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Özellikle TYT sınavlarında çıkabilecek yorumsal sorular için temel bilgilerin önemi vurgulanmaktadır."]},"endTime":789,"title":"Matematik Dersi: Eşitsizlikler ve Çözüm Kümeleri","beginTime":0}],"fullResult":[{"index":0,"title":"Dersin Tanıtımı","list":{"type":"unordered","items":["Yeni bir günün başlangıcı ve yeni bir dersin başlangıcı olarak bu video çekiliyor.","Altıncı adımda basitlik, yedinci adımda mutlak değer konuları ele alınacak.","Temel konuları anlamak TYT'de mutlak değer sorularını daha rahat çözmeyi sağlayabilir."]},"beginTime":5,"endTime":76,"href":"/video/preview/3032508966229972852?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=5&ask_summarization=1"},{"index":1,"title":"Eşitsizlik Tanımı","list":{"type":"unordered","items":["Eşitsizlik, x > 4 gibi bir ifadeyi gösterir ve geniş olan taraf büyük, dar olan taraf küçük anlamına gelir.","Eşitsizlik iki türlü okunabilir: x > 4 veya 4 \u003c x, ikisi de doğru olur.","Eşitsizlikte tam sayı kelimesi zorunlu değildir, x > 4 ise x 4'ten büyük her değeri alabilir."]},"beginTime":76,"endTime":189,"href":"/video/preview/3032508966229972852?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=76&ask_summarization=1"},{"index":2,"title":"Çözüm Kümesi ve Aralıklar","list":{"type":"unordered","items":["Çözüm kümesi, eşitsizliğin çözümlerini gösteren bir kümedir ve ÇK ile gösterilir.","Açık aralık (4,∞) şeklinde yazılır, bu durumda sayı 4 değerini almaz ama 4'ten büyük her değer alır.","Kapalı aralık [4,∞) şeklinde yazılır, bu durumda sayı 4 değerini alır."]},"beginTime":189,"endTime":354,"href":"/video/preview/3032508966229972852?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=189&ask_summarization=1"},{"index":3,"title":"Eşitsizlik İşaretleri ve Çözüm Kümesi","list":{"type":"unordered","items":["Eşitsizlikte hangi sayı varsa, çözüm kümesinde mutlaka bu sayı bulunmalıdır.","Eşitlik varsa kapalı aralık, eşitlik yoksa açık aralık kullanılır.","Eksi sonsuz daima açık aralık olarak gösterilir."]},"beginTime":354,"endTime":412,"href":"/video/preview/3032508966229972852?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=354&ask_summarization=1"},{"index":4,"title":"Sayı Doğrusu ve Aralıklar","list":{"type":"unordered","items":["Sayı doğrusunda taralı bölgeler, belirli aralıkları ifade eder; yuvarlak nokta açık aralık, koyu nokta ise kapalı aralık gösterir.","Açık aralıkta nokta yuvarlak olduğunda, o nokta dahil edilmez; kapalı aralıkta ise nokta koyu olduğunda, o nokta dahil edilir.","Sayı doğrusunda sonsuzluk, artı sonsuz veya eksi sonsuz olarak gösterilir ve bu değerler yazmaya gerek yoktur."]},"beginTime":417,"endTime":464,"href":"/video/preview/3032508966229972852?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=417&ask_summarization=1"},{"index":5,"title":"Aralıkların Yazımı","list":{"type":"unordered","items":["Sayı doğrusunda gösterilen aralıklar, açık veya kapalı nokta durumuna göre yazılır; örneğin 3'ten büyük sayılar (3,∞) şeklinde yazılır.","Eksi sonsuz ile -2 arasında kapalı aralık (-∞,-2] şeklinde gösterilir.","Eksi 3 ile 5 arasında kapalı aralık (-3,5] şeklinde yazılır."]},"beginTime":464,"endTime":562,"href":"/video/preview/3032508966229972852?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=464&ask_summarization=1"},{"index":6,"title":"Karmaşık Aralıklar","list":{"type":"unordered","items":["2/3 ile 10/3 arasında kapalı aralık (2/3,10/3] şeklinde gösterilir.","4 ile 13 arasında açık aralık (4,13) şeklinde yazılır.","-∞ ile 7/2 arasında açık aralık (-∞,7/2) şeklinde gösterilir."]},"beginTime":562,"endTime":693,"href":"/video/preview/3032508966229972852?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=562&ask_summarization=1"},{"index":7,"title":"Aralıkların Gösterimi ve Kullanımı","list":{"type":"unordered","items":["Sayı doğrusunda aralıklar, eşitlik durumuna göre gösterilir; eşitlik varsa kapalı nokta, yoksa açık nokta kullanılır.","Eşitlik varsa içi doldurulmuş nokta, yoksa içi boş nokta kullanılır.","Örnek olarak x>3 ve 2≤x≤5 gibi aralıkların çözüm kümeleri yazılabilir."]},"beginTime":693,"endTime":783,"href":"/video/preview/3032508966229972852?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=693&ask_summarization=1"}],"linkTemplate":"/video/preview/3032508966229972852?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Yedi Adımda Temel Matematik (Tyt-Kpss-Ales-Dgs) 6. 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Öğretmen, Mehmet adında bir öğrenciden bahsederek konuyu açıklamaktadır.","Videoda temel kavramlar konusu kapsamında en büyük değer, en küçük değer, en az değer ve en çok değer bulma soruları, toplamları verilen sayıların çarpım değerlerini bulma, çarpımları verilen sayıların toplam değerlerini hesaplama ve tam sayılarla ilgili çeşitli problemler adım adım çözülmektedir. İçerik, klasik soruların çözümünden yeni nesil beceri temelli sorulara geçiş yapmaktadır.","Öğretmen, \"farklı\" kelimesinin önemini vurgulayarak sayıların birbirine ne kadar yakın seçildiğinde çarpım değerinin arttığını, uzak seçildiğinde ise toplam değerinin arttığını açıklamaktadır. Video, ikinci dersin sonunda sona erer ve öğretmen, temel kavramlar konusunun daha fazla video ile devam edeceğini belirtmektedir."]},"endTime":1943,"title":"Matematik Dersi: Temel Kavramlar ve Soru Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Temel Kavramlar Soru Çözümüne Giriş","list":{"type":"unordered","items":["Videoda temel kavramların soru çözümüne geçiliyor, önce sayı kümelerini tanımlama üzerine bir video yapılmıştı.","Temel kavramlar sorularında karşınıza çıkacak sorular en az, en çok, en büyük ve en küçük değer soruları olacak.","Bu soru yapılarının çözüm sistemleri mantık ve sayı kümesindeki seçimler üzerine kuruludur."]},"beginTime":3,"endTime":59,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=3&ask_summarization=1"},{"index":1,"title":"Farklı Rakamlarla En Büyük ve En Küçük Değer","list":{"type":"unordered","items":["İlk soruda abc farklı rakamlar olmak üzere ifadenin en büyük değeri ve en küçük değerinin toplamı soruluyor.","En büyük değeri bulmak için 3×8, 4×9 ve c=7 seçilirken, en küçük değeri bulmak için 3×1, 4×3 ve c=2 seçilir.","En büyük değer (67) ve en küçük değer (5) toplamı 72 olarak bulunur."]},"beginTime":59,"endTime":226,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=59&ask_summarization=1"},{"index":2,"title":"İşaretli İfadelerde En Büyük ve En Küçük Değer","list":{"type":"unordered","items":["İkinci soruda x, y, z birer rakam olmak üzere ifadenin en büyük değeri en küçük değerinden kaç fazla olduğu soruluyor.","En büyük değerde x ve y=9, z=0 seçilirken, en küçük değerde x=2, y=5 ve z=9 seçilir.","En büyük değer (63) ile en küçük değer (-27) arasındaki fark 90 olarak bulunur."]},"beginTime":226,"endTime":350,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=226&ask_summarization=1"},{"index":3,"title":"Oran Orantı Problemi","list":{"type":"unordered","items":["Üçüncü soruda a, b, c pozitif tam sayı olmak üzere 4a=3b ve 3b=5c olduğuna göre abc toplamının en az değeri soruluyor.","Oran orantı yöntemiyle a:b=15:20 ve b:c=20:12 ilişkisi bulunur.","En küçük pozitif tam sayı 1 için a=15, b=20, c=12 seçilir ve toplamları 47 olarak bulunur."]},"beginTime":350,"endTime":492,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=350&ask_summarization=1"},{"index":4,"title":"Toplamları Verilen Sayıların Çarpımı","list":{"type":"unordered","items":["Dördüncü soruda x ve y doğal sayı olmak üzere x+y=13 olduğuna göre x×y en çok kaç olduğu soruluyor.","İki sayının toplamı verilmişse, bu sayıları birbirine yakın seçmek çarpım değerini maksimize eder.","x=6 ve y=7 seçilince x×y=42 olarak bulunur."]},"beginTime":492,"endTime":629,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=492&ask_summarization=1"},{"index":5,"title":"Farklı Pozitif Tam Sayılarla Çarpım Problemleri","list":{"type":"unordered","items":["Soruda x, y, z farklı pozitif tam sayılardır ve toplamları 16'dır.","Çarpım değerini maksimize etmek için sayıları birbirine ne kadar yakın seçersek o kadar artar.","Farklı pozitif tam sayılar olması şartıyla x=4, y=5, z=7 seçilerek x×y×z=140 cevabı bulunur."]},"beginTime":637,"endTime":771,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=637&ask_summarization=1"},{"index":6,"title":"Toplama Problemi Çözümü","list":{"type":"unordered","items":["abc farklı pozitif tam sayılardır ve 3x+4y+z=67 eşitliği verilmiştir.","y'nin en büyük değerini bulmak için x ve z'ye en küçük farklı pozitif tam sayılar verilmelidir.","x=2, y=15, z=1 seçilerek x+y+z=18 cevabı bulunur."]},"beginTime":771,"endTime":1000,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=771&ask_summarization=1"},{"index":7,"title":"Çarpma ve Toplama Problemleri","list":{"type":"unordered","items":["Çarpımın verilip toplamanın sorulduğu soru türlerine geçiş yapılıyor.","x×y=56 olduğunda, sayıları birbirine ne kadar yakın seçersek o iki sayının toplamı en küçük değeri alır.","Video ders notunun videoları izlemek kadar faydalı olduğu belirtiliyor."]},"beginTime":1000,"endTime":1096,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=1000&ask_summarization=1"},{"index":8,"title":"Negatif Tam Sayı Problemi","list":{"type":"unordered","items":["Soruda pozitif tam sayı yerine negatif tam sayı istendiğinde dikkatli olunmalı.","x×y=12 ve y×z=20 koşullarında negatif tam sayılar için x=-3, y=-4, z=-5 değerleri en büyük toplamı verir.","Negatif tam sayılar için x+y+z toplamının en büyük değeri -12'dir."]},"beginTime":1098,"endTime":1241,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=1098&ask_summarization=1"},{"index":9,"title":"Pozitif Tam Sayı Problemi","list":{"type":"unordered","items":["x\u003cy\u003cz koşulu altında z×(y-2)=21×x denklemi verilmiş ve x+y+z toplamının en küçük değeri isteniyor.","x=1, y=5, z=7 değerleri denklemi sağlayarak x+y+z toplamının en küçük değerini verir.","x+y+z toplamının en küçük değeri 13'tür."]},"beginTime":1241,"endTime":1418,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=1241&ask_summarization=1"},{"index":10,"title":"Çarpım Problemi","list":{"type":"unordered","items":["a×b+a×c=12 koşulu altında abc çarpımının alabileceği en büyük değer isteniyor.","a=1, b=6, c=6 değerleri abc çarpımının en büyük değerini verir (1×6×6=36).","a=2, b=3, c=3 değerleri abc çarpımının daha küçük bir değerini verir (2×3×3=18)."]},"beginTime":1418,"endTime":1554,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=1418&ask_summarization=1"},{"index":11,"title":"Eşitsizlik Problemi","list":{"type":"unordered","items":["a\u003cb\u003cc koşulu altında a+b+c=44 ve b=15 değerleri verilmiş.","Eşitsizlik sırasına sadık kalarak a, b ve c değerleri hesaplanmalıdır."]},"beginTime":1554,"endTime":1596,"href":"/video/preview/638221662820050195?parent-reqid=1765340891291817-14581333593507699405-balancer-l7leveler-kubr-yp-vla-207-BAL&text=Al%C3%A8s+Demil+-+Topic&t=1554&ask_summarization=1"},{"index":12,"title":"Sayılar Kuramı Problemi Çözümü","list":{"type":"unordered","items":["Öğretmen, bir sayılar kuramı problemi çözüyorken, A, B, C ve D olmak üzere dört değişkenin değerlerini belirlemek için bir kriter sunuyor.","B değişkenine 15 verildiğinde, A değişkeni 15'ten küçük değerler alırken, C değişkeni 15'ten büyük değerler alacak.","A değişkeninin en büyük değeri 14 olabilir, ancak C'nin 15'ten büyük olması gereği nedeniyle A'nın en büyük değeri 13 olur ve A'nın alabileceği toplam 13 farklı değer 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Öğretmen, tahtada sorular çözerken öğrencilere adım adım çözüm yöntemlerini göstermektedir.","Video, matematik temel kavramlarını ele almaktadır. İlk bölümde sıralı ikili (iki bilinmeyenli denklem) ve çapraz katsayı yöntemi konuları işlenirken, ikinci bölümde çarpım tablosu, sayı problemleri ve denklem kurma soruları çözülmektedir. Son bölümde ise doğal sayılar konusu üzerinden çeşitli soru tipleri ele alınmaktadır.","Videoda doğal sayılarla ilgili sıralı ikili bulma, toplamları verilen ifadelerin çarpımlarının en büyük değerini bulma, kova taşıma problemi, polinom bölmesi yapma ve doğal sayı olma koşullarını sağlayan x değerlerinin toplamını hesaplama gibi çeşitli soru tipleri çözülmektedir. 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