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Öğretmen, tabanlar aynıysa üstlerin eşit olması, tabanları farklı olan üslü sayıların düzenlenmesi, ikili üslü denklemler, tek ve çift üslü denklemler, tabanın 1'den büyük veya küçük olduğu durumlarda üslerin değişimi ve üslü sayıların sıralanması gibi konuları örneklerle açıklamaktadır.","Videoda 21'den 28'e kadar olan sorular çözülmekte ve her bir çözümün adım adım gösterilmektedir. Ayrıca, üslü sayıların gerçel gösterimleri konusu da işlenmekte ve bir sonraki derste köklü sayıların gerçel gösterimleri konusunun işleneceği duyurulmaktadır. Öğretmen, temel matematik eksikliklerini gidermek ve öğrencilerin üniversite sınavlarına hazırlanmalarına yardımcı olmayı amaçlamaktadır."]},"endTime":2635,"title":"Matematik Dersi: Üslü Sayılar ve Denklemler","beginTime":0}],"fullResult":[{"index":0,"title":"Üslü Sayılar Konusuna Giriş","list":{"type":"unordered","items":["Z takımı okula destek kamplarından matematiğe hoş geldiniz mesajı ile ders başlıyor.","İlk temanın içerisindeki ilk konu gerçel sayıların üstü gösterimleri olarak belirtiliyor.","Üslü sayıların defterini dürecek iki ders anlatımı yapılacak ve en temelden en tepeye çıkarılacak."]},"beginTime":0,"endTime":27,"href":"/video/preview/14247680051624425705?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=0&ask_summarization=1"},{"index":1,"title":"Temel Matematik Eksiklikleri İçin Öneriler","list":{"type":"unordered","items":["İlköğretimden gelen matematik eksiklikleri (toplama, çıkarma, denklem kurma) olanlar için on günde temel atmak garanti kampı öneriliyor.","Kitabın içerisindeki konular tamamen dokuzuncu sınıf konuları olup, temel oluşturulduktan sonra daha iyi anlaşılabilecek.","Bu derste üstü denklemler ve üsteliklere bakılacak, konular genişletilecek çünkü üniversite sınavında da karşınıza gelecek."]},"beginTime":27,"endTime":84,"href":"/video/preview/14247680051624425705?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=27&ask_summarization=1"},{"index":2,"title":"Üstü Denklemlerin İlk Durumu","list":{"type":"unordered","items":["Üstü denklemlerin ilk durumu, tabanlar aynıysa üstlerin birbirine eşit olması gerektiği.","İlk sayı sıfırdan farklı, eksi birden farklı ve birden farklı olmak üzere, çünkü birim bütün kuvvetleri bir olduğu için bu özelliği sağlamaz.","Tabanlar aynıysa eşit olabilmeleri için üstler de birbirlerine eşit 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çarpılır."]},"beginTime":444,"endTime":730,"href":"/video/preview/14247680051624425705?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=444&ask_summarization=1"},{"index":6,"title":"İkili Üslü Sayı Denklemleri","list":{"type":"unordered","items":["İkili üslü sayı denklemlerinde aynı tabanlı olanlar alt alta getirilir.","Aynı tabanlı üslü sayı denklemlerinde üstlerin oranı, denklemin diğer tarafındaki üstlerin oranına eşittir.","İkili üslü sayı denklemlerinde, bir denklemdeki bilgi diğer denklemde yerine konularak çözüm yapılır."]},"beginTime":730,"endTime":967,"href":"/video/preview/14247680051624425705?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=730&ask_summarization=1"},{"index":7,"title":"Üslü Denklemlerde Tabanların Eşitliği","list":{"type":"unordered","items":["Üslü denklemlerde üstler aynı ve tabanlar farklı olduğunda, üstler eşitse tabanlar da eşit 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Denklemlerde Özel Durumlar","list":{"type":"unordered","items":["Üslü denklemlerde üstler çift sayı ise, tabanlar ya birbirine eşit olabilir ya da birbirine eksi işaretli olabilir.","Üslü denklemlerde üstler tek sayı ise, tabanlar direkt birbirine eşit olmalıdır.","Üslü denklemlerde tabanlar farklıysa ve üstler tam sayı ise, üstlerin sıfır olması gerekir."]},"beginTime":1447,"endTime":1614,"href":"/video/preview/14247680051624425705?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1447&ask_summarization=1"},{"index":10,"title":"Bir Sayının Kuvvetinin Bir Olması Durumu","list":{"type":"unordered","items":["Bir sayının sıfırıncı kuvveti birdir, ancak taban sıfıra eşit olmamalıdır çünkü sıfır üzeri sıfır belirsizliği vardır.","Bir sayının birinci kuvveti bir olabilmesi için taban bir olmalıdır çünkü birin bütün kuvvetleri birdir.","Bir sayının n'inci kuvveti bir olabilmesi için taban eksi bir olmalı ve n çift bir sayı olmalıdır."]},"beginTime":1616,"endTime":1728,"href":"/video/preview/14247680051624425705?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1616&ask_summarization=1"},{"index":11,"title":"Örnek Sorular","list":{"type":"unordered","items":["27. soruda 8x+2'nin yedinci kuvveti bir olduğunda, tabanın bir olması gerektiği için 8x+2=1 denklemi çözülür ve x=-1/8 bulunur.","28. soruda (x-2)^(x²-6x)=1 olduğunda, tabanın bir olması için x-2=1 denklemi çözülür ve x=3 bulunur.","Üstün sıfır olması için x²-6x=0 denklemi çözülür ve x=0 veya x=6 bulunur, ancak x-2≠0 koşulu gereği x=0 hariç tutulur.","Tabanın eksi bir olması ve üstün çift olması için x=-1+2=1 bulunur, ancak üst çift olmadığı için bu çözüm geçersizdir."]},"beginTime":1728,"endTime":1944,"href":"/video/preview/14247680051624425705?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1728&ask_summarization=1"},{"index":12,"title":"Üslü Sayıların Karşılaştırılması","list":{"type":"unordered","items":["İki'nin kuvvetleri (2², 2³, 2⁴) büyüdükçe sonuçları da büyür.","Bir bölü iki'nin kuvvetleri (1/2², 1/2³, 1/2⁴) büyüdükçe sonuçları küçülür.","Tabanın değeri, üslü sayıların karşılaştırılmasında önemli bir faktördür."]},"beginTime":1949,"endTime":2016,"href":"/video/preview/14247680051624425705?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1949&ask_summarization=1"},{"index":13,"title":"Tabanların Bileşik ve Basit Kesir Olması","list":{"type":"unordered","items":["Taban bileşik kesir (1'den büyük) ise, a üzeri x > a üzeri y olduğunda x > y olur.","Taban basit kesir (0,1 aralığında) ise, a üzeri x > a üzeri y 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Sınıf Din Kültürel Bilgisi: Bilgi ve İnanç Ünitesi","beginTime":0}],"fullResult":[{"index":0,"title":"Dersin İçeriği","list":{"type":"unordered","items":["Ders, İslam'da bilginin kaynakları, İslam inancında imanın mahiyeti ve Kur'an'dan mesajlar (İsra Suresi 36 ve Mülk Suresi 23 ayetleri) konularını içerecek.","Ders kapsamında 6 test ve 5 klasik soru çözülecek, ayrıca kanalda soru çözüm ve yazılı videosu da bulunabilir."]},"beginTime":3,"endTime":51,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=3&ask_summarization=1"},{"index":1,"title":"İslam'da Bilgi ve İnsan İhtiyacı","list":{"type":"unordered","items":["İslam'a göre insan doğuştan bilme ve öğrenme özellikleri (fıtrat) ile gelmiştir.","İnsan, diğer varlıklardan ayıran okuma, düşünme, anlama, yazma, uygulama ve paylaşma gibi özelliklerle bilgi edinir.","İnsanın en önemli özelliği iradedir, irade eşittir seçebilme özgürlüğü."]},"beginTime":51,"endTime":97,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=51&ask_summarization=1"},{"index":2,"title":"Bilginin Kaynakları","list":{"type":"unordered","items":["İslam'a göre bilginin gerçek kaynağı Allah'tır ve bu vahiydir.","Allah her şeyi bilendir ve insana bilmediklerini öğretendir, bu sıfatına \"el- alim\" denir.","Bilgi, İslam alimleri tarafından ilim ve marifet kavramlarıyla ifade edilir; ilim bir şeyi bilmektir, marifet ise derin bilgi ve anlayışa ulaşmaktır."]},"beginTime":97,"endTime":198,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=97&ask_summarization=1"},{"index":3,"title":"İslam Alimlerine Göre Bilgi Kaynakları","list":{"type":"unordered","items":["İslam alimlerine göre üç çeşit bilgi kaynağı vardır: doğru haber, selim akıl ve salim duyular.","Selim akıl, insanı sorumlu kılan düşünme ve anlama yeteneksidir, sebep-sonuç ilişkisi içerisinde mevcut verilerden hareketle muhakeme eder.","Selim akıl, doğru karar vermesini sağlayan, olumsuzluktan etkilenmeyen, yaratılıştaki temizliği ve saflığını koruyan akıldır."]},"beginTime":198,"endTime":445,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=198&ask_summarization=1"},{"index":4,"title":"Sadık Haber","list":{"type":"unordered","items":["Sadık haber, bilgi edinme yollarından biridir ve İslam'a göre vahiy ve peygamberlerden gelen haberlerin tamamını kapsar.","Sadık haber iki kısma ayrılır: mütevatir haber ve peygamberlerden gelen haber.","Mütevatir haber, yalan söylemesi mümkün olmayan bir topluluğun ilettiği haberdir, Kur'an-ı Kerim bize mütevatir bir şekilde gelmiştir."]},"beginTime":445,"endTime":556,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=445&ask_summarization=1"},{"index":5,"title":"Vahiy Kavramı","list":{"type":"unordered","items":["Vahiy, akıl ve duyularımızı bilemeyeceğimiz konularda (cennet, cehennem, ölümden sonraki hayat) bilgi sahibi olmamızı sağlar.","Vahiyde inanç esasları, ibadetler, ahlak, sosyal ilişkiler ve ahiret hayatı hakkında bilgiler verilir.","Akıl ve duyularla elde edilemeyen hususlarda insanı rehberlik eder."]},"beginTime":556,"endTime":604,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=556&ask_summarization=1"},{"index":6,"title":"İslam'da Bilgi Kaynakları","list":{"type":"unordered","items":["İslam dinine göre bilgi edinme yollarından biri salim duyu organlarıdır; işitme, görme, koku alma, tatma ve dokunma gibi beş duyu organı ile edinilen bilgilerdir.","İslam'a göre bilginin güç kaynağı olan selim akıl, doğru haber ve salim duyular nesnel bilgi kaynağıdır ve bu üç kaynak birlikte işletilerek bilgiye ulaşılması gerekir.","Bu üç kaynağın dışında sezgi, rüya, keşif ve ilham gibi nesnel olmayan, herkes için bağlayıcı olmayan bilgi kaynakları da vardır."]},"beginTime":606,"endTime":722,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=606&ask_summarization=1"},{"index":7,"title":"Rüya, Keşif ve İlahi Bilgi","list":{"type":"unordered","items":["Rüya, uyku sırasında zihinde belirlenen görüntülerdir ve Kur'an-ı Kerim'de Yusuf kıssasında geçen rüyalar örnek olarak gösterilmiştir.","İlahi bilgi kaynakları olarak ilham (gönle doğan şey) ve keşif (aklın üstünde olduğu için gayp olan bazı şeyleri bilmektir) kabul edilir fakat bağlayıcılıkları yoktur.","Keşif özellikle tasavvufta kullanılır ve doğru olabildiği gibi yanlış yerde kişiyi yöneltebileceği için tehlikeli bir bilgi kaynağıdır."]},"beginTime":722,"endTime":769,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=722&ask_summarization=1"},{"index":8,"title":"Bilgi ve İslam","list":{"type":"unordered","items":["Peygamberimiz \"öğreten, öğrenen, dinleyen ya da seven ol. Beşincisi olma, helak olursun\" hadisinde bilgiyle iç dışlı olunmaması gerektiğini vurgulamıştır.","Doğru bilgi, içinde şüphe barındırmayan, kesin ve güven duyulan bilgidir; doğru karar alabilmek ve doğru davranışları sergileyebilmek için gereklidir.","İslam, bilgi kaynağının güvenilir olması konusunda özel bir önem verir ve aldığımız haberlerin doğruluğunu araştırmamızı isteyen Kur'an ayetleri vardır."]},"beginTime":769,"endTime":888,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=769&ask_summarization=1"},{"index":9,"title":"Bilginin Ahlakı ve Faydalı Bilgi","list":{"type":"unordered","items":["Faydalı bilgi hem kişinin kendisine hem de başkalarına yararlı olacaktır.","Resulullah \"faydası faydasız bilgiden Allah'a sığınırım\" demiştir; insan önce kendisine sonra da şahsiyetini geliştirecek yönünde bilgiler edinmelidir.","İslam inancında imanın mahiyetiyle ilgili olarak inanç ve iman kavramları birbirinden farklıdır; inanç daha genel bir kavramken, iman özellikle bir dine inanmak anlamındadır."]},"beginTime":888,"endTime":978,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=888&ask_summarization=1"},{"index":10,"title":"İman ve İnanç Sistemleri","list":{"type":"unordered","items":["İslam akaidi, İslam dininin iman esaslarını konu alan bir ilim dalıdır ve imanın temelinde koşulsuz şartsız Allah'a inanmak vardır.","İman kelime olarak güven duygusu içinde tasdik etmek, tereddüt etmeden gönül huzuruna bağlanmak anlamına gelir; inanan kişiye mümin, inkar edene kafir denir.","İman dini bir terim olarak kişinin Allah'ın varlığını, birliğini, sıfatlarını, peygamberlerini, ahiret gününü ve bunlardan başka iman edilmesi gereken şeyleri kalp ile tasdik etmek ve dil ile ikrar etmektir."]},"beginTime":978,"endTime":1074,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=978&ask_summarization=1"},{"index":11,"title":"Kalp ve Dil İmanı","list":{"type":"unordered","items":["İman esası kalp ile tasdik etmek (onaylamak) ve dil ile ikrar etmektir; kalbin inanması kişiye en temel şartlardan biridir.","Kalpten inanmayan fakat çıkarları için diliyle mümin olduğunu söyleyen kişiye münafık denir ve bu kişiler kafirden daha tehlikelidir.","İman-bilgi ilişkisinde, mümin olmanın ilk ifadesi olan kelime-i şehadet söylerken kişi bildiğini yani Allah'ın varlığına, peygamberin onun kulu olduğuna şahitlik eder."]},"beginTime":1074,"endTime":1166,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1074&ask_summarization=1"},{"index":12,"title":"İman ve Amel İlişkisi","list":{"type":"unordered","items":["İman etmekten sonra amel (uygulama) gelir, amel iradeye dayanan her türlü iş ve davranıştır.","İman ile amel arasında sıkı bir ilişki vardır çünkü insan inandığı gibi yaşar, inanmadığı şekilde yaşamaz.","Dini vecibeleri bilerek yerine getirmeyen bir mümin günah işlemiş olur (fasık olur) ancak inkar etmediği sürece dinden çıkmaz."]},"beginTime":1181,"endTime":1233,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1181&ask_summarization=1"},{"index":13,"title":"Taklidi ve Tahkiki İman","list":{"type":"unordered","items":["İman ikiye ayrılır: taklidi iman ve tahkiki iman.","Taklidi iman, araştırmadan, delillere dayanmadan çevrenin yönlendirmesiyle oluşan imandır.","Tahkiki iman ise delillere, bilgi, araştırma ve kavrama dayalı imandır.","Taklidi iman geçerli olsa da zayıftır ve küçük engeller karşısında şüpheye düşürebilir.","Tahkiki imana ulaşan kişi evreni ve yaratılışı incelediği için dini hükümleri hakkında bilgi sahibi olur ve Allah'ın diğer varlıklarla ilişkisini sağlam temeller üzerine şekillendirir."]},"beginTime":1233,"endTime":1361,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1233&ask_summarization=1"},{"index":14,"title":"Kur'an'dan Mesajlar","list":{"type":"unordered","items":["İsrâ Suresi 36. ayette \"Hakkında kesin bilgi sahibi olmadığın şeyin peşine düşme\" denilmiştir.","Bu ayette kulak, göz ve kalbin sorumluluğu vurgulanmıştır.","Mülk Suresi 23. ayette insanı yaratan ve sayısız nimet veren Allah'a karşı nankörlük yapılmaması istenmiştir."]},"beginTime":1361,"endTime":1430,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1361&ask_summarization=1"},{"index":15,"title":"Bilgi Kaynakları ve İman","list":{"type":"unordered","items":["İslami bilginin temel kaynağı vahiydir.","İslam alimleri bilgi kaynaklarını akıl, salim duyular ve sadık haber olarak üç'e ayırır.","Rüya, ilham ve keşif gibi kişiye özel, nesnel olmayan bilgi kaynakları da vardır.","Bilgi iman için tek başına yeterli değildir, koşulsuz, önyargısız bir şekilde inanmak gerekir.","Bilgi hem kişiye hem topluma yararlı olmalıdır."]},"beginTime":1430,"endTime":1488,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1430&ask_summarization=1"},{"index":16,"title":"Test Soruları","list":{"type":"unordered","items":["İslam'a göre bağlayıcılığı olmayan bilgi kaynağı rüyadır.","İslam bağnazlığı ve taassubu önermez, akletmeyi (düşünmeyi) önerir.","İslam vahyin rehberliğine teslim olmayı, bilgiyi över ve bilgili olmayı tavsiye eder.","Hücurat Suresi 6. ayette temel mesaj, yanlışı düşünmek için haber verenlerin doğruluğunu araştırmamız gerektiğidir.","Rüyalar doğru bilgi için vazgeçilmez kaynaklar değildir çünkü öznel kaynaklardır.","İman kelime olarak güven duygusu içinde tasdik etmek, tereddüt ve şüphe etmeden gönül huzuruyla bağlamak anlamına gelir, zıttı inkardır."]},"beginTime":1488,"endTime":1730,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1488&ask_summarization=1"},{"index":17,"title":"Bilgi Kaynakları Hakkında Soru","list":{"type":"unordered","items":["Verilen cümlelerde tanıtılan bilgi kaynağı sorusu ele alınıyor.","Doğru bilginin kaynağı vahiy olarak belirtiliyor.","Yüce Allah'ın varlığını, birliğini ve peygamberin gönderiliş amaçlarını vahiy verdiğini vurguluyor."]},"beginTime":1731,"endTime":1780,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1731&ask_summarization=1"},{"index":18,"title":"Kanal Bilgileri","list":{"type":"unordered","items":["9. sınıf dini dersi bir ünite konusu olan bilgi inancı konusu uzun uzun işlenmiş.","Çözümlü video ve yazılı hazırlık videosunda bu konuyla ilgili soru çözümleri bulunabilir.","Web adresi \"www.ozakadem.net\" olarak belirtiliyor ve en yakın zamanda PDF içeriklerin yüklenmesi planlanıyor."]},"beginTime":1780,"endTime":1833,"href":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1780&ask_summarization=1"}],"linkTemplate":"/video/preview/5329794757802269669?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Religious Culture and Moral Knowledge 9th Grade Unit 1 Knowledge and 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Sınıf Matematik MEB 1. Dönem 1. Yazılı ... 9TH Grade MEB Mathematics BOOK Pages 76-77-78-79 -81-84 Applications and IT'S YOUR TURN // 9TH Grade 9T...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4009793/c9a2ff85bb011cbe4b969a1e1cae7e97/564x318_1"},"target":"_self","position":"13","reqid":"1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=videoid:7806022286531793815","teaser":[{"list":{"type":"unordered","items":["Bu video, bir öğretmen/eğitmen tarafından sunulan 9. sınıf matematik dersinde eşlik ve benzerlik konusundaki problemlerin çözüldüğü eğitim içeriğidir. Eğitmen, tahtada çizimler yaparak ve adım adım açıklamalar vererek problemleri çözmektedir.","Videoda toplam dört farklı matematik problemi çözülmektedir. İlk problem fotoğraf makinesinin en eski formu olan iğne deliği ve kamera obscura ile ilgili, ikinci problem şehir planlayıcısı Hatice Hanım'ın park tasarımları, üçüncü problem tahta velilerin metal desteği ve tahterevelli yüksekliği, son problem ise Necati'nin iki farklı lambanın gölge problemi üzerinden çözülmektedir.","Her problem için eğitmen, temel orantı teoremi ve benzerlik kavramlarını kullanarak detaylı çözüm yöntemlerini göstermektedir. Özellikle Necati'nin gölge problemi üzerinden kağıt üzerinde çizim yaparak çözüm süreci adım adım anlatılmaktadır."]},"endTime":1873,"title":"9. Sınıf Matematik: Eşlik ve Benzerlik Problemleri Çözüm Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Eşlik ve Benzerlik Problemleri","list":{"type":"unordered","items":["Dokuzuncu sınıf matematik ders kitabında eşlik ve benzerlikle ilgili problemlere giriş yapılıyor.","Fotoğraf makinesinin en eski formu olarak kabul edilen iğne deliği ve kamera obscura düzenekinde, ışık geçirmez kutunun bir yüzeyine açılan delikten geçen ışık, nesnenin baş aşağı bir görüntüsünü oluşturur.","Görselde kelebek kuralı olarak adlandırılan iki benzer üçgen bulunur ve bu üçgenlerin açıları ve kenarları arasındaki ilişkiler incelenir."]},"beginTime":2,"endTime":76,"href":"/video/preview/7806022286531793815?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=2&ask_summarization=1"},{"index":1,"title":"Benzerlik Problemlerinin Çözümü","list":{"type":"unordered","items":["Nesne ve nesnenin karanlık kutudaki görüntüsünün oluşturduğu üçgenler benzerdir ve benzerlik ilişkisi OB=OB' ve AB=AB' şeklinde ifade edilir.","Karanlık kutuda oluşan görüntünün uzunluğunu bulmak için iki üçgenin oranlı iki kenarı ve kalemin uzunluğu bilinmelidir.","Nesnenin uzunluğu verildiğinde karanlık kutuda oluşan görüntünün uzunluğunu bulmak için oran-kenar oranı ile kalemin kutudaki görüntüsü arasındaki ilişki kullanılır."]},"beginTime":76,"endTime":237,"href":"/video/preview/7806022286531793815?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=76&ask_summarization=1"},{"index":2,"title":"Park Tasarımı Problemi","list":{"type":"unordered","items":["Şehir planlayıcısı Hatice Hanım, dikdörtgen ve daire şeklindeki alanlar için iki farklı park tasarımı oluşturmuştur.","Parklara çocuklar için oyun alanları eklenecek ve bu alanların boyut ve şekil bakımından aynı olması, parkın geometrik şekline ve yerleşimine uyumlu olması gerekmektedir.","Parkların taslak planlarında öteleme, yansıma ve dönme dönüşümleri kullanılmıştır."]},"beginTime":237,"endTime":471,"href":"/video/preview/7806022286531793815?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=237&ask_summarization=1"},{"index":3,"title":"Park Tasarımının Matematiksel İfadesi","list":{"type":"unordered","items":["Parkın içinde oluşturulacak oyun alanları için dairenin yarıçapı ve dikdörtgenin kenar uzunlukları bilinmelidir.","Oyun alanlarının şekli ve konumları matematiksel olarak ifade edilebilir.","Oyun alanlarının park düzenine uyumlu olması için altıgen ve daire şeklinde tasarlanabilir."]},"beginTime":471,"endTime":753,"href":"/video/preview/7806022286531793815?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=471&ask_summarization=1"},{"index":4,"title":"Örnek Problem Çözümü","list":{"type":"unordered","items":["Uzun kenar uzunluğu 600 m ve çevre uzunluğu 2 km olan dikdörtgen şeklinde bir parkın iki giriş kapısı bulunmaktadır.","Parka giriş kapılarına ve merkez noktalarına eşit uzaklıkta bulunan eş ve simetrik ikizkenar üçgen şeklinde iki havuz yapılacaktır.","Havuzların eşit uzun kenarlarının uzunlukları 125 metre, taban uzunluğu 200 metredir."]},"beginTime":753,"endTime":959,"href":"/video/preview/7806022286531793815?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=753&ask_summarization=1"},{"index":5,"title":"Havuz Problemi Çözümü","list":{"type":"unordered","items":["Havuzun tepe noktası güney girişine 195 metre uzaklıkta ve ikizkenar üçgenin yüksekliği 75 metre olarak hesaplanmıştır.","Havuzların taban kenarları bulundukları yöndeki kapıya 115 metre uzaklıkta konumlandırıldığında, üçgenlerin tepe noktalarının birbirine uzaklığı 220 metre olarak bulunmuştur."]},"beginTime":975,"endTime":1263,"href":"/video/preview/7806022286531793815?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=975&ask_summarization=1"},{"index":6,"title":"Tahtevelli Problemi Çözümü","list":{"type":"unordered","items":["Tahtevelli eşit kollu olmayan bir yapıda, A ucu yere değdiğinde B ucunun yerden yüksekliği 120 santimetre, B ucu yere değdiğinde A ucunun yerden yüksekliği 60 santimetre olarak ölçülmüştür.","Tahtevelli eşit kollu olacak şekilde tasarlanırsa, A ucunun yere inmesi durumunda B ucunun yerden yüksekliği 80 santimetre olarak hesaplanmıştır.","Tahta veli şekil birdeki konumda iken AK 30 santimetredir ve zemine paralel konumda dengede kalabilmesi için metal desteğin tahta parçasının B tarafına doğru 15 santimetre hareket ettirilmesi gerekir."]},"beginTime":1263,"endTime":1588,"href":"/video/preview/7806022286531793815?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1263&ask_summarization=1"},{"index":7,"title":"Lamba Direği Problemi Çözümü","list":{"type":"unordered","items":["Doğrusal bir yol üzerinde bulunan A ve B noktalarına yerleştirilmiş iki lamba direği arasında 2 metre boyunda olan Necati yer almaktadır.","A ve B noktaları arasındaki uzaklık 18 metredir, A ve B direklerindeki lambaların yerden yüksekliği sırasıyla 6 ve 10 metredir.","Lambalardan herhangi birinin oluşturduğu gölgenin boyu 3 metre olarak hesaplanmıştır."]},"beginTime":1588,"endTime":1750,"href":"/video/preview/7806022286531793815?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1588&ask_summarization=1"},{"index":8,"title":"Benzerlik Problemi Çözümü","list":{"type":"unordered","items":["Bir lambanın boyu altı metre, Necati'nin boyu iki metredir.","Soldaki lambanın boyu altı metre, sağdaki lambanın boyu on metredir.","Benzerlik kurularak x/x+y = 2/6 denklemi elde edilir ve sadeleştirilerek x+y = 3 bulunur."]},"beginTime":1763,"endTime":1838,"href":"/video/preview/7806022286531793815?parent-reqid=1765317984451626-1943877215341560284-balancer-l7leveler-kubr-yp-sas-87-BAL&text=MizzQ9thgrade&t=1763&ask_summarization=1"},{"index":9,"title":"Denklemin Çözümü","list":{"type":"unordered","items":["İçler dışlar çarpımı yapılarak y = 2x ilişkisi elde edilir.","Lambalar arasındaki mesafe 18 metre olduğundan 3x = 18 denklemi kurulur.","Denklem çözülerek x = 6 bulunur, yani Necati'nin gölgesinin uzunluğu 6 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