This document contains the solutions to 5 math exercises for a middle school exam in Morocco. The first exercise involves solving equations with fractions. The second uses percentages to interpret data in a table on the number of male and female students. The third involves solving several equations for the variable x. The fourth requires calculating the area and circumference of an equilateral triangle and a circle that touches its sides. The fifth finds the surface area and volume of a cube.

1. ‫ﺍﻟﻭﻁﻨﻴﺔ‬ ‫ﺍﻟﺘﺭﺒﻴﺔ‬ ‫ﻭﺯﺍﺭﺓ‬
‫ﺒﻌﺩ‬ ‫ﻋﻥ‬ ‫ﺍﻟﺘﻜﻭﻴﻥ‬ ‫ﻭ‬ ‫ﻟﻠﺘﻌﻠﻴﻡ‬ ‫ﺍﻟﻭﻁﻨﻲ‬ ‫ﺍﻟﺩﻴﻭﺍﻥ‬
‫ﺍﻟــﻤـﺴـﺘﻭﻯ‬ ‫ﺍﻤﺘﺤﺎﻥ‬ ‫ﺇﺠـﺎﺒـﺔ‬ ‫ﺘﺼﻤﻴﻡ‬–‫ﻤــﺎﻱ‬ ‫ﺩﻭﺭﺓ‬2009
‫ﺍﻟﻤــﺎﺩﺓ‬:‫ﺭﻴﺎﻀﻴﺎﺕ‬ ‫ﺍﻟﻤﺴﺘﻭﻯ‬:‫ﻤﺘﻭﺴﻁ‬ ‫ﺃﻭﻟﻰ‬
‫اﻟﻌــﻼﻣــﺔ‬
‫آﺎﻣﻠﺔ‬ ‫ﻣﺠﺰ‬‫أة‬
‫اﻹﺝﺎﺑﺔ‬ ‫ﻋﻨﺎﺻﺮ‬ ‫اﻟﻤﻮﺿﻮع‬ ‫ﻣﺤﺎور‬
4
1.5 + 1
1.5
‫اﻷول‬ ‫اﻟﺘﻤﺮﻳﻦ‬ ‫ﺡﻞ‬)4‫ﻥﻘﻂ‬(
4
48
192
)2;
3
2
1648
1632
48
32
)1 ==
÷
÷
=
4
48
192
48
32
48
160
48
32
3
10
)3 ==+=+=A
‫اﻟﻜﺴﺮﻳﺔ‬ ‫اﻷﻋﺪاد‬
4
1
1
1
1
‫اﻟﺜﺎﻥﻲ‬ ‫اﻟﺘﻤﺮﻳﻦ‬ ‫ﺡﻞ‬)4‫ﻥﻘﻂ‬(
1(*‫ﻟﻠﺬآﻮر‬ ‫اﻟﻤﺆوﻳﺔ‬ ‫اﻟﻨﺴﺒﺔ‬:54 %
‫ﻟﻺﻥﺎث‬ ‫اﻟﻤﺆوﻳﺔ‬ ‫اﻟﻨﺴﺒﺔ‬:46 %
2(*‫اﻟﺠﺪول‬:
‫اﻟﺬآﻮر‬‫اﻹﻥﺎث‬‫اﻟﺘﻼﻣﻴﺬ‬
1412‫اﻟﻌﺪد‬
54%46%‫اﻟﻤﺌﻮﻳﺔ‬ ‫اﻟﻨﺴﺒﺔ‬
97°83°‫اﻟﻤﻤﺜﻠﺔ‬ ‫اﻟﺰاوﻳﺔ‬
‫اﻟﻤﺨﻄﻂ‬:
‫اﻟﺬآﻮر‬97°‫اﻹﻥﺎث‬83°
‫ﺕﻨ‬‫ﻈﻴﻢ‬
‫ﻣﻌﻄﻴﺎت‬
4
1.5
1
1.5
‫اﻟﺜﺎﻟﺚ‬ ‫اﻟﺘﻤﺮﻳﻦ‬ ‫ﺡﻞ‬)3‫ﻥﻘﻂ‬(
2
2
4
==x ‫إذن‬
2
1
2
5
−=x ‫أي‬
2
5
2
1
=+x *
x = 18 ‫إذن‬ x = 15 + 3 ‫أي‬ x – 3 = 15 *
x = 26 ÷ 5 ‫إذن‬ 5 × x = 26 *
‫إذن‬:5,2=x
‫اﻟﻤﻌﺎدﻻت‬
1/2

2. 1
6 × 3 , 1 4
p = = 9 , 4 2
2
4
1
1
1
1
‫اﻟ‬ ‫اﻟﺘﻤﺮﻳﻦ‬ ‫ﺡﻞ‬‫ﺮاﺑﻊ‬)4‫ﻥﻘﻂ‬(
1(*‫رﺱﻢ‬]AB[‫اﻟﻨﻘﻄﺔ‬ ‫و‬C
2(*AB = AC = BC = 6 cm
ABC‫ﻣﺘﻘﺎ‬ ‫ﻣﺜﻠﺚ‬‫اﻷﺿﻼع‬ ‫ﻳﺲ‬
3(*‫اﻟﺪاﺉﺮة‬ ‫ﻥﺼﻒ‬ ‫ﻣﺤﻴﻂ‬
P1
‫هﻮ‬ ‫اﻟﺸﻜﻞ‬ ‫ﻣﺤﻴﻂ‬:6×2+P = 9,42
P = 21,42 cm
‫اﻟﻤﺜﻠﺚ‬
‫اﻟﺪاﺉﺮة‬
)‫اﻟﻤﺴﺎﺡﺔ‬ ، ‫اﻟﻤﺤﻴﻂ‬(
4 2
2
‫اﻟﺨﺎﻣﺲ‬ ‫اﻟﺘﻤﺮﻳﻦ‬ ‫ﺡﻞ‬)4‫ﻥﻘﻂ‬(
1(*‫اﻟﻤﻜﻌﺐ‬ ‫ﺱﻄﺢ‬ ‫ﻣﺴﺎﺡﺔ‬:6 = 49 cm2
÷294
2(*‫اﻟﻤﻜﻌﺐ‬ ‫ﺡﺠﻢ‬:= 343 cm3
7×49
‫اﻟﻤﺠﺴﻤﺎت‬)‫اﻟﻤﻜﻌﺐ‬(
2/2