المهارات_الأساسية_المرحلة_المتوسطة

‫('&‪!\"#!$\"%#$.%/!+,,\"),*#-+,$,,%-‬‬ ‫اﻟﻤﻬﺎرات اﻷﺳﺎﺳﻴﺔ‬ ‫اﻟﻤﺮﺣﻠﺔ اﻟﻤﺘﻮﺳﻄﺔ‬ ‫إﻋﺪاد ‪:‬‬ ‫أ ‪ .‬ﻧﻮال اﻟﻤﻄﻴﺮي ‪.‬‬ ‫أ ‪ .‬ﻧﻮرة اﻟﺤﺮﺑﻲ ‪.‬‬ ‫أ ‪ .‬أﺷﻮاق اﻟﺤﺠﻴﻠﻲ ‪.‬‬ ‫‪0+12 3 ' 4*+5% 06#2‬‬

‫ﺛﺎﻟﺚ‬ ‫ﺛﺎﻧﻲ‬ ‫أول‬ ‫ﻣﺘﻮﺳﻂ ﻣﺘﻮﺳﻂ ﻣﺘﻮﺳﻂ‬ . 7=1K:/; I;@8J; • . 7Y=YZ/; I;@8J; • . <\"J; ' ?#>/; • . LM#N+O=P 72CQ* • . D+=EAF/; G=HCH • . 7=[\\/; D3I+FA/; • . 7RS+T$A/; D+FEUA/; • . D3I+FA/; • . G\"+:$/;' 71K:/; • . D+:2+1$A/; • 789:/; <=2+>% • . +2;'9/; V=S D+WXF/; • .]#5Y/; ' D+^+KA/; • .?@A/; ' 729BCA/; . D3+A$^3; • ‫ـ‬١‫ـ‬

)E=5Y/; _;#`( ' )SCY/; aM#* ' bC=[A/; &;#* ' )*+1=YK/; M@S / aI+K/; : ,S ]#\"CA/; cdEA8 e=5KH cH @W f*gS +AE8 cB@=h* 7[\"#$A/; 7E^CAE/ D+=i+2C/; aI+A/ 7=\"+\"J; D;M+RA/; jkkl | mnn 0;@2o cWM pYH ,q jkkl | rj| sj t2M+H umn , vrl , nulv , r w%IC/; cWM ‫ـ‬٢‫ـ‬

7%@>% V=E\"CA/;' x+=1*J; yC`( zE8 ]XK/;' aXZ/;' V=A/+F/; {M |@AY/; … @FS +%( 7[\"#$A/; 7E^CAE/ 7=\"+\"J; D;M+RA/; cd2@2( V=S ]@>* a@}+h/; +R=P ;'@5H ~( ;#•C*' fS €h$:2 +•FP+* +A• E8 fEF52 ~( z/#A/; V=E}+\" ‫ـ‬٣‫ـ‬

‫اﻟﻤﻬﺎرات اﻷﺳﺎﺳﻴﺔ‬ ‫ﻟﻠﺼﻒ اﻷول ﻣﺘﻮﺳﻂ‬ ‫ـ‪٤‬ـ‬

‫اﻟﻘﻮى واﻷﺳﺲ‬ ‫ﺗﺬﮐﺮ‬ ‫;‪: 7Kh* )P e%+F/; {Ci aM#‚ zE8 a#>/; G$B‬‬ ‫اﻷس‬ ‫‪v ✕ v✕ v=l v‬‬ ‫اﻟﻌﻮاﻣﻞ‪٤٢‬‬ ‫;\"‪D;C% „X- X%+8 v I@F/; eAF$‬‬ ‫= ‪٢ ✕٢✕٢✕ ٢‬‬ ‫‪7=\"+=>/; 7ƒ=Z/+S ?#>/; 7S+$B‬‬ ‫اﻷﺳﺎس‬ ‫;^‪: 7A=>/; GK‬‬ ‫ﺗﺮﺑﯿﻊ‬ ‫‪٢‬‬ ‫‪ku = m ✕ m = s m‬‬ ‫‪٣‬‬ ‫ﺗﮑﻌﯿﺐ‪٢٢‬‬ ‫;\"‪V=HC% X%+8 m I@F/; eAF$‬‬ ‫اﻟﺼﯿﻐﺔ اﻟﺘﻲ ﺗﮑﺘﺐ ﻓﯿﻬﺎ اﻷﻋﺪاد‬ ‫اﻟﺼﯿﻐﺔ اﻟﻘﯿﺎﺳﯿﺔ‬ ‫‪7=\"J; 7ƒ=Z/+S I;@8J; 7S+$B‬‬ ‫دون أﺳﺘﻌﻤﺎل اﻷس‬ ‫;‪: 7=\"J; 7ƒ=Z/+S k ✕ k ✕ k G$B‬‬ ‫اﻟﺼﯿﻐﺔ اﻷﺳﯿﺔ اﻟﺼﯿﻐﺔ اﻟﺘﻲ ﺗﮑﺘﺐ ﻓﯿﻬﺎ اﻷﻋﺪاد‬ ‫‪lk = k ✕ k ✕ k‬‬ ‫ﺑﺈﺳﺘﻌﻤﺎل اﻷس‬ ‫;‪l #q LJ+P ;…/ D;C% „X- X%+8 eAF$\";' L+\"J; #q k I@F/‬‬ ‫ـ‪٧‬ـ‬

‫ﺗﺮﺗﻴﺐ اﻟﻌﻤﻠﻴﺎت‬ ‫ﺗﺬﮐﺮ‬ ‫اﻟﻨﺎﺗﺞ‬ ‫اﻟﺠﻤﻊ واﻟﻄﺮح‬ ‫اﻟﻀﺮب واﻟﻘﺴﻤﺔ‬ ‫اﻟﻘﻮى‬ ‫اﻷﻗﻮاس‬ ‫;^‪+R*J 3'( ˆC[* : 7A=W GK‬‬ ‫*‪+R*J 3'( €A5‬‬ ‫;^‪: 7A=W GK‬‬ ‫‪V=\"#>/; V=S‬‬ ‫‪V=\"#>/; V=S‬‬ ‫‪= ( k + u )・・- lu‬‬ ‫‪l = jl ・・- lu‬‬ ‫('•@ ‪?#>/; 7A=W‬‬ ‫=‬ ‫) ‡ † ‪k ÷ l( j‬‬ ‫نقسم‬ ‫‪lk = k ÷ l k‬‬ ‫‪cK>* jv = k ÷ vk‬‬ ‫ـ‪٥‬ـ‬

‫اﻟﻤﻌﺎدﻻت‬ ‫‪١‬‬ ‫س ‪١-‬‬ ‫ﻣﺎهﻲ اﻟﻘﯿﻤﺔ اﻟﺘﻲ ﺗﺠﻌﻞ هﺬﻩ اﳌﻌﺎدﻟﻪ ﺻﺤﯿﺤﺔ ؟‬ ‫‪١١‬‬ ‫س ‪٣ = ١-‬‬ ‫هﻲ ﺟﻤﻠﺔ ﺗﺤﺘﻮي ﻋﻠﻲ ﻋﺒﺎرﺗﯿﻦ‬ ‫اﳌﻌﺎدﻟﺔ‬ ‫ﺗﻔﺼﻞ ﺑﯿﻨﻬﻤﺎ إﺷﺎرة‬ ‫اﳌﺴﺎواة ) = (‬ ‫^‪: +•=:q‰ 7/I+FA/; e‬‬ ‫ﻣﻌﺎدﻟﺔ ﺟﻤﻊ‬ ‫^‪: +•=:q‰ 7/I+FA/; e‬‬ ‫ﻣﻌﺎدﻟﺔ ﻃﺮح‬ ‫‪m= k+Š‬‬ ‫{ † ‡ = ‪sr‬‬ ‫‪l=Š‬‬ ‫‪m= k+l‬‬ ‫‡‪sr = ‡ † s‬‬ ‫‪m=m‬‬ ‫{ = ‡‪s‬‬ ‫‪sr = sr‬‬ ‫^‪: +•=:q‰ 7/I+FA/; e‬‬ ‫ﻣﻌﺎدﻟﺔ اﻟﻘﺴﻤﺔ‬ ‫^‪: +=• :q‰ 7/I+FA/; e‬‬ ‫ﻣﻌﺎدﻟﺔ اﻟﻀﺮب‬ ‫‪-n‬‬ ‫‪n=L‬‬ ‫‪-n‬‬‫=‬ ‫‪l‬‬ ‫‪・・・・n Lsk‬‬ ‫{=‪k‬‬ ‫‪jv = { k‬‬ ‫‪jv = k ✕ k‬‬ ‫=‬ ‫‪l‬‬ ‫ـ‪٦‬ـ‬ ‫‪n‬‬ ‫=‬ ‫‪jv = jv‬‬

‫ﻣﻘﺎﻳﻴﺲ اﻟﻨﺰﻋﺔ اﻟﻤﺮﻛﺰﻳﺔ واﻟﻤﺪى‬ ‫ﺗﺬﮐﺮ‬ ‫أحسب المتوسط الحسابي ‪ -‬الوسيط ‪ -‬المنوال ‪ -‬المدى‬ ‫اﳌﺘﻮﺳﻂ اﻟﺤﺴﺎﺑﻲ‬ ‫لهذه البيانات ‪:‬‬ ‫هﻮ ﻣﺠﻤﻮع اﻟﺒﯿﺎﻧﺎت ﻣﻘﺴﻮﻣﺎ ‪ b‬ﻋﺪد ﻣﻔﺮداﺗﻬﺎ‬ ‫‪٨- ١١- ٩ - ٨ - ١٠‬‬ ‫المتوسط الحسابي = ‪٨ + ١١+ ٩ + ٨ + ١٠‬‬ ‫اﻟﻮﺳﯿﻂ‬ ‫‪٥‬‬ ‫‪٤٦‬‬ ‫ﺗﺮﺗﯿﺐ اﻟﺒﯿﺎﻧﺎت إﻣﺎ ﺗﺼﺎﻋﺪﯾﺎ أو ﺗﻨﺎزﻟﯿﺎ‬ ‫‪٥‬‬ ‫= ‪٩٫٢‬‬ ‫=‬ ‫* إذا ﮐﺎن ﻋﺪد ﻣﻔﺮدات اﻟﺒﯿﺎﻧﺎت ﻓﺮدﯾﺎ ﯾﮑﻮن اﻟﻮﺳﯿﻂ اﻟﻌﺪد اﻟﻮاﻗﻊ‬ ‫‪ m‬اﳌﻨﺘﺼﻒ‬ ‫الوسيط = ‪١١ - ١٠ - ٩ - ٨ - ٨‬‬ ‫* إذا ﮐﺎﻧﺖ ﻋﺪد اﻟﺒﯿﺎﻧﺎت زوﺟﯿﺎ ﻓﺈن اﻟﻮﺳﯿﻂ هﻮ ﻣﺘﻮﺳﻂ اﻟﻌﺪدﯾﻦ‬ ‫عدد البيانات ) ‪ ( ٥‬إذًا عددها فرد ًيا‬ ‫اﳌﺘﺠﺎورﯾﻦ ‪ m‬اﳌﻨﺘﺼﻒ‬ ‫*‬ ‫الوسيط = ‪٩‬‬ ‫اﳌﺪى‬ ‫اﳌﻨﻮال‬ ‫المدى = ‪٣ = ٨ - ١١‬‬ ‫المنوال = ‪٨‬‬ ‫هﻮ اﻟﻔﺮق ﺑﯿﻦ أﮐﺒﺮ وأﺻﻐﺮ ﻋﺪد‬ ‫هﻮ اﻟﻌﺪد اﻷﮐﺜﺮ ﺗﮑﺮارًا‬ ‫ـ‪٨‬ـ‬

‫اﻟﻤﻬﺎرات اﻷﺳﺎﺳﻴﺔ‬ ‫ﻟﻠﺼﻒ اﻟﺜﺎﻧﻲ ﻣﺘﻮﺳﻂ‬ ‫ـ‪٩‬ـ‬

‫اﻟﻌﻤﻠﻴﺎت اﻟﺤﺴﺎﺑﻴﺔ ﻋﻠﻰ اﻷﻋﺪاد اﻟﺼﺤﻴﺤﺔ‬ Ž=YZ/; I@F/; { … • l† • s† • j† • r • j •s • l •… } 78#A5A/; V% I@8 b( #q 71/+K/; 7Y=YZ/; I;@8J; 71•#A/; 7Y=YZ/; I;@8J; † aM+`•S 7W#1K% G$dH• ' r V% eW( 7Y=Y‚ I;@8( )q +R*'@S '( + aM+`•S 7W#1K% G$d•H' r V% C1B( 7Y=Y‚ I;@8( )q G/+\" 3' G•#% <=/ ChZ/; || | || || | | ٤- ٣- ٢- ١- ٠ ١+ ٢+ ٣+ ٤+ 7AK>/;' {CU/; ˆC[/;' €A5/; )1EK/; f•#/; )S+52‹; f•#/; G•#% D;M+`‹; pRS+TH ;‰o ・・-⎯⎯✕ D;M+`‹; pRS+TH ;‰o ✚✚ D;M+`‹; pRS+TH ;‰o ⎯⎯⎯⎯ G/+\" D;M+`‹; phE$Œ; ;‰o ✚ €A5*' aM+`‹; <h* ✚ €A5*' aM+`‹; <h* D;M+`‹; phE$Œ; ;‰o )FW;#/; f•#/; ˆC[*' C1BJ; I@F/; aM+`o …Œg* ⎯✚ ⌄ ✚jn † = l † v u+ = ‡ ✚ k j‡ † = m - n † ]+,%( aM+,`o G$d,•H 3 +,%@:,8 n † = l -.. sk † I@,8 f,*( ):F,2 ;…,RP I@F,/; ‫ ـ‬١٠ ‫ـ‬ G•#%

‫اﻟﻤﻌﺎدﻻت اﻟﺨﻄﻴﺔ‬ \" = \" a;'+KA/; aM+`o +AR:=S eZhH V=HM+18 zE8 b#$YH 7EA• )q 7/I+FA/; 7Y=Y‚ 7/I+FA/; eF5H )$/; C=ƒ$AE/ 72I@F/; 7A=>/; #q 7/I+FA/; e^ 7AK>/; D3I+F% ˆC[/; D3I+F% €A5/; D3I+F% zE8 7/I+FA/; V% yC‘ eB pAKW ;‰o )PC‘ XB V% fKh* I@F/; p^C‘ ;‰o )PC‘ z/o fKh* I@F/; phi( ;‰o +PC‘ z>12 ChZ/; C=N I@8 V=2'+K$% 7/I+FA/; +PC‘ z>12 7/I+FA/; V=2'+K$% 7/I+FA/; +PC‘ z>12 7/I+FA/; V=2'+K$% 7/I+FA/; v =s+L k =l†L v†=Ls s†= s† l+=l+ ’vs’† = ’Ls’s ’’k ’= L’’ ’’m’= ’L’ l† = L ‫ ـ‬١١ ‫ـ‬

‫اﻟﻨﺴﺒﺔ واﻟﺘﻨﺎﺳﺐ‬ s D;Cd/; I@8 z/o x+WM9/; D;Cd/; I@8 71K* 71K:/; k x;CAY/; V=S 7*M‫ا‬+>% )q ~+2'+K$% G\"+:H bJ )/I+1$/; {CU/; +5H+* l =j V=$=AB v l s=v j s 7AK>/; &+AF$\"+S 7/#R5A/; c=>/; I+52‹ )/I+1$/; {CU/; eAF$K•2 G\"+:$/; _١_٠_ = __٥_ ?'+K$H 7/+^‫ ا‬#q G\"+:$/; ٢٢ ‫ك‬ +R=P eWJ; zE8 ~3@F% '( ~+$1K* ٥ ٢٢ = ١٠ ‫ك‬ ١١٠ = ‫ ك‬١٠ “ e%+F% zE8 7AK>/+S ١_١_٠_ = ‫__ك‬١_٠ ١٠ ١٠ ١١ = ‫ك‬ ‫ ـ‬١٢ ‫ـ‬

‫اﻟﻌﻼﻗﺎت ﺑﻴﻦ اﻟﺰواﻳﺎ‬ +RH+\"+=W GKYS +2;'9/; ”:ZH ~+$2'+K$A/; ~+$2';9/;' L(C/+S ~+$ES+>$A/; ~+$2';9/; ~+$>S+[$% L+=>/; )P s V=HM'+5$% C=N ~+$2';6 +Aq +2;'9/; ”=:ZH lj V=A=>$K% €‘+>H V8 V=$5H+:/; k ~+HM'+5$A/; ~+$2';9/; ٥ ٥ ٥ ur V% eW( jnr b'+KH ur b'+KH V=HM'+5$% C=N ~+$2';6 +Aq ٥ jnr '٥ ur V=S aI+^‫ا‬72';6 ‫ا‬7A=>$K% 72';6 7A}+W‫ ا‬72';6 sj €‘+>H V8 V=$5H+:/; 7•Ch:‫ا‬% 72';6 V=A=>$K% +2;'9/;' c=>$KA/; D+WX8 ~+$=EŒ;I ~+$2';6 ~+$E%+d$A/; ~+$2';9/; ~+$%+$$A/; ~+$2';9/; ~+$=•M+Œ ~+$2';6 0#A5% ~+$2';6 +Aq 0#A5% ~+$2';6 +Aq ٥jnr b'+K2 +AR\"+=W ٥ ur b'+K2 +AR\"+=W V=A=>$KA/; •M+Œ €>H )$/; +2;'9/; )q sj V=A=>$KA/; V=S €>H )$/; +2;'9/; )q k l‡ sj ‫نك‬ 4=•M+Œ ~+$/I+1$% ~+$2';6 v 4=EŒ;I ~+$/I+1$% ~+$2';6 nm sj V=,,HM'+5$,,% C=,,N ~+$=,,•M+,,Œ ~+$,,2';6 +A,,q V=,,HM'+5$,,% C=,,N ~+$=E,,Œ;I ~+$,,2';6 +A,,q €‘+>/; V% V=$hE$\\% V=$R• )P ~+F>H €‘+>/; V% V=$hE$\\% V=$R• )P ~+F>H €[>,,,2 b…,,,/; c=>$,,,KA/; #,,,q €,,,‘+>,,,/; ~+HC–+:$% ~+$2';6 COB( '( V=A=>$K% 7=E,,,Œ;I +A,,,q@,,,^( V=,,,HM'+5$,,,% C=,,,N ~+$,,,2';6 +A,,,q €‘+>/; V% a@^;' 7R• )P ~+F>H 7=•M+Œ ?CŒJ;' ‫ ـ‬١٣ ‫ـ‬

‫ل = اﻟﻄﻮل‬ ‫اﻟﻤﺴﺎﺣﺎت واﻟﺤﺠﻮم‬ ‫ض = اﻟﻌﺮض‬ ‫ق = اﻟﻘﺎﻋﺪة‬ ‫ﻣﺴﺎﺣﺔ اﻟﻤﺜﻠﺚ‬ ‫ﻣﺴﺎﺣﺔ اﻟﻤﺴﺘﻄﻴﻞ‬ ‫ﻣﺴﺎﺣﺔ اﻟﻤﺮﺑﻊ‬ ‫ع = اﻻرﺗﻔﺎع‬ ‫ﻧﻖ = ﻧﺼﻒ اﻟﻘﻄﺮ‬ ‫م=ل×ض‬ ‫م = ) ﻃﻮل اﻟﻀﻠﻊ ( ‪٢‬‬ ‫ق ×ع‬ ‫‪١‬‬ ‫م=‬ ‫ﻣﺴﺎﺣﺔ اﻟﺪاﺋﺮة‬ ‫‪٢‬‬ ‫م = ط ﻧﻖ ‪٢‬‬ ‫ﻣﺴﺎﺣﺔ اﻷﺷﻜﺎل اﻟﻤﺮﻛﺒﺔ‬ ‫ﻣﺴﺎﺣﺔ ﺷﺒﻪ اﻟﻤﻨﺤﺮف‬ ‫‪&+d`( z/o f$}95$S cW GBCA/; edT/; 7^+K% {+KY/‬‬ ‫×ع‬ ‫) ق‪ + ١‬ق‪( ٢‬‬ ‫‪١‬‬ ‫م=‬ ‫‪. +RFA•;' D+^+KA/; wEH GK^; c- +R$^+K% yCFH‬‬ ‫‪٢‬‬ ‫ﺣﺠﻢ اﻻﺳﻄﻮاﻧﺔ‬ ‫ﺣﺠﻢ اﻟﻬﺮم‬ ‫ﺣﺠﻢ اﻟﻤﻨﺸﻮر‬ ‫ˆ = ™ *˜ ‪0 s‬‬ ‫رﺑﺎﻋﻲ‬ ‫رﺑﺎﻋﻲ‬ ‫)& × — × ‪( 0‬‬ ‫‪١‬‬ ‫=‬ ‫ˆ‬ ‫ˆ=&×—×‪0‬‬ ‫‪٣‬‬ ‫ﺣﺠﻢ اﻟﻤﺨﺮوط‬ ‫ﺛﻼﺛﻲ‬ ‫ﺛﻼﺛﻲ‬ ‫‪١‬‬ ‫‪0s‬‬ ‫*˜‬ ‫™‬ ‫‪٣‬‬ ‫ˆ=‬ ‫×‪(0)(0‬‬ ‫_‬ ‫‪١‬‬ ‫)‬ ‫‪١‬‬ ‫=‬ ‫ˆ‬ ‫×‪(0)(0‬‬ ‫)_‬ ‫‪١‬‬ ‫ˆ=‬ ‫‪٢‬‬ ‫‪٣‬‬ ‫‪٢‬‬ ‫اﻟﻤﺴﺎﺣﺔ اﻟﺠﺎﻧﺒﻴﺔ واﻟﻜﻠﻴﺔ ﻟﻠﻬﺮم‬ ‫اﻟﻤﺴﺎﺣﺔ اﻟﺠﺎﻧﺒﻴﺔ واﻟﻜﻠﻴﺔ ﻟﻺﺳﻄﻮاﻧﺔ‬ ‫اﻟﻤﺴﺎﺣﺔ اﻟﺠﺎﻧﺒﻴﺔ واﻟﻜﻠﻴﺔ ﻟﻠﻤﻨﺸﻮر‬ ‫‪& Ž%‬‬ ‫‪١‬‬ ‫•‪= ,‬‬ ‫اﻟﻤﺴﺎﺣﺔ اﻟﺠﺎﻧﺒﻴﺔ ‪:‬‬ ‫اﻟﻤﺴﺎﺣﺔ اﻟﺠﺎﻧﺒﻴﺔ ‪0 ˜* ™ s = ,• :‬‬ ‫اﻟﻤﺴﺎﺣﺔ اﻟﺠﺎﻧﺒﻴﺔ ‪0 Ž% = ,• :‬‬ ‫‪٢‬‬ ‫اﻟﻤﺴﺎﺣﺔ اﻟﻜﻠﻴﺔ ‪:‬‬ ‫اﻟﻤﺴﺎﺣﺔ اﻟﻜﻠﻴﺔ ‪s ˜* ™ s + ,• = “ :‬‬ ‫اﻟﻤﺴﺎﺣﺔ اﻟﻜﻠﻴﺔ ‪] s + ,• = “ :‬‬ ‫“ = •‪] + ,‬‬ ‫ـ ‪ ١٤‬ـ‬

‫اﺣﺘﻤﺎل اﻟﺤﻮادث اﻟﻤﺮﻛﺒﺔ‬ 71BCA/; 7-I+Y/; COB( '( V=$[=KS V=$-I+^ V% ~#d$H 7E>$KA/; C=N „I;#Y/; 7E>$KA/; „I;#Y/; ?CŒJ; „I;#Y/; )P „I;#Y/; ?@^o šH+* C-›2 ?CŒJ; „I;#Y/; )P „I;#Y/; ?@^o šH+* C-›2 3 ( ( @FS { ) ˆ ( ( ) ˆ = ( { 'œ ( ) ˆ ( { ) ˆ ( ( ) ˆ = ( { 'œ ( ) ˆ + •?C,Œ( DC=$,Œ; c,- 7R,B+,P 71,^ DC=$,Œ; ;‰o +( V=PCY/; XB &+A$^; +% +•^+hH ~+$1Y/; ~#dH ~( &+A$^; +% ++ j’v‡ = ( 7^+hH z/'J; 71Y/; ) ˆ ’vj = ( ( yC^ zE8 M;'@/; ŠC>/; ”W#H ) ˆ ’j = ( ( yC^ 7W+[S M+=$Œ; ) ˆ ’jk‡ = ( 7^+hH 7=*+O/; 71Y/; ) ˆ m j’js = j j k’sj = ’mj ’vj = ( ( V=PCY/; XB ) ˆ ’j//k‡ j’//v‡ = (ˆ+hH ~+$1Y/; ) ˆ lk ‫ ـ‬١٥ ‫ـ‬

‫اﻟﻤﻬﺎرات اﻷﺳﺎﺳﻴﺔ‬ ‫ﻟﻠﺼﻒ اﻟﺜﺎﻟﺚ ﻣﺘﻮﺳﻂ‬ ‫ـ ‪ ١٦‬ـ‬

‫اﻷﻋﺪاد اﻟﻨﺴﺒﻴﺔ‬ ‫اﻟﻌﺪد اﻟﻨﺴﺒﻲ ‪. CKB aM#‚ zE8 f$S+$B VdA2 b…/; I@F/; #q :‬‬ ‫اﻟﺠﻤﻊ واﻟﻄﺮح ذات‬ ‫اﻟﻌﻤﻠﻴﺎت ﻋﻠﻰ اﻷﻋﺪاد اﻟﻨﺴﺒﻴﺔ‬ ‫اﻟﻤﻘﺎﻣﺎت اﻟﻤﺘﺸﺎﺑﻬﺔ‬ ‫‪١١‬‬ ‫=‬ ‫‪٩+ ٢‬‬ ‫=‬ ‫‪٩‬‬ ‫‪+‬‬ ‫‪٢‬‬ ‫‪٣‬‬ ‫÷‬ ‫‪٤‬‬ ‫‪٥‬‬ ‫×‬ ‫‪٤‬‬ ‫‪٥‬‬ ‫‪٥‬‬ ‫‪٥‬‬ ‫‪٥‬‬ ‫‪٢‬‬ ‫‪٩‬‬ ‫‪٦‬‬ ‫‪٣‬‬ ‫‪٩ - ٧-‬‬ ‫=‬ ‫‪٩‬‬ ‫‪−‬‬ ‫‪٧-‬‬ ‫‪{#E>%‬‬ ‫‪٥× ٤‬‬ ‫=‬ ‫‪١٠‬‬ ‫‪١٠‬‬ ‫‪&#YH‬‬ ‫‪٦×٣‬‬ ‫‪&9:2‬‬ ‫‪٨-‬‬ ‫=‬ ‫‪٢ ÷ ١١٠٦-‬‬ ‫=‬ ‫‪(٩ -) +‬‬ ‫= ‪٧-‬‬ ‫‪٢‬‬ ‫×‬ ‫‪٤‬‬ ‫=‬ ‫= ‪٢ ÷ ٢٠‬‬ ‫‪٥‬‬ ‫‪٢ ÷ ١٠‬‬ ‫‪١٠‬‬ ‫‪٣‬‬ ‫‪٩‬‬ ‫=‬ ‫‪٢ ÷ ١٨‬‬ ‫×‬ ‫‪٤‬‬ ‫‪٢‬‬ ‫‪٣×٩‬‬ ‫= ‪١٠‬‬ ‫‪٨‬‬ ‫‪٩‬‬ ‫اﻟﺠﻤﻊ واﻟﻄﺮح ذات‬ ‫‪٢٧‬‬ ‫=‬ ‫اﻟﻤﻘﺎﻣﺎت اﻟﻤﺨﺘﻠﻔﺔ‬ ‫اﻟﻀﺮب‬ ‫‪٤‬‬ ‫‪+‬‬ ‫‪٢‬‬ ‫اﻟﻘﺴﻤﺔ‬ ‫‪٣‬‬ ‫‪٥‬‬ ‫×‪(٤×٥)+(٣‬‬ ‫)‪٢‬‬ ‫=‬ ‫اﻟﺠﻤﻊ‬ ‫)‪(٣×٥‬‬ ‫اﻟﻄﺮح‬ ‫‪٢٦‬‬ ‫‪= ٢٠ + ٦‬‬ ‫=‬ ‫‪١٥‬‬ ‫‪١٥‬‬ ‫ـ ‪ ١٧‬ـ‬

‫ﻧﻈﺮﻳﺔ ﻓﻴﺜﺎﻏﻮرس‬ 72';9/; eS+>2 CH#/; +Aq ~+W+K/; &#‘( #q' 7A}+>/; ~;…E/; ~+FEU/; s{ +s ( =s,• 72';6 ~XdT2 .EOA/; )P €Ei . 72';9/; c}+>/; . 7A}+W ‫ﻋﻜﺲ‬ ‫ﻧﻈﺮﻳﺔ‬ ‫ﻧﻈﺮﻳﺔ ﻓﻴﺜﺎﻏﻮرس‬ ‫ﻓﻴﺜﺎﻏﻮرس‬ I@^ .c\" jl • c\" js • c\" ‡ : 0XiJ; &;#‘( ‫جـ سم‬ s{ +s ( =s,• . 3 ]( 72';9/; c}+W .EOA/; ~+B ;‰o +% ‫ سم‬٣ s k + s l =s,• s{ +s ( =s,• ‫ سم‬٤ jv + u = s,• s‡ = s ‡ ‫ ل‬jkk = s js V=PC[E/ )F=SC$/; M…5/; …ŒgS s‡ = s,• CH#/; jvu = s jl ‫ ـ‬١٨ ‫ـ‬ s‡ = s,• s‡ +jkk = jvu jvu = jvu ‡±= ,• . 72';9/; c}+W .EOA/; ;‰o . c\" ‡=&#R5A/; €EU/; &#‘ ;‰o

‫اﻟﻤﻀﻠﻌﺎت اﻟﻤﺘﺸﺎﺑﻬﺔ‬ ‫رﻣﺰ اﻟﺘﺸﺎﺑﻪ ~‬ ‫اﻟﻤﻀﻠﻊ ‪. 4>Eƒ% X• d` ~#d2 .=YS +R$2+R* 7F‘+>$% ?#$K% )P 7A=>$KA/; €[>/; V% 78#A5% :‬‬ ‫إذا ﺗﺸﺎﺑﻪ ﻣﻀﻠﻌﺎن ﻓﺈن‬ ‫(‘‪71\"+:$% aC–+:$A/; +AR8Xi( &;#‬‬ ‫‪7>S+[$% aC–+:$A/; +Aq+2;'6‬‬ ‫^@‪. 3 ]( ~+RS+T$% ~+FEUA/; ~+B+% ;‰o I‬‬ ‫‪L‬‬ ‫‪0‬‬ ‫{‬ ‫(‬ ‫‪Š‬‬ ‫•‪,‬‬ ‫;‪. 7>S+[$% aC–+:$A/; +2;'9/‬‬ ‫‪٤‬‬ ‫=‬ ‫‪٢٤‬‬ ‫=‬ ‫‪٢٠‬‬ ‫=‬ ‫‪١٦‬‬ ‫‪٣‬‬ ‫‪١٨‬‬ ‫‪١٥‬‬ ‫‪١٢‬‬ ‫‪0ŠL‬‬ ‫( { •‪~ ,‬‬ ‫ـ ‪ ١٩‬ـ‬

‫اﻟﻤﺘﺒﺎﻳﻨﺎت‬ . ( > ) V% Cƒ‚( '( ( < ) V% C1B( V29%C/; @^( zE8 eA$TH )$/; 7=i+2C/; 7EA5/; : ‫اﻟﻤﺘﺒﺎﻳﻨﺔ‬ 7AK>/; {CU/; : ‫ﺣﻞ اﻟﻤﺘﺒﺎﻳﻨﺎت‬ €A5/; l× n ≥ ≥ŠŠ٣١ × l ks† < L m j‡ > n − L sk mm n+>n+ 7:2+1$A/; aM+`o C=ƒ$H3 7:2+1$A/; aM+`o C=ƒ$H3 v† < L sl > L ‫ن‬ sk < L v† s† × n < ٢- × s† v† v† 7:2+1$A/; aM+`o C=ƒ$H3 7:2+1$A/; aM+`o C=ƒ$H k† > L jv† > ~ ˆC[/; 7:2+1$A/; aM+`o C=ƒ$H k† ≤ m + & m -≤ m - . G/+\" I@8 zE8 cK>* '( {CU* +%@:8 7:2+1$A/; aM+`o C=ƒ$H jj† ≤ & ‫ ـ‬٢٠ ‫ـ‬ 7:2+1$A/; aM+`o C=ƒ$H3

‫ـ ‪ ٢١‬ـ‬

twitter.com/ D+h/›A/; D+S+K^ https:// ‫ ﻧﻮرﻩ اﻟﺤﺮﺑﻲ‬/‫أ‬ mobile.twitter.c ‫ ﻧﻮال اﳌﻄﯿﺮي‬/‫أ‬anan66661 ‫ أﺷﻮاق اﻟﺤﺠﯿﻠﻲ‬/‫أ‬https:// om/ twitter.com/ noura_ali909 Ashwaq_math D+=i+2C/; 7FPM 78#A5% D+S+K^ https:// https:// https:// https://twitter.com/ www.snapchat.com/ youtube.com/ www.instagra maths0120?s=11 add/maths0120 channel/ m.com/ UCSuTr4xQF93 /math0120 Snapchat yTcyBhRr-jhg Instagram Twitter You Tube https://t.me/ https://t.me/ https://t.me/ https://t.me/ RAFAHTHEBO RAFAH_middl RAFAH_mid RAFAH_middl OKS e3 dle2 e12 ‫اﳌﮑﺘﺒﺔ اﻟﺮﻗﻤﯿﺔ‬ ‫ﺛﺎﻟﺚ ﻣﺘﻮﺳﻂ‬ ‫أول ﻣﺘﻮﺳﻂ ﺛﺎﻧﻲ ﻣﺘﻮﺳﻂ‬ 7FPM D;#:W' D+S+K^ €=A• 7P+i‹ https:// ‫اﺿﻐﻂ هﻨﺎ‬linktr.ee/ maths120 ‫ ـ‬٢٢ ‫ـ‬