8. Sınıf Öğreniyorum Serisi Matematik Soru Bankası

["Uyguluyorum Daire Grafi\u011fi Test 36 5. A\u015fa\u011f\u0131daki daire grafi\u011fi 72 ki\u015filik bir gruptaki \u201cEn sev- di\u011finiz meyve nedir?\u201d sorusuna verilen cevaplar\u0131n 7. A\u015fa\u011f\u0131daki daire grafi\u011finde bir arazide bulunan 1200 da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6stermektedir. a\u011fac\u0131n t\u00fcrlerine g\u00f6re da\u011f\u0131l\u0131m\u0131 verilmi\u015ftir. Grafik: Gruptakilerin Cevaplar\u0131n\u0131n Da\u011f\u0131l\u0131m\u0131 Grafik: A\u011fa\u00e7lar\u0131n T\u00fcrlerine G\u00f6re Da\u011f\u0131l\u0131m\u0131 Portakal 30\u00b0 G\u00fcrgen Me\u015fe 30\u00b0 \u00c7am \u015eeftali 80\u00b0 160\u00b0 Muz Palamut \u00c7ilek Karpuz Arazide bulunan me\u015fe a\u011fa\u00e7lar\u0131n\u0131n say\u0131s\u0131 \u00e7am a\u011fa\u00e7- lar\u0131n\u0131n say\u0131s\u0131n\u0131n iki kat\u0131, palamut a\u011fa\u00e7lar\u0131n\u0131n say\u0131s\u0131- \u201cKarpuz\u201d cevab\u0131na ait daire diliminin merkez a\u00e7\u0131s\u0131 \u201c\u00c7ilek\u201d cevab\u0131na ait daire diliminin merkez a\u00e7\u0131s\u0131ndan 1 fazlad\u0131r. n\u0131n 3 \u2019\u00fc kadard\u0131r. Buna g\u00f6re \u00e7ilek cevab\u0131n\u0131 veren ki\u015fi say\u0131s\u0131 en fazla Buna g\u00f6re arazideki g\u00fcrgen a\u011fa\u00e7lar\u0131n\u0131n say\u0131s\u0131 ka\u00e7t\u0131r? ka\u00e7t\u0131r? A) 7 B) 8 C) 9 D) 10 A) 300 B) 400 C) 500 D) 600 6. A\u015fa\u011f\u0131daki daire grafi\u011finde bir \u015firketin gelirlerinin \u00e7e- 8. A\u015fa\u011f\u0131daki daire grafi\u011finde bir ma\u011fazada sat\u0131lan k\u0131- \u015fitli sekt\u00f6rlere g\u00f6re da\u011f\u0131l\u0131m\u0131 verilmi\u015ftir. yafetlerin \u00fcr\u00fcn gruplar\u0131na g\u00f6re da\u011f\u0131l\u0131m\u0131 verilmi\u015ftir. Grafik: \u015eirketin Gelirlerinin 36\u00b0 %15 Ti\u015f\u00f6rt %43 %20 Kazak G\u00f6mlek %30 \u015eort Otomotiv Tar\u0131m Turizm Buna g\u00f6re bu \u015firketin gelirlerinin da\u011f\u0131l\u0131m\u0131n\u0131n Sat\u0131lan ti\u015f\u00f6rt say\u0131s\u0131, g\u00f6mlek say\u0131s\u0131ndan 27 az ol- y\u00fczde ka\u00e7\u0131 turizm sekt\u00f6r\u00fcne aittir? du\u011funa g\u00f6re ma\u011fazada ka\u00e7 \u015fort sat\u0131lm\u0131\u015ft\u0131r? A) 21 B) 29 C) 47 D) 57 A) 162 B) 171 C) 180 D) 189 150 8. S\u0131n\u0131f","Verileri Uygun Grafikle G\u00f6sterme ve Grafikler Aras\u0131 D\u00f6n\u00fc\u015f\u00fcmler Yapma \u2022 Verilerdeki de\u011fi\u015fimi incelemek i\u00e7in en uygun grafi\u011fin \u00e7izgi grafi\u011fi, \u2022 Verileri kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in en uygun grafi\u011fin s\u00fctun grafi\u011fi, \u2022 Veri grubu i\u00e7indeki bir verinin b\u00fct\u00fcn i\u00e7erisindeki oran\u0131n\u0131 g\u00f6stermek i\u00e7in en uygun grafi\u011fin daire grafi\u011fi oldu\u011funu \u00f6\u011frenmi\u015ftik. Baz\u0131 veriler s\u0131kl\u0131k tablosu ya da \u00e7e\u015fitli grafikler ile g\u00f6sterildikten sonra bu verilere bak\u0131larak uygun \u015fekilde ba\u015fka bir grafik \u00e7izilebilir. \u00d6rnek: Bir ailedeki d\u00f6rt karde\u015fin ya\u015flar\u0131 a\u015fa\u011f\u0131daki gibi \u00f6nce s\u0131kl\u0131k tablosunda g\u00f6sterilip daha sonra s\u00fctun grafi\u011fine d\u00f6n\u00fc\u015ft\u00fcr\u00fclebilir. Tablo: Karde\u015flerin Ya\u015flar\u0131 Grafik: Karde\u015flerin Ya\u015flar\u0131 Ki\u015fi Ahmet Burak Cansu Duru Ya\u015f Ya\u015f 15 3 10 7 15 10 Ki\u015fi 7 3 Ahmet Burak Cansu Duru 36 1. A\u015fa\u011f\u0131daki tabloda bir \u015fehrin \u00fc\u00e7 g\u00fcnl\u00fck hava s\u0131cakl\u0131k 2. A\u015fa\u011f\u0131daki tabloda aylara g\u00f6re bir k\u00fct\u00fcphaneden de\u011ferleri verilmi\u015ftir. \u00f6d\u00fcn\u00e7 al\u0131nan kitap say\u0131lar\u0131 verilmi\u015ftir. Tablo: Hava S\u0131cakl\u0131k De\u011ferleri Tablo: \u00d6d\u00fcn\u00e7 Al\u0131nan Kitap Say\u0131lar\u0131 G\u00fcn Pazartesi Sal\u0131 \u00c7ar\u015famba Ay Ocak \u015eubat Mart Nisan Say\u0131 110 130 100 140 S\u0131cakl\u0131k (\u00b0C) 15 12 19 Bu verilere uygun \u00e7izgi grafi\u011fi \u00e7iziniz. Bu verilere uygun s\u00fctun grafi\u011fi \u00e7iziniz. 8. S\u0131n\u0131f 151","Verileri Uygun Grafikle G\u00f6sterme ve Grafikler Aras\u0131 D\u00f6n\u00fc\u015f\u00fcmler Yapma 3. A\u015fa\u011f\u0131daki grafikte \u00fc\u00e7 y\u0131l boyunca bir \u015firkette \u00e7al\u0131\u015fan 4. A\u015fa\u011f\u0131daki daire grafi\u011finde 1 L\u2019lik kar\u0131\u015f\u0131k meyve suyu personel say\u0131s\u0131n\u0131n cinsiyete g\u00f6re say\u0131lar\u0131 verilmi\u015ftir. yap\u0131m\u0131nda kullan\u0131lan baz\u0131 i\u00e7eceklerin t\u00fcrlerine g\u00f6re Grafik: \u015eirkette \u00c7al\u0131\u015fanlar\u0131n Say\u0131s\u0131 da\u011f\u0131l\u0131m\u0131 verilmi\u015ftir. Say\u0131 Grafik: Kar\u0131\u015f\u0131k Meyve Suyu Yap\u0131m\u0131nda Kullan\u0131lan Kad\u0131n \u0130\u00e7ecekler 60 Erkek 50 Vi\u015fne Elma 40 72\u00b0 Mango 30 0 Y\u0131l 2020 2021 2022 a) Bu verilere uygun s\u00fctun grafi\u011fi \u00e7iziniz. a) Bu verilere uygun tablo olu\u015fturunuz. b) Bu verilere uygun \u00e7izgi grafi\u011fi \u00e7iziniz. b) Kad\u0131n personel say\u0131s\u0131n\u0131n y\u0131llara g\u00f6re da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6steren daire grafi\u011fi \u00e7iziniz. c) \u00c7izdi\u011finiz iki grafi\u011fin birbirlerine g\u00f6re \u00fcst\u00fcn veya zay\u0131f durumlar\u0131n\u0131 yaz\u0131n\u0131z. 152 8. S\u0131n\u0131f","Test Uygun Grafikle G\u00f6sterme ve Grafikler Aras\u0131 Uyguluyorum 37 D\u00f6n\u00fc\u015f\u00fcmler Yapma 1. ve 2. sorular\u0131 a\u015fa\u011f\u0131daki bilgilere g\u00f6re cevapla- 3. A\u015fa\u011f\u0131daki \u00e7izgi grafi\u011finde Cem\u2019in d\u00f6rt g\u00fcn boyunca y\u0131n\u0131z. kumbaras\u0131nda bulunan para miktar\u0131 g\u00f6sterilmi\u015ftir. Para Miktar\u0131 (TL) A\u015fa\u011f\u0131daki tabloda bir geziye kat\u0131lacak \u00f6\u011frenci say\u0131- lar\u0131n\u0131n s\u0131n\u0131f seviyelerine g\u00f6re da\u011f\u0131l\u0131m\u0131 verilmi\u015ftir. 180 150 Tablo: Geziye Kat\u0131lacak \u00d6\u011frenci Say\u0131lar\u0131 5. S\u0131n\u0131f K\u0131z Erkek 90 6. S\u0131n\u0131f 15 20 60 7. S\u0131n\u0131f 15 15 8. S\u0131n\u0131f 20 15 0 1 2 3 4 G\u00fcn 10 20 Cem\u2019in d\u00f6rt g\u00fcnde biriktirdi\u011fi toplam para mikta- r\u0131n\u0131n g\u00fcnlere g\u00f6re da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6steren daire gra- fi\u011fi a\u015fa\u011f\u0131dakilerden hangisidir? 1. Bu verilere uygun s\u00fctun grafi\u011fi a\u015fa\u011f\u0131dakilerden A) B) hangisidir? 3.G\u00fcn 4.G\u00fcn 3.G\u00fcn 4.G\u00fcn 60\u00b0 A) Say\u0131 K\u0131z B) Say\u0131 K\u0131z Erkek Erkek 60\u00b0 120\u00b0 60\u00b0 20 20 2.G\u00fcn 1.G\u00fcn 2.G\u00fcn 1.G\u00fcn 15 15 10 10 55 56 7 8 S\u0131n\u0131flar 56 7 8 S\u0131n\u0131flar C) Say\u0131 K\u0131z D) Say\u0131 K\u0131z C) D) Erkek Erkek 20 20 3.G\u00fcn 4.G\u00fcn 15 15 S\u0131n\u0131flar 2.G\u00fcn 60\u00b0 4.G\u00fcn 10 10 3.G\u00fcn 120\u00b0 5 5 60\u00b0 60\u00b0 60\u00b0 60\u00b0 56 7 8 1.G\u00fcn 1.G\u00fcn 2.G\u00fcn S\u0131n\u0131flar 56 7 8 2. K\u0131z \u00f6\u011frencilerin s\u0131n\u0131f seviyelerine g\u00f6re da\u011f\u0131l\u0131m\u0131 4. Bir \u015fehirdeki se\u00e7im sonu\u00e7lar\u0131n\u0131 g\u00f6stermek i\u00e7in daire grafi\u011fi ile g\u00f6sterildi\u011finde 8. s\u0131n\u0131flara ait da- a\u015fa\u011f\u0131daki g\u00f6sterim \u015fekillerinden hangisini kul- ire diliminin merkez a\u00e7\u0131s\u0131n\u0131n \u00f6l\u00e7\u00fcs\u00fc ka\u00e7 derece lanmak daha uygundur? olur? A) S\u0131kl\u0131k tablosu B) \u00c7izgi grafi\u011fi C) S\u00fctun grafi\u011fi D) Daire grafi\u011fi A) 60 B) 80 C) 90 D) 120 8. S\u0131n\u0131f 153","Uyguluyorum Uygun Grafikle G\u00f6sterme ve Grafikler Aras\u0131 Test D\u00f6n\u00fc\u015f\u00fcmler Yapma 37 5. Nesrin haftal\u0131k ders \u00e7al\u0131\u015fma program\u0131na g\u00f6re her 6. Bir yay\u0131nevine ait K k\u0131rtasiyesindeki kitaplar\u0131n say\u0131- dersten belirli bir s\u00fcre \u00e7al\u0131\u015fma plan\u0131 yap\u0131yor. s\u0131n\u0131n t\u00fcrlerine g\u00f6re da\u011f\u0131l\u0131m\u0131 a\u015fa\u011f\u0131daki tabloda veril- mi\u015ftir. A\u015fa\u011f\u0131daki s\u00fctun grafi\u011finde Nesrin\u2019in ders \u00e7al\u0131\u015fma saatleri g\u00f6sterilmi\u015ftir. Tablo: K K\u0131rtasiyesindeki Kitaplar\u0131n Say\u0131s\u0131 Ders Kitap T\u00fcr\u00fc Say\u0131 Ekinlik Defteri 340 T\u00fcrk\u00e7e Soru Bankas\u0131 350 Matematik Deneme Seti 390 Fen B. L k\u0131rtasiyesindeki; etkinlik defteri say\u0131s\u0131, K k\u0131rtasiye- Sosyal B. sindekinden 40 az, soru bankas\u0131 say\u0131s\u0131 K k\u0131rtasiye- sindekinden 40 fazlad\u0131r. \u0130ng 369 S\u00fcre \u0130ki k\u0131rtasiyenin deneme seti say\u0131lar\u0131 birbirine e\u015fit saat saat saat oldu\u011funa g\u00f6re L k\u0131rtasiyesindeki kitaplar\u0131n t\u00fcrle- rine g\u00f6re da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6steren daire grafi\u011fi a\u015fa\u011f\u0131- Buna g\u00f6re bu programa uygun daire grafi\u011fi a\u015fa- dakilerden hangisidir? \u011f\u0131dakilerden hangisi olabilir? A) B) A) B) Soru 40\u00b0 40\u00b0 Soru Deneme Bankas\u0131 40\u00b0 Bankas\u0131 Seti Deneme 150\u00b0 80\u00b0 Set1i 05\u00b0 40\u00b0 150\u00b0 80\u00b0 80\u00b0 60\u00b0 Etkinlik Etkinlik Defteri Defteri C) D) C) D) Etkinlik Soru 60\u00b0 40\u00b0 120\u00b0 50\u00b030\u00b0 Deneme Soru Defteri Bankas\u0131 40\u00b0 30\u00b0 Seti Bankas\u0131 130\u00b0 150\u00b0 120\u00b0 130\u00b0 130\u00b0 Deneme Seti Etkinlik Defteri 154 8. S\u0131n\u0131f","Test Veri Analizi Ba\u015far\u0131yorum 38 1. ve 2. sorular\u0131 a\u015fa\u011f\u0131daki bilgilere g\u00f6re cevaplay\u0131n\u0131z. Bir firman\u0131n \u00fcretti\u011fi sak\u0131z kutusunda kendi i\u00e7lerinde \u00f6zde\u015f muzlu, \u00e7ilekli ve naneli sak\u0131z paketleri bulunmaktad\u0131r. Kutudaki paket sak\u0131zlar\u0131n toplam k\u00fctlesinin t\u00fcrlerine g\u00f6re da\u011f\u0131l\u0131m\u0131 daire grafi\u011finde, sak\u0131zlar\u0131n say\u0131lar\u0131 ise s\u00fctun gra- fi\u011finde g\u00f6sterilmi\u015ftir. Grafik: Sak\u0131zlar\u0131n Toplam K\u00fctlesinin Da\u011f\u0131l\u0131m\u0131 Grafik: Sak\u0131zlar\u0131n T\u00fcrlerine G\u00f6re Say\u0131s\u0131 Say\u0131 Naneli 14 \u00c7ilekli 120\u00b0 96\u00b0 10 8 Muzlu 0 T\u00fcr Naneli \u00c7ilekli Muzlu Muzlu sak\u0131zlar\u0131n toplam k\u00fctlesi, \u00e7ilekli sak\u0131zlar\u0131n toplam k\u00fctlesinden 28 g eksiktir. 1. Buna g\u00f6re kutudaki naneli sak\u0131zlardan bir tanesinin k\u00fctlesi ka\u00e7 gramd\u0131r? D) 7 A) 4 B) 5 C) 6 2. Bu firma benzer \u015fekilde \u00f6zde\u015f sak\u0131z paketlerini kullanarak a\u015fa\u011f\u0131daki gibi yeni kutularda sat\u0131\u015f yapmaktad\u0131r. Sak\u0131z Kutusu 5 Muzlu 6 \u00c7ilekli Buna g\u00f6re bu yeni kutudaki sak\u0131zlar\u0131n toplam k\u00fctlesi ka\u00e7 gramd\u0131r? A) 84 B) 78 C) 71 D) 63 8. S\u0131n\u0131f 155","Ba\u015far\u0131yorum Veri Analizi Test 38 3. A\u015fa\u011f\u0131da bir tiyatro oyununun may\u0131s ay\u0131 i\u00e7indeki 3 farkl\u0131 g\u00f6steriminde sat\u0131lan tam ve indirimli bilet say\u0131lar\u0131 verilmi\u015ftir. Bilet Say\u0131s\u0131 150 \u0130ndirimli 120 Tam 90 60 0 G\u00f6sterim 8 May\u0131s 15 May\u0131s 22 May\u0131s G\u00f6sterimi G\u00f6sterimi G\u00f6sterimi Bu sinema salonunda indirimli biletin \u00fccretinin tam bilet \u00fccretine oran\u0131 1 \u2019dir. 2 Buna g\u00f6re bu 3 g\u00f6sterim i\u00e7in izleyicilerin \u00f6dedi\u011fi toplam \u00fccretin g\u00f6sterimlere g\u00f6re da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6steren da- iresel grafik a\u015fa\u011f\u0131dakilerden hangisi olabilir? A) B) 15 22 22 15 May\u0131s May\u0131s May\u0131s May\u0131s 8 8 May\u0131s May\u0131s C) D) 8 22 8 15 May\u0131s May\u0131s May\u0131s May\u0131s 15 110\u00b0 May\u0131s 22 May\u0131s 156 8. S\u0131n\u0131f","Test Veri Analizi Ba\u015far\u0131yorum 38 4. ve 5. sorular\u0131 a\u015fa\u011f\u0131daki bilgilere g\u00f6re cevaplay\u0131n\u0131z. A\u015fa\u011f\u0131daki daire grafi\u011finde bir caddede 2021 y\u0131l\u0131nda yeni internet aboneli\u011fi alan m\u00fc\u015fteri say\u0131lar\u0131n\u0131n internet \u015firketle- rine g\u00f6re da\u011f\u0131l\u0131m\u0131 verilmi\u015ftir. S\u00fctun grafi\u011finde ise bu caddedeki 2022 y\u0131l\u0131nda yeni abonelik alan m\u00fc\u015fterilerin say\u0131lar\u0131 g\u00f6sterilmi\u015ftir. Grafik: 2021 Y\u0131l\u0131ndaki Yeni M\u00fc\u015fterilerin Da\u011f\u0131l\u0131m\u0131 Grafik: 2022 Y\u0131l\u0131ndaki Yeni M\u00fc\u015fterilerin Da\u011f\u0131l\u0131m\u0131 L Say\u0131 M 72\u00b0 52 50 168\u00b0 48 K 0 \u015eirket K LM 2022 y\u0131l\u0131nda K marka abonelik alan m\u00fc\u015fteri say\u0131s\u0131 bir \u00f6nceki y\u0131la g\u00f6re %20 azalm\u0131\u015ft\u0131r. 4. Buna g\u00f6re 2021 y\u0131l\u0131nda M marka abonelik alan m\u00fc\u015fteri say\u0131s\u0131 ka\u00e7t\u0131r? A) 60 B) 72 C) 84 D) 96 5. L marka internetin 2021 ve 2022 y\u0131llar\u0131ndaki yeni m\u00fc\u015fterilerden al\u0131nan ayl\u0131k kullan\u0131m \u00fccreti s\u0131ras\u0131yla 100 ve 130 TL\u2019dir. Buna g\u00f6re iki y\u0131lda L marka yeni aboneliklerden elde edilen ayl\u0131k toplam gelir miktarlar\u0131 fark\u0131 ka\u00e7 lira olabilir? A) 2900 B) 2600 C) 2400 D) 2100 8. S\u0131n\u0131f 157","Ba\u015far\u0131yorum Veri Analizi Test 38 6. 50 \u00fclkeyi gezen Mustafa\u2019n\u0131n gezdi\u011fi \u00fclkelerin k\u0131talara g\u00f6re say\u0131s\u0131 a\u015fa\u011f\u0131daki d\u00fcnya k\u0131talar haritas\u0131 \u00fczerinde veril- mi\u015ftir. 66 13 11 Kuzey Avrupa Asya Amerika Afrika Avusturalya G\u00fcney Amerika 20 Antartika Mustafa\u2019n\u0131n gezdi\u011fi toplam \u00fclke say\u0131s\u0131n\u0131n k\u0131talara g\u00f6re da\u011f\u0131l\u0131m\u0131 karton \u00fczerine \u00e7izilen daire grafi\u011finde g\u00f6steriliyor. Ard\u0131ndan bu k\u0131talara ait daire dilimleri kesilerek \u00e7\u0131kar\u0131l\u0131yor. Buna g\u00f6re a\u015fa\u011f\u0131dakilerden hangisi bu daire dilimlerinden birisi de\u011fildir? A) O B) %40 %26 O C) D) %22 %14 O O 158 8. S\u0131n\u0131f","Test Veri Analizi Ba\u015far\u0131yorum 38 7. Aylin\u2019in kumbaras\u0131nda bulunan maden\u00ee paralar\u0131n T\u00fcrk Liras\u0131 cinsinden de\u011ferleri ve say\u0131lar\u0131 a\u015fa\u011f\u0131daki s\u00fctun grafi- \u011finde \u00fcsl\u00fc ifadelerle g\u00f6sterilmi\u015ftir. Madeni Paralar\u0131n Say\u0131lar\u0131 (Adet) 5.23 5.22 6 2-2 10-1 Madeni Paralar\u0131n 0 De\u011ferleri (TL) 20 2-1 Grafikte verilen maden\u00ee paralar\u0131n lira cinsinden toplam tutarlar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131 daire grafi\u011finde g\u00f6sterildi\u011finde 50 Kr\u2019luk madeni paralara ait daire diliminin merkez a\u00e7\u0131s\u0131 ka\u00e7 derece olur? A) 60 B) 90 C) 120 D) 150 8. A\u015fa\u011f\u0131daki e\u015f aral\u0131kl\u0131 say\u0131 do\u011frusunda ocak ay\u0131 sonunda \u00fc\u00e7 ki\u015finin kilogram cinsinden k\u00fctlelerinin kar\u015f\u0131l\u0131k geldi\u011fi noktalar i\u015faretlenmi\u015ftir. Aslan Burak Cenk 74 79 Tabloda ise bu \u00fc\u00e7 ki\u015finin \u015fubat, mart ve nisan ay\u0131 sonlar\u0131nda k\u00fctlelerinin bir \u00f6nceki aya g\u00f6re de\u011fi\u015fimi tam say\u0131larla g\u00f6sterilmi\u015ftir. Ki\u015fi \u015eubat Mart Nisan Aslan +3 \u20131 +5 Burak \u20131 +2 +2 Cenk +3 \u20132 \u20133 \u00d6rne\u011fin Aslan\u2019\u0131n k\u00fctlesi \u015fubat ay\u0131nda bir \u00f6nceki ocak ay\u0131na g\u00f6re 3 kg artm\u0131\u015f, mart ay\u0131nda ise \u015fubat ay\u0131na g\u00f6re 1 kg azalm\u0131\u015ft\u0131r. Buna g\u00f6re nisan ay\u0131 sonunda \u00fc\u00e7 ki\u015finin toplam k\u00fctlesinin ki\u015filere g\u00f6re da\u011f\u0131l\u0131m\u0131 daire grafi\u011fiyle g\u00f6sterildi- \u011finde Cenk\u2019e ait daire diliminin merkez a\u00e7\u0131s\u0131 ka\u00e7 derece olur? A) 114 B) 117 C) 120 D) 123 8. S\u0131n\u0131f 159","Ba\u015far\u0131yorum Veri Analizi Test 38 9. A\u015fa\u011f\u0131daki tabloda bir yemek yar\u0131\u015fmas\u0131na kat\u0131lan yar\u0131\u015fmac\u0131lara j\u00fcri taraf\u0131ndan verilebilecek \u00fc\u00e7 sembol ve bu sem- bollerin kar\u015f\u0131l\u0131k geldi\u011fi puan de\u011ferleri verilmi\u015ftir. Grafik: Yar\u0131\u015fmac\u0131lar\u0131n Puanlar\u0131 Puan Sembol Puan De\u011feri 18 15 10 9 8 5 4 \u00d6mer \u00d6yk\u00fc Yar\u0131\u015fmac\u0131lar 3 2 Asya Bu yar\u0131\u015fmaya kat\u0131lan \u00fc\u00e7 yar\u0131\u015fmac\u0131n\u0131n j\u00fcrilerden ald\u0131klar\u0131 toplam sembol say\u0131lar\u0131 ise s\u00fctun grafi\u011finde g\u00f6sterilmi\u015ftir. Buna g\u00f6re \u00fc\u00e7 yar\u0131\u015fmac\u0131n\u0131n toplam puanlar\u0131n\u0131n yar\u0131\u015fmac\u0131lara g\u00f6re da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6steren daire grafi\u011fi a\u015fa\u011f\u0131- dakilerden hangisidir? A) B) C) D) Asya \u00d6mer Asya \u00d6mer Asya \u00d6mer 100\u00b0 125\u00b0 Asya \u00d6mer 108\u00b0 108\u00b0 100\u00b0 180\u00b0 145\u00b0 \u00d6yk\u00fc \u00d6yk\u00fc \u00d6yk\u00fc 60\u00b0 \u00d6yk\u00fc 160 8. S\u0131n\u0131f","3 \u00dcN\u0130TE BAS\u0130T OLAYLARIN OLMA OLASILI\u011eI VE CEB\u0130RSEL 8. SINIF \u0130FADELER VE \u00d6ZDE\u015eL\u0130KLER Basit Olaylar\u0131n Olma Olas\u0131l\u0131\u011f\u0131 Cebirsel \u0130fadeler ve \u00d6zde\u015flikler Kazan\u0131mlar; Bir olaya ait olas\u0131 durumlar\u0131 belirler. M.8.5.1.1 \u201cDaha fazla\u201d, \u201ce\u015fit\u201d, \u201cdaha az\u201d olas\u0131l\u0131kl\u0131 olaylar\u0131 ay\u0131rt eder, M.8.5.1.2 \u00f6rnek verir. M.8.5.1.3 M.8.5.1.4 E\u015fit \u015fansa sahip olan olaylarda her bir \u00e7\u0131kt\u0131n\u0131n olas\u0131l\u0131k de\u011ferinin e\u015fit oldu\u011funu ve bu de\u011ferin 1\/n oldu\u011funu a\u00e7\u0131klar. Olas\u0131l\u0131k de\u011ferinin 0 ile 1 aras\u0131nda (0 ve 1 d\u00e2hil) oldu\u011funu anlar. Basit bir olay\u0131n olma olas\u0131l\u0131\u011f\u0131n\u0131 hesaplar. M.8.5.1.5 Basit cebirsel ifadeleri anlar ve farkl\u0131 bi\u00e7imlerde yazar. M.8.2.1.1 Cebirsel ifadelerin \u00e7arp\u0131m\u0131n\u0131 yapar. M.8.2.1.2 \u00d6zde\u015flikleri modellerle a\u00e7\u0131klar. M.8.2.1.3 Cebirsel ifadeleri \u00e7arpanlara ay\u0131r\u0131r. M.8.2.1.4","\u00dcN\u0130TE NOTLANDIRMA \u00dcN\u0130TE \u00d6NCEL\u0130KLER\u0130M \u00dcN\u0130TEDEK\u0130 MOOD NOTLARIM F\u0130K\u0130RLER\u0130M FORM\u00dcLLER","Basit Olaylar\u0131n Olma Olas\u0131l\u0131\u011f\u0131 Olas\u0131 Durumlar\u0131 Belirleme \u2022 Bir olas\u0131l\u0131k deneyinde elde edilebilecek sonu\u00e7lar\u0131n her birine \u00e7\u0131kt\u0131 denir. \u00d6rnek: Zar\u0131n havaya at\u0131lmas\u0131 deneyinde \u00fcst y\u00fcze 1, 2, 3, 4, 5 ve 6 gelmesi deneyin \u00e7\u0131kt\u0131lar\u0131d\u0131r. \u2022 Bir deneyde ger\u00e7ekle\u015fmesini istedi\u011fimiz veya istemedi\u011fimiz durumlara olay denir. \u00d6rnek: Zar\u0131n at\u0131lmas\u0131 deneyinde \u00fcst y\u00fcze 3\u2019ten b\u00fcy\u00fck say\u0131 gelmesi bir olayd\u0131r. \u2022 Bir deneyde b\u00fct\u00fcn \u00e7\u0131kt\u0131lar\u0131n olu\u015fturdu\u011fu durumlara olas\u0131 durumlar denir. \u00d6rnek: Zar\u0131n at\u0131lmas\u0131 deneyinde \u00fcst y\u00fcze 1, 2, 3, 4, 5 ve 6 gelecek \u015fekilde toplam 6 olas\u0131 durum vard\u0131r. Bir olay\u0131n olmas\u0131n\u0131n ya da olmamas\u0131n\u0131n matematiksel de\u011ferine o olay\u0131n olas\u0131l\u0131\u011f\u0131 denir. 37 2. Bar\u0131\u015f a\u015fa\u011f\u0131daki masada bulunan oyuncaklardan bir tanesini se\u00e7mek istiyor. 1. Nisa a\u015fa\u011f\u0131daki tepside bulunan nesnelerden bir ta- nesini se\u00e7mek istiyor. Buna g\u00f6re Nisa\u2019n\u0131n ka\u00e7 farkl\u0131 se\u00e7im yapabilece- \u011fini bulunuz. Buna g\u00f6re Bar\u0131\u015f\u2019\u0131n ka\u00e7 farkl\u0131 se\u00e7im yapabilece- \u011fini bulunuz. 8. S\u0131n\u0131f 163","Basit Olaylar\u0131n Olma Olas\u0131l\u0131\u011f\u0131 3. A\u015fa\u011f\u0131da verilen olaylara ait t\u00fcm olas\u0131 durumlar\u0131 4. A\u015fa\u011f\u0131da \u00fczerlerinde birer do\u011fal say\u0131 yazan renkli yaz\u0131n\u0131z. toplara g\u00f6re sorular\u0131 cevaplay\u0131n\u0131z. a) Bir madeni para havaya at\u0131ld\u0131\u011f\u0131nda \u00fcst y\u00fcz\u00fcn\u00fcn 7 12 16 22 g\u00f6r\u00fcn\u00fcm\u00fc. mavi mavi mavi k\u0131rm\u0131z\u0131 25 30 33 41 b) Bir zar havaya at\u0131ld\u0131\u011f\u0131nda \u00fcst y\u00fcz\u00fcne gelen say\u0131- k\u0131rm\u0131z\u0131 mor mor mor n\u0131n \u00e7ift olmas\u0131. a) Bu toplardan rastgele se\u00e7ilen bir tanesinin mor renk olmas\u0131 olay\u0131na ait olas\u0131 durumlar\u0131n say\u0131s\u0131 ka\u00e7t\u0131r? c) Bir zar havaya at\u0131ld\u0131\u011f\u0131nda \u00fcst y\u00fcz\u00fcne gelen say\u0131- n\u0131n 2\u2019den b\u00fcy\u00fck olmas\u0131. b) Bu toplardan rastgele se\u00e7ilen bir tanesinin \u00fcze- rinde tek say\u0131 yazma olay\u0131na ait \u00e7\u0131kt\u0131lar\u0131 yaz\u0131n\u0131z. \u00e7) 1\u2019den 20\u2019ye kadar numaraland\u0131r\u0131lm\u0131\u015f \u00f6zde\u015f kart- lardan rastgele se\u00e7ilen bir tanesinin asal numaral\u0131 olmas\u0131. d) Be\u015f se\u00e7enekten olu\u015fan bir test sorusunda i\u015faret- c) Renginin ba\u015f harfi \u201cm\u201d olan toplar i\u00e7inden rastgele lenebilecek se\u00e7enek say\u0131s\u0131. se\u00e7ilen bir tanesinin \u00fczerinde tam kare say\u0131 yaz- ma olay\u0131na ait olas\u0131 durumlar\u0131n say\u0131s\u0131 ka\u00e7t\u0131r? e) Haftan\u0131n g\u00fcnleri i\u00e7inden rastgele se\u00e7ilen bir g\u00fc- \u00e7) Bu toplardan rastgele se\u00e7ilen bir tanesinin \u00fcze- n\u00fcn hafta sonu olmas\u0131. rinde yazan say\u0131n\u0131n farkl\u0131 rakamlardan olu\u015fmas\u0131 olay\u0131na ait \u00e7\u0131kt\u0131lar\u0131 yaz\u0131n\u0131z. 164 8. S\u0131n\u0131f","Test Olas\u0131 Durumlar\u0131 Belirleme Uyguluyorum 39 1. \u201cATAT\u00dcRK\u201d kelimesinin harfleri \u00f6zde\u015f kartlara yaz\u0131- 4. Bir \u00e7ift zar havaya at\u0131l\u0131yor ve zarlar\u0131n \u00fcst y\u00fcz\u00fcne ge- l\u0131p bo\u015f bir torbaya at\u0131l\u0131yor. len say\u0131lar \u00e7arp\u0131l\u0131yor. Buna g\u00f6re torbadan rastgele se\u00e7ilen bir kart\u0131n Buna g\u00f6re a\u015fa\u011f\u0131dakilerden hangisi bu olaya ait t\u00fcm olas\u0131 durumlar\u0131n\u0131n say\u0131s\u0131 ka\u00e7t\u0131r? olas\u0131 durumlardan biri de\u011fildir? A) 6 B) 7 C) 8 D) 9 A) 36 B) 30 C) 14 D) 4 2. 5. Y\u0131l\u0131n aylar\u0131 \u00f6zde\u015f kartlara yaz\u0131larak bo\u015f bir torbaya KARI\u015eIK at\u0131l\u0131yor. 5 s\u00fctl\u00fc Buna g\u00f6re bu torbadan rastgele se\u00e7ilen bir kartta 6 \u00e7ilekli yazan ay\u0131n yaz mevsimi olma olay\u0131na ait \u00e7\u0131kt\u0131lar 7 limonlu a\u015fa\u011f\u0131dakilerden hangisidir? A) May\u0131s, haziran, temmuz B) Haziran, temmuz, a\u011fustos C) May\u0131s, haziran, temmuz, a\u011fustos D) Haziran, temmuz, a\u011fustos, eyl\u00fcl Yukar\u0131daki kutudan rastgele se\u00e7ilen bir \u00e7ikolata i\u00e7in ka\u00e7 farkl\u0131 olas\u0131 durum vard\u0131r? A) 12 B) 14 C) 16 D) 18 6. A\u015fa\u011f\u0131da bir s\u00fct \u015fi\u015fesi g\u00f6sterilmi\u015ftir. 3. A\u015fa\u011f\u0131daki tabloda bir seminere kat\u0131lan bilim insanla- r\u0131n\u0131n \u00fclkelerine g\u00f6re say\u0131lar\u0131 verilmi\u015ftir. Kat\u0131ld\u0131\u011f\u0131 \u00dclke Ki\u015fi Say\u0131s\u0131 6 Litre T\u00fcrkiye 14 Almanya 10 \u015ei\u015fedeki litre cinsinden s\u00fct miktar\u0131n\u0131n 50\u2019den k\u00fc\u00e7\u00fck \u0130ngiltere 12 do\u011fal say\u0131 katlar\u0131 \u00f6zde\u015f ka\u011f\u0131tlara yaz\u0131larak bo\u015f bir \u0130talya 8 torbaya at\u0131l\u0131yor. Buna g\u00f6re bu seminere kat\u0131lan ki\u015filer aras\u0131ndan Buna g\u00f6re bu torbadan rastgele se\u00e7ilen bir ka\u011f\u0131t- rastgele se\u00e7ilen bir ki\u015fi i\u00e7in olas\u0131 durum say\u0131s\u0131 ta yazan say\u0131 i\u00e7in a\u015fa\u011f\u0131dakilerden hangisi olas\u0131 ka\u00e7t\u0131r? durumlardan biridir? A) 44 B) 43 C) 42 D) 41 A) 28 B) 32 C) 36 D) 40 8. S\u0131n\u0131f 165","Uyguluyorum Olas\u0131 Durumlar\u0131 Belirleme Test 39 7. A\u015fa\u011f\u0131da bir kitapl\u0131ktaki ders kitaplar\u0131 g\u00f6sterilmi\u015ftir. 10. A\u015fa\u011f\u0131da i\u00e7inde sar\u0131, k\u0131rm\u0131z\u0131 ve mavi renkli olmak \u00fczere toplam 70 bilyenin bulundu\u011fu bir torbadaki sar\u0131 ve k\u0131rm\u0131z\u0131 bilye say\u0131lar\u0131 g\u00f6sterilmi\u015ftir. T\u00fcrk\u00e7e 21 sar\u0131 T\u00fcrk\u00e7e 36 k\u0131rm\u0131z\u0131 Matematik Matematik Matematik Fen Bilgisi Sosyal Bilgiler Bu kitaplardan rastgele se\u00e7ilen bir tanesi i\u00e7in Bu bilyeden rastgele se\u00e7ilen bir tanesinin mavi a\u015fa\u011f\u0131dakilerden hangisi olas\u0131 durumlardan biri renkli olmas\u0131 ile ilgili olas\u0131 durumlar\u0131n say\u0131s\u0131 ka\u00e7- de\u011fildir? t\u0131r? A) T\u00fcrk\u00e7e B) Matematik A) 13 B) 17 C) 20 D) 23 C) Sosyal Bilgiler D) \u0130ngilizce 8. K\u00fctleleri 7 kg, 11 kg, 12 kg ve 15 kg olan d\u00f6rt \u00e7uval- 11. 96 say\u0131s\u0131n\u0131n t\u00fcm pozitif tam say\u0131 \u00e7arpanlar\u0131 \u00f6zde\u015f dan iki tanesi rastgele al\u0131n\u0131yor. kartlara yaz\u0131larak bo\u015f bir kutuya at\u0131l\u0131yor. Buna g\u00f6re al\u0131nan iki \u00e7uval\u0131n toplam k\u00fctlesinin 20 Buna g\u00f6re bu torbadan rastgele se\u00e7ilen bir kartta kg\u2019dan az oldu\u011fu olas\u0131 durumlar\u0131n say\u0131s\u0131 ka\u00e7t\u0131r? yazan say\u0131n\u0131n sadece iki \u00e7arpan\u0131 oldu\u011fu olas\u0131 du- rumlar\u0131n say\u0131s\u0131 ka\u00e7t\u0131r? A) 2 B) 3 C) 4 D) 5 A) 1 B) 2 C) 3 D) 4 9. Bir \u00e7i\u00e7ek\u00e7ide 20 papatya, 18 g\u00fcl ve 24 nergis bulun- 12. \u0130ki zar havaya at\u0131ld\u0131\u011f\u0131nda \u00fcst y\u00fcze gelen say\u0131lar\u0131n maktad\u0131r. toplam\u0131n\u0131n 7 oldu\u011fu olas\u0131 durumlar\u0131n say\u0131s\u0131 ka\u00e7- t\u0131r? Buna g\u00f6re rastgele se\u00e7ilen bir \u00e7i\u00e7e\u011fin nergis olma olay\u0131na ait \u00e7\u0131kt\u0131 say\u0131s\u0131, g\u00fcl olma olay\u0131na ait A) 3 B) 4 C) 5 D) 6 \u00e7\u0131kt\u0131 say\u0131s\u0131ndan ka\u00e7 fazlad\u0131r? A) 2 B) 4 C) 6 D) 8 166 8. S\u0131n\u0131f","Test Olas\u0131 Durumlar\u0131 Belirleme Ba\u015far\u0131yorum 40 1. A\u015fa\u011f\u0131da \u015eekil 1\u2019de be\u015f farkl\u0131 kolonya bidonunda bulunan kolonya miktar\u0131 \u00fcsl\u00fc ifadelerin \u00e7arp\u0131m\u0131 \u015feklinde verilmi\u015ftir. 23.3.5 23.52 32.52 22.52 75 mL mL mL 24.5 mL mL mL \u015eekil 1 \u015eekil 2 Bu bidonlardan bir tanesi se\u00e7ilerek \u015eekil 2\u2019de kapasitesi 200 mL olan ve i\u00e7inde 75 mL kolonya bulunan \u015fi\u015feye ta\u015fma olmayacak bi\u00e7imde tamam\u0131n\u0131 doldurmak isteniliyor. Buna g\u00f6re se\u00e7ilebilecek kolonya bidonu i\u00e7in ka\u00e7 farkl\u0131 olas\u0131 durum vard\u0131r? D) 4 A) 1 B) 2 C) 3 2. Lunaparka giden Ali, oyuncaklara binmek i\u00e7in 4 TL\u2019ye sat\u0131lan kartlardan bir tane al\u0131p bir miktar y\u00fckleme yap\u0131yor. Ard\u0131ndan bu kart i\u00e7in y\u00fckleme ve kart paras\u0131 d\u00e2hil 34 TL \u00f6deme yap\u0131yor. Tablo: Oyuncaklar\u0131n Bini\u015f Fiyat\u0131 Oyuncak \u0130smi 1 Ki\u015filik Bini\u015f Fiyat\u0131 Gondol 24 Korku T\u00fcneli 30 Kamikaze 16 \u00c7arp\u0131\u015fan Araba 22 Ali\u2019nin y\u00fckleme yapt\u0131\u011f\u0131 bu kartta her 15 TL\u2019lik y\u00fcklemeye 8 TL hediye y\u00fckleme yap\u0131l\u0131yor ve Ali bu kartla yukar\u0131da fiyatlar\u0131 verilen oyuncaklardan ikisine birer kez biniyor. Buna g\u00f6re a\u015fa\u011f\u0131dakilerden hangisi Ali\u2019nin binmi\u015f olabilece\u011fi oyuncaklar\u0131 g\u00f6steren olas\u0131 durumlardan biri de\u011fildir? A) Gondol ve kamikaze B) Korku t\u00fcneli ve kamikaze C) Gondol ve \u00e7arp\u0131\u015fan araba D) Korku t\u00fcneli ve \u00e7arp\u0131\u015fan araba 8. S\u0131n\u0131f 167","Ba\u015far\u0131yorum Olas\u0131 Durumlar\u0131 Belirleme Test 40 3. A\u015fa\u011f\u0131daki geometri tahtas\u0131nda, bir lastik tahtan\u0131n A, B ve C \u00e7ivilerine ge\u00e7irilerek \u00fc\u00e7gensel b\u00f6lge elde edilmi\u015ftir. AB 1 br 1 br Lasti\u011fin C k\u00f6\u015fesi \u00e7\u0131kar\u0131larak di\u011fer \u00e7ivilerden birine ge\u00e7iriliyor ve yeni bir \u00fc\u00e7gensel b\u00f6lge elde ediliyor. Buna g\u00f6re elde edilen \u00fc\u00e7gensel b\u00f6lgenin alan\u0131n\u0131n 9 br2 den fazla oldu\u011fu olas\u0131 durumlar\u0131n say\u0131s\u0131 ka\u00e7t\u0131r? A) 6 B) 8 C) 10 C) 12 4. A\u015fa\u011f\u0131da eni 6 cm olan dikd\u00f6rtgen \u015feklinde bir \u015ferit g\u00f6sterilmi\u015ftir. 6 cm Bu \u015ferit her seferinde enine paralel bi\u00e7imde kesilerek \u015fekildeki gibi yedi par\u00e7aya ayr\u0131l\u0131yor. Par\u00e7alar\u0131n santimetre cinsinden uzunluklar\u0131n\u0131n ise en k\u00fc\u00e7\u00fck asal say\u0131dan ba\u015flanacak bi\u00e7imde k\u00fc\u00e7\u00fckten b\u00fcy\u00fc\u011fe s\u0131ras\u0131yla farkl\u0131 bir asal say\u0131ya e\u015fit oldu\u011fu g\u00f6r\u00fcl\u00fcyor. Buna g\u00f6re bu par\u00e7alardan bir tanesinin \u00f6n y\u00fcz\u00fcn\u00fcn alan\u0131n\u0131n 40 cm2 den fazla oldu\u011fu ka\u00e7 olas\u0131 durum var- d\u0131r? A) 2 B) 3 C) 4 D) 5 168 8. S\u0131n\u0131f","Olas\u0131 Durumlar\u0131 Kar\u015f\u0131la\u015ft\u0131rma Bir olas\u0131l\u0131k deneyinde elde edilebilecek sonu\u00e7lar\u0131n her birine \u00e7\u0131kt\u0131 dedi\u011fimizi bir \u00f6nceki b\u00f6l\u00fcmde g\u00f6rm\u00fc\u015ft\u00fck. Bir olaya ait olas\u0131 durumlar kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda; \u2022 \u00c7\u0131kt\u0131 say\u0131s\u0131 fazla olan olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 daha fazlad\u0131r. \u2022 \u00c7\u0131kt\u0131 say\u0131s\u0131 az olan olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 daha azd\u0131r. \u2022 \u00c7\u0131kt\u0131 say\u0131s\u0131 e\u015fit olan olaylar\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 e\u015fittir. \u00d6rnek: A\u015fa\u011f\u0131daki tabloda bir s\u0131n\u0131ftaki \u00f6\u011frencilerin en sevdikleri meyvelere g\u00f6re say\u0131lar\u0131 verilmi\u015ftir. \u00c7ilek Portakal Kiraz Karpuz 10 7 6 7 Bu s\u0131n\u0131ftan rastgele se\u00e7ilen bir \u00f6\u011frencinin; \u2022 \u00e7ilek sevme olas\u0131l\u0131\u011f\u0131, kiraz sevme olas\u0131l\u0131\u011f\u0131ndan daha fazlad\u0131r. \u2022 karpuz sevme olas\u0131l\u0131\u011f\u0131, \u00e7ilek sevme olas\u0131l\u0131\u011f\u0131ndan daha azd\u0131r. \u2022 portakal sevme olas\u0131l\u0131\u011f\u0131, karpuz sevme olas\u0131l\u0131\u011f\u0131na e\u015fittir. 38 2. A\u015fa\u011f\u0131daki tabloda bir kamptaki 7 ve 8. s\u0131n\u0131f \u00f6\u011frenci- lerinin cinsiyetlerine g\u00f6re say\u0131s\u0131 verilmi\u015ftir. 1. A\u015fa\u011f\u0131daki kutuda e\u015f b\u00fcy\u00fckl\u00fckte ve farkl\u0131 \u00e7e\u015fit kura- biyeler vard\u0131r. S\u0131n\u0131f K\u0131z Erkek 7.S\u0131n\u0131f 21 16 10 Elmal\u0131 8. S\u0131n\u0131f 23 18 14 F\u0131nd\u0131kl\u0131 10 Portakall\u0131 8 \u00c7ikolatal\u0131 a) 7. s\u0131n\u0131f \u00f6\u011frencilerinden rastgele se\u00e7ilen bir \u00f6\u011fren- cinin hangi cinsiyetli olma olas\u0131l\u0131\u011f\u0131 daha fazlad\u0131r? Kutudan rastgele bir kurabiye se\u00e7ilmesi deneyinde; b) Erkek \u00f6\u011frencilerden rastgele se\u00e7ilen bir \u00f6\u011frenci- a) Se\u00e7ilme olas\u0131l\u0131\u011f\u0131 en fazla olan \u00e7e\u015fidi bulunuz. nin hangi s\u0131n\u0131ftan olma olas\u0131l\u0131\u011f\u0131 daha azd\u0131r? b) Se\u00e7ilme olas\u0131l\u0131\u011f\u0131 en az olan \u00e7e\u015fidi bulunuz. c) Kamptan rastgele se\u00e7ilen bir \u00f6\u011frencinin 7. s\u0131n\u0131f erkek mi 8. s\u0131n\u0131f k\u0131z m\u0131 olma olas\u0131l\u0131\u011f\u0131 daha fazla- c) Se\u00e7ilme olas\u0131l\u0131klar\u0131 e\u015fit olan \u00e7e\u015fitleri bulunuz. d\u0131r? 8. S\u0131n\u0131f 169","Olas\u0131 Durumlar\u0131 Kar\u015f\u0131la\u015ft\u0131rma 3. A\u015fa\u011f\u0131da e\u015f b\u00fcy\u00fckl\u00fckteki b\u00f6lmelerden olu\u015fan \u00e7ark 4. A\u015fa\u011f\u0131da bir konferans salonundaki koltuklar\u0131n dolu- \u00e7evriliyor. luk durumu g\u00f6sterilmi\u015ftir. 1 3 1.S\u0131ra 5 2 2.S\u0131ra 3.S\u0131ra 5 5 4.S\u0131ra 5.S\u0131ra 33 45 24 Dolu Bo\u015f A BCDEF Okun g\u00f6sterdi\u011fi say\u0131n\u0131n; A\u015fa\u011f\u0131daki bo\u015fluklara \u201cdaha fazla\u201d, \u201cdaha az\u201d veya a) Hangi say\u0131 olma olas\u0131l\u0131\u011f\u0131 en fazlad\u0131r? \u201ce\u015fit\u201d yaz\u0131n\u0131z. a) 3. s\u0131radan se\u00e7ilen bir koltu\u011fun dolu olma olas\u0131l\u0131\u011f\u0131, bo\u015f olma olas\u0131l\u0131\u011f\u0131na g\u00f6re ............... olas\u0131l\u0131kl\u0131d\u0131r. b) Hangi say\u0131 olma olas\u0131l\u0131\u011f\u0131 en azd\u0131r? c) Hangi say\u0131lar\u0131n olma olas\u0131l\u0131klar\u0131 birbirine e\u015fittir? b) 4. s\u0131radan se\u00e7ilen bir koltu\u011fun dolu olma olas\u0131l\u0131\u011f\u0131, bo\u015f olma olas\u0131l\u0131\u011f\u0131na g\u00f6re ............... olas\u0131l\u0131kl\u0131d\u0131r. \u00e7) Asal say\u0131 olma olas\u0131l\u0131\u011f\u0131 m\u0131, tam kare olma olas\u0131l\u0131- \u011f\u0131 m\u0131 daha fazlad\u0131r? d) \u00c7ift say\u0131 olma olas\u0131l\u0131\u011f\u0131 m\u0131, tek say\u0131 olma olas\u0131l\u0131\u011f\u0131 c) C s\u00fctunundaki bo\u015f koltuklardan se\u00e7ilen bir ta- m\u0131 daha azd\u0131r? nesinin tek s\u0131rada olma olas\u0131l\u0131\u011f\u0131, \u00e7ift s\u0131rada olma olas\u0131l\u0131\u011f\u0131na g\u00f6re ............... olas\u0131l\u0131kl\u0131d\u0131r. 170 8. S\u0131n\u0131f","Test Olas\u0131 Durumlar\u0131 Kar\u015f\u0131la\u015ft\u0131rma Uyguluyorum 41 1. A\u015fa\u011f\u0131da e\u015f b\u00fcy\u00fckl\u00fckteki renkli pullar g\u00f6sterilmi\u015ftir. 4. Her biri e\u015f b\u00f6lmelendirilmi\u015f a\u015fa\u011f\u0131daki \u00e7arklar M M Y MM M K d\u00f6nd\u00fcr\u00fcl\u00fcyor. Bu \u00e7ark durdu\u011funda ibrenin x harfi olan dilimi g\u00f6sterme olas\u0131l\u0131\u011f\u0131 hangisinde en KSKSMKS azd\u0131r? Bu pullar i\u00e7inden rastgele se\u00e7ilen bir tanesinin A) B) hangi renk olma olas\u0131l\u0131\u011f\u0131 en fazlad\u0131r? xx z A) Sar\u0131 B) K\u0131rm\u0131z\u0131 C) Mavi D) Ye\u015fil x xy x 2. A\u015fa\u011f\u0131daki kavanozlarda \u00fczerinde yazan say\u0131 kadar C) D) kart bulunmaktad\u0131r. xy xt yx xz z yz 20 15 25 30 5. Bir rafta 14 T\u00fcrk\u00e7e, 10 Fen Bilimleri ve 6 Matematik I. II. III. IV. kitab\u0131 vard\u0131r. Kavanozlar\u0131n her birinde bir hediye kart\u0131 oldu\u011fu- Bu raftan en az ka\u00e7 kitap al\u0131n\u0131rsa kalan kitab\u0131n na g\u00f6re hangisinde hediye kart\u0131n\u0131n \u00e7ekilme ola- T\u00fcrk\u00e7e, Fen Bilimleri ve Matematik olma olas\u0131l\u0131k- s\u0131l\u0131\u011f\u0131 en azd\u0131r? lar\u0131 birbirine e\u015fit olur? A) I. B) II. C) III. D) IV. A) 12 B) 11 C) 10 D) 9 3. Bir kalemlikte 5 t\u00fckenmez, 11 kur\u015fun, 7 ke\u00e7eli ve 11 6. \u201cMATEMAT\u0130K\u201d kelimesindeki harfler \u00f6zde\u015f kartlara u\u00e7lu kalem vard\u0131r. yaz\u0131larak bo\u015f bir torbaya at\u0131l\u0131yor. Buna g\u00f6re bu kalemlerden rastgele se\u00e7ilen bir ta- Buna g\u00f6re bu torbadan rastgele se\u00e7ilen bir kartta nesinin hangi kalem t\u00fcrlerine ait olmas\u0131 e\u015fit ola- yazan harfin hangi harf olma olas\u0131l\u0131\u011f\u0131 M olma ola- s\u0131l\u0131kl\u0131d\u0131r? s\u0131l\u0131\u011f\u0131na e\u015fit olabilir? A) T\u00fckenmez ve u\u00e7lu B) Ke\u00e7eli ve kur\u015fun C) Kur\u015fun ve u\u00e7lu D) T\u00fckenmez ve ke\u00e7eli A) A B) E C) \u0130 D) K 8. S\u0131n\u0131f 171","Uyguluyorum Olas\u0131 Durumlar\u0131 Kar\u015f\u0131la\u015ft\u0131rma Test 41 7. Okunu\u015fu \u201c\u0130ki y\u00fcz altm\u0131\u015f alt\u0131 milyon y\u00fcz altm\u0131\u015f \u00fc\u00e7 bin 10. A\u015fa\u011f\u0131da bulunan torbalardaki k\u0131rm\u0131z\u0131 ve beyaz bilye y\u00fcz k\u0131rk\u201d olan do\u011fal say\u0131n\u0131n rakamlar\u0131 \u00f6zde\u015f kartlara say\u0131lar\u0131 verilmi\u015ftir. yaz\u0131l\u0131p bo\u015f bir torbaya at\u0131l\u0131yor. K\u0131rm\u0131z\u0131: 7 K\u0131rm\u0131z\u0131: 8 Buna g\u00f6re bu torbadan rastgele se\u00e7ilen bir kartta Beyaz: 5 Beyaz: 8 a\u015fa\u011f\u0131daki rakamlardan hangisinin yazma olas\u0131l\u0131\u011f\u0131 en fazlad\u0131r? A Torbas\u0131 B Torbas\u0131 A) 3 B) 4 C) 5 D) 6 K\u0131rm\u0131z\u0131: 9 K\u0131rm\u0131z\u0131: 10 Beyaz: 10 Beyaz: 13 C Torbas\u0131 D Torbas\u0131 8. Sema y\u00fczeylerinde 1, 2, 3, 3, 4 ve 5 rakamlar\u0131n\u0131n bu- Buna g\u00f6re hangi torbadan rastgele al\u0131nan bir bil- lundu\u011fu, Seda ise 1, 1, 1, 2, 3 ve 4 rakamlar\u0131n\u0131n bu- yenin k\u0131rm\u0131z\u0131 olma olas\u0131l\u0131\u011f\u0131 en fazlad\u0131r? lundu\u011fu e\u015fit b\u00fcy\u00fckl\u00fckteki zarlar\u0131 birer kez at\u0131yorlar. A) A B) B C) C D) D Buna g\u00f6re \u00fcst y\u00fcze a\u015fa\u011f\u0131daki say\u0131lardan hangisi- nin geldi\u011finde yar\u0131\u015fmay\u0131 Seda\u2019n\u0131n kazanma ola- s\u0131l\u0131\u011f\u0131 daha fazlad\u0131r? A) 1 B) 2 C) 3 D) 4 11. Bir kafeden sipari\u015f edilen 33 pidenin 7\u2019si sucuklu, geri kalanlar\u0131 kavurmal\u0131 ya da kar\u0131\u015f\u0131kt\u0131r. Bu pidelerden rastgele se\u00e7ilen bir tanesinin sucuklu olma olas\u0131l\u0131\u011f\u0131 en az, kar\u0131\u015f\u0131k olma olas\u0131l\u0131\u011f\u0131 en fazlad\u0131r. Buna g\u00f6re pidelerden en az ka\u00e7 tanesi kar\u0131\u015f\u0131kt\u0131r? 9. Bir okuldaki 32 \u00f6\u011fretmen ve 160\u2019\u0131 k\u0131z olmak \u00fczere A) 12 B) 13 C) 14 D) 15 300 \u00f6\u011frencinin isimlerinin yaz\u0131l\u0131 oldu\u011fu kartlardan rastgele se\u00e7ilen bir kart\u0131n; I. \u00d6\u011fretmene ait olma olas\u0131l\u0131\u011f\u0131, k\u0131z \u00f6\u011frenciye ait olma olas\u0131l\u0131\u011f\u0131ndan azd\u0131r. II. Erkek \u00f6\u011frenciye ait olma olas\u0131l\u0131\u011f\u0131, \u00f6\u011fretmen ait olma olas\u0131l\u0131\u011f\u0131ndan fazlad\u0131r. III. K\u0131z \u00f6\u011frenciye ait olma olas\u0131l\u0131\u011f\u0131, erkek \u00f6\u011frenciye 12. Rakamlar\u0131n yaz\u0131l\u0131 oldu\u011fu \u00f6zde\u015f kartlardan rast- ait olma olas\u0131l\u0131\u011f\u0131na e\u015fittir. gele se\u00e7ilen bir kartta yazan rakam i\u00e7in a\u015fa\u011f\u0131da- ifadelerinden hangileri do\u011frudur? kilerden hangisinin olma olas\u0131l\u0131\u011f\u0131 daha fazlad\u0131r? A) Yaln\u0131z I. B) Yaln\u0131z II. A) Tek olma B) 5\u2019ten k\u00fc\u00e7\u00fck olma C) I ve II. D) I ve III. C) 3\u2019ten b\u00fcy\u00fck olma D) Asal olma 172 8. S\u0131n\u0131f","Test Olas\u0131 Durumlar\u0131 Kar\u015f\u0131la\u015ft\u0131rma Ba\u015far\u0131yorum 42 1 ve 2. sorular\u0131 birbirinden ba\u011f\u0131ms\u0131z olarak cevapland\u0131r\u0131n\u0131z. Kur\u015fun kalemler, kalemin yap\u0131m\u0131nda kullan\u0131lan kur\u015funun sertli\u011fine g\u00f6re H, F veya B s\u0131n\u0131f\u0131 olarak grupland\u0131r\u0131l\u0131r. H grubundaki kalemler sert, F grubundaki kalemler orta, B grubundaki kalemler yumu\u015fak s\u0131n\u0131f\u0131ndad\u0131r. A\u015fa\u011f\u0131da baz\u0131 kalemlerin fiyatlar\u0131 ve bu kalemlerin sertlik s\u0131n\u0131flar\u0131 verilmi\u015ftir. (Harflerin \u00f6n\u00fcndeki rakamlar\u0131n sertlik s\u0131n\u0131f\u0131na etkisi yoktur.) 28\u00a5 30\u00a5 23\u00a5 36\u00a5 25\u00a5 32\u00a5 24\u00a5 29\u00a5 36\u00a5 H B 4B 4H F H B F 2B 1. Ayaz bu kalemlerden birini rastgele se\u00e7iyor. Buna g\u00f6re Ayaz\u2019\u0131n se\u00e7ti\u011fi kalem i\u00e7in a\u015fa\u011f\u0131daki olaylardan hangisinin olma olas\u0131l\u0131\u011f\u0131 daha fazlad\u0131r? A) Sertlik s\u0131n\u0131f\u0131na g\u00f6re orta grupta olma B) Sertlik s\u0131n\u0131f\u0131na g\u00f6re sert grupta olma C) Lira cinsinden fiyat\u0131na g\u00f6re 5 ile b\u00f6l\u00fcnebilme D) Lira cinsinden fiyat\u0131na g\u00f6re 7\u2019nin kat\u0131 olma 2. Ege bu kalemlerden birini rastgele se\u00e7iyor. Buna g\u00f6re Ege\u2019nin se\u00e7ti\u011fi kalemin hangi iki \u00f6zellikte olmas\u0131 birbirine e\u015fit olas\u0131l\u0131ktad\u0131r? A) Sertlik s\u0131n\u0131f\u0131na g\u00f6re orta, lira cinsinden fiyat\u0131na g\u00f6re asal say\u0131 olma B) Sertlik s\u0131n\u0131f\u0131na g\u00f6re yumu\u015fak, lira cinsinden fiyat\u0131na g\u00f6re tam kare olma C) Sertlik s\u0131n\u0131f\u0131na g\u00f6re sert, lira cinsinden fiyat\u0131na g\u00f6re \u00e7ift say\u0131 olma D) Sertlik s\u0131n\u0131f\u0131na g\u00f6re orta, lira cinsinden fiyat\u0131na g\u00f6re tek say\u0131 olma 8. S\u0131n\u0131f 173","Ba\u015far\u0131yorum Olas\u0131 Durumlar\u0131 Kar\u015f\u0131la\u015ft\u0131rma Test 42 3. A\u015fa\u011f\u0131da bir okulun 11 ki\u015fiden olu\u015fan futbol tak\u0131m\u0131n\u0131n t\u00fcm oyuncular\u0131n\u0131n forma numaralar\u0131 g\u00f6sterilmi\u015ftir. 2 9 16 Oyuncular\u0131n forma numaralar\u0131 bir \u00f6r\u00fcnt\u00fc olu\u015fturmaktad\u0131r. Buna g\u00f6re bu oyunculardan rastgele se\u00e7ilen bir oyuncunun forma numaras\u0131 i\u00e7in a\u015fa\u011f\u0131dakilerden hangisinin olas\u0131l\u0131\u011f\u0131 daha azd\u0131r? A) 40\u2019tan b\u00fcy\u00fck olma B) 25\u2019ten k\u00fc\u00e7\u00fck olma C) 20\u2019den b\u00fcy\u00fck 40\u2019tan k\u00fc\u00e7\u00fck olma D) 30\u2019dan b\u00fcy\u00fck 50\u2019den k\u00fc\u00e7\u00fck olma 4. Bir kitap\u00e7\u0131 roman, hik\u00e2ye ve \u015fiir kitab\u0131 olmak \u00fczere toplam 120 kitab\u0131 bir rafa yerle\u015ftirmi\u015ftir. Bu raftan rastgele se\u00e7ilen bir kitab\u0131n roman olma olas\u0131l\u0131\u011f\u0131 en fazla, hik\u00e2ye kitab\u0131 olma olas\u0131l\u0131\u011f\u0131 en azd\u0131r. Buna g\u00f6re rafa dizilen bu kitaplar\u0131n da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6steren daire grafi\u011fi a\u015fa\u011f\u0131dakilerden hangisi olabilir? A) B) Hik\u00e2ye \u015eiir Hik\u00e2ye Roman 125\u00b0 84\u00b0 116\u00b0 105\u00b0 Roman \u015eiir C) D) Hik\u00e2ye \u015eiir Hik\u00e2ye 108\u00b0 Roman 120\u00b0 120\u00b0 Roman \u015eiir 174 8. S\u0131n\u0131f","Olas\u0131l\u0131k De\u011feri ve Kesin Olay \u2013 \u0130mk\u00e2ns\u0131z Olay E\u015fit \u015fansa sahip olan olaylarda her bir \u00e7\u0131kt\u0131n\u0131n olas\u0131l\u0131k de\u011feri e\u015fittir. Bu olas\u0131l\u0131k de\u011feri de 1 \u2019dir. \u201cn\u201d olas\u0131 durum n say\u0131s\u0131n\u0131 g\u00f6stermektedir. \u00d6rnek: Bir zar havaya at\u0131ld\u0131\u011f\u0131nda 1, 2, 3, 4, 5 ve 6 rakamlar\u0131ndan her birinin \u00fcst y\u00fcze gelmesi e\u015f olas\u0131l\u0131kl\u0131d\u0131r 1 ve bu olas\u0131l\u0131k de\u011feri 6 \u2019d\u0131r. \u2022 Her durumda ger\u00e7ekle\u015fecek olaylara kesin olay denir. \u00d6rnek: Zar havaya at\u0131ld\u0131\u011f\u0131nda \u00fcst y\u00fcze 7\u2019den k\u00fc\u00e7\u00fck rakam gelmesi kesin olayd\u0131r. Kesin olaylar\u0131n ger\u00e7ek- le\u015fme olas\u0131l\u0131\u011f\u0131 1\u2019dir. Ger\u00e7ekle\u015fmesi m\u00fcmk\u00fcn olmayan olaylara imk\u00e2ns\u0131z olay denir. \u00d6rnek: Zar havaya at\u0131ld\u0131\u011f\u0131nda \u00fcst y\u00fcze iki basamakl\u0131 bir say\u0131 gelmesi imk\u00e2ns\u0131z olayd\u0131r. \u0130mk\u00e2ns\u0131z olaylar\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 0\u2019d\u0131r. 39 2. A\u015fa\u011f\u0131daki olaylar\u0131n olas\u0131l\u0131k de\u011ferini belirleyiniz. 1. A\u015fa\u011f\u0131daki ifadelerde bo\u015f b\u0131rak\u0131lan yerleri, \u201ce\u015f ola- a) \u201cKONSER\u201d kelimesinin harflerinden rastgele se- s\u0131l\u0131kl\u0131d\u0131r\u201d ya da \u201ce\u015f olas\u0131l\u0131kl\u0131 de\u011fildir\u201d \u015feklinde dol- \u00e7ilen bir harfin \u201cN\u201d olma olas\u0131l\u0131\u011f\u0131 durunuz. a) Bir madeni paran\u0131n havaya at\u0131lmas\u0131nda \u00fcst y\u00fcze tura veya yaz\u0131 gelme olay\u0131 .............. b) 24 \u00f6\u011frencinin bulundu\u011fu bir s\u0131n\u0131f listesinden rast- b) Bir g\u00fcn i\u00e7inde her saat ba\u015f\u0131 \u00e7alan alarm\u0131n saat gele se\u00e7ilen bir \u00f6\u011frenci i\u00e7in her bir \u00e7\u0131kt\u0131 .............. 10.00\u2019da \u00e7alma olas\u0131l\u0131\u011f\u0131 c) Bir zar havaya at\u0131ld\u0131\u011f\u0131nda \u00fcst y\u00fcze gelen say\u0131n\u0131n c) 1\u2019den 20\u2019ye kadar numaraland\u0131r\u0131lm\u0131\u015f kartlardan 2 ya da tek say\u0131 olmas\u0131 .............. rastgele se\u00e7ilen birinde 7 yazma olas\u0131l\u0131\u011f\u0131 \u00e7) 3 k\u0131rm\u0131z\u0131, 3 mavi ve 2 mor top i\u00e7inden rastgele \u00e7) Haftan\u0131n g\u00fcnlerinden rastgele se\u00e7ilen bir g\u00fcn\u00fcn \u201cs\u201d harfi ile ba\u015flama olas\u0131l\u0131\u011f\u0131 se\u00e7ilen bir topun k\u0131rm\u0131z\u0131, mavi ya da mor olmas\u0131 .............. 8. S\u0131n\u0131f 175","Olas\u0131l\u0131k De\u011feri ve Kesin Olay \u2013 \u0130mk\u00e2ns\u0131z Olay 3. A\u015fa\u011f\u0131da verilen olaylardan kesin olaylar\u0131n \u00f6n\u00fcne 4. A\u015fa\u011f\u0131daki kartlarda birer hayvan resmi bulunmakta- \u201c1\u201d, imk\u00e2ns\u0131z olaylar\u0131n \u00f6n\u00fcne \u201c0\u201d yaz\u0131n\u0131z. d\u0131r. a) (.......) Bir raftaki cep telefonlar\u0131ndan rastgele Kartal Aslan K\u00f6pek se\u00e7ilen bir tanesinin tablet olmas\u0131. b) (.......) 444 say\u0131s\u0131n\u0131n rakamlar\u0131n\u0131n yaz\u0131l\u0131 oldu\u011fu Kedi Kartal Fare kartlardan rastgele se\u00e7ilen bir tanesinde \u201c4\u201d yazmas\u0131. A\u015fa\u011f\u0131daki ifadelerden do\u011fru olanlar\u0131n ba\u015f\u0131na \u201cD\u201d, yanl\u0131\u015f olanlar\u0131n ba\u015f\u0131na \u201cY\u201d yaz\u0131n\u0131z. c) (.......) Sadece kad\u0131n sporcular\u0131n bulundu\u011fu bir gruptan rastgele se\u00e7ilen bir sporcunun Bu kartlardan rastgele se\u00e7ilen bir tanesinde; kad\u0131n olmas\u0131. a) (.......) Hayvan resmi bulunmas\u0131 kesin olayd\u0131r. \u00e7) (.......) Yaz mevsiminin aylar\u0131n\u0131n yaz\u0131l\u0131 oldu\u011fu b) (.......) Kedi resmi bulunmas\u0131 ile fare resmi bu- kartlardan rastgele se\u00e7ilen bir tanesinde lunmas\u0131 e\u015f olas\u0131l\u0131kl\u0131d\u0131r. \u201cEyl\u00fcl\u201d yazmas\u0131. c) (.......) Ta\u015f\u0131t resmi bulunmas\u0131 imk\u00e2ns\u0131z olayd\u0131r. d) (.......) 10\u2019a tam b\u00f6l\u00fcnebilen say\u0131lar i\u00e7inden se\u00e7i- len bir tanesinin 5\u2019e ile tam b\u00f6l\u00fcnmesi. \u00e7) (.......) Kartal resmi bulunmas\u0131 ile aslan resmi bulunmas\u0131 e\u015f olas\u0131l\u0131kl\u0131d\u0131r. e) (.......) 1 k\u0131rm\u0131z\u0131, 2 pembe, 3 siyah bilye i\u00e7eri- sinden rastgele se\u00e7ilen bir bilyenin mavi 1 renkli olmas\u0131. d) (.......) Her bir kart\u0131n olas\u0131l\u0131k de\u011feri 6 \u2019d\u0131r. f) (.......) Rakamlar\u0131n yaz\u0131l\u0131 oldu\u011fu kartlardan rast- gele se\u00e7ilen bir tanesinde \u201cm\u201d yazmas\u0131. g) (.......) 30\u2019un \u00e7arpanlar\u0131n\u0131n oldu\u011fu kartlardan rastgele se\u00e7ilen bir tanesinde rasyonel say\u0131 yazmas\u0131. 176 8. S\u0131n\u0131f","Bir Olay\u0131n Olma Olas\u0131l\u0131\u011f\u0131 \u2022 Olas\u0131l\u0131k, bir olay\u0131n olma \u015fans\u0131na ili\u015fkin \u00f6l\u00e7\u00fcmd\u00fcr. Bir Olay\u203an Olma Olas\u203al\u203a\u20ac\u203a = \u2039stenilen olas\u203a durum say\u203as\u203a T\u00fcm olas\u203a durum say\u203as\u203a \u00d6rnek: Bir zar havaya at\u0131ld\u0131\u011f\u0131nda \u00fcst y\u00fcze gelen say\u0131n\u0131n \u00e7ift olma olas\u0131l\u0131\u011f\u0131n\u0131 bulal\u0131m. \u0130stenilen olas\u0131 durumlar = 2, 4, 6 T\u00fcm olas\u0131 durumlar = 1, 2, 3, 4, 5, 6 Olas\u203al\u203ak = \u2039stenen olas\u203a durum say\u203as\u203a = 3 tane (2, 4, 6) = 3 = 1 T\u00fcm olas\u203a durum say\u203as\u203a 6 tane (1, 2, 3, 4, 5, 6) 6 2 \u2022 Bir olay\u0131n olma olas\u0131l\u0131\u011f\u0131 en az 0, en fazla 1 olmak \u00fczere (0 ve 1 d\u00e2hil) bu iki de\u011fer aras\u0131ndad\u0131r. \u00d6rnek: \u2022 1 ; 0, 2; %41Bir olay\u203an olma olas\u203al\u203a\u20ac\u203a olabilir. \u2022 7 ; 1, 3; %2, 101Bir olay\u203an olma olas\u203al\u203a\u20ac\u203a olamaz. 3 6 40 \u00e7) \u0130ki basamakl\u0131 bir say\u0131 yazma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? 1. A\u015fa\u011f\u0131daki \u00f6zde\u015f toplar bo\u015f bir torbaya at\u0131l\u0131yor. 123 15 d) Asal rakam yazma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? Bu torbadan rastgele al\u0131nan bir topun \u00fczerinde; a) 11 yazma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? NOT: Bir olay\u0131n olma olas\u0131l\u0131\u011f\u0131 ile olmama ola- s\u0131l\u0131\u011f\u0131n\u0131n toplam\u0131 1\u2019dir. b) Rakam yazma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? 2. A\u015fa\u011f\u0131da ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 verilen olaylar\u0131n ger\u00e7ekle\u015fmeme olas\u0131l\u0131klar\u0131n\u0131 bulunuz. a) 1 b) 3 5 7 c) 7\u2019den k\u00fc\u00e7\u00fck bir say\u0131 yazma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? c) 0,2 \u00e7) 0,6 d) 1 e) %42 8. S\u0131n\u0131f 177","Bir Olay\u0131n Olma Olas\u0131l\u0131\u011f\u0131 3. A\u015fa\u011f\u0131da Nisan 2022 ay\u0131na ait takvim g\u00f6sterilmi\u015ftir. 4. A\u015fa\u011f\u0131da bir s\u0131n\u0131ftaki \u00f6\u011frencilerin sa\u00e7 renklerine g\u00f6re say\u0131lar\u0131 verilmi\u015ftir. Nisan 2022 Pzt Sal\u0131 \u00c7ar\u015f Per\u015f Cuma Cmt Paz Cinsiyet Kumral Sar\u0131\u015f\u0131n Kahverengi K\u0131z 7 3 6 1 23 3 2 8 4 5 6 7 8 9 10 Erkek 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Buna g\u00f6re a\u015fa\u011f\u0131daki sorular\u0131 cevaplay\u0131n\u0131z. 25 26 27 28 29 30 a) Bu s\u0131n\u0131ftan rastgele se\u00e7ilen bir \u00f6\u011frencinin; Bu aydan rastgele se\u00e7ilen bir g\u00fcn\u00fcn; \u2022 kumral sa\u00e7l\u0131 olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? a) hafta sonuna ait olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? \u2022 sar\u0131\u015f\u0131n erkek olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? b) per\u015fembe g\u00fcn\u00fc olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? \u2022 kahverengi sa\u00e7l\u0131 k\u0131z olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? c) \u201cc\u201d harfi ile ba\u015flamama olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? \u00e7) numaras\u0131n\u0131n bir say\u0131n\u0131n karesi ya da k\u00fcp\u00fc olma b) Erkek \u00f6\u011frencilerden rastgele se\u00e7ilen bir \u00f6\u011f- olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? rencinin; \u2022 kumral sa\u00e7l\u0131 olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? d) numaras\u0131n\u0131n iki basamakl\u0131 olmama olas\u0131l\u0131\u011f\u0131 ka\u00e7- \u2022 sar\u0131\u015f\u0131n olmama olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? t\u0131r? 178 8. S\u0131n\u0131f","Bir Olay\u0131n Olma Olas\u0131l\u0131\u011f\u0131 5. A\u015fa\u011f\u0131daki grafikte bir kul\u00fcpteki sporcular\u0131n bran\u015fla- 6. A\u015fa\u011f\u0131da bir k\u00fcp\u00fcn a\u00e7\u0131n\u0131m\u0131 verilmi\u015ftir. r\u0131na g\u00f6re say\u0131lar\u0131 verilmi\u015ftir. \u00e675 Grafik: Sporcular\u0131n Bran\u015flar\u0131 Say\u0131 \u00a78 \u00e620 \u00e624 \u00e632 35 25 \u00e627 20 15 Bu k\u00fcp kapat\u0131l\u0131yor ve kar\u015f\u0131l\u0131kl\u0131 y\u00fczlerinde yazan sa- y\u0131lar\u0131 \u00e7arp\u0131larak elde edilen sonu\u00e7lar \u00f6zde\u015f kartlara yaz\u0131l\u0131p bo\u015f bir torbaya at\u0131l\u0131yor. Buna g\u00f6re bu torbadan \u00e7ekilen kartta yazan say\u0131- 0 Bran\u015f n\u0131n irrasyonel olma olas\u0131l\u0131\u011f\u0131n\u0131 bulunuz. Voleybol Basketbol Futbol Hentbol Bu sporculardan rastgele se\u00e7ilen bir tanesinin; a) Voleybol bran\u015f\u0131ndan olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? b) Hentbol bran\u015f\u0131ndan olma olas\u0131l\u0131\u011f\u0131 futbol bran\u015f\u0131n- 7. Kenarlar\u0131n\u0131n uzunluklar\u0131 1 dm ve 8 dm olan dikd\u00f6rt- dan olma olas\u0131l\u0131\u011f\u0131ndan ka\u00e7ta ka\u00e7 fazlad\u0131r? gen bi\u00e7imindeki kartonun \u00f6n y\u00fcz\u00fc \u015fekildeki gibi farkl\u0131 renklere boyanm\u0131\u015ft\u0131r. Bu renklerin her birinin kapla- d\u0131\u011f\u0131 karesel b\u00f6lgelerin alanlar\u0131 birbirine e\u015fittir. 8 dm 1 dm Bu karton, par\u00e7alarda ayn\u0131 renk olmayacak \u015fekilde iki par\u00e7aya ayr\u0131lacakt\u0131r. Buna g\u00f6re par\u00e7alardan birinin boyal\u0131 y\u00fcz\u00fcn\u00fcn alan\u0131n\u0131n, di\u011ferinin boyal\u0131 y\u00fcz\u00fcn\u00fcn alan\u0131n\u0131n 3 kat\u0131 olma olas\u0131l\u0131\u011f\u0131n\u0131 bulunuz. c) Basketbol bran\u015f\u0131ndan olmama olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? 8. S\u0131n\u0131f 179","Uyguluyorum Bir Olay\u0131n Olma Olas\u0131l\u0131\u011f\u0131 Test 43 1. Bir k\u00fcmesteki hayvanlar\u0131n 6\u2019s\u0131 \u00f6rdek, 2\u2019si horoz, 4\u2019\u00fc 4. Bir olay\u0131n olma olas\u0131l\u0131\u011f\u0131n\u0131n de\u011feri a\u015fa\u011f\u0131dakiler- tavuktur. den hangisi olamaz? Bu k\u00fcmesin kap\u0131s\u0131ndan ilk \u00e7\u0131kan hayvan\u0131n tavuk A) 0 B) 0,18 7 11 C) 8 D) 10 olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? A) 1 1 2 3 4 B) 3 C) 3 D) 4 2. 1 L = 1000 mL 5. 36 ki\u015filik bir s\u0131n\u0131ftan rastgele se\u00e7ilen bir \u00f6\u011frencinin 4 A\u015fa\u011f\u0131daki \u015fi\u015felerde bulunan zeytinya\u011f\u0131 miktarlar\u0131 ve- rilmi\u015ftir. k\u0131z olma olas\u0131l\u0131\u011f\u0131 9 \u2019dur. Buna g\u00f6re bu s\u0131n\u0131ftaki erkek \u00f6\u011frenci say\u0131s\u0131 ka\u00e7- t\u0131r? A) 16 B) 18 C) 20 D) 24 1200 900 1150 950 850 mL mL mL mL mL Bu \u015fi\u015felerden rastgele se\u00e7ilen bir tanesinde 1 L\u2019den fazla zeytinya\u011f\u0131 bulunma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? 4 3 2 1 A) 5 B) 5 C) 5 D) 5 6. 70 sayfal\u0131k bir kitapta rastgele i\u015faretlenen bir sayfan\u0131n numaras\u0131n\u0131n 5\u2019in kat\u0131 olma olas\u0131l\u0131\u011f\u0131 ka\u00e7- 3. t\u0131r? A) 1 1 C) 2 2 7 B) 5 7 D) 5 Yukar\u0131daki afi\u015fte yazan s\u00f6z\u00fcn her harfi \u00f6zde\u015f kartla- 7. Bir torbada bulunan 10 k\u0131rm\u0131z\u0131, 6 mavi ve 4 ye\u015fil ra yaz\u0131l\u0131p bo\u015f bir torbaya at\u0131l\u0131yor. toptan rastgele al\u0131nan bir topun mavi renkli olma olas\u0131l\u0131\u011f\u0131 y\u00fczde ka\u00e7t\u0131r? Buna g\u00f6re bu torbadan rastgele \u00e7ekilen bir kart\u0131n \u00fczerinde sesli harf yazma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? 3 9 C) 1 D) 4 A) 20 B) 30 C) 40 D) 50 A) 7 B) 20 2 7 180 8. S\u0131n\u0131f","Test Bir Olay\u0131n Olma Olas\u0131l\u0131\u011f\u0131 Uyguluyorum 43 8. A\u015fa\u011f\u0131daki olaylardan kesin olay olanlar\u0131n kar\u015f\u0131s\u0131n- 11. 1\u2019den 50\u2019ye kadar olan do\u011fal say\u0131lar \u00f6zde\u015f kartlara daki kutucuk ye\u015fil, imk\u00e2ns\u0131z olay olanlar\u0131n kar\u015f\u0131s\u0131n- yaz\u0131larak ters \u00e7evriliyor. daki kutucuk k\u0131rm\u0131z\u0131 renkle boyanacakt\u0131r. Buna g\u00f6re bu kartlardan rastgele al\u0131nan bir tane- Haftan\u0131n g\u00fcnlerinden rastgele se\u00e7ilen bir g\u00fcn\u00fcn 6 harfli olmas\u0131. sinde yazan say\u0131n\u0131n karek\u00f6k\u00fcn\u00fcn veya karek\u00f6- Rakamlar aras\u0131ndan rastgele se\u00e7ilen bir rakam\u0131n bir basamakl\u0131 olmas\u0131. k\u00fcn\u00fcn en yak\u0131n oldu\u011fu asal say\u0131n\u0131n 5 olma ola- Y\u0131l\u0131n aylar\u0131ndan rastgele se\u00e7ilen bir ay\u0131n 35 g\u00fcn olmas\u0131. s\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? Buna g\u00f6re kutucuklar\u0131n do\u011fru boyanm\u0131\u015f hali 9 1 11 6 a\u015fa\u011f\u0131dakilerden hangisidir? A) 50 B) 5 C) 50 D) 25 A) B) C) D) 12. Telefonuna rakamlardan olu\u015fun 6 haneli bir \u015fifre ko- yan Cansu, \u015fifrenin ilk 5 rakam\u0131n\u0131 do\u011fru giriyor, son rakam\u0131 ise hat\u0131rlam\u0131yor. Buna g\u00f6re Cansu\u2019nun rastgele girdi\u011fi son hane- nin yanl\u0131\u015f olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? 1 1 8 9 A) 10 B) 9 C) 9 D) 10 9. Toplam 26 kalemin bulundu\u011fu bir kutudaki kalemler- 13. A\u015fa\u011f\u0131daki torbalarda bulunan renkleri d\u0131\u015f\u0131nda \u00f6zde\u015f den 7\u2019si k\u0131rm\u0131z\u0131, 9\u2019u mavi, kalanlar\u0131 siyaht\u0131r. bilyelerin say\u0131s\u0131 verilmi\u015ftir. Buna g\u00f6re bu torbadan rastgele al\u0131nan bir kale- min siyah olma olas\u0131l\u0131\u011f\u0131 ile mavi olmama olas\u0131l\u0131- \u011f\u0131n\u0131n toplam\u0131 ka\u00e7t\u0131r? 25 B) 1 27 14 A) 26 C) 26 D) 13 6 Siyah 5 Siyah 8 Beyaz 3 Beyaz 1.Torba 2.Torba 10. Bir sepetteki sa\u011flam elmalar\u0131n say\u0131s\u0131n\u0131n 6 kat\u0131, \u00e7\u00fcr\u00fck 1. torbadan rengine bak\u0131lmadan 4 bilye al\u0131n\u0131p 2. tor- elmalar\u0131n say\u0131s\u0131n\u0131n 7 kat\u0131na e\u015fittir. baya at\u0131l\u0131yor. Buna g\u00f6re bu sepetten rastgele al\u0131nan bir elma- Buna g\u00f6re son durumda 2. torbadan rastgele al\u0131- nan bir bilyenin siyah olma olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131dakiler- n\u0131n \u00e7\u00fcr\u00fck olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? den hangisi olabilir? 13 13 6 7 1 5 3 5 A) 42 B) 21 C) 13 D) 13 A) 3 B) 2 C) 4 D) 6 8. S\u0131n\u0131f 181","Ba\u015far\u0131yorum Bir Olay\u0131n Olma Olas\u0131l\u0131\u011f\u0131 Test 44 1. Leyla ve Ak\u0131n\u2019\u0131n renkleri d\u0131\u015f\u0131nda \u00f6zde\u015f olan oyuncak par\u00e7alar\u0131 a\u015fa\u011f\u0131da say\u0131lar\u0131yla verilmi\u015ftir. Leyla\u2019n\u0131n Ak\u0131n\u2019\u0131n Par\u00e7alar\u0131 Par\u00e7alar\u0131 10 Adet 6 Adet 7 Adet 11 Adet \u0130ki arkada\u015f kendi par\u00e7alar\u0131yla yap\u0131labilecek en fazla say\u0131da a\u015fa\u011f\u0131daki \u015fekilleri yapm\u0131\u015flard\u0131r. Kalan par\u00e7alar\u0131 da bo\u015f bir torbaya atm\u0131\u015flard\u0131r. Buna g\u00f6re torbadan rastgele \u00e7ekilen bir par\u00e7an\u0131n olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? A) 4 B) 1 3 D) 1 7 2 C) 8 4 2. A\u015fa\u011f\u0131da e\u015f kare \u015feklinde b\u00f6lmelerden olu\u015fan kartonun her bir b\u00f6lmesine 1\u2019den 12\u2019ye kadar do\u011fal say\u0131lar yaz\u0131lm\u0131\u015ft\u0131r. 1 2 3 4 5 6 7 8 9 10 11 12 Bu kartondan ard\u0131\u015f\u0131k 5 do\u011fal say\u0131n\u0131n yaz\u0131l\u0131 oldu\u011fu dikd\u00f6rtgen bir par\u00e7a kesilerek at\u0131l\u0131yor. Daha sonra kalan kareler e\u015f par\u00e7alar halinde ayr\u0131larak bo\u015f bir torbaya konuluyor. Buna g\u00f6re torbadan rastgele al\u0131nan par\u00e7an\u0131n \u00fczerinde asal say\u0131 yazma olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131dakilerden hangisi olamaz? A) 1 B) 2 3 D) 4 7 7 C) 7 7 3. Yanda bir apartman\u0131n kap\u0131s\u0131nda \u015fifre girmek i\u00e7in kullan\u0131lan tu\u015f tak\u0131m\u0131 g\u00f6sterilmi\u015ftir. D\u00f6rt basamakl\u0131 bir \u015fifre ile bu apartmana giri\u015f yap\u0131l\u0131rken \u015fifreyi olu\u015fturan rakamlar\u0131n bir k\u0131sm\u0131 \u015fekildeki gibi a\u015f\u0131nm\u0131\u015ft\u0131r. Bu \u015fifrenin pozitif tam say\u0131 \u00e7arpanlar\u0131ndan birinin 10 oldu\u011fu bilinmektedir. Buna g\u00f6re \u015fifrenin 4 say\u0131s\u0131n\u0131n kat\u0131 olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? 1 B) 1 A) 3 2 2 3 C) 3 D) 4 182 8. S\u0131n\u0131f","Test Bir Olay\u0131n Olma Olas\u0131l\u0131\u011f\u0131 Ba\u015far\u0131yorum 44 4. Bir ara\u015ft\u0131rma kapsam\u0131nda bir derne\u011fe \u00fcye olan 18 ki\u015fiye internet \u00fczerinden bir form g\u00f6nderilmi\u015ftir. \u00dcyelerin cinsi- yetlerine g\u00f6re formu doldurup doldurmad\u0131klar\u0131 a\u015fa\u011f\u0131daki gibi g\u00f6sterilmi\u015ftir. \u00dcye \u0130smi Cinsiyeti Formu Doldurma \u00dcye \u0130smi Cinsiyeti Formu Doldurma Durumu Durumu A... Kad\u0131n \ufffd H... Kad\u0131n \ufffd B... Erkek \ufffd I... Kad\u0131n \ufffd C... Kad\u0131n \ufffd \u0130... Kad\u0131n \ufffd \u00c7... Kad\u0131n \ufffd J... Erkek \ufffd D... Kad\u0131n \ufffd K... Erkek \ufffd E... Erkek \ufffd L... Kad\u0131n \ufffd F... Kad\u0131n \ufffd M... Erkek \ufffd G... Erkek \ufffd N... Kad\u0131n \ufffd Formu dolduran \u00fcyeler \ufffd, doldurmayan \u00fcyeler \ufffd ile ifade edilmi\u015ftir. Buna g\u00f6re formu dolduran \u00fcyeler aras\u0131ndan rastgele se\u00e7ilen bir \u00fcyenin kad\u0131n olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? 2 3 C) 1 3 A) 5 B) 5 2 D) 4 5. A\u015fa\u011f\u0131da \u00ca450 cm uzunlu\u011funda dikd\u00f6rtgen \u015feklinde bir k\u00e2\u011f\u0131t g\u00f6sterilmi\u015ftir. \u00ca450 cm Hakan \u00d6\u011fretmen T\u00fcbitak Bilim Fuar\u0131\u2019nda g\u00f6revli \u00f6\u011frencilerden sorumlu \u00f6\u011frenciyi se\u00e7mek i\u00e7in bir \u00e7ekili\u015f yapmak istiyor. \u00c7ekili\u015f i\u00e7in bu k\u00e2\u011f\u0131d\u0131 \u00a72 cm\u2019lik e\u015f par\u00e7alara ay\u0131r\u0131p bir \u00f6r\u00fcnt\u00fc olu\u015fturacak bi\u00e7imde par\u00e7alar\u0131 \u015fekildeki gibi boyuyor. Ard\u0131ndan boyal\u0131 par\u00e7alar\u0131n her birini keserek bo\u015f bir kutuya at\u0131yor ve bu \u00f6\u011frencilerden bir k\u00e2\u011f\u0131d\u0131 rastgele se\u00e7melerini istiyor. Mor k\u00e2\u011f\u0131d\u0131 se\u00e7en \u00f6\u011frencinin sorumlu olaca\u011f\u0131n\u0131 s\u00f6yl\u00fcyor. Buna g\u00f6re bir \u00f6\u011frencinin sorumlu olma olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r? 4 1 2 4 A) 15 B) 3 C) 3 D) 5 8. S\u0131n\u0131f 183","Cebirsel \u0130fadeler ve \u00d6zde\u015flikler Basit Cebirsel \u0130fadeleri Farkl\u0131 Bi\u00e7imlerde Yazma \u2022 En az bir de\u011fi\u015fkeni bulunan ve i\u015flem i\u00e7eren ifadelere cebirsel ifadeler denir. \u00d6rne\u011fin; 3x + 4y \u2013 6z; 2a2 + 5b \u2013 7; m \u2013 8n ..... birer cebirsel ifadedir. \u2022 Cebirsel ifadelerdeki her harf bir say\u0131y\u0131 temsil eder. Bu y\u00fczden bu harflere bilinmeyen (de\u011fi\u015fken) denir. \u00d6rne\u011fin; 3x+ 4y \u2013 6z cebirsel ifadesinde de\u011fi\u015fkenler x, y ve z\u2019dir. 2a2 + 5b \u2013 7 cebirsel ifadesinde de\u011fi\u015fkenler a ve b\u2019dir. \u2022 Cebirsel ifadelerde toplama veya \u00e7\u0131karma i\u015flemi ile birbirinden ayr\u0131lan her ifadeye terim denir. \u00d6rne\u011fin; 3x + 4y \u2013 6z cebirsel ifadesinin terimleri 3x, 4y ve \u20136z\u2019dir. \u2022 Her bir terimde de\u011fi\u015fken d\u0131\u015f\u0131ndaki say\u0131lara katsay\u0131 denir. \u00d6rne\u011fin; 3x + 4y \u2013 6z cebirsel ifadesinin katsay\u0131lar\u0131 3, 4 ve \u20136\u2019d\u0131r. \u2022 De\u011fi\u015fkeni olmayan terimlere sabit terim denir. \u00d6rne\u011fin; 2a2 + 5b \u2013 7 cebirsel ifadesinin sabit terimi \u20137\u2019dir. 41 c) 19x3\u00b7y \u2022 Terim(ler):....................................................... 1. A\u015fa\u011f\u0131daki cebirsel ifadelerde istenenleri bulunuz. \u2022 De\u011fi\u015fken(ler): ................................................. a) 4a + 7c \u2022 Katsay\u0131(lar): .................................................... \u2022 Terim(ler):....................................................... \u2022 Sabit Terim: .................................................... \u2022 De\u011fi\u015fken(ler): ................................................. \u2022 Katsay\u0131(lar): .................................................... \u00e7) 10m2 \u2013 7m + 6 \u2022 Sabit Terim: .................................................... \u2022 Terim(ler):....................................................... \u2022 De\u011fi\u015fken(ler): ................................................. b) \u20135x2 + 12 \u2022 Katsay\u0131(lar): .................................................... \u2022 Terim(ler):....................................................... \u2022 Sabit Terim: .................................................... \u2022 De\u011fi\u015fken(ler): ................................................. \u2022 Katsay\u0131(lar): .................................................... NOT: Sabit terim de bir katsay\u0131d\u0131r. \u2022 Sabit Terim: .................................................... 184 8. S\u0131n\u0131f","Cebirsel \u0130fadeler ve \u00d6zde\u015flikler NOT: De\u011fi\u015fkenleri ve de\u011fi\u015fkenlerin kuvvetleri NOT: Bir cebirsel ifade birden fazla farkl\u0131 bi- ayn\u0131 olan terimlere benzer terim denir. \u00e7imlerde g\u00f6sterilebilir. \u00d6rne\u011fin; \u201312a ve 7a benzer terimlerdir. \u00d6rne\u011fin; 8a2 cebirsel ifadesi Toplama ve \u00e7\u0131karma i\u015flemi benzer terimler aras\u0131nda \u20ba 4\u00b72\u00b7a2, 4\u00b72\u00b7a\u00b7a, 10a2 \u2013 2a2, 5a2 + 3a2 gibi farkl\u0131 yap\u0131l\u0131r. bi\u00e7imlerde g\u00f6sterilir. 2. A\u015fa\u011f\u0131daki i\u015flemleri yap\u0131n\u0131z. 3. A\u015fa\u011f\u0131daki ifadeleri 3\u2019er farkl\u0131 g\u00f6sterimle yaz\u0131n\u0131z. a) 4a + 2a \u2013 3a = .................................................. a) 12x2 \u2022 ....................................................................... b) 11x \u2013 7x \u2013 9x = ................................................. \u2022 ....................................................................... \u2022 ....................................................................... c) 6m + 3m \u2013 7 = .................................................. b) a2b \u00e7) 8x \u2013 y \u2013 6x + 3y = ............................................. \u2022 ....................................................................... d) 10a2 + 7a \u2013 a2 \u2013 6 =.......................................... \u2022 ....................................................................... \u2022 ....................................................................... c) \u20138m2 \u2022 ....................................................................... \u2022 ....................................................................... \u2022 ....................................................................... e) (20x2 \u2013 5) \u2013 (13x2 \u2013 2) = ................................... \u00e7) 2x + 2y f) (3c \u2013 5) \u2013 (9 + 4c) =........................................... \u2022 ....................................................................... \u2022 ....................................................................... \u2022 ....................................................................... 8. S\u0131n\u0131f 185","Cebirsel \u0130fadelerin \u00c7arp\u0131m\u0131 Cebirsel ifadeler \u00e7arp\u0131l\u0131rken \u00e7arpman\u0131n toplama veya \u00e7\u0131karma i\u015flemi \u00fczerine da\u011f\u0131lma \u00f6zelli\u011finden yararlan\u0131l\u0131r. Bi- rinci \u00e7arpandaki terimler ikinci \u00e7arpandaki terimlerle ayr\u0131 ayr\u0131 \u00e7arp\u0131l\u0131r. \u00c7\u0131kan sonu\u00e7ta benzer terimler toplan\u0131r veya \u00e7\u0131kar\u0131l\u0131r. \u00d6rnek: \u2022 3\u00b7(7x \u2013 2) = 3\u00b77x \u2013 3\u00b72 = 21x \u2013 6 \u2022 (2x + 3)\u00b7(4x\u20131) = 2x\u00b74x \u2013 2x\u00b71 + 3\u00b74x \u2013 3\u00b71 = 8x2 \u2013 2x + 12x \u2013 3 = 8x2 \u20132x + 12x \u2013 3 = 8x2 + 10x \u2013 3 42 g) (\u2013m)\u00b7m2 = ........................................................ \u011f) abc\u00b7ab = .......................................................... 1. A\u015fa\u011f\u0131daki \u00e7arpma i\u015flemlerini yap\u0131n\u0131z. a) a\u00b7a = .............................................................. b) 3\u00b72x = .............................................................. h) (\u20132)\u00b7x\u00b7(\u2013x2) =.................................................. c) (\u20134c)\u00b72 = .......................................................... \u0131) 10x\u00b7(\u2013x2y) = ...................................................... \u00e7) 5x\u00b76x =............................................................. i) y\u00b7(\u20132y)\u00b73y = ..................................................... d) 8\u00b72\u00b74a =.......................................................... j) 4d\u00b7(\u20135e2) = ....................................................... e) 7x\u00b7(\u2013x) = .......................................................... k) (\u20136a)\u00b7(\u20133c) = ................................................... f) 3a\u00b74ab = ........................................................... l) x2\u00b7(\u20132xy)\u00b7xy2 =................................................. 186 8. S\u0131n\u0131f","Cebirsel \u0130fadelerin \u00c7arp\u0131m\u0131 3. A\u015fa\u011f\u0131daki i\u015flemlerin sonu\u00e7lar\u0131n\u0131 bulunuz. a) (x + 2)\u00b7(x + 3) = ............................................... 2. A\u015fa\u011f\u0131daki i\u015flemlerin sonu\u00e7lar\u0131n\u0131 bulunuz. a) 2\u00b7(3a + 4) = ..................................................... b) \u20136\u00b7(8x \u2013 3) = ................................................... b) (x + y)\u00b7(x \u2013 y) = ............................................... c) \u2013(2c + 5) = ....................................................... c) (2x + 5)\u00b7(3x + 4) = ........................................... \u00e7) y\u00b7(3y + 10) = .................................................... \u00e7) (x \u2013 8)\u00b7(2x \u2013 1) = ............................................. d) 3a\u00b7(4a2 \u2013 7) = ................................................. d) (x \u2013 5)\u00b7(x \u2013 5) = .............................................. e) \u20136x\u00b7(3x3 \u2013 1) = ................................................ e) (5 \u2013 2x)\u00b7(3x \u2013 4) = ........................................... f) a\u00b7(10x + 6) = .................................................... f) (3a \u2013 5)\u00b7(4 + 9a) = ........................................... g) 6m\u00b7(8n \u2013 7m) = ............................................... g) (2x + 3)\u00b7(2x \u2013 3) = .......................................... 8. S\u0131n\u0131f 187","Cebirsel \u0130fadelerin \u00c7arp\u0131m\u0131 4. x 1 5. A\u015fa\u011f\u0131da kenar uzunluklar\u0131 birim cinsinden veri- x 1 len d\u00f6rtgenlerin alanlar\u0131n\u0131 bulunuz. x2 x 11 1 a) Yukar\u0131da verilen cebir karolar\u0131 kullan\u0131larak mo- x+3 dellenen a\u015fa\u011f\u0131daki i\u015flemleri yap\u0131n\u0131z. a) x+3 b) b) 2x 6x-1 c) 2a+3 2a-3 c) \u00e7) 2m+1 \u00e7) 15-m 188 8. S\u0131n\u0131f","Cebirsel \u0130fadelerin \u00c7arp\u0131m\u0131 6. A\u015fa\u011f\u0131daki \u015fekillerde boyal\u0131 b\u00f6lgelerin alanlar\u0131n\u0131 bulunuz. (\u220f yerine 3 al\u0131n\u0131z.) a) 2a cm b) (x+5)cm 1 cm 2a cm 3x cm 5 cm 3 cm (4x+7) cm c) \u00e7) 3 cm (4m+6) cm 4a cm (10-a) cm (5m+4) cm (6a+1) cm 7. A\u015fa\u011f\u0131da zemini ve odalar\u0131 dikd\u00f6rtgen bi\u00e7iminde olan bir evin plan\u0131 g\u00f6sterilmi\u015ftir. Buna g\u00f6re evin b\u00f6l\u00fcmle- rinin ve evin toplam alan\u0131n\u0131 bulunuz. xx 4x Banyo : ......................................................... y+3 Banyo Koridor Mutfak : ......................................................... 2y Koridor : ......................................................... Mutfak Salon Tuvalet : ......................................................... Oda1 Oda2 Salon : ......................................................... WC 2y Oda 1 : ......................................................... Oda 2 : ......................................................... Toplam Alan: :................................................. 8. S\u0131n\u0131f 189","Uyguluyorum Basit Cebirsel \u0130fadeler ve Test Cebirsel \u0130fadelerin \u00c7arp\u0131m\u0131 45 1. 2\u00b7(a \u2013 2) \u20133\u00b7b cebirsel ifadesinin en sade h\u00e2li i\u00e7in; 5. I. 4 terimlidir. (3a+1)cm O II. Sabit terimi \u20134\u2019t\u00fcr. III. Katsay\u0131lar toplam\u0131 \u20135\u2019tir. ifadelerinden hangileri do\u011frudur? A) Yaln\u0131z II B) II ve III Yukar\u0131da verilen O merkezli \u00e7emberin \u00e7evre uzun- C) I ve III D) I, II ve III lu\u011funu santimetre cinsinden veren cebirsel ifade a\u015fa\u011f\u0131dakilerden hangisidir? (\u220f yerine 3 al\u0131n\u0131z.) A) 9a + 3 B) 9a + 6 C) 18a + 6 D) 18a + 9 2. \u20138\u00b73x \u00e7arp\u0131m\u0131 a\u015fa\u011f\u0131dakilerden hangisine e\u015fittir? A) \u20135x B) \u201311x C) \u201321x D) \u201324x 6. 2 x-y 3. \u00b7 x+y I. m.m.m = m3 II. 4a.5a = 20a2 \u00b7 III. 2x2.(-x)=-2x3 ? IV. 3y2.4y3=12y6 Yukar\u0131daki tahtada yazan e\u015fitliklerin tamam\u0131n\u0131n Yukar\u0131da verilen \u015femada \u201c?\u201d yerine a\u015fa\u011f\u0131dakiler- do\u011fru olmas\u0131 i\u00e7in hangi e\u015fitli\u011fin silinmesi gere- den hangisi yaz\u0131lmal\u0131d\u0131r? kir? A) I. B) II. C) III. D) IV. A) 2x2 \u2013 2y2 B) 2x2 + 2y2 C) 2x2 \u2013 2y2 + 2xy D) 2x2 + 2y2 \u2013 2xy 4. x\u00b7(7 \u2013 x2) \u00e7arp\u0131m\u0131 a\u015fa\u011f\u0131dakilerden hangisine e\u015fit- 7. 30mn2 ifadesi a\u015fa\u011f\u0131dakilerden hangisine e\u015fit de- tir? \u011fildir? A) 7x2 + x2 B) 7x \u2013 x2 A) 15m\u00b72n2 B) 10m2\u00b73n C) 7x + x2 D) 7x \u2013 x3 C) 6\u00b75mn2 D) 40mn2 \u2013 10mn2 190 8. S\u0131n\u0131f","Test Basit Cebirsel \u0130fadeler ve Uyguluyorum 45 Cebirsel \u0130fadelerin \u00c7arp\u0131m\u0131 8. x 1 11. A = 3x \u2013 2 x x2 x 1 B = x\u00b7(2x \u2013 1) x1 1 e\u015fitliklerine g\u00f6re B \u2013 A i\u015fleminin sonucu ka\u00e7t\u0131r? Yukar\u0131da verilen cebir karolar\u0131 kullan\u0131larak, A) 2x2\u2013 4x + 2 B) 2x2 \u2013 6x C) 4x2 \u2013 2x + 4 D) 4x2 \u2013 4x 12. A\u015fa\u011f\u0131da uzunluklar\u0131 verilen dikd\u00f6rtgen \u015feklindeki k\u0131rm\u0131z\u0131 karton ile kare \u015feklindeki mavi karton 5\u2019er cm\u2019lik k\u0131s\u0131mlar\u0131 \u00fcst \u00fcste gelecek bi\u00e7imde \u00e7ak\u0131\u015ft\u0131r\u0131l- m\u0131\u015ft\u0131r. (10x+10) cm \u015fekildeki gibi modellenen i\u015flem a\u015fa\u011f\u0131dakilerden (5x+5) cm hangisidir? A) (3x + 1)\u00b7(2x + 1) B) (3x + 1)\u00b7(2x \u2013 1) 5 cm C) (3x \u2013 1)\u00b7(2x + 1) D) (3x \u2013 1)\u00b7(2x \u2013 1) Buna g\u00f6re son durumda olu\u015fan \u015feklin \u00f6n y\u00fcz\u00fc- 9. Tanesi (3x + 1) TL olan kalemlerden 20 tane alan bir n\u00fcn alan\u0131n\u0131 santimetrekare cinsinden veren i\u015flem k\u0131rtasiyeci bu kalemlerin her birini (5x + 3) TL\u2019den a\u015fa\u011f\u0131dakilerden hangisidir? sat\u0131yor. A) (15x + 15)\u00b7(5x + 10) B) (15x + 10)\u00b7(5x + 5) C) (10x + 5)\u00b7(5x + 5) D) (10x + 10)\u00b7(5x + 10) Buna g\u00f6re k\u0131rtasiyecinin t\u00fcm kalemlerin sat\u0131\u015f\u0131n- dan elde etti\u011fi k\u00e2r\u0131 lira cinsinden g\u00f6steren cebir- 13. sel ifade a\u015fa\u011f\u0131dakilerden hangisidir? (m + 6)\u00b7(m + x) A) 40x + 40 B) 40x + 20 \u00e7arp\u0131m\u0131nda katsay\u0131lar toplam\u0131 21 oldu\u011funa g\u00f6re C) 20x + 40 D) 20x + 20 x ka\u00e7t\u0131r? A) 1 B) 2 C) 3 D) 4 10. 14. (ab \u2013 5b)\u00b7(3a \u2013 1) (8x + 3)\u00b7(4x \u2013 1) = Ax2 \u2013 Bx + C \u00e7arp\u0131m\u0131 a\u015fa\u011f\u0131dakilerden hangisine e\u015fittir? A) 3a2b \u2013 15ab B) 3ab2 \u2013 16ab \u2013 5b oldu\u011funa g\u00f6re A + B + C i\u015fleminin sonucu ka\u00e7t\u0131r? C) 3a2b \u2013 16ab D) 3a2b \u201316ab + 5b A) 25 B) 28 C) 29 D) 33 8. S\u0131n\u0131f 191","Ba\u015far\u0131yorum Cebirsel \u0130fadelerin \u00c7arp\u0131m\u0131 Test 46 1. A\u015fa\u011f\u0131da bir zemine soldan hizal\u0131 olarak yerle\u015ftirilmi\u015f kal\u0131nl\u0131klar\u0131 e\u015fit \u00fc\u00e7 \u00e7ubuktan birinin uzunlu\u011fu ile baz\u0131 \u00e7ubuklar aras\u0131ndaki uzunluk farklar\u0131 verilmi\u015ftir. (2x+15) cm (x+5) cm x cm Bu \u00e7ubuklardan ye\u015fil ve mavi renkli olanlar a\u015fa\u011f\u0131daki gibi birer k\u00f6\u015fesi \u00e7ak\u0131\u015facak bi\u00e7imde yerle\u015ftirilip i\u00e7 b\u00f6lgesi dik- d\u00f6rtgen \u015feklinde olan bir \u00e7er\u00e7eve elde ediliyor. Buna g\u00f6re elde edilen bu \u00e7er\u00e7evenin i\u00e7 b\u00f6lgesindeki dikd\u00f6rtgenin alan\u0131n\u0131 santimetrekare cinsinden veren cebirsel ifade a\u015fa\u011f\u0131dakilerden hangisidir? A) 6x2 + 100x + 400 B) 6x2 + 80x + 400 C) 4x2 + 100x + 200 D) 4x2 + 80x + 200 2. A\u015fa\u011f\u0131da \u015eekil 1\u2019de dikd\u00f6rtgen bi\u00e7iminde bir arsan\u0131n k\u00f6\u015fesine dikd\u00f6rtgen bi\u00e7iminde hobi bah\u00e7esi yap\u0131lm\u0131\u015ft\u0131r. Bu hobi bah\u00e7esinin uzun kenarlar\u0131 ok y\u00f6n\u00fcnde 6 m uzat\u0131larak \u015eekil 2\u2019deki g\u00f6r\u00fcn\u00fcm elde ediliyor. (x+4)m (x-2)m \u015eekil 1 \u015eekil 2 \u015eekil 2\u2019de arsan\u0131n kalan k\u0131sm\u0131n\u0131n metrekare cinsinden alan\u0131n\u0131n hobi bah\u00e7esinin alan\u0131ndan (x2 -10) m2 fazla oldu\u011fu biliniyor. Buna g\u00f6re arsan\u0131n tamam\u0131n\u0131n alan\u0131n\u0131 metrekare cinsinden veren cebirsel ifade a\u015fa\u011f\u0131dakilerden hangisidir? A) 5x2 + 16x \u2013 30 B) 3x2 + 16x \u2013 50 C) 3x2 + 8x \u2013 30 D) 2x2 + 8x \u2013 50 192 8. S\u0131n\u0131f","Test Cebirsel \u0130fadelerin \u00c7arp\u0131m\u0131 Ba\u015far\u0131yorum 46 3. A\u015fa\u011f\u0131da ekran\u0131 dikd\u00f6rtgen bi\u00e7iminde olan tablette a\u00e7\u0131k olan uygulama kare bi\u00e7imindedir. (x+3) cm 4 cm (x+3) cm 4 cm Bu uygulaman\u0131n \u00e7evre uzunlu\u011fu (4x + 12) cm olup uygulaman\u0131n, tabletin kenarlar\u0131na uzakl\u0131klar\u0131 \u015fekildeki gibidir. Tabletin ekran d\u0131\u015f\u0131ndaki k\u0131sm\u0131n\u0131n kal\u0131nl\u0131\u011f\u0131 2 cm oldu\u011funa g\u00f6re tabletin bir y\u00fcz\u00fcn\u00fcn alan\u0131n\u0131 santimetrekare cinsinden veren cebirsel ifade a\u015fa\u011f\u0131dakilerden hangisidir? A) 6x2 + 45x \u2013 15 B) 6x2 + 46x + 15 C) 3x2 + 58x + 195 D) 3x2 + 58x \u2013 195 4. \u015eekil 1\u2019de birim cinsinden baz\u0131 uzunluklar\u0131 verilen \u00f6n y\u00fcz\u00fc mavi, arka y\u00fcz\u00fc k\u0131rm\u0131z\u0131 renkli yamuk bi\u00e7imindeki k\u00e2\u011f\u0131t kesikli \u00e7izgiler boyunca kendi \u00fczerine katland\u0131\u011f\u0131nda \u015eekil 2\u2019deki gibi dikd\u00f6rtgen g\u00f6r\u00fcn\u00fcm olu\u015fmu\u015ftur. 4x+2 3x+1 \u015eekil 1 2x-2 \u015eekil 2 \u015eekil 2\u2019de olu\u015fan \u015feklin \u00e7evre uzunlu\u011fu 20x br oldu\u011funa son durumda mavi g\u00f6r\u00fcnen y\u00fcz\u00fcn alan\u0131 ka\u00e7 bi- rimkaredir? A) 14x2 + x \u2013 3 B) 14x2 + 4x \u2013 6 C) 7x2 + 13x \u2013 6 D) 7x2 + x \u2013 3 8. S\u0131n\u0131f 193","\u00d6zde\u015flikler \u0130\u00e7inde bilinmeyen bulunan ve bu bilinmeyenin her de\u011feri i\u00e7in do\u011fru olan e\u015fitli\u011fe \u00f6zde\u015flik denir. Denklem ise bilinmeyenin baz\u0131 de\u011ferleri i\u00e7in do\u011fru olan e\u015fitliklerdir. \u00d6rnek: \u2022 3x + 1 = 7 e\u015fitli\u011finde x de\u011feri sadece 2 oldu\u011funda e\u015fitlik do\u011fru oldu\u011fu i\u00e7in, bu e\u015fitlik denklemdir. \u2022 4\u00b7(x + 2) = 4x + 8 e\u015fitli\u011fi x\u2019in t\u00fcm de\u011ferleri i\u00e7in do\u011fru oldu\u011fundan bu e\u015fitlik \u00f6zde\u015fliktir. \u2022 x2 = 16 e\u015fitli\u011fi x\u2019in sadece 4 veya \u20134 de\u011ferleri i\u00e7in do\u011fru oldu\u011fundan bu e\u015fitlik denklemdir. 43 2. A\u015fa\u011f\u0131daki cebirsel ifadelerin \u00f6zde\u015fini bulunuz. a) 2x\u00b7(4y + 5) = .................................................... 1. A\u015fa\u011f\u0131daki e\u015fitliklerden hangilerinin denklem, hangilerinin \u00f6zde\u015flik oldu\u011funu bulunuz. a) 5\u00b7(x \u2013 1) = 3x + 11 \u00a1........................................ b) (4a + 3)\u00b7(2a \u2013 1) = ........................................... b) 2 + 3\u00b7(x + 1) = 2\u00b7(x + 2) + x + 1 \u00a1 .................. c) (2m + 1)\u00b7(4 \u2013 n) =............................................. c) 7a + 3 = 8a + 1 \u00a1 ............................................. \u00e7) (a \u2013 4)\u00b7(a + 4) = a2 \u2013 16 \u00a1............................... \u00e7) (a2 + 2a) + (1 \u2013 4a) = ........................................ d) 3 = 4\u00b7(x \u2013 2) + 11 \u2013 4x \u00a1 ................................. d) (y \u2013 8)\u00b7(3y + 2) = ............................................. e) x\u00b7(x + 6) = 02 \u2013 5x + 1 \u00a1.................................. e) (a + b)2 =........................................................... f) (a + 3)\u00b7(a + 3) = a2 + 6a + 9 \u00a1 ......................... f) n\u00b7(n + 2) \u2013 n2 + 1 = ........................................... 194 8. S\u0131n\u0131f","Tam Kare \u00d6zde\u015flikler \u0130ki Terimin Toplam\u0131n\u0131n Karesi \u00d6zde\u015fli\u011fi ^a + bh2 = a2 + 2ab + b2 \u0130ki terimin toplam\u0131n\u0131n karesi al\u0131n\u0131rken, birinci terimin karesi, birinci ile ikinci terimin \u00e7arp\u0131mlar\u0131n\u0131n iki kat\u0131 ve ikinci terimin karesi toplan\u0131r. \u00d6rnek: \u2022 ^x + 3h2 = x2 + 2\u00b73\u00b7x + 32 = x2 + 6x + 9 144462x4443 6 9 \u2022 ^3a + 4h2 = ^3ah2 + 2\u00b73a\u00b74 + 42 = 9a2 + 24a + 16 14492a4243 14442424a44443 6 16 44 2. A\u015fa\u011f\u0131da verilen tam kare ifadelerin \u00f6zde\u015fini bu- lunuz. 1. A\u015fa\u011f\u0131da verilen ifadelerin \u00f6zde\u015fini bulunuz. a) (c + 1)2 = ........................................................... a) (x + 5)\u00b7(x + 5) =................................................ b) (a + 2b)\u00b7(a + 2b) = ........................................... b) (2x + y)2 =......................................................... c) (m + 7)\u00b7(m + 7) = ............................................. c) (8 + m)2 =.......................................................... \u00e7) (2x + 3y)\u00b7(2x + 3y) = ........................................ \u00e7) (4x + 2y)2 = ....................................................... d) (4a + 2b)\u00b7(4a + 2b) = ....................................... d) (2x + yz)2 = ....................................................... e) (2m + 5n)\u00b7(2m + 5n) = ..................................... e) (10 + xy)2 = ....................................................... 8. S\u0131n\u0131f 195","\u0130ki Terimin Toplam\u0131n\u0131n Karesi \u00d6zde\u015fli\u011finin Modellenmesi a b Yandaki \u015fekilde boyal\u0131 b\u00f6lgenin alan\u0131 a a2 a.b a ^a + bh2 = a2 + 2ab + b2 b a.b b2 b a b 45 \u00e7) n 4m n 1. A\u015fa\u011f\u0131da verilen boyal\u0131 b\u00f6lgelerin alan\u0131n\u0131 g\u00f6ste- ren \u00f6zde\u015flikleri yaz\u0131n\u0131z. 4m a) x y x y d) 5a 6b 5a b) 2a b 2a b 6b e) 7y 2x 2x c) 3x 2y 2y 3x 7y 196 8. S\u0131n\u0131f","\u0130ki Terimin Fark\u0131n\u0131n Karesinin \u00d6zde\u015fli\u011fi ^a - bh2 = a2 - 2ab + b2 \u0130ki terimin fark\u0131n\u0131n karesi al\u0131n\u0131rken, birinci terimin karesi, birinci ile ikinci terimin \u00e7arp\u0131mlar\u0131n\u0131n eksi iki kat\u0131 ve ikinci terimin karesi toplan\u0131r. \u00d6rnek: \u2022 ^x - 4h2 = x2 - 2\u00b74\u00b7x + 42 = x2 - 8x + 16 14444-28x44443 6 16 \u2022 ^3a - 5h2 = ^3ah2 - 2\u00b73a\u00b75 + 52 = 9a2 - 30a + 25 14492a4243 144-443204a4443 6 25 46 2. A\u015fa\u011f\u0131da verilen tam kare ifadelerin \u00f6zde\u015fini bu- lunuz. 1. A\u015fa\u011f\u0131da verilen ifadelerin \u00f6zde\u015fini bulunuz. a) (a \u2013 1)2 = ........................................................... a) (x \u2013 3)\u00b7(x \u2013 3) =................................................ b) (a \u2013 5b)\u00b7(a \u2013 5b) = ........................................... b) (x \u2013 2y)2 =......................................................... c) (2m \u2013 4n)\u00b7(2m \u2013 4n) = ..................................... c) (5 \u2013 c)2 =........................................................... \u00e7) (6 \u2013 x)\u00b7(6 \u2013 x) =................................................ \u00e7) (3x \u2013 4y)2 = ....................................................... d) (7x \u2013 10y)\u00b7(7x \u2013 10y) =..................................... d) (2a \u2013 6ab)2 = .................................................... e) (mn \u2013 3n)\u00b7(mn \u2013 3n) = ..................................... e) (12 \u2013 xy)2 = ....................................................... 8. S\u0131n\u0131f 197","\u0130ki Terimin Fark\u0131n\u0131n Karesi \u00d6zde\u015fli\u011finin Modellenmesi a-b b Yandaki \u015fekilde boyal\u0131 b\u00f6lgenin alan\u0131 ^a - bh2 = a2 - 2ab + b2 a-b (a-b).(a-b) b.(a-b) a-b a b b.(a-b) b.b b a-b b a 47 \u00e7) 1. A\u015fa\u011f\u0131da verilen boyal\u0131 b\u00f6lgelerin alan\u0131n\u0131 g\u00f6ste- 3n 4m ren \u00f6zde\u015flikleri yaz\u0131n\u0131z. 3n 10x a) y 7n 4m x y d) 6y x b) b b 3a 3a 2y 6y c) 2y 10x 5x e) 7n 9m 9m 5x 198 8. S\u0131n\u0131f","\u0130ki Kare Fark\u0131 \u00d6zde\u015fli\u011fi ^a - bh\u00b7^a + bh = a2 - b2 \u0130ki terimin fark\u0131 ile toplam\u0131n\u0131n \u00e7arp\u0131m\u0131 bu terimlerin karelerinin fark\u0131na e\u015fittir. \u00d6rnek: \u2022 (x + 5)\u00b7(x \u2013 5) = x\u00b7x \u2013 5\u00b75 = x2 \u2013 25 \u2022 (a + 2b)\u00b7(a \u2013 2b) = a\u00b7a \u2013 2b\u00b72b = a2 \u2013 4b2 48 2. A\u015fa\u011f\u0131da verilen tam kare ifadelerin \u00f6zde\u015fini bu- lunuz. 1. A\u015fa\u011f\u0131da verilen ifadelerin \u00f6zde\u015fini bulunuz. a) x2 \u2013 9 = ............................................................. a) (x + y)\u00b7(x \u2013 y) = ................................................ b) (a + 3)\u00b7(a \u2013 3) = ............................................... b) 4a2 \u2013 1 = ........................................................... c) (6 + m)\u00b7(6 \u2013 m) = ............................................. c) 25 \u2013 x2 = ........................................................... \u00e7) (2x + 3y)\u00b7(2x \u2013 3y) = ........................................ \u00e7) 9a2 \u2013 25b2 =...................................................... d) (7a + 8b)\u00b7(7a \u2013 8b) = ....................................... d) 100x2 \u2013 81y2 =................................................... e) (ab + 2c)\u00b7(ab \u2013 2c) =........................................ e) 16a2b2 \u2013 49c2 =................................................. f) cx + 1 m\u00b7cx - 1 m = ......................................... f) 36x2 - 64 = ..................................................... 10 10 121 8. S\u0131n\u0131f 199"]