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Eğitmen, öğrencilere hitap ederek adım adım problemleri çözmektedir.","Videoda işçi havuz problemleri üzerine odaklanılmakta ve toplam 18 sorudan oluşan bir test çözülmektedir. Sorular, işçilerin bir işi tek başına veya birlikte ne kadar sürede tamamlayabilecekleri, havuzların doldurulma ve boşaltılma süreleri gibi konuları içermektedir. Her soru için doğru orantı ve birim zaman kavramları kullanılarak çözüm yöntemleri gösterilmektedir.","Eğitmen, her sorunun çözümünü detaylı olarak açıklamakta ve doğru cevabı belirtmektedir. Problemler genellikle muslukların havuzu doldurma veya boşaltma süreleri, iki kişinin birlikte işi tamamlama süreleri ve iş-hız ilişkisi gibi konuları içermektedir."]},"endTime":1083,"title":"İşçi Havuz Problemleri Test Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"İşçi Havuz Problemleri Testi Tanıtımı","list":{"type":"unordered","items":["Ders, işçi havuz problemlerinden bir test çözmeyi içermektedir.","Testin PDF formatında sitede bulunabilir ve online olarak çözülebilir.","Test sonrası başarı yüzdesi görülebilir ve yapamadığınız sorular dinlenebilir."]},"beginTime":16,"endTime":36,"href":"/video/preview/14947372440243472951?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=16&ask_summarization=1"},{"index":1,"title":"İlk Soru - Ümit'in İş Hızı","list":{"type":"unordered","items":["Ümit bir işin üçte birini sekiz saatte yapıyorsa, aynı işin yarısını kaç saatte yapar sorusu sorulmuştur.","Doğru orantı kurularak çözüm yapılmıştır.","Ümit'in işin yarısını altı saatte yapacağı bulunmuştur."]},"beginTime":36,"endTime":120,"href":"/video/preview/14947372440243472951?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=36&ask_summarization=1"},{"index":2,"title":"İkinci Soru - Osman'ın İş Hızı","list":{"type":"unordered","items":["Osman bir işin tamamını otuzaltı günde yapabiliyorsa, sekiz gün çalışırsa işin kaçta kaçı bitmiş olur sorusu sorulmuştur.","Doğru orantı kurularak çözüm yapılmıştır.","Osman'ın sekiz günde işin iki dokuzunu bitireceği bulunmuştur."]},"beginTime":120,"endTime":188,"href":"/video/preview/14947372440243472951?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=120&ask_summarization=1"},{"index":3,"title":"Üçüncü Soru - İlhan ve Murat'ın İş Hızı","list":{"type":"unordered","items":["İlhan tek başına yirmi günde, Murat tek başına otuz günde bir işi bitirebiliyorsa, aynı işi birlikte kaç günde yapabilirler sorusu sorulmuştur.","Birim zamanda yapacakları iş miktarları hesaplanmıştır.","İlhan ve Murat'ın birlikte işin on iki günde bitirebilecekleri 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bulunmuştur."]},"beginTime":265,"endTime":361,"href":"/video/preview/14947372440243472951?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=265&ask_summarization=1"},{"index":5,"title":"Beşinci Soru - Yasin ve Elif'in İş Hızı","list":{"type":"unordered","items":["Yasin işin yarısını beş günde, Elif işin çeyreğini beş günde bitirebiliyorsa, ikisi birlikte aynı işin tamamını kaç günde yaparlar sorusu sorulmuştur.","Birim zamanda yapacakları iş miktarları hesaplanmıştır.","Yasin ve Elif'in birlikte işin üçte bir günde bitirebilecekleri bulunmuştur."]},"beginTime":361,"endTime":447,"href":"/video/preview/14947372440243472951?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=361&ask_summarization=1"},{"index":6,"title":"Altıncı Soru - İki Musluktan Havuz Doldurma","list":{"type":"unordered","items":["Bir havuzu dolduran iki musluktan birincisi havuzu tek başına kırk saatte, ikincisi ise aynı havuzu tek başına elli saatte dolduruyor.","İkisi birlikte aynı havuzu kaç saatte doldurabilir sorusu sorulmuştur.","İki musluktan birlikte havuzu ikiyüz dokuz saatte doldurabilecekleri 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hesaplanmıştır."]},"beginTime":566,"endTime":650,"href":"/video/preview/14947372440243472951?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=566&ask_summarization=1"},{"index":9,"title":"İş Problemleri","list":{"type":"unordered","items":["Tarık bir işi tek başına e günde, İlayda aynı işi tek başına 2e günde yapabiliyor ve ikisi birlikte bu işi 4 günde yapabiliyorlarsa, e değeri 6 olarak bulunmuştur.","Tabloda boş bir havuzu dolduran iki musluğun ve dolu bir havuzu boşaltan iki musluğun tek başlarına havuzu doldurma ve boşaltma süreleri gösterilmiştir.","Dolduran musluklar havuz boşken aynı anda açılırsa, havuz 10 saatte 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Eğitmen, zorlu bir zil sorusunu adım adım çözmektedir.","Videoda, dört, altı ve sekiz dakikalık aralıklarla çalan üç zilin dördüncü kez birlikte çaldıkları zamana kadar toplam kaç zil sesi duyulacağı sorusu ele alınmaktadır. Eğitmen önce normal çözüm yöntemini göstererek zillerin birlikte çaldıkları zamanları hesaplamakta, ardından sorunun püf noktasını vurgulayarak kümeler konusunu kullanarak çözümü detaylı şekilde açıklamaktadır. Sonuç olarak, sorunun doğru cevabının 32 olduğu gösterilmektedir."]},"endTime":433,"title":"Zil Sorusu ve Kümeler Konusu Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Zil Sorusunun Tanıtımı","list":{"type":"unordered","items":["Dört, altı ve sekiz dakikalık aralıklarla çalan üç saat aynı anda kuruluyor.","Ziller dördüncü kez birlikte çaldıkları zamana kadar toplam kaç zil sesi duyulur soruluyor.","Ziller birlikte çaldıklarında tek ses duyulmaktadır, bu durum sorunun püf noktasıdır."]},"beginTime":0,"endTime":51,"href":"/video/preview/5319802545258327516?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=0&ask_summarization=1"},{"index":1,"title":"Zillerin Birlikte Çalma Zamanları","list":{"type":"unordered","items":["Dört, altı ve sekiz'in OKEK'i yirmidört olduğundan, üç zil ilk defa yirmidört dakika sonra birlikte çalıyor.","Dördüncü kez birlikte çaldıkları zamana kadar toplam doksanaltı dakika geçiyor.","Dört dakikada bir çalan zil, altı dakikada bir çalan zil ve sekiz dakikalık zil farklı zamanlarda çalıyor."]},"beginTime":51,"endTime":143,"href":"/video/preview/5319802545258327516?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=51&ask_summarization=1"},{"index":2,"title":"Kümeler Probleminin Çözümü","list":{"type":"unordered","items":["Sorunun çözümü kümeler problemine dönüştürülüyor.","Dört dakikada bir çalan zil A kümesi, altı dakikada bir çalan zil B kümesi, sekiz dakikalık zil C kümesi olarak düşünülüyor.","Toplam zil sesi sayısı, A birleşim B birleşim C kümesinin eleman sayısı olarak hesaplanıyor."]},"beginTime":143,"endTime":220,"href":"/video/preview/5319802545258327516?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=143&ask_summarization=1"},{"index":3,"title":"Kümelerin Eleman Sayılarının Hesaplanması","list":{"type":"unordered","items":["A kümesinin eleman sayısı: 96/4 = 24","B kümesinin eleman sayısı: 96/6 = 16","C kümesinin eleman sayısı: 96/8 = 12"]},"beginTime":220,"endTime":265,"href":"/video/preview/5319802545258327516?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=220&ask_summarization=1"},{"index":4,"title":"Kesişim Kümelerinin Eleman Sayıları","list":{"type":"unordered","items":["A kesişim B'nin eleman sayısı: 96/12 = 8","A kesişim C'nin eleman sayısı: 96/8 = 12","B kesişim C'nin eleman sayısı: 96/24 = 4"]},"beginTime":265,"endTime":416,"href":"/video/preview/5319802545258327516?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=265&ask_summarization=1"},{"index":5,"title":"Sonuç Hesaplama","list":{"type":"unordered","items":["A kesişim B kesişim C'nin eleman sayısı 4 olduğundan, bu değer matematiksel işlemden çıkarılıyor.","Toplam zil sesi sayısı: 24 + 16 + 12 - 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Eğitmen, öğrencilere hitap ederek çeşitli matematik sorularını adım adım çözmektedir.","Videoda temel matematik işlemlerini içeren bir testin çözümü sunulmaktadır. İçerikte işlem önceliği, kesirlerin sadeleştirilmesi, denklem çözme, denklem sistemleri, pozitif ve negatif tam sayılar, rakam problemleri gibi konular ele alınmaktadır. Eğitmen her soruyu detaylı olarak açıklamakta ve çözüm yöntemlerini göstermektedir.","Video, matematik temel becerilerini geliştirmek isteyenler için faydalı bir kaynak niteliğindedir. Eşitlikleri alt alta toplama, çapraz çarpım yapma ve değer atama gibi çözüm teknikleri de videoda gösterilmektedir."]},"endTime":1040,"title":"Temel Matematik Problemleri Çözüm Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Temel İşlem Yeteneği Soruları","list":{"type":"unordered","items":["İlk soruda 1-2, 3-4, 5-6 ve 7-1 işlemlerinin sonucu -1 olarak hesaplanıp, 7 ile toplandığında sonuç 4 bulunur.","İkinci soruda işlem önceliğine göre önce çarpma işlemi yapılır: (-3)×2=-6, (-1)×2=-2, toplam 9 olarak hesaplanır.","Üçüncü soruda önce parantez içindeki işlem yapılır: -5×(-4)=20, sonra çarpma işlemi: -5×20=-100, sonuç -15 olarak bulunur."]},"beginTime":6,"endTime":138,"href":"/video/preview/16933890286929396119?channelId=d3d3LnlvdXR1YmUuY29tO1VDNHlKUVMtdE5HdVVwbUpiQ1dHbzM5Zw%3D%3D&how=tm&parent-reqid=1751811120227539-14510308439976551205-balancer-l7leveler-kubr-yp-sas-123-BAL&text=NetSporTV+HD&t=6&ask_summarization=1"},{"index":1,"title":"İşlem Önceliği ve Sayı 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Eğitmen, kar-zarar problemlerini detaylı bir şekilde anlatmaktadır.","Videoda kar-zarar problemlerinin temel kavramları (maliyet, satış fiyatı, kar ve zarar) açıklanmakta ve toplam yedi farklı örnek problem çözülmektedir. Örnekler arasında yüzde kar hesaplamaları, indirim uygulamaları ve etiket fiyat üzerinden kar hesaplamaları bulunmaktadır. Ayrıca, bir tüccarın parasının farklı oranlarıyla mal satın alıp satışından elde ettiği kar-zarar oranları hesaplanmaktadır.","Her problem için adım adım çözüm yöntemi gösterilmekte ve matematiksel işlemler detaylı olarak açıklanmaktadır. Özellikle bir tüccarın 100 TL başlangıç parasıyla A malından %60 kar, B malından %50 zarar eden problemi farklı yöntemlerle çözülmekte ve her iki çözümde de tüccarın %6 zarar ettiği sonucuna varılmaktadır."]},"endTime":946,"title":"Kar-Zarar Problemleri Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Kar-Zarar Problemlerinde Temel Kavramlar","list":{"type":"unordered","items":["Kar-zarar problemlerini incelemek için maliyet ve satış fiyatı kavramlarını bilmek gerekir.","Maliyet, malın alış fiyatıdır.","Satış fiyatı, maliyet fiyatına kazanmak istenen kar miktarı eklenerek hesaplanır.","Mal maliyet fiyatının altında satıldığında zarar edilir ve satış fiyatı maliyet fiyatından zarar miktarı çıkarılarak 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Öğretmen önce A kümesinin eleman sayısı m, B kümesinin eleman sayısı n olduğunda A'dan B'ye tanımlanabilen fonksiyon sayısının n üzeri m olduğunu formülle açıklar, ardından bu formülü çeşitli örneklerle pekiştirir. Daha sonra örten fonksiyonlar ve sabit fonksiyonlar konusunu şema çizerek açıklar.","Öğretmen, formüllere çok takılmamak ve mantığı anlamak gerektiğini vurgular. Videoda A'dan B'ye ve B'den A'ya tanımlanabilen fonksiyon sayıları, fonksiyon olmayan bağıntıların sayısı, birebir fonksiyonların sayısı ve birebir örten fonksiyonların sayısı gibi konular ele alınmaktadır. Ayrıca A kümesinin eleman sayısı m, B kümesinin eleman sayısı n olduğunda A'dan B'ye tanımlanabilen sabit fonksiyon sayısının her zaman n olduğunu ve bunun A kümesinin eleman sayısına eşit olduğunu belirtmektedir."]},"endTime":788,"title":"Fonksiyon Sayıları Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Fonksiyon Sayıları","list":{"type":"unordered","items":["Bu ders, fonksiyonlar konusunun üçüncü dersi olup, fonksiyon sayılarına ilişkin kısa bir ders içermektedir.","A kümesinin eleman sayısı m, B kümesinin eleman sayısı n ise, A'dan B'ye tanımlanabilen fonksiyon sayısı n üzeri m'dir.","Fonksiyon olma şartı, tanım kümesinde açıkta eleman kalmaması ve her elemanın değer kümesinde yalnız bir görüntüsü 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