َّ‫ّي‬‫ل‬ُ‫ٱلك‬� َ‫ة‬ َ‫ِ�ساح‬ ْ‫ٱمل‬�‫و‬ َ‫ة‬َّ‫ِبي‬‫ن‬‫ٱجلا‬� َ‫ة‬ َ‫ٱملِ�ساح‬� ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬�
ِ‫ة‬َ‫ن‬�َ‫و‬ ِ‫ط‬ ْ‫�س‬ُ‫أ‬ ْ‫ِل‬‫ل‬
َ‫ة‬َّ‫ّي‬‫ل‬ُ‫ٱلك‬� َ‫ة‬ َ‫ِ�ساح‬ ْ‫ٱمل‬�‫و‬ َ‫ة‬َّ‫ِبي‬‫ن‬‫ٱجلا‬� َ‫ة‬ َ‫�ساح‬ِ‫ٱمل‬� ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬�
: ْ‫ن‬َ‫أ‬� ‫ا‬ً‫ْم‬‫ل‬ ِ‫ع‬ ِ‫ِم‬‫ئ‬‫ٱلقا‬� ِ‫ور‬ ُ‫و�س‬ُ‫ْم‬‫ل‬ِ‫ل‬
BF = 9dm َ‫و‬ 2,8dm ُ‫ه‬ ِ‫فاع‬ِ‫ت‬ ْ‫ار‬ ٍ‫ف‬ ِ‫ر‬ َ‫ح‬ْ‫ن‬ُ‫م‬ ُ‫ه‬ْ‫ب‬ ِ‫�ش‬ ABCD ‫و‬
2
34
1
DC = 7dm ; AB = 2,5dm ; BC = 5dm ; AD = 4dm
h = 9 cm
r = 6 cm
15 cm
8 cm
12 cm
7cm
10 cm
2cm
ِ‫ة‬َ‫د‬ِ‫�لقاع‬ُ‫يط‬ُ‫م‬
ُ‫ِفاع‬‫ت‬ ْ‫ِر‬�
ُ‫ِفاع‬‫ت‬ ْ‫ِر‬�َ‫ي‬ ِ‫ه‬ ُ‫ة‬َّ‫ي‬‫ِب‬‫ن‬‫�جلا‬ ُ‫ة‬ َ‫ِ�ساح‬‫مل‬�
ِ‫ت‬ َ‫يل‬ ِ‫َط‬‫ت‬ ْ‫�س‬ُ ْ‫�مل‬ ُ‫ة‬ َ‫�ساح‬ِ‫م‬
ِ‫ة‬َ‫ث‬‫ل‬َّ‫ث‬‫�ل‬
ِ‫ة‬َ‫د‬ ِ‫�لقاع‬ ُ‫يط‬ ُ‫م‬

15. 16
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
‫األدوات‬ ‫ابستعمال‬
‫هندسية‬
.ٍّ‫ي‬ ِ‫س‬َ‫د‬ْ‫ن‬َ‫ه‬ ٍ‫ل‬ْ‫ك‬ َ‫ش‬ ِ‫ء‬‫شا‬ْ‫ن‬ِ‫إ‬ ُ‫ة‬َ‫د‬‫عا‬ِ‫إ‬ ♦
.ِ‫ة‬َّ‫سي‬َ‫د‬ْ‫ن‬َ‫ه‬‫ال‬ ِ‫وات‬َ‫د‬َ‫اْأل‬ ِ‫ال‬َ‫م‬ْ‫ع‬ِ‫ت‬ ْ‫س‬ِ‫اب‬ ُ‫لَه‬ ٍ‫ف‬ْ‫ص‬َ‫و‬ ْ‫ِن‬‫م‬ ‫ا‬ً‫ق‬‫ِال‬‫ط‬ْ‫ن‬‫ا‬ ٍّ‫ي‬ ِ‫س‬َ‫د‬ْ‫ن‬َ‫ه‬ ٍ‫ل‬ْ‫ك‬ َ‫ش‬ ُ‫شاء‬ْ‫ن‬ِ‫إ‬ ♦
ٌ‫ة‬َّ‫ي‬‫�س‬َ‫د‬ْ‫ن‬ َ‫ه‬ ٌ‫ْ�ساء�ت‬‫ن‬ِ‫إ‬�
ُ‫س‬ْ‫ر‬ َّ‫الد‬
43
ُ‫َّر‬‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬َ‫و‬ ُ‫م‬َ‫ه‬ْ‫ف‬َ‫أ‬
Constructions géométriques
.ِ‫ة‬‫سي‬‫سية‬‫ة‬ ‫ند‬‫ند‬‫د‬ ‫اله‬ ِ‫وات‬‫الهن‬ ِ‫وات‬‫ن‬ ‫األد‬ ِ‫مال‬‫ا‬ ِ‫مال‬‫ا‬ ِ‫ال‬ ‫ع‬‫عم‬‫م‬ ِ‫ت‬‫تع‬‫ع‬ ‫س‬‫ست‬‫ت‬ ِ‫اب‬ِ‫اب‬ِ ‫له‬‫له‬‫ه‬ ٍ‫صف‬‫صف‬‫ف‬ ‫و‬ ‫ِن‬‫ِن‬‫من‬ ‫ا‬‫من‬ ‫ا‬‫ن‬ ‫ِالق‬‫ط‬‫م‬ ‫ِالقا‬‫ط‬‫م‬ ‫ا‬ ‫ان‬‫ِالق‬‫ط‬‫ان‬‫ِالق‬‫ط‬ ٍٍ‫ي‬ ِ‫ندس‬‫ند‬‫د‬ ‫ه‬‫هن‬‫ن‬ ٍ‫ل‬ٍ‫ل‬ٍ ‫ك‬‫كل‬‫ل‬ ‫ش‬‫شك‬‫ك‬ ‫نشاء‬‫نشاء‬‫شاء‬ ِ‫إ‬ِ‫إ‬ِ♦ ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬
379 - 42
487 - 56
666 - 34
2489 - 67
: ‫لى‬ َ‫ع‬ ٍّ‫ي‬ ِ‫�س‬َ‫د‬ْ‫ن‬ َ‫ه‬ ٍ‫ل‬ْ‫ك‬ َ‫�س‬ ِ‫ْ�ساء‬‫ن‬ِ‫إ‬� ِ‫ة‬َ‫عاد‬ِ‫إ‬� َ‫د‬ْ‫ن‬ ِ‫ع‬ ُ‫�ص‬ِ‫ر‬ ْ‫ح‬َ‫أ‬� •
ِ‫ه‬ِ‫ت‬‫قيا�س��ا‬‫ل��ى‬ َ‫ع‬َ‫و‬ ِ‫ل‬ْ‫��ك‬ َّ‫ٱل�س‬� ِ ِ‫نا���ر‬ َ‫ع‬‫ل��ى‬ َ‫ع‬ ِ‫ف‬ُّ‫��ر‬َ‫ع‬َّ‫ت‬‫ٱل‬� -
‫؛‬ ِ‫��ة‬ َ‫ح‬َ َ‫ت‬ْ‫ق‬ُ‫مل‬‫ٱ‬�
ِ‫د‬��َ‫ْي‬‫ل‬‫ٱ‬‫ا‬ِ‫ب‬ ِ‫ة‬ َ‫ور‬ ََّ‫ٱل���ر‬� َ‫د‬��ْ‫ن‬ ِ‫ع‬ ٍّ‫ْريب��ي‬‫ق‬َ‫ت‬ ٍ‫ل‬ْ‫��ك‬ َ‫�س‬ ِ‫��م‬ ْ‫�س‬ َ‫ر‬ -
َ‫وي��ن‬ْ‫ك‬َ‫ت‬ َ‫��ك‬ِ‫ل‬َ‫ذ‬ ُ‫ي��ح‬ِ‫ت‬ُ‫ي‬ . ٍ‫د�ة‬َ‫أ‬� ِّ‫ي‬َ‫أ‬� ِ‫مال‬ْ‫ع‬َ‫ت‬�� ْ‫��س‬ َ‫ون‬ُ‫د‬
‫؛‬ ُ‫ه‬ُ‫ؤ‬‫و‬‫��ا‬ َ‫ْ�س‬‫ن‬ِ‫إ‬� ِ‫ر�د‬ُ‫��م‬ْ�‫ٱل‬� ِ‫ل‬ْ‫��ك‬ َََّ‫ٱل�س‬� ْ‫��ن‬ َ‫ع‬ ٍ‫ة‬َ‫��ر‬ْ‫ك‬ِ‫ف‬
ِ‫و�ت‬َ‫د‬ َ‫أ‬� ِ‫تي��ار‬ ْ‫و�خ‬ ِ‫�س��اء‬ْ‫ن‬ِ‫إ‬‫ل‬‫ٱ‬� ِ‫ط��و�ت‬ ُ‫خ‬ ِ‫د‬��‫دي‬ْ َ‫ت‬ -
‫؛‬ ِ‫��ة‬َ‫م‬ِ‫ئ‬‫ال‬ُ‫مل‬‫ٱ‬� ِ‫��م‬ ْ‫�س‬ َََّ‫ٱلر‬�
‫؛‬ ٍ‫قان‬ْ‫ت‬ ِ‫إ‬‫ا‬ِ‫ب‬ ِ‫ل‬ْ‫ك‬ َّ‫ٱل�س‬� ِ‫�ساء‬ْ‫ن‬ِ‫إ‬� -
‫َّ��ذي‬َ‫ل‬‫ٱ‬� ِ‫ل‬َْ‫ك‬�� َّ‫ٱل�س‬� ِ‫يا�س��ات‬ِ‫ق‬ ِ‫��ة‬َ‫م‬ِ‫ئ‬‫ال‬ُ‫م‬ ْ‫��ن‬ِ‫م‬ ِ‫ّ��ق‬ُ‫ق‬ َ‫ح‬ََّ‫ت‬‫ٱل‬� -
. ِ‫ي��ات‬ َ‫ط‬ْ‫ع‬ُ‫مل‬‫ٱ‬� َ‫��ع‬َ‫م‬ ُ‫ه‬ُ‫ؤ‬‫و‬‫��ا‬ َ‫ْ�س‬‫ن‬ِ‫إ‬� َّ َ‫ت‬
ِ‫ة‬َّ‫�سي‬َ‫د‬ْ‫ن‬َ‫ٱله‬� ِ‫ال‬َ‫ك‬ ْ‫�س‬َ‫أ‬‫ال‬‫ٱ‬� ‫َى‬‫ل‬ َ‫ع‬ ِ‫موز‬ُّ‫ٱلر‬� ِ‫�ص‬ْ‫ع‬َ‫ب‬ ‫نى‬ْ‫ع‬ َ‫م‬ •
ِ‫ف‬ َ‫�س‬َ‫ت‬ْ‫ن‬ُ‫م‬ I ْ‫ي‬َ‫أ‬�
: ً‫َال‬‫ث‬َ‫م‬ 897 - 53 ِ‫اب‬ َ‫ِس‬‫ح‬ِ‫ل‬
: ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫ن‬ َ‫و‬ 897 ْ‫ن‬ِ‫م‬ 50 ُ‫ح‬َ‫ر‬ْ‫ط‬َ‫ن‬
897 - 50 = 847
: 847 ْ‫ن‬ِ‫م‬ 3 ُ‫ح‬َ‫ر‬ْ‫ط‬َ‫ن‬ َّ‫م‬ُ‫ث‬
847 - 3 = 844
897 - 53 = 844 : ْ‫ن‬َ‫ذ‬ِ‫إ‬
: ‫ا‬َ‫ذ‬َ‫ك‬َ‫ه‬ ِ‫ِساب‬‫ح‬‫ال‬ ُ‫ْديم‬‫ق‬َ‫ت‬ ُ‫ن‬ِ‫ك‬ْ ُ‫ي‬
897 - 53 = 897 - 50 - 3
= 847 - 3 = 844
758 - 35
524 - 13
279 - 28
1568 - 45
♦
♦
♦
♦
♦
♦
♦
♦
GJ = JK = KF
EI = GI]GE[
BOA= BOC
^ ^MON = NOC
^ ^
G

16. 17
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
:ٍ‫بيعية‬ ْ‫َر‬‫ت‬ ٍ‫ة‬َ‫ق‬ َ‫ر‬ َ‫و‬ ‫لى‬ َ‫ع‬ َ‫ل‬ْ‫ك‬ َََّ‫ٱل�س‬� ُ‫ئ‬ ِ‫�س‬ْ‫ن‬ُ‫أ‬�
ُ ْ‫ي‬ َ‫غ‬ ِ‫ل‬ْ‫ك‬ َّ‫ٱل�س‬� ِ‫�ساء‬ْ‫ِن‬‫إ‬‫ال‬ ُ‫د‬َ‫م‬ ْ‫ح‬َ‫أ‬� ‫ها‬َ‫ع‬َ‫ّب‬َ‫ت‬� ‫ِي‬‫ت‬َّ‫ل‬َ� ُ‫طو�ت‬ُ‫ٱخل‬�
َ‫ل‬ْ‫ك‬ َّ‫ٱل�س‬� ُ‫ئ‬ ِ‫�س‬ْ‫ن‬ُ‫أ‬� َّ‫م‬ُ‫ث‬ ِ‫طو�ت‬ُ‫ٱخل‬� ِ‫ِه‬‫ذ‬ َ‫ه‬ ُ‫ّب‬ِ‫ت‬ َ‫ر‬ُ‫أ‬� . ٍ‫ة‬َ‫َب‬‫ت‬ ْ‫ر‬ َ‫م‬
ِ‫ل‬ْ‫ك‬ َّ‫ِال�س‬‫ب‬ ِ‫�ساء‬ْ‫ِن‬‫إ‬‫ال‬� ِ‫ل‬ ِ‫ر�ح‬ َ‫م‬ ْ‫ن‬ ِ‫م‬ ٍ‫َة‬‫ل‬ َ‫ح‬ ْ‫ر‬ َ‫م‬ ََّ‫ل‬ُ‫ك‬ ْ‫ط‬ُ‫ب‬ ْ‫ر‬َ‫أ‬�
. ِ‫ب‬ ِ‫نا�س‬ُ‫�مل‬
. ٍّ‫ي‬ ِ‫�س‬َ‫د‬ْ‫ن‬ َ‫ه‬ ٍ‫ل‬ْ‫ك‬ َ‫�س‬ ِ‫اء‬ َ‫�س‬ْ‫ِن‬‫إ‬ ِ‫ال‬ ٍ‫ة‬َ‫َّب‬‫ت‬َ‫ر‬ ُ‫م‬ َ‫ل‬ ِ‫ر�ح‬ َ‫م‬ 3 ِ‫ِه‬‫ذ‬ َ‫ه‬
‫ا‬ً‫ع‬َّ‫ب‬ َ‫ر‬ُ‫م‬ ُ‫م‬ ُ‫�س‬ ْ‫ر‬َ‫أ‬� : 1 ُ‫َة‬‫ل‬ َ‫ح‬ ْ‫ر‬َ‫�مل‬
ِ‫ع‬َّ‫ب‬ َ‫ُر‬‫مل‬� ُّ‫ري‬ َ‫ط‬َ‫ق‬ ُ‫م‬ ُ‫�س‬ ْ‫ر‬َ‫أ‬� : 2 ُ‫َة‬‫ل‬ َ‫ح‬ ْ‫ر‬َ‫�مل‬
ٍ‫ع‬ ُ‫قاط‬َ‫ت‬ ُ‫ة‬ َ‫ط‬ْ‫ق‬ُ‫ن‬ ‫ها‬ ُ‫ز‬َ‫ك‬ ْ‫ر‬َ‫م‬ ‫ي‬ِ‫ت‬َّ‫ل‬َ� َ‫ة‬ َ‫ر‬ِ‫ئ‬�ّ‫د‬‫�ل‬ ُ‫م‬ ُ‫�س‬ ْ‫ر‬َ‫أ‬� : 3 ُ‫َة‬‫ل‬ َ‫ح‬ ْ‫ر‬َ‫�مل‬
ِ‫ع‬َّ‫ب‬ َ‫ر‬ُ‫ْم‬‫ل‬ِ‫ل‬ ِ‫ة‬َ‫ع‬َ‫ب‬ ْ‫ر‬َ‫أ‬‫ل‬� ِ‫و�س‬ُ‫ؤ‬‫و‬ ُّ‫�لر‬ َ‫ن‬ِ‫م‬ ُّ‫ر‬ُ َ‫ت‬ َ‫و‬ ِ‫ع‬َّ‫ب‬ َ‫ُر‬‫مل‬� ُّ‫ري‬ َ‫ط‬َ‫ق‬
: ُ‫ث‬ْ‫ي‬ َ‫ح‬ ، َ‫�ساء‬ْ‫ي‬َ‫ب‬ ٍ‫ة‬َ‫ق‬ َ‫ر‬ َ‫و‬ ‫لى‬ َ‫ع‬ ‫ّايل‬َ‫ت‬‫ٱل‬� َ‫ل‬ْ‫ك‬ ََّ‫ٱل�س‬� ُ‫ئ‬ ِ‫�س‬ْ‫ن‬ُ‫أ‬�
: ُ‫ُه‬‫ن‬ ِّ‫َو‬‫ل‬ُ‫أ‬� َ‫و‬ َ‫ل‬ْ‫ك‬ َََّ‫ٱل�س‬� ُ‫ئ‬ ِ‫�س‬ْ‫ن‬ُ‫أ‬�
: ِ‫�ساء‬ِْ‫ن‬‫إ‬ ْ‫ال‬َ� �‫ذ‬َ‫ِه‬‫ل‬ َ‫ب‬ ِ‫نا�س‬ُ ْ‫مل‬َ� َ‫ل‬ْ‫ك‬ َََّ‫ٱل�س‬� ُ‫د‬ِّ‫د‬ َ‫ح‬ُ‫أ‬�
1
3
5
6
4
،ٌ َّ‫ي‬َ‫ع‬ُ‫م‬ ، ٌ‫ع‬َّ‫ب‬ َ‫ر‬ُ‫م‬ : ‫يها‬ّ‫م‬ َ‫�س‬ُ‫أ‬� َ‫و‬ َ‫ة‬َ‫الي‬ّ‫ت‬‫�ل‬ َ‫كال‬ ْ‫�س‬َ‫أ‬‫ل‬� ُ‫ف‬ َّ‫ر‬َ‫ع‬َ‫ت‬َ‫أ‬� •
. ٌ‫ّث‬َ‫ل‬َ‫ث‬ُ‫م‬ ، ٍ‫ف‬ ِ‫ر‬ َ‫ح‬ْ‫ن‬ُ‫م‬ ُ‫ه‬ْ‫ب‬ ِ‫�س‬ ، ِ‫الع‬ ْ‫�س‬َ‫أ‬‫ل‬� ‫و�زي‬َ‫ت‬ُ‫م‬ ، ٌ‫طيل‬َ‫ت‬ ْ‫�س‬ُ‫م‬
. 4,6cm ِ‫ه‬ِ‫ْع‬‫ل‬ ِ‫�س‬ َ‫ا�س‬َ‫ي‬ِ‫ق‬ ABDC ِ‫ع‬َّ‫ب‬ َ‫ر‬ُ‫م‬ ُ‫اء‬ َ‫�س‬ْ‫ن‬‫إ‬� )a(
.E, F, H, G ِ‫ْط‬‫ق‬ُّ‫ن‬‫�ل‬ َ‫ن‬ِ‫م‬ ُّ‫ر‬ُ َ‫ت‬ O ‫ها‬ ُ‫ز‬َ‫ك‬ْ‫ر‬َ‫م‬ ٍِ‫ة‬َ‫ِر‬‫ئ‬�‫د‬ ُ‫اء‬ َ‫�س‬ْ‫ن‬‫إ‬� )b(
.O‫ا‬َ‫م‬ِ‫ه‬ِ‫ع‬ ِ‫قاط‬ُ‫ت‬ َ‫ة‬ َ‫ط‬ْ‫ق‬ُ‫ن‬ َ‫و‬ ]HF[‫و‬ ]EG[ ْ‫ي‬َ‫ت‬َ‫ع‬ ْ‫ط‬ِ‫ق‬‫�ل‬ ُ‫اء‬ َ‫�س‬ْ‫ن‬‫إ‬� )c(
. ِ‫ع‬َّ‫ب‬ َ‫ُر‬‫مل‬� ِ‫الع‬ ْ‫�س‬ َ‫أ‬� ُ‫ات‬َ‫ف‬ ِ‫�س‬َ‫ت‬ْ‫ن‬ُ‫م‬ H, G, F, E ِ‫ط‬ْ‫ق‬ُّ‫ن‬‫�ل‬ ُ‫اء‬ َ‫�س‬ْ‫ن‬‫إ‬� )d(
.]EF[ َ‫ة‬َ‫ع‬ ْ‫ط‬ِ‫ق‬‫�ل‬ َ‫ئ‬ ِ‫�س‬ْ‫ن‬ُ‫أ‬� )a(
AB = 6cm : ُ‫ث‬ْ‫ي‬ َ‫ح‬ ABCD َ‫يال‬ ِ‫يط‬ِ‫ت‬ ْ‫�س‬ُ‫م‬ َ‫ئ‬ ِ‫�س‬ْ‫ن‬ُ‫أ‬� )b(
BC = 4cm
.EFB َ‫ّث‬َ‫ل‬َ‫ث‬ُ‫مل‬� َ‫ئ‬ ِ‫�س‬ْ‫ن‬ُ‫أ‬� )c(
َ‫ف‬ َ‫�س‬َ‫ت‬ّ‫ن‬ُ‫م‬ F َ‫ة‬ َ‫ط‬ّ‫ق‬ُّ‫ن‬‫�ل‬ ‫و‬ ]DC[ َ‫ف‬ َ‫�س‬َ‫ت‬ّ‫ن‬ُ‫م‬ E َ‫ة‬ َ‫ط‬ّ‫ق‬ُّ‫ن‬‫�ل‬ ُ‫د‬ِّ‫د‬ َ‫ح‬ُ‫أ‬� )d(
. ]AD[
AE = 3cm ‫و‬ 8cm ِ‫ه‬ِ‫ْع‬‫ل‬ ِ‫�س‬ ُ‫قيا�س‬ ٌ‫ع‬َّ‫ب‬ َ‫ر‬ُ‫م‬ ABCD
2
)1(
)a(
)c(
)d(
)b(
)3()2( )4(

17. 18
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
.ِ‫ة‬َ‫ب‬ ِ‫ناس‬ُ‫الم‬ ِ‫ة‬َ‫ِد‬‫ع‬‫القا‬ ِ‫يق‬ِ‫ب‬ْ‫ط‬َ‫ت‬ِ‫ب‬ ِ‫ت‬َ‫ِيال‬‫ط‬َ‫ت‬ ْ‫س‬ُ‫الْم‬ ‫وازي‬َ‫ت‬ُ‫م‬َ‫و‬ ِ‫ب‬َّ‫ع‬َ‫ك‬ُ‫الم‬ ِ‫م‬ْ‫ج‬َ‫ح‬ ُ‫ساب‬ِ‫ح‬ ♦
ُ‫م‬ ْ‫ج‬َ ْ‫ل‬َ� : ِ‫يلت‬ ِ‫َط‬‫ت‬ ْ‫�س‬ُ ْ‫ٱمل‬� ‫َو�زي‬‫ت‬ ُ‫م‬ َ‫و‬ ُ‫ب‬ََّ‫ع‬َ‫ك‬ُ ْ‫مل‬َ�
ُ‫س‬ْ‫ر‬ َّ‫الد‬
44
ُ‫َّر‬‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬َ‫و‬ ُ‫م‬َ‫ه‬ْ‫ف‬َ‫أ‬
Le cube et le parallélépipède : le volume
ِ ِ ِ ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬
8 x 3 = .......
8 x 7 = .......
8 x 11 = .......
8 x 2 = .......
8 x 6 = .......
8 x 10 = .......
8 x 1 = .......
8 x 5 = .......
8 x 9 = .......
8 x 0 = .......
8 x 4 = .......
8 x 8 = .......
:َ‫هو‬ a ُ‫ه‬ُ‫ف‬ ْ‫ر‬ َ‫ح‬ ِ‫ب‬ََّ‫ع‬َ‫ك‬ ُ‫م‬ ٌ‫م‬ ْ‫ج‬ َ‫ح‬ •b َ‫و‬ a ِ‫ِه‬‫ف‬‫رو‬ ُ‫ح‬ ُ‫ِيا�ص‬‫ق‬ ٍ‫يلت‬ ِ‫َط‬‫ت‬ ْ‫�س‬ ُ‫م‬ ‫َو�زي‬‫ت‬ ُ‫م‬ ٌ‫م‬ ْ‫ج‬ َ‫ح‬ •
: ‫هو‬ c‫و‬
: َّ‫ن‬ِ‫إ‬‫ا‬َ‫ف‬ ً‫ل‬َ‫ث‬ َ‫م‬ a = 3cm َ‫كان‬ �‫ذ‬ِ‫إ‬� •
: ّ‫ن‬ِ‫إ‬‫ا‬َ‫ف‬ a = 2cm َ‫كان‬ �‫ذ‬ِ‫إ‬� •
ِ‫ِفاع‬‫ت‬ ْ‫ر‬ ِ‫�ال‬ ِ‫ف‬ ِ‫ة‬َ‫د‬ ِ‫�لقاع‬ ِ‫ة‬ َ‫�ساح‬ ِ‫م‬ ُ‫�ء‬َ‫د‬ ُ‫ج‬ َ‫ِك‬‫ل‬َ‫ذ‬َ‫ك‬ َ‫هو‬ V •
: ً‫ل‬َ‫ث‬ َ‫م‬ َ‫كان‬ �‫ذ‬ِ‫إ‬� •
c = 2cm َ‫و‬ b = 3cm ‫و‬ a = 5cm
: َّ‫ن‬ِ‫إ‬‫ا‬َ‫ف‬ •
ِ‫ا�ص‬َ‫ي‬ِ‫ق‬ْ‫ل‬� ِ‫ة‬َ‫د‬ ْ‫ح‬ َ‫و‬ ِ‫�ص‬ْ‫ف‬َ‫ن‬ِ‫ب‬ ‫ا‬َ‫ْه‬‫ن‬ َ‫ع‬ ٌ َّ‫ب‬َ‫ع‬ َ‫م‬ c َ‫و‬ b َ‫و‬ a •
َ‫ل‬َ‫و‬ْ‫د‬َ‫ج‬ ُ‫ّر‬َ‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬
ِ‫ف‬ ِ‫ب‬ْ‫ر‬َّ‫ض‬‫ال‬
8
V = a x a x a = a3
3 x 3 x 3 = 27
2 x 2 x 2 = 8
V = 27cm3
V = 8cm3
V = a x b x c
َ‫و‬
5 x 2 x 3 = 30V = 30cm3
َ‫و‬
َ‫و‬

18. 19
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
: ِ ْ‫َي‬‫ت‬َ‫ق‬‫ي‬ِ‫ر‬ َ‫ِط‬‫ب‬ a ِ‫ف‬ ْ‫ر‬َ‫�ل‬ ِ‫�ت‬َ‫ذ‬ ِ‫ة‬َ‫ب‬َّ‫ع‬َ‫ك‬ُ ْ‫مل‬َ� ِ‫ة‬َ‫ْب‬‫ل‬ُ‫ْع‬‫ل‬َ� ِ‫ء‬ ْ‫َل‬ ِ‫مل‬ ِ‫ة‬ َ‫م‬ ِ‫ز‬ ّ‫�لل‬
1cm
1cm
1cm
ِ‫ة‬َ‫غي‬ َّ‫�ل�س‬ ِ‫بات‬ََّ‫ع‬َ‫ك‬ُ ْ‫مل‬َ� َ‫د‬َ‫د‬ َ‫ع‬ ُ‫ُب‬‫ت‬ ْ‫ك‬َ‫أ‬�
: ‫ها‬َ‫م‬ ْ‫ج‬ َ‫ح‬ ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬� َ‫و‬ ُ‫ه‬َ‫ِب‬‫ن‬‫ا‬ َ‫ج‬ ِ‫ة‬َ‫ْب‬‫ل‬ُ‫ْع‬‫ل‬َ� ِ‫ء‬ ْ‫َل‬ ِ‫مل‬ ِ‫ة‬ َ‫م‬ ِ‫ز‬ ّ‫�لل‬
1cm
1cm
1cm
ِ‫ة‬َ‫غي‬ َّ‫�ل�س‬ ِ‫بات‬ََّ‫ع‬َ‫ك‬ُ ْ‫مل‬َ� َ‫د‬َ‫د‬ َ‫ع‬ ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬�
ِ‫ت‬ َ‫يل‬ ِ‫ط‬َ‫ت‬ ْ‫�س‬ُ ْ‫مل‬َ� ‫َو�زي‬‫ت‬ ُ‫م‬ َ‫و‬ ِ‫ب‬َّ‫ع‬َ‫ك‬ُ ْ‫مل‬َ� َ‫م‬ ْ‫ج‬ َ‫ح‬ ُ‫ب‬ ُ‫�س‬ ْ‫ح‬َ‫أ‬�
: V َ‫هو‬ ُ‫ه‬ُ‫م‬ ْ‫ج‬ َ‫ح‬ َ‫و‬ L ، l ، h َ‫ي‬ ِ‫ه‬ ِ‫ت‬ َ‫يل‬ ِ‫ط‬َ‫ت‬ ْ‫�س‬ُ ْ‫مل‬َ� ‫َو�زي‬‫ت‬ ُ‫م‬ ُ‫عاد‬ْ‫ب‬َ‫أ‬�
ِ: ‫ل‬ َ‫و‬ْ‫د‬َ ْ‫جل‬َ� َ‫ء‬ ْ‫ل‬ َ‫م‬ ُ‫ل‬ِ‫م‬ ْ‫ك‬ُ‫أ‬�
2
3
4
1
1 ‫لطريقة‬َ�
ِ‫ة‬َ‫ْب‬‫ل‬ُ‫�لع‬ ‫يف‬ ِ‫قات‬َ‫ب‬ َّ‫�لط‬ ُ‫د‬ُ‫د‬ َ‫ع‬
ٍ‫ة‬َ‫ق‬َ‫ب‬ َ‫ط‬ ِّ‫ل‬ُ‫ك‬ ‫يف‬ ِ‫بات‬َّ‫ُكَع‬‫مل‬� ُ‫د‬ُ‫د‬ َ‫ع‬
ِ‫ة‬َ‫ْب‬‫ل‬ُ‫�لع‬ ‫يف‬ ِ‫بات‬َّ‫ُكَع‬‫مل‬� ُ‫د‬ُ‫د‬ َ‫ع‬
V = …… cm3
2 ‫�لطريقة‬
a = …..cm
V = a x a x a
V = …….cm3
7cm5cm
65cm
10cm
V = ……V = ……
l (cm) 4 3 7 . . .
L (cm) 5 2 . . . 8
h (cm) 7 . . . 6 9
V (cm3) . . . 36 84 144
L
l
h
3 cm
4 cm
6 cm

19. 20
ُ‫ة‬‫ــــ‬َّ‫ي‬ِ‫و‬َ‫ئ‬ِ‫م‬ْ‫ل‬‫ٱ‬ ُ‫ة‬‫ـ‬َ‫ب‬ ْ‫س‬ِّ‫ن‬‫ل‬َ‫ا‬
ُ‫س‬ْ‫ر‬ َّ‫الد‬
45
Le pourcentage
ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬. ‫اه‬ُ‫ساب‬ِ‫ح‬َ‫و‬ ِ‫ة‬َّ‫وي‬َ‫ئ‬ِ‫م‬‫ال‬ ِ‫ة‬َ‫ب‬ ْ‫س‬ِّ‫ن‬‫ال‬ ُ‫هوم‬ْ‫ف‬َ‫م‬ ♦
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
3
4
7
4
6
5
6
5
12
80
15
60
●
●
●
●
ُ‫َّر‬‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬َ‫و‬ ُ‫م‬َ‫ه‬ْ‫ف‬َ‫أ‬
.ٍ‫ة‬َ‫ن‬ َ‫س‬ ِ‫ة‬َّ‫د‬ُ‫م‬ِ‫ل‬ ِ‫ه‬ْ‫ي‬َ‫د‬َ‫ل‬ ٍ‫ع‬َ‫ود‬ُ‫م‬ ٍّ
‫ي‬ِ‫ال‬َ‫م‬ ٍ‫غ‬َ‫ل‬ْ‫ب‬َ‫م‬ ّ
ِ‫ل‬ُ‫ك‬ ْ‫ن‬َ‫ع‬ ُ‫ك‬ْ‫ن‬َ‫ب‬ْ‫ل‬‫ٱ‬ ‫يها‬ِّ‫د‬َ‫ؤ‬ُ‫ي‬ ‫تي‬َّ‫ٱل‬ ُ‫ة‬َّ‫ي‬ ِ‫و‬َ‫ئ‬ِ‫م‬ْ‫ل‬‫ٱ‬ ُ‫ة‬َ‫ب‬ ْ‫س‬ِّ‫ٱلن‬ َ‫و‬ُ‫ه‬ ِ‫ة‬َ‫د‬ِ‫ائ‬َ‫ف‬ْ‫ل‬‫ٱ‬ ُ‫ر‬ْ‫ع‬ ِ‫س‬●
.َ‫م‬ِ‫اه‬َ‫ر‬َ‫د‬ 7 ُ‫ك‬ْ‫ن‬َ‫ب‬ْ‫ل‬‫ٱ‬ ‫ا‬َ‫ه‬ْ‫ن‬َ‫ع‬ ‫ي‬ّ‫د‬َ‫ؤ‬ُ‫ي‬ ٍ‫ة‬َ‫ل‬ِ‫كام‬ ِ‫ة‬َ‫ن‬ َ‫س‬ َ‫ة‬َّ‫د‬ُ‫م‬ ِ‫ك‬ْ‫ن‬َ‫ب‬ْ‫ل‬‫ٱ‬ ‫في‬ ُ‫ع‬َ‫تود‬ ٍ‫م‬َ‫ه‬ْ‫ر‬ِ‫د‬ 100 ُّ‫ل‬ُ‫ك‬ : ‫ي‬ِ‫ن‬ْ‫ع‬َ‫ي‬ ‫ا‬َ‫ذ‬َ‫ه‬َ‫ف‬ 7 % ‫و‬ُ‫ه‬ ً‫ل‬َ‫ث‬ِ‫م‬ ‫ة‬َ‫د‬ِ‫فائ‬ْ‫ل‬‫ا‬ ُ‫ر‬ْ‫ع‬ ِ‫س‬ َ‫كان‬ ‫ذا‬ِ‫إ‬●
.َ‫مال‬ ْ‫س‬ْ‫أ‬َّ‫ٱلر‬ ‫ى‬ّ‫م‬ َ‫س‬ُ‫ي‬ ِ‫ك‬ْ‫ن‬َ‫ب‬ْ‫ل‬‫ٱ‬ ‫في‬ ُ‫ع‬َ‫مود‬ْ‫ل‬‫ٱ‬ ُ‫غ‬َ‫ل‬ْ‫ب‬َ‫م‬ْ‫ل‬َ‫ا‬ ●
.َ‫ة‬َّ‫ي‬ ِ‫و‬َ‫ن‬ َّ‫ٱلس‬ َ‫ة‬َ‫د‬ِ‫فائ‬ْ‫ل‬‫ٱ‬ ‫ى‬ّ‫سم‬ُ‫ت‬ ٍ‫ة‬َ‫ن‬ َ‫س‬ ِ‫ة‬َّ‫د‬ُ‫م‬ِ‫ل‬ ُ‫ة‬َ‫د‬ِ‫فائ‬ْ‫ل‬َ‫ا‬●
: ‫ة‬َ‫ل‬ِ‫ث‬ْ‫َم‬‫أ‬ ،ٍ‫ة‬َّ‫ي‬ ِ‫و‬َ‫ئ‬ِ‫م‬ ٍ‫ة‬َ‫ب‬ ْ‫س‬ِ‫ن‬ ِ‫ثيل‬ْ‫م‬َ‫ت‬ِ‫ل‬ ٍ‫ة‬َ‫ط‬ِ‫ر‬ ْ‫َش‬‫أ‬ ْ‫َو‬‫أ‬ ٍ‫ع‬َ‫ط‬ِ‫ق‬ ُ‫مال‬ْ‫ع‬ِ‫ت‬ ْ‫اس‬ ُ‫ن‬ِ‫ك‬ْ‫م‬ُ‫ي‬●
2 ‫نضرب‬ ،ً‫َال‬‫ث‬َ‫م‬ 10 ْ‫ِن‬‫م‬ َ‫اب‬ َ‫ِس‬‫ح‬ِ‫ل‬
: 5 ‫على‬ ‫النتيجة‬ ‫ونقسم‬ 10 ‫ف‬
: ْ‫ن‬َ‫ذ‬ِ‫إ‬.4 : ‫هي‬ 10 ‫من‬
‫من‬
‫من‬
‫من‬
‫من‬
2
5
2
5
(2 x 10) : 5 = 20 : 5
= 4
ِ
: ‫ة‬َ َ‫أ‬ ،‫ة‬َّ ‫ة‬ ‫ة‬َ ْ َ‫أ‬ َ‫أ‬ َ ُ
‫ة‬َ‫ن‬‫نة‬‫ة‬ َ ‫ة‬َّ‫د‬ُ ‫ل‬ ‫ه‬َْ‫د‬َ‫ل‬‫لد‬‫د‬ ‫ع‬َ‫ود‬ُ ّ
‫ال‬َ ‫غ‬َ‫ل‬‫لغ‬‫غ‬ َْ ‫ل‬ّ‫ل‬ّ ُ‫ك‬‫كل‬‫ل‬ُ‫ك‬ُ ْ‫ن‬َ‫ع‬‫عن‬‫ن‬ ُ‫ك‬ُ‫ك‬ُ ْ‫ن‬‫نك‬‫ك‬ َْ‫ل‬‫ٱ‬ ‫يها‬ْ‫ل‬‫ٱ‬ ‫يها‬ْ ّ‫د‬َ‫ؤ‬ّ‫ؤ‬ّ‫ؤد‬‫د‬َ‫ؤ‬َُ‫ي‬ ‫تي‬‫يؤ‬ ‫تي‬‫ؤ‬ُ‫ي‬ ‫تي‬ُ َّ‫ٱل‬‫ي‬ ‫ٱلتي‬‫ي‬ ‫تي‬َّ‫ٱل‬َّ ُ‫ة‬َّ َ‫ئ‬ ْ‫ل‬‫ٱ‬ْ‫ل‬‫ٱ‬ْ ُ‫ة‬َ ْ ‫ٱلن‬ّ‫ن‬‫ٱل‬ّ َُ‫ه‬ ‫ة‬َ‫ائد‬‫ائد‬‫د‬ َ‫ف‬‫فائ‬‫ائ‬ ْ‫ل‬‫ٱ‬‫ٱلف‬‫ف‬ْ‫ل‬‫ٱ‬ْ ُْ‫ع‬
100%
75%
10%
َّ‫ل‬ُ‫ك‬ َّ‫ن‬َ‫أ‬� �َ‫ذ‬َ‫ه‬ ‫ي‬ِ‫ن‬ْ‫ع‬َ‫ي‬ ِ‫َاء‬ ْ‫�مل‬ ْ‫ن‬ِ‫م‬ 65 %‫َى‬‫ل‬ َ‫ع‬ ِ‫ان‬ َ‫�س‬ْ‫ن‬ ِ‫إ‬ ْ‫�ل‬ ُ‫م‬ ْ‫�س‬ ِ‫ج‬ ‫ي‬ِ‫و‬َ‫ت‬ ْ‫ح‬َ‫ي‬ ●
.ِ‫َاء‬ ْ‫�مل‬ ْ‫ن‬ِ‫م‬ 65kg‫َى‬‫ل‬ َ‫ع‬‫ي‬ِ‫و‬َ‫ت‬ْ َ‫ت‬ 100kg ُ‫ه‬ُ‫ت‬َ‫ل‬ْ‫ت‬ُ‫ك‬ ٍ‫�سان‬ْ‫ن‬ِ‫إ‬�
: ِ‫ار‬َ‫ر‬ ْ‫َز‬ْ‫ال‬‫َى‬‫ل‬ َ‫ع‬ ُ‫ع‬ُ‫اب‬َ‫ت‬َّ‫ت‬‫ِال‬‫ب‬ ُ‫ط‬َ‫غ‬ ْ‫�س‬َ‫ن‬ ِ‫ة‬َ‫ب‬ َ‫�س‬ ْ‫ُح‬ ْ‫ِامل‬‫ب‬ 35kg �ِ‫ب‬ ْ‫ن‬ِ‫م‬ 80 % ِ‫َ�ساب‬ ِ‫ل‬ ●
25
100
25% 1
4
= =
5
100
50% 1
2
= =
75
100
75% 3
4
= =
100 40
65 .............
kg ‫بـ‬ ‫إنسان‬ ‫كتلة‬
kg ‫بـ‬ ‫املاء‬ ‫كتلة‬
35 x 80 % =
َّ‫ل‬
.‫�لربع‬‫ي‬ِ‫ن‬ْ‫ع‬َ‫ت‬25 % ‫ة‬َ‫ب‬ ْ‫�س‬ِ‫ن‬:
.‫�لن�سف‬‫ي‬ِ‫ن‬ْ‫ع‬َ‫ت‬ 50 % ‫ة‬َ‫ب‬ ْ‫�س‬ِ‫ن‬:
.‫أرباع‬�‫ثالثة‬‫ي‬ِ‫ن‬ْ‫ع‬َ‫ت‬ 75 % ‫ة‬َ‫ب‬ ْ‫�س‬ِ‫ن‬ :
●
●
●

20. 21
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
.32kg ِ‫بـ‬ ِ‫ه‬ِ‫م‬ ْ‫س‬ ِ‫ج‬ ‫في‬ ِ‫ماء‬ْ‫ل‬‫ٱ‬ ُ‫ة‬َ‫ل‬ْ‫ت‬ُ‫ك‬ ُ‫ر‬َّ‫د‬َ‫ق‬ُ‫ت‬َ‫و‬ 40kg ٌ‫ان‬‫و‬َ‫ي‬َ‫ح‬ ُ‫ن‬ ِ‫ز‬َ‫ي‬
. ِ‫ان‬‫و‬َ‫ي‬َ‫ح‬ْ‫ل‬‫ٱ‬ ِ‫م‬ ْ‫س‬ ِ‫ج‬ ‫ي‬ِ‫ف‬ ِ‫ماء‬ْ‫ل‬‫ا‬ ِ‫ة‬َ‫ل‬ْ‫ت‬ُ‫ك‬ِ‫ل‬ َ‫ة‬َّ‫ي‬ ِ‫و‬َ‫ئ‬ِ‫م‬ْ‫ل‬‫ا‬ َ‫ة‬َ‫ب‬ ْ‫س‬ِّ‫لن‬َ‫ا‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬ ●
1
2
3
4
5
6
7
8
21
: 850 ‫ى‬َ‫ل‬ِ‫إ‬ ‫ميها‬ِّ‫ل‬َ‫ع‬َ‫ت‬ُ‫م‬ ُ‫د‬َ‫د‬َ‫ع‬ ُ‫ل‬ ِ‫ص‬َ‫ي‬ ٍ‫ة‬ َ‫س‬َ‫ر‬ْ‫د‬َ‫م‬ ‫ي‬ِ‫ف‬ 80% ٍ‫جاح‬َّ‫ٱلن‬ ُ‫ة‬َ‫ب‬ ْ‫س‬ِ‫ن‬ ْ‫ت‬َ‫غ‬َ‫ل‬َ‫ب‬
.ٍ‫ة‬َ‫ب‬ ِ‫اس‬َ‫ن‬َ‫ت‬ُ‫م‬ ٍ‫اد‬َ‫د‬ْ‫َع‬‫أ‬ َ‫ل‬ َ‫و‬ْ‫د‬َ‫ج‬ ُ‫ل‬ِ‫م‬ْ‫ع‬َ‫ت‬ ْ‫َس‬‫أ‬َ‫و‬ ‫ا‬‫و‬‫ح‬َ‫ج‬َ‫ن‬ َ‫ين‬ِ‫ذ‬َّ‫ال‬ َ‫ِّمي‬‫ل‬َ‫َع‬‫ت‬ُ‫مل‬‫ٱ‬ َ‫د‬َ‫د‬َ‫ع‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬ ●
100 850
80 ................
َ‫ِّمي‬‫ل‬َ‫َع‬‫ت‬ُ‫ِلم‬‫ل‬ ُّ‫ِي‬‫ل‬ُ‫ك‬ْ‫ل‬‫ٱ‬� ُ‫د‬َ‫د‬َ‫ْع‬‫ل‬َ�
�‫و‬ ُ‫ح‬َ َ‫ن‬ ِ‫ين‬َّ‫ذ‬‫ٱل‬� ُ‫د‬َ‫د‬ َ‫ع‬
: ِ‫ة‬َّ‫ي‬ ِ‫و‬َ‫ئ‬ِ‫م‬ ٍ‫ب‬ َ‫س‬ِ‫ن‬ ‫ى‬َ‫ل‬ِ‫إ‬ َ‫ة‬َّ‫ي‬ِ‫ر‬ ْ‫س‬َ‫ك‬ْ‫ل‬‫ٱ‬ َ‫اد‬َ‫د‬ْ‫َع‬ْ‫ٱل‬ ُ‫ل‬ ِّ‫و‬َ‫َح‬‫أ‬
7
100
= ........ 3
20
= ........ 4
25
= ........ 8
200
= ........
. ٍ‫اض‬َ‫َر‬‫أ‬ َ‫ن‬ِ‫م‬ ُ‫ن‬ َّ‫و‬َ‫ك‬َ‫ت‬َ‫ي‬ ‫ى‬ّ‫ق‬َ‫ب‬َ‫ت‬ ‫ما‬َ‫و‬ ،ِ‫ة‬َّ‫ي‬ ِ‫ض‬ْ‫َر‬ْ‫ٱل‬ ِ‫ة‬َ‫ر‬ُ‫ك‬ْ‫ل‬‫ٱ‬ ِ‫ة‬َ‫ساح‬ِ‫م‬ ِ‫ع‬‫مو‬ْ‫ج‬َ‫م‬ ْ‫ن‬ِ‫م‬ 70% َ‫ة‬َ‫ب‬ ْ‫س‬ِ‫ن‬ ُ‫حار‬ِ‫ب‬ْ‫ل‬‫ٱ‬ ُ‫ل‬ِّ‫ك‬ َ‫ش‬ُ‫ت‬
.‫ي‬ ِ‫اض‬َ‫َر‬ْ‫ل‬ِ‫ل‬ َ‫ة‬َّ‫ي‬ ِ‫و‬َ‫ئ‬ِ‫م‬ْ‫ل‬‫ٱ‬ َ‫ة‬َ‫ب‬ ْ‫س‬ِّ‫ٱلن‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬ ●
‫في‬ ٍ‫ة‬َ‫ع‬َ‫مود‬ َ‫ساميل‬َ‫ر‬ َ‫ة‬َّ‫د‬ِ‫ع‬ ُ‫ن‬ِّ‫ي‬َ‫ب‬ُ‫ي‬ ‫الي‬ّ‫ت‬‫ٱل‬ ُ‫ل‬ ْ‫دو‬َ‫ج‬ْ‫ل‬َ‫ا‬
.5,6% ِ‫ر‬ْ‫ع‬ ِ‫س‬ِ‫ب‬ ٍ‫ك‬ْ‫ن‬َ‫ب‬
ِ‫ة‬َّ‫ي‬ ِ‫و‬َ‫ن‬ َّ‫ٱلس‬ ِ‫ة‬َ‫د‬ِ‫فائ‬ْ‫ل‬‫ٱ‬ ِ‫ساب‬ِ‫ح‬ِ‫ب‬ ِ‫ل‬ َ‫و‬ْ‫د‬َ‫ج‬ْ‫ل‬‫ٱ‬ َ‫ء‬ْ‫ل‬َ‫م‬ ُ‫م‬ِ‫م‬ْ‫ت‬ُ‫أ‬●
.ٍ‫ة‬َ‫ن‬ َ‫س‬ ِ‫رور‬ُ‫م‬ َ‫د‬ْ‫ع‬َ‫ب‬ ِ‫غ‬ِ‫بال‬َ‫م‬ْ‫ل‬‫ٱ‬‫و‬
)ِ‫م‬ َ‫ه‬ ْ‫ر‬ِّ‫ِالد‬‫ب‬( ُ‫�ساميل‬َّ‫�لر‬10040010003500
)ِ‫م‬ َ‫ه‬ ْ‫ر‬ِّ‫ِالد‬‫ب‬( ُ‫ة‬َّ‫ي‬ِ‫َو‬‫ن‬ َّ‫�ل�س‬ ُ‫ة‬َ‫د‬ِ‫ئ‬‫ْفا‬‫ل‬�5,6...............
ٍ‫ة‬َ‫ن‬ َ‫�س‬ ِ‫رور‬ ُ‫م‬ َ‫د‬ْ‫ع‬َ‫ب‬ ُ‫َغ‬‫ل‬ْ‫َب‬ ْ‫�مل‬
)ِ‫م‬ َ‫ه‬ ْ‫ر‬ِّ‫ِالد‬‫ب‬(
105,6...............
‫ها‬ِ‫ن‬َ‫م‬َ‫ث‬ ُ‫فيض‬ْ‫خ‬َ‫ت‬ َّ‫م‬َ‫ت‬ ،840DH َ‫و‬ُ‫ه‬ ٍ‫ة‬َ‫ضاع‬ِ‫ب‬ ُ‫ن‬َ‫م‬َ‫ث‬ َ‫ان‬َ‫ك‬
: ِ‫فيض‬ْ‫خ‬َّ‫ٱلت‬ َ‫غ‬َ‫ل‬ْ‫ب‬َ‫م‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬ .8% ِ‫ة‬َ‫ب‬ ْ‫س‬ِ‫ن‬ِ‫ب‬
ِ‫في�ص‬ ْ‫َّخ‬‫ت‬‫ٱل‬� َ‫ل‬ْ‫ب‬َ‫ق‬ ُ‫ن‬َ‫م‬َّ‫ث‬‫ل‬َ�.....100
ِ‫في�ص‬ ْ‫َّخ‬‫ت‬‫ٱل‬� ُ‫َغ‬‫ل‬ْ‫ب‬ َ‫م‬..........
. ِ‫س‬ِ‫ب‬‫ل‬َ‫م‬ْ‫ل‬‫ا‬ ِ‫ة‬َ‫ن‬ِ‫م‬ْ‫ث‬َ‫أ‬ ‫في‬ 15% ُ‫ه‬ُ‫ر‬ْ‫د‬َ‫ق‬ ً‫ا‬‫فيض‬ْ‫خ‬َ‫ت‬ ٌ‫ر‬َ‫ج‬ْ‫ت‬َ‫م‬ ُ‫ح‬َ‫ن‬ْ‫م‬َ‫ي‬‫ْعادي‬‫ل‬� ُ‫ن‬َ‫م‬َّ‫ث‬‫�ل‬ِ‫ة‬َ‫َب‬‫ل‬ َّ‫لط‬َ�‫و‬ ِ‫ذ‬‫َّلمي‬‫ت‬‫لل‬ ُ‫ن‬َ‫م‬َّ‫ث‬‫�ل‬
ِ‫لم‬ ْ‫ع‬َ‫أ‬ ْ‫�ال‬ ُ‫د‬ ِ‫ْج‬‫ن‬ ُ‫م‬
ِ‫لوم‬ُ‫ْع‬‫ل‬� ُ‫تاب‬ِ‫ك‬
َ‫َة‬‫ن‬ ْ‫م‬ِ‫د‬ َ‫و‬ َ‫َة‬‫ل‬‫لي‬َ‫ك‬
60
25
35
..........
..........
..........
َّ‫َن‬‫أ‬ ُ‫ت‬َ‫م‬ِ‫ل‬َ‫ع‬ ‫ذا‬ِ‫إ‬ ، ِ‫ناك‬ْ‫َب‬ْ‫ٱل‬ ِ‫د‬َ‫َح‬‫أ‬ ‫في‬ ٍ‫ة‬َ‫ل‬ِ‫كام‬ ٍ‫ة‬َ‫ن‬ َ‫س‬ ِ‫ة‬َّ‫د‬ُ‫م‬ِ‫ل‬ ً‫ا‬‫م‬َ‫ه‬ْ‫ر‬ِ‫د‬ 13000 ُ‫ه‬ُ‫ر‬ْ‫د‬َ‫ق‬ ً‫ا‬‫ي‬ِ‫مال‬ ً‫ا‬‫غ‬َ‫ل‬ْ‫ب‬َ‫م‬ ُ‫ة‬ َ‫ش‬ِ‫عائ‬ ُ‫ة‬َ‫د‬ِّ‫ي‬ َ‫ٱلس‬ ِ‫ت‬َ‫ع‬َ‫د‬ ْ‫َو‬‫أ‬
.ٍ‫م‬َ‫ه‬ْ‫ر‬ِ‫د‬ 4,5 ‫ـ‬ِ‫ب‬ ُ‫زيد‬َ‫ت‬ ٍ‫م‬َ‫ه‬ْ‫ر‬ِ‫د‬ 100 َّ‫ل‬ُ‫ك‬
.ُ‫ة‬ َ‫ش‬ِ‫عائ‬ ُ‫ة‬َ‫د‬ِّ‫ي‬ َ‫ٱلس‬ ُ‫ه‬ْ‫ن‬ِ‫م‬ ُ‫فيد‬َ‫ت‬ ْ‫س‬َ‫ت‬ َ‫س‬ ‫ذي‬َّ‫ٱل‬ َ‫غ‬َ‫ل‬ْ‫ب‬َ‫م‬ْ‫ل‬‫ٱ‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬ ●
ُ‫فيض‬ْ‫خ‬َ‫ت‬ َ‫ة‬َ‫ِبار‬‫ع‬ْ‫اَل‬ َّ‫ن‬ِ‫إ‬
ُ‫ع‬َ‫ض‬ْ‫خ‬َ‫ت‬ 100DH َّ‫كُل‬ َّ‫ن‬َ‫أ‬ ‫ني‬ْ‫ع‬َ‫ت‬ 15%
ِ‫ء‬‫دا‬َ‫أ‬ َ‫ض‬َ‫و‬ِ‫ع‬ ‫ذا‬َ‫ك‬َ‫ه‬َ‫و‬ .15DH ُ‫ه‬ُ‫ر‬ْ‫َد‬‫ق‬ ٍ‫فيض‬ْ‫خ‬َ‫ت‬ِ‫ل‬
.85DH ‫ي‬ّ‫د‬َ‫ؤ‬ُ‫ن‬ 100DH
.ِ‫ة‬َ‫ب‬َ‫ل‬َّ‫ٱلط‬َ‫و‬ ِ‫يذ‬ِ‫م‬ َ‫ل‬َّ‫لت‬ِ‫ل‬ ِ‫ة‬َ‫ب‬ ْ‫س‬ِّ‫بٱلن‬ 15% ُ‫يض‬ِ‫ف‬ْ‫خ‬َ‫ت‬ : ُ‫ة‬َّ‫ي‬ِ‫ٱآلت‬ ُ‫ة‬َ‫ت‬ِ‫ف‬ َّ‫ٱلل‬ ُ‫يق‬ِ‫ل‬ْ‫ع‬َ‫ت‬ َّ‫م‬َ‫ت‬ ِ‫ة‬َ‫ب‬َ‫ت‬ْ‫ك‬َ‫م‬ْ‫ل‬‫ٱ‬ ‫ي‬ِ‫ف‬
: ُ‫ل‬ِ‫م‬ْ‫ك‬ُ‫أ‬َ‫و‬ َ‫ل‬ َ‫و‬ْ‫د‬َ‫ج‬ْ‫ل‬‫ٱ‬ ُ‫ظ‬ِ‫ح‬َ‫ال‬ُ‫أ‬ ●
.
.

21. 22
ُ‫م‬ْ‫ج‬َ‫ح‬ْ‫ل‬‫ٱ‬ : ُ‫ة‬َ‫م‬ِ‫قائ‬ْ‫ل‬‫ٱ‬ ُ‫ة‬َ‫ن‬‫ا‬‫و‬‫ط‬ ْ‫ُس‬ْ‫ٱل‬َ‫و‬ ُ‫م‬ِ‫قائ‬ْ‫ل‬‫ٱ‬ ُ‫ـور‬ ُ‫ش‬ ْ‫و‬َ‫م‬ْ‫ل‬َ‫ا‬
ُ‫س‬ْ‫ر‬ َّ‫الد‬
46
Le prisme droit et le cylindre droit : le volume
ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬.ِ‫ة‬َ‫ب‬ ِ‫ناس‬ُ‫الم‬ ِ‫د‬ِ‫ع‬‫َوا‬‫ق‬‫ال‬ ِ‫يق‬ِ‫ب‬ْ‫ط‬َ‫ت‬ِ‫ب‬ ِ‫ة‬َ‫ِم‬‫ئ‬‫القا‬ ِ‫ة‬َ‫ن‬‫طوا‬ ْ‫ُْس‬‫اَأل‬َ‫و‬ ِ‫م‬ِ‫ئ‬‫القا‬ِ‫ر‬‫شو‬ْ‫و‬‫الم‬ ِ‫م‬ْ‫ج‬َ‫ح‬ ُ‫ساب‬ِ‫ح‬ ♦
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
‫جدول‬ ُ‫ـر‬‫ـ‬‫ك‬‫ـذ‬َ‫ت‬َ‫أ‬
.9 ‫ف‬ ‫الضرب‬
9 x 3 = . . . . . ; 9 x 2 = . . . . . ; 9 x 1 = . . . . . ; 9 x 0 = . . . . .
9 x 7 = . . . . . ; 9 x 6 = . . . . . ; 9 x 5 = . . . . . ; 9 x 4 = . . . . .
9 x 11 = . . . . . ; 9 x 10 = . . . . . ; 9 x 9 = . . . . . ; 9 x 8 = . . . . .
‫ونتائج‬ ٌ‫ة‬‫ص‬َ‫ال‬ُ‫خ‬
. h ِ‫ِفاع‬‫ت‬ ْ‫ر‬ ْ‫ٱال‬� َ‫و‬ B ِ‫ة‬َ‫د‬ ِ‫ْقاع‬‫ل‬‫ٱ‬� ِ‫ة‬ َ‫�ساح‬ ِ‫م‬ ُ‫د�ء‬ ُ‫ج‬ ‫و‬ ُ‫ه‬ ِ‫ِئم‬‫ا‬َ‫ق‬ْ‫ل‬‫ٱ‬� ِ‫�سور‬ ْ‫َو‬ ْ‫ٱمل‬� ُ‫م‬ ْ‫ج‬ َ‫ح‬ ●
.h ِ‫تفاع‬ ْ‫ِر‬ ْ‫�ال‬ َ‫و‬ B ِ‫ة‬َ‫د‬ ِ‫ْقاع‬‫ل‬� ِ‫ة‬ َ‫�ساح‬ ِ‫م‬ ُ‫د�ء‬ ُ‫ج‬ َ‫و‬ ُ‫ه‬ ِ‫ة‬َ‫ِم‬‫ئ‬‫ْقا‬‫ل‬� ِ‫ة‬َ‫ن‬�َ‫طو‬ ْ‫�س‬ُ‫أ‬ ْ‫�ال‬ ُ‫م‬ ْ‫ج‬ َ‫ح‬ ●
V = B x h
V = B x h
V = π x r x r x h
‫قاعدة‬
‫قاعدة‬
‫قاعدة‬
‫قاعدة‬

22. 23
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
: ‫هو‬ ‫قائم‬ ‫موشور‬ ‫حجم‬ V
.‫االرتفاع‬ h ‫و‬ ‫القاعدة‬ ‫مساحة‬ B ‫حيث‬
‫ـقاعدة‬‫ـ‬‫ل‬‫ا‬ ُ‫ة‬َ‫اح‬ َ‫ِس‬‫م‬
: )ُ‫ن‬َّ‫ي‬َ‫ع‬ُ‫(م‬
: ُ‫ـم‬ْ‫ـج‬َ‫اَلْح‬
‫ْقاعدة‬‫ـ‬‫ل‬‫ا‬ ُ‫ة‬َ‫اح‬ َ‫ِس‬‫م‬
: )‫قائم‬ ‫ثلث‬ُ‫(م‬
: ُ‫ـم‬ْ‫ـج‬َ‫اَلْح‬
: ِ‫ة‬‫ـوان‬‫ط‬‫األس‬ ُ‫ـم‬ْ‫ـج‬َ‫ح‬: ِ‫ة‬‫ـوان‬‫ط‬‫األس‬ ُ‫ـم‬ْ‫ـج‬َ‫ح‬
: ِ‫ة‬َ‫ِد‬‫ع‬‫اَلْقا‬ ُ‫ة‬َ‫ِساح‬‫م‬: ِ‫ة‬َ‫ِد‬‫ع‬‫اَلْقا‬ ُ‫ة‬َ‫ِساح‬‫م‬
‫الْقاعدة‬ ُ‫ة‬َ‫اح‬ َ‫ِس‬‫م‬
: )ِ‫ع‬‫األضال‬ ‫(متوازي‬
: ُ‫ـم‬ْ‫ـج‬َ‫اَلْح‬
‫الْقاعدة‬ ُ‫ة‬َ‫اح‬ َ‫ِس‬‫م‬
: )‫(مثلث‬
: ُ‫ـم‬ْ‫ـج‬َ‫اَلْح‬
ِ‫ة‬‫ُسطوان‬ ِ‫أل‬ V ُ‫م‬ْ‫ج‬َ‫اَلْح‬
: ‫هو‬ ‫قائمة‬
h ‫و‬ ‫القاعدة‬ ‫مساحة‬ B ‫حيث‬
.‫االرتفاع‬
: ٍ‫م‬ِ‫قائ‬ ٍ‫شور‬ ْ‫و‬َ‫م‬ ِ
ّ‫ل‬ُ‫ك‬ َ‫م‬ْ‫ج‬َ‫ح‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
: ٍ‫ة‬َ‫م‬ِ‫قائ‬ ٍ‫ة‬َ‫ن‬‫ا‬‫و‬ُ‫ط‬ ْ‫ُس‬‫أ‬ ِ
ّ‫ل‬ُ‫ك‬ َ‫م‬ْ‫ج‬َ‫ح‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
: ٍ‫ة‬َ‫م‬ِ‫قائ‬ ٍ‫ة‬َ‫ن‬‫ا‬‫و‬ُ‫ط‬ ْ‫ُس‬‫أ‬ ِ
ّ‫ل‬ُ‫ك‬ َ‫م‬ْ‫ج‬َ‫ح‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
: ِ‫ح‬َ‫ب‬ ْ‫س‬َ‫م‬ْ‫ل‬‫ا‬ َ‫م‬ْ‫ج‬َ‫ح‬ ُ‫ب‬ ُ‫س‬ْ‫َح‬‫أ‬
1
2
4
3
5
. . . x . . . = . . . cm3 . . . x . . . = . . . cm3 . . . x . . . = . . . cm3
6,5cm
8cm2
4cm
7cm2 5cm
12cm2
V = B x h
V = B x h
V = . . . . . . cm3 V = . . . . . . cm33cm
7cm
2cm
10cm
. . . x . . . = . . . cm2
. . . x . . . = . . . cm3. . . x . . . = . . . cm3 . . . x . . . = . . . cm3 . . . x . . . = . . . cm3
= . . . cm2
= . . . cm2 = . . . cm2
6cm
5cm 4cm 8cm
8cm
5cm
5cm
5cm
3cm
4cm
6 cm
6 cm
3 cm
. . . x . . .
. . . x . . . . . . x . . .
2
2 2
. . . x . . . x p = . . . cm2. . . x . . . x p = . . . cm2
. . . x . . . = . . . cm3
. . . x . . . = . . . cm3
3cm
7cm 10cm
4cm
5m
12m
1,5m
4cm
6m
4m
//
///
///
///
//

23. 24
ِ‫قياس‬ْ‫ل‬‫ٱ‬ ُ‫ـدات‬َ‫ح‬َ‫و‬ : ُ‫ة‬‫ـ‬َ‫ع‬ َّ‫ٱلس‬َ‫و‬ ُ‫ـم‬ْ‫ـج‬َ‫ح‬ْ‫ل‬َ‫ا‬
ُ‫س‬ْ‫ر‬ َّ‫الد‬
47
Volume et contenance : unités de mesure
ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬.ِ‫ة‬َ‫ع‬ َّ‫الس‬َ‫و‬ ٍ‫م‬ْ‫ج‬َ‫الْح‬ ِ‫ِياس‬‫ق‬ ِ‫ات‬َ‫د‬َ‫ح‬َ‫و‬ ُ‫ال‬َ‫م‬ْ‫ع‬ِ‫ت‬ ْ‫اس‬ ♦
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
7
8
18
17
5
4
7
6
12
13
9
8
9
2
1
2
23
65
105
213
7
6
1054
2136
●
●
●
●
●
●
‫ونتائج‬ ٌ‫ة‬‫ص‬َ‫ال‬ُ‫خ‬
.l ‫ر‬ْ‫ت‬ِّ‫ل‬‫ال‬
َ
‫ي‬ِ‫ه‬ ‫ة‬َ‫ع‬ َّ‫لس‬َ‫ا‬ ِ‫قياس‬ِ‫ل‬ ُ‫ة‬َ‫ي‬ ِ‫َساس‬ْ‫ل‬َ‫ا‬ ُ‫ة‬َ‫د‬ْ‫ح‬َ‫و‬ْ‫ل‬َ‫ا‬ ●
.hl ‫و‬ dal : ‫هي‬ ‫ر‬ْ‫ت‬ِّ‫ل‬‫ال‬ ُ‫فات‬َ‫ضاع‬ُ‫م‬ ●
. ml ‫و‬ cl ‫و‬ dl : ‫هي‬ ‫ر‬ْ‫ت‬ِّ‫ل‬‫ال‬ ‫اء‬‫ز‬ْ‫َج‬‫أ‬●
.َ‫ة‬َ‫ع‬ َّ‫الس‬ ِ‫ياس‬ِ‫ق‬ ِ‫ويل‬ْ‫ح‬َ‫ت‬ ‫لى‬َ‫ع‬ ُ‫د‬ِ‫ساع‬ُ‫ي‬ ‫الي‬َّ‫الت‬ ُ‫ل‬ َ‫و‬ْ‫د‬َ‫ج‬ْ‫ل‬َ‫ا‬ ●
‫دات‬َ‫ح‬َ‫و‬ َ‫و‬ َ‫ة‬َ‫ع‬ َّ‫الس‬ ِ‫ياس‬ِ‫ق‬ ‫دات‬َ‫ح‬َ‫و‬َ َ‫ن‬ْ‫ي‬َ‫ب‬ َ‫ة‬َ‫ق‬‫ل‬َ‫ع‬ْ‫ل‬َ‫ا‬ ‫الي‬ّ‫ت‬‫ال‬ ُ‫ل‬ َ‫و‬ْ‫د‬َ‫ج‬ْ‫ل‬َ‫ا‬ ُ‫ن‬ِّ‫ي‬َ‫ب‬ُ‫ي‬ ●
: ‫ى‬‫ر‬ْ‫ُخ‬‫أ‬ ‫لى‬ِ‫إ‬ ٍ‫ة‬‫د‬َ‫ح‬َ‫و‬ ْ‫ن‬ِ‫م‬ ِ‫ياس‬ِ‫ق‬ ِ‫ويل‬ْ‫ح‬َ‫ت‬ ‫لى‬َ‫ع‬ ُ‫د‬ِ‫ساع‬ُ‫وي‬ ِ‫م‬ْ‫ج‬َ‫الح‬ ‫ياس‬ِ‫ق‬
: ِ‫ن‬ْ‫ي‬َ‫ر‬ ْ‫كَس‬ ِ‫ة‬َ‫ن‬َ‫قار‬ُ‫ِم‬‫ل‬ ِ‫اَلْحاالت‬ ِ‫ض‬ْ‫ع‬َ‫ب‬ ِ‫ف‬
: َّ‫َن‬ ِ‫أل‬ 19
23
> 7
6
: ً‫َال‬‫ث‬َ‫م‬ 1 َ‫ع‬َ‫م‬ ‫اه‬ْ‫ِن‬‫م‬ ٌ‫د‬ِ‫ح‬‫وا‬ َّ‫كُل‬ ُ‫ن‬ِ‫ر‬‫قا‬ُ‫ن‬
‫و‬
‫و‬
‫و‬
‫و‬
‫و‬
‫و‬
7
6
19
23
> 1 1 >‫و‬ ‫أكبر‬ ‫الْبسط‬
ِ‫م‬‫المقا‬ ‫من‬ُ‫َر‬‫غ‬ْ‫ص‬َ‫أ‬ ‫الْبسط‬
ِ‫م‬‫المقا‬ ‫من‬
1cm
1cm
1cm
1cm3 = 1ml 1dm3 = 1l
1dl1l 1ml
)‫تقربيا‬ ‫قطرة‬ 20(
1cl
1dm
1dm
1dm
459dm3
= 459l
459dm3
= 45900cl
hl dal l dl cl ml
7 8 2 0
m3
dm3
cm3
mm3
hl dal l dl cl ml
4 5 9 0 0
78,2l = 7820cl
: ِ‫ن‬ْ‫ي‬ َ‫ر‬ ْ‫س‬َ‫ك‬ َّ‫ل‬ُ‫ك‬ ُ‫ن‬ ِ‫ُقار‬‫أ‬

24. 25
ُ‫ن‬َّ‫ر‬ َ‫َم‬‫ت‬َ‫أ‬ َ‫و‬ ُ‫ق‬ِّ‫ب‬ َ‫ط‬ُُ‫أ‬
: ٍ‫ء‬
ْ
‫ي‬ َ‫ش‬ ُّ‫َي‬‫أ‬ ْ‫ع‬ ِ‫ض‬ِ‫ي‬ ْ‫م‬َ‫ل‬َ‫و‬ ُ‫ه‬َّ‫ل‬ُ‫ك‬ ََ‫ل‬َ‫ت‬ْ‫ام‬ َ‫ناء‬ ِْ‫ٱل‬ َّ‫َن‬‫أ‬ َ‫ظ‬َ‫الح‬َ‫و‬ ٍ‫ب‬َّ‫ع‬َ‫ك‬ُ‫م‬ ِ‫ل‬ْ‫ك‬ َ‫ش‬ ‫لى‬َ‫ع‬ ٍ‫اء‬َ‫ن‬ِ‫إ‬ ‫ي‬ِ‫ف‬ ِ‫اء‬َ‫م‬ْ‫ل‬‫ٱ‬ ‫ن‬ِ‫م‬ ‫ا‬ً‫ر‬ْ‫ت‬ِ‫ل‬ ‫دي‬ْ‫ه‬َ‫م‬ َ‫غ‬َ‫ر‬ْ‫ف‬َ‫أ‬
: ِ‫ال‬َ‫ث‬ِ‫م‬ْ‫ل‬‫ٱ‬ ‫ي‬ِ‫ف‬ ‫ما‬َ‫ك‬ ُ‫ط‬ِ‫ب‬ْ‫َر‬‫أ‬
: ُ‫ل‬ِ‫م‬ْ‫ك‬ُ‫أ‬َ‫و‬ ِ‫ويلت‬ْ‫ح‬َّ‫ٱلت‬ ‫ي‬‫ـر‬ْ‫ُج‬‫أ‬
: ُ‫ل‬ِ‫م‬ْ‫ك‬ُ‫أ‬َ‫و‬ َ‫ج‬َّ‫ر‬َ‫د‬ُ‫م‬ْ‫ل‬‫ٱ‬ َ‫ناء‬ ِْ‫ٱل‬ ُ‫ظ‬ِ‫ح‬َ‫ال‬ُ‫أ‬
: ُ‫ل‬ِّ‫ث‬َ‫م‬ُ‫ت‬ ٍ‫ة‬َ‫يج‬ِ‫ر‬ْ‫د‬َ‫ت‬ َّ‫ل‬ُ‫ك‬●
: َ‫ـو‬ُ‫ه‬ ِ‫ناء‬ ِْ‫ٱل‬ ‫في‬ ِ‫اء‬َ‫م‬ْ‫ل‬‫ٱ‬ ُ‫م‬ْ‫ج‬َ‫ح‬●
: ُ‫ل‬ِ‫م‬ْ‫ك‬ُ‫أ‬َ‫و‬ ِ‫ن‬ْ‫ي‬َ‫ج‬َّ‫ر‬َ‫د‬ُ‫م‬ْ‫ل‬‫ٱ‬ ِ‫ن‬ْ‫ي‬َ‫نائ‬ ِ‫ٱل‬ ُ‫ظ‬ِ‫ح‬َ‫ال‬ُ‫أ‬
: َ‫ـو‬ُ‫ه‬ ِ‫ر‬َ‫ج‬َ‫ح‬ْ‫ل‬‫ٱ‬ ِ‫ة‬َ‫ع‬ْ‫ط‬ِ‫ق‬ ُ‫م‬ْ‫ج‬َ‫ح‬●
: ٍ‫ة‬َ‫ل‬‫ا‬َ‫ح‬ ِ
ّ‫ل‬ُ‫ك‬ ‫ي‬ِ‫ف‬ َ‫ب‬ ِ‫ناس‬ُ‫م‬ْ‫ل‬‫ٱ‬ َ‫م‬ْ‫ج‬َ‫ح‬ْ‫ل‬‫ٱ‬ ُ‫ب‬ُ‫ت‬ْ‫ك‬َ‫أ‬
: ٍ‫ة‬َ‫ل‬‫ا‬َ‫ح‬ ِ
ّ‫ل‬ُ‫ك‬ ‫ي‬ِ‫ف‬ َ‫ب‬ ِ‫اس‬َ‫ن‬ُ‫م‬ْ‫ل‬‫ا‬ َ‫م‬ْ‫ج‬َ‫ح‬ْ‫ل‬‫ٱ‬ ُ‫ب‬ُ‫ت‬ْ‫ك‬َ‫أ‬
1
2
3
4
5
6
1 dm3
1 m3
1 cm3
1
1 000
1
1 000
l
l
l
1 l
138 ml = . . . l
145 cl = . . . l
1
2
l = 50 . . .
1
4
l = 25 . . .
25 dl = . . . cl
10 hl = . . . l
1,5 l = . . . dm3
0,5 l = . . . cm3
10 l = . . . m3
. . . l
l l l
200 ml
100ml
. . . ml
1010
3030
2020
4040
50 clcl50
10
‫ه‬. . . . . . dm3
. . . . . . . cm3 . . . . . . mm3 . . . . . . . m3 . . . . . . . dm3
0,5 0,50,5 0,5
1 11 1llll
25
1 dm
1 dm
1 dm

25. 26
‫ِيا‬‫ن‬ْ‫ه‬ِ‫ذ‬ ُ‫ب‬ ُ‫س‬ْ‫ح‬َ‫أ‬
ُ‫ة‬َ‫ط‬ ّ
ِ‫س‬َ‫و‬َ‫ت‬ُ‫م‬ْ‫ل‬‫ٱ‬ ُ‫ة‬َ‫ع‬ْ‫ر‬ ُّ‫ٱلس‬‫و‬ ُ‫ة‬َّ‫ي‬ِ‫م‬ْ‫ج‬َ‫ح‬ْ‫ل‬‫ٱ‬ ُ‫ة‬َ‫ل‬ْ‫ت‬ُ‫ك‬ْ‫ل‬‫ٱ‬َ‫و‬ ِ‫م‬‫ي‬ِ‫صام‬َّ‫ٱلت‬ ُ‫م‬َّ‫ل‬ ُ‫س‬ : ُ‫ة‬َّ‫بي‬ ُ‫ناس‬َّ‫ٱلت‬
: ً‫َال‬‫ث‬َ‫م‬ 60 ْ‫ِن‬‫م‬ 5% ٍ‫ِساب‬‫ح‬ِ‫ل‬
: 100 ‫لَى‬َ‫ع‬ ُ‫م‬ ِ‫ْس‬‫ق‬ُ‫ن‬َ‫و‬ 60 ‫ف‬ 5 ُ‫ب‬ِ‫ر‬ْ‫ض‬َ‫ن‬
.3 َ‫ِي‬‫ه‬ 60 ْ‫ِن‬‫م‬ 5% ْ‫ن‬َ‫ذ‬ِ‫إ‬
ُ‫ر‬ ُ‫ش‬ُ‫ع‬‫ال‬ ُ‫ل‬ِّ‫ث‬َُ‫ت‬ 10%
َ‫ع‬ْ‫ب‬ُُ‫الر‬ ُ‫ل‬ِّ‫ث‬َُ‫ت‬ 25%
ُ‫ف‬ْ‫ص‬ِّ‫ن‬‫ال‬ ُ‫ل‬ِّ‫ث‬َُ‫ي‬ 50%
ٍ‫ع‬َ‫اب‬ْ‫ر‬ََ‫أ‬ َ‫ة‬َ‫الث‬َ‫ث‬ ُ‫ل‬ِّ‫ث‬َُ‫ت‬ 75%
ُ‫س‬ْ‫ر‬ َّ‫الد‬
48
ُ‫َّر‬‫ك‬َ‫ذ‬َ‫ت‬َ‫أ‬َ‫و‬ ُ‫م‬َ‫ه‬ْ‫ف‬َ‫أ‬
Proportionnalité : Echelle, masse volumique
ْ
ُ‫َّم‬‫ل‬َ‫ع‬َ‫ت‬َ‫أ‬
. ِ‫ِساب‬‫ح‬‫ال‬ ِ‫ف‬ ِ‫ه‬ُ‫مال‬ْ‫ع‬ِ‫ت‬ ْ‫واس‬ ٍ‫م‬‫مي‬ْ‫ص‬َ‫ت‬ ِ‫م‬َّ‫ل‬ َ‫س‬ ُ‫د‬‫ا‬َ‫يح‬ِ‫إ‬ ♦
.ِ‫ة‬َّ‫مي‬ْ‫ج‬َ‫الح‬ ِ‫ة‬َ‫ل‬ْ‫ت‬ُ‫ك‬‫ال‬ ِ‫ال‬َ‫م‬ْ‫ع‬ِ‫ت‬ ْ‫س‬ِ‫اب‬ ٍ‫ساب‬ِ‫ح‬ ُ‫راء‬ْ‫ج‬ِ‫إ‬ ♦
.ِ‫ة‬َ‫ق‬َ‫ْر‬‫غ‬َ‫ت‬ ْ‫س‬ُ‫اَلْم‬ ِ‫ة‬َّ‫د‬ُ‫الم‬ ِ‫و‬َ‫أ‬ ِ‫ة‬َ‫ع‬‫ْطو‬‫ق‬َ‫الم‬ ِ‫ة‬َ‫ف‬‫سا‬َ‫الم‬ ِ‫و‬َ‫أ‬ ِ‫ة‬َ‫ط‬ ِّ‫س‬َ‫و‬َ‫ت‬ُ‫الم‬ ِ‫ة‬َ‫ع‬ْ‫ر‬ ُّ‫الس‬ ُ‫ساب‬ِ‫ح‬ ♦
240 ْ‫ن‬ ِ‫م‬ 50% ●
300 ْ‫ن‬ ِ‫م‬ 10% ●
500 ْ‫ن‬ ِ‫م‬ 1% ●
42 ْ‫ن‬ ِ‫م‬ 200% ●
460 ْ‫ن‬ ِ‫م‬ 25% ●
320 ْ‫ن‬ ِ‫م‬ 75% ●
530 ْ‫ن‬ ِ‫م‬ 20% ●
195 ْ‫ن‬ ِ‫م‬ 100% ●
(5 x 60) : 100 = 3
.ِ‫ة‬َ‫ِي‬‫ق‬‫ِي‬‫ق‬َ ْ‫ٱل‬� ِ‫�سافات‬َ ْ‫ٱمل‬� َ‫ع‬ َ‫م‬ ٌٍ‫ة‬َ‫ب‬ ِ‫َا�س‬‫ن‬َ‫ت‬ ُ‫م‬ ٍ‫يم‬ِ‫م‬ ْ‫َ�س‬‫ت‬ ْ‫و‬َ‫أ‬� ٍ‫ة‬ َ‫يط‬ِ‫ر‬ َ‫خ‬ ‫َى‬‫ل‬ َ‫ع‬ ُ‫ات‬َ‫َ�ساف‬ ْ‫مل‬َ� ●
.ِ‫يم‬ِ‫م‬ ْ‫َّ�س‬‫ت‬‫�ل‬ ‫َى‬‫ل‬ َ‫ع‬ ِ‫افات‬ َ‫�س‬َ ْ‫ٱمل‬� ‫ىل‬ِ‫إ‬� ِ‫ة‬َّ‫ِي‬‫ق‬‫ِي‬‫ق‬َ ْ‫ٱل‬� ِ‫افات‬ َ‫َ�س‬ ْ‫ٱمل‬� َ‫ن‬ ِ‫م‬ َ‫ِقال‬‫ت‬ْ‫ن‬ ْ‫ٱال‬� ُ‫ن‬ِّ‫ك‬َ ُ‫ي‬ ‫ِي‬‫ذ‬َّ‫ل‬‫ٱ‬� ِ‫ب‬ ُ‫َّنا�س‬‫ت‬‫ٱل‬� َ‫ل‬ ِ‫ام‬َ‫ع‬ ُ‫م‬ َ‫َّم‬‫ل‬ ُّ‫ٱل�س‬� ‫ي‬ِّ‫م‬ َ‫ُ�س‬‫ن‬ ●
.250m ْ‫ي‬َ‫أ‬� ِ‫َة‬‫ق‬‫ِي‬‫ق‬َ ْ‫ٱل‬� ِ‫ف‬ 25000cm ُ‫ل‬ِّ‫ث‬َ ُ‫ت‬ ِ‫يم‬ِ‫م‬ ْ‫َّ�س‬‫ت‬‫ٱل‬� ‫َى‬‫ل‬ َ‫ع‬ 1cm َّ‫ن‬َ‫أ‬� ‫ِي‬‫ن‬ْ‫َع‬‫ت‬ 1
25000
ُ‫ة‬ َ‫بار‬ِ‫ْع‬‫ل‬‫ٱ‬� : ‫ال‬َ‫ث‬ ِ‫م‬ ●
: َ‫ي‬ ِ‫ه‬ َ‫ة‬ َ‫ط‬ ِّ‫�س‬َ‫َو‬‫ت‬ُ‫�مل‬ ُ‫َه‬‫ت‬ َ‫ع‬ْ ُ‫�ش‬ َّ‫ن‬ِ‫إ‬‫ا‬َ‫ف‬ ِ‫ات‬ َ‫اع‬ َّ‫ِال�س‬‫ب‬ t ٍ‫ة‬َّ‫ني‬ َ‫م‬ َ‫ز‬ ٍ‫ة‬َّ‫د‬ ُ‫م‬ ِ‫ف‬ ِ‫�ت‬ ْ‫ت‬ ِ‫ْكيلوم‬‫ل‬َ‫ا‬ِ‫ب‬ d َ‫ة‬َ‫�ساف‬ َ‫م‬ ٌ‫ك‬ِّ‫ر‬ َ‫َح‬‫ت‬ ُ‫م‬ ٌ‫م‬ ْ‫�س‬ ِ‫ج‬ ُ‫ع‬ َ‫ط‬ْ‫ق‬َ‫ي‬ ‫ا‬ َ‫م‬َ‫د‬ْ‫ن‬ ِ‫ع‬ ●
ِ‫ة‬ َ‫ع‬ْ ُّ‫�ل�ش‬ ِ‫ف‬ َ‫ة‬َّ‫د‬ُ‫�مل‬ ُ‫ِب‬ ْ‫َ�ش‬‫ن‬ ِ‫ة‬َّ‫ف‬ِ‫ا‬‫�س‬ُ‫�مل‬ ِ‫اب‬ َ‫�س‬ِ ِ‫ل‬●
: v ‫لى‬ َ‫ع‬ d ُ‫م‬ ِ‫�س‬ْ‫ق‬ُ‫ن‬ d ِ‫ة‬َ‫ف‬‫َ�سا‬‫مل‬� ِ‫ع‬ ْ‫َط‬‫ق‬ِ‫ل‬ ِ‫ة‬َّ‫ني‬ َ‫م‬َّ‫�لز‬ ِ‫ة‬َّ‫د‬ُ‫�مل‬ ِ‫�ساب‬ِ ِ‫ل‬ َ‫و‬ ●
÷ 25000 x 25000
1 0,04 40 2
25000 1000 1000000 50000
cm ‫ِـ‬‫ب‬ ‫التصميم‬ ‫عىل‬ ُ‫سافات‬َ‫م‬ْ‫ل‬َ‫ا‬
cm ‫ِـ‬‫ب‬ ‫الحقيقية‬ ُ‫سافات‬َ‫م‬ْ‫ل‬َ‫ا‬
‫ْقيا�ص‬‫ل‬� ‫وحدة‬ ‫نف�ص‬ ‫�عتماد‬ ‫ينبغي‬
َ‫ِه‬‫ذ‬ َ‫ه‬ ْ‫ن‬ ِ‫م‬ ...1m3 ،1dm3 ،1cm3 ٍ‫ة‬َّ‫ي‬ِ‫م‬ ْ‫ج‬ َ‫ح‬ ٍ‫ة‬َ‫د‬ ْ‫ح‬ َ‫و‬ ُ‫َة‬‫ل‬ْ‫ت‬ُ‫ك‬ َ‫ي‬ ِ‫ه‬ )... ٌ‫ت‬ْ‫ي‬ َ‫ز‬ ، ٌ‫اء‬ َ‫م‬ ، ٌ‫ب‬ َ‫�س‬ َ‫خ‬ ،ٌ‫د‬‫دي‬ َ‫(ح‬ ٍ‫ة‬ َ‫ِ�س‬‫ن‬‫ا‬ َ‫َج‬‫ت‬ ُ‫م‬ ٍ‫ة‬َّ‫اد‬َ ِ‫مل‬ ُ‫ة‬َّ‫ي‬ِ‫م‬ ْ‫ج‬َ ْ‫ٱل‬� ُ‫َة‬‫ل‬ْ‫ت‬ُ‫ك‬ْ‫ل‬َ� ●
: ً‫ة‬َّ‫اد‬َ ْ‫ٱمل‬�
: ِ‫ة‬َّ‫ِي‬‫ل‬‫َّا‬‫ت‬‫ٱل‬� ِ‫د�ت‬ َ‫ح‬َ‫ْو‬‫ل‬‫ٱ‬� ‫ى‬َ‫د‬ ْ‫ح‬ِ‫إ‬‫ا‬ِ‫ب‬ ِ‫ة‬َّ‫ي‬ِ‫م‬ ْ‫ج‬َ ْ‫ٱل‬� ِ‫َة‬‫ل‬ْ‫ت‬ُ‫ك‬ْ‫ل‬� ْ‫ن‬ َ‫ع‬ ُ َّ‫ب‬َ‫ع‬ُ‫ي‬ ●
،‫ا‬َ‫ه‬ِ‫م‬ ْ‫ج‬ َ‫ح‬ َ‫ع‬ َ‫م‬ ٌ‫ة‬َ‫ب‬ ِ‫َنا�س‬‫ت‬ ُ‫م‬ ٍ‫ة‬ َ‫ِ�س‬‫ن‬‫ا‬ َ‫َج‬‫ت‬ ُ‫م‬ ٍ‫ة‬َّ‫ماد‬ ُ‫َة‬‫ل‬ْ‫ت‬ُ‫ك‬ ُ‫َكون‬‫ت‬ ●
.ُ‫م‬ ْ‫ج‬َ ْ‫ل‬َ� َ‫و‬ ُ‫ه‬ v ‫و‬ ُ‫َة‬‫ل‬ْ‫ت‬ُ‫ك‬ْ‫ل‬� َ‫ي‬ ِ‫ه‬ m ُ‫ث‬ْ‫ي‬ َ‫ح‬ .ِ‫ة‬َّ‫اد‬ ْ‫�مل‬ ِ‫ه‬ِ‫ذ‬َ‫ِه‬‫ل‬ َ‫ة‬َّ‫ي‬ِ‫م‬ ْ‫ج‬َ ْ‫�ل‬ َ‫َة‬‫ل‬ْ‫ت‬ُ‫ك‬ْ‫ل‬� ‫ى‬َّ‫م‬ َ‫�س‬ُ‫ي‬ m
v
ِ‫ب‬ ُ‫َّنا�س‬‫ت‬‫�ل‬ ُ‫ل‬ ِ‫عام‬ ُ‫م‬
‫الكتلة‬
‫الحجم‬
‫الحجمية‬ ‫الكتلة‬
t kg g
m3 dm3 cm3
t/m3 kg/dm3 g/cm3
َ ْ 3 3 3
َّ ُ َ ْ ُ ٌ َ ٌ َ َ ٌ َ َّ َ ُ َّ َ ْ‫ٱل‬�َ‫ٱل‬�َ ْ‫ٱل‬�ْ ُ َ ْ ُ ْ َ
: َ ‫ه‬ َ‫ة‬ َ‫ط‬‫طة‬‫ة‬ ّ َ‫َو‬‫ت‬‫تو‬‫و‬ ُ‫مل‬‫ملت‬‫ت‬ � ُ‫َه‬‫ت‬‫ته‬‫ه‬ َ‫ع‬‫عت‬‫ت‬ ْ ُ ََّّّ‫ان‬َ‫ف‬‫فا‬‫ا‬ ‫ات‬ َ‫اع‬‫اعات‬‫ات‬ َ‫اع‬َ ّ‫ال�س‬‫ال�ساع‬‫اع‬ ّ‫ال�س‬َّ‫ال�س‬ََّّ‫ال�س‬َّّ ‫ب‬‫بال�س‬‫ال�س‬ t ‫ة‬ََّّّ‫ي‬‫ن‬‫نية‬‫ة‬ّ‫ي‬‫ن‬َّ‫ني‬ََّّ‫ي‬‫ن‬َّّ َ َ‫ز‬ ‫ة‬ََّّّ‫د‬ ُ ‫ف‬ ‫�ت‬ ْ‫كيلومت‬‫كيلومت‬‫ت‬ ْ‫ل‬‫لكيلوم‬‫كيلوم‬ َ‫ا‬‫ب‬‫با‬‫ا‬ d َ‫ة‬َ‫�ساف‬‫�سافة‬‫ة‬ َ ٌ‫ك‬ّ َ‫َح‬‫ت‬‫تح‬‫ح‬ ُ ٌ ْ ‫ج‬ ُ‫ع‬ َ‫ط‬‫طع‬‫ع‬ ْ‫ق‬‫قط‬‫ط‬ َ‫ي‬ ‫ا‬‫يق‬ ‫ا‬‫ق‬َ‫ي‬ ‫ا‬َ َ َ‫د‬ْ‫ن‬‫ند‬‫د‬ ‫ع‬‫عن‬‫ن‬ ●●
v
:: ِ ٍ ٍ ‫ف‬ ِ
‫لى‬ َ d
ِِV = d
t
(Km/h)
d = t x V (Km)
t = d
V
(h)