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ifadeleri doğru bulunuyor.","A kümesi B kümesinde bulunmuyor ve C kümesinin elemanları 1, 2, 3, 4, 5 olabilir.","C kümesinin elemanlarının toplamının alabileceği değerler toplamı 38 olarak bulunuyor ve cevap B seçeneğinde yer alıyor."]},"beginTime":687,"endTime":881,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=687&ask_summarization=1"},{"index":8,"title":"Doğrusal Fonksiyonlar ve Sıralama","list":{"type":"unordered","items":["ABC birer gerçek sayı olmak üzere, f, g, h doğrusal fonksiyonları verilmiş ve sıfırların değerleri a, b, c olarak belirlenmiştir.","f(x+3) fonksiyonu, f(x) fonksiyonunu 3 birim sola öteler.","h(x) = -f(x) eşitliği, f(x) fonksiyonunun y eksenine göre simetrik olduğunu gösterir.","Sıfırların değerleri a=e, b=b, c=c olarak bulunmuş ve a, b, c'nin sıralaması e seçeneğine eşittir."]},"beginTime":882,"endTime":1009,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=882&ask_summarization=1"},{"index":9,"title":"Küme Problemi","list":{"type":"unordered","items":["A birleşim B kümesinin eleman sayısı 15, A fark B kümesinin eleman sayısı 17, B fark A kümesinin eleman sayısı 5 ve A çarpı B kümesinin eleman sayısı 35 verilmiştir.","A fark B kümesinin eleman sayısı ya 5 ya da 7 olabilir, ancak A çarpı B kümesinin eleman sayısı 35 olduğundan A fark B kümesinin eleman sayısı 5'tir.","A birleşim B kümesinin eleman sayısı, A çarpı B kümesinin eleman sayısı, B çarpı A kümesinin eleman sayısı ve A kesişim B kümesinin eleman sayısı kullanılarak 151 olarak hesaplanmıştır."]},"beginTime":1009,"endTime":1136,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=1009&ask_summarization=1"},{"index":10,"title":"Denklem Sorusu","list":{"type":"unordered","items":["Verilen ifadeye göre değeri bulunması istenmiştir.","Katsayıları aynı olan ifadeler ortak çarpan parantezine alınarak düzenlenmiştir.","Kökler toplamı ve çarpımı kullanılarak ifade 12 olarak bulunmuştur."]},"beginTime":1136,"endTime":1226,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=1136&ask_summarization=1"},{"index":11,"title":"Polinom Sorusu","list":{"type":"unordered","items":["Üçüncü dereceden bir polinom fonksiyonu verilmiş ve x=6 ile bölümünden kalanı bulunması istenmiştir.","Polinomun kökleri x=1, x=-2 ve x=1 olarak belirlenmiştir.","P(25) değeri kullanılarak a=2 bulunmuş ve P(3) değeri 13 olarak hesaplanmıştır."]},"beginTime":1226,"endTime":1413,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=1226&ask_summarization=1"},{"index":12,"title":"Logaritma Sorusu","list":{"type":"unordered","items":["logₐ(729) ifadesinin tam sayı olması için a'nın hangi değerleri alabileceği sorulmuştur.","729 sayısı 3⁶ olarak ifade edilebilir.","a'nın 3, 9, 27 veya 81 olabileceği, ancak 81 değeri 64'e tam bölünmediği için geçersiz olduğu belirlenmiştir."]},"beginTime":1413,"endTime":1472,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=1413&ask_summarization=1"},{"index":13,"title":"Logaritma ve Aritmetik Dizi Problemleri","list":{"type":"unordered","items":["Bir logaritma probleminde, a'nın dört farklı değeri bulunuyor ve bunlar işaretleniyor.","B'nin küpü başa alınarak 1/3 çarpı logaritma b tabanında a ifadesi elde ediliyor ve bu ifadenin tam sayı olması için b'nin 3 veya 9 olabileceği bulunuyor.","B'nin farklı değerlerinin toplamı 12 olarak hesaplanıyor."]},"beginTime":1476,"endTime":1607,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=1476&ask_summarization=1"},{"index":14,"title":"Aritmetik Dizi Problemi","list":{"type":"unordered","items":["Ortak farkı r olan bir aritmetik dizide, a₅ = 2 + 4d şeklinde ifade ediliyor.","a₃ + 14d \u003c 60 ve a₄ + 28d > 60 farklı durumlar inceleniyor.","d'nin alabileceği tam sayı değerlerinin çarpımı 12 olarak bulunuyor."]},"beginTime":1607,"endTime":1723,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=1607&ask_summarization=1"},{"index":15,"title":"Binom Açılımı Problemi","list":{"type":"unordered","items":["(2 + 1/a)⁷ ifadesinin katsayılar toplamı 120 - 128 olarak veriliyor.","a = -1/4 olarak bulunuyor ve (2 - 4x²)⁷ ifadesi elde ediliyor.","x¹⁰ ve x⁸ terimlerinin katsayıları hesaplanarak bölümü 20 olarak bulunuyor."]},"beginTime":1723,"endTime":2019,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=1723&ask_summarization=1"},{"index":16,"title":"Kalem Paylaşımı Problemi","list":{"type":"unordered","items":["Üç özdeş kalemlikte toplam 12 kalem bulunuyor.","Kalemler 1, 2 ve 3 kalemlik kalemliklere yerleştiriliyor.","Akif, Can ve Can isimli üç arkadaşa her birine 4 kalem düşecek şekilde paylaşım yapılıyor."]},"beginTime":2019,"endTime":2086,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=2019&ask_summarization=1"},{"index":17,"title":"Dörtlü Kalemlerin Tamamlanması","list":{"type":"unordered","items":["Dörtlü kalemleri tamamlamak için üç farklı ihtimal vardır: 1+1+2, 2+2 veya 3+1.","Akif, Birkan ve Can'ın kendi arasında yer değiştirmeleri 3 faktöriyel (6) durumda meydana gelir."]},"beginTime":2089,"endTime":2141,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=2089&ask_summarization=1"},{"index":18,"title":"Kesirlerin Tam Sayı Olma Olasılığı","list":{"type":"unordered","items":["Kübra, Ahmet, Günay ve Yusuf'un kesirlerini farklı kutulara yerleştiriyor ve tüm sonuçların tam sayı olma olasılığı soruluyor.","Tüm durumlar 6 faktöriyel (720) olurken, istenen durumlar 18'dir.","İstenen durumda 720/18 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 = 40/1 ="]},"beginTime":2141,"endTime":2607,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=2141&ask_summarization=1"},{"index":19,"title":"Türev Problemi Çözümü","list":{"type":"unordered","items":["f(x) = x³g(x²+1) fonksiyonunun türevi alınarak f'(x) = 3x²g(x²+1) + x²g'(x²+1) + k bulunur.","f(-1) = -1g(1) + 3 ve g(1) = 2, g'(1) = 4 değerleri kullanılarak k = -3 bulunur.","f'(-1) = 10 + k/3 = 7/3 olarak hesaplanır ve cevap D seçeneğinde yer alır."]},"beginTime":2610,"endTime":2771,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=2610&ask_summarization=1"},{"index":20,"title":"Fonksiyonun Artan ve Azalan Bölgeleri","list":{"type":"unordered","items":["f'(x) fonksiyonunun grafiği, artan ve azalan bölgeleri gösterir; kritik nokta 8'dir.","Fonksiyon 8'den önce azalan, 8'den sonra artan olup, minimum noktası 60'dır.","f(1), f(3) ve f(5) değerleri için, azalan fonksiyonda fonksiyon içi büyüdükçe değeri küçülür, bu nedenle f(5) en büyük değerdir."]},"beginTime":2771,"endTime":2853,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=2771&ask_summarization=1"},{"index":21,"title":"Teğet Doğrusu Problemi","list":{"type":"unordered","items":["f(x) = (x+5)/(x-2) fonksiyonunun türevi f'(x) = -7/(x-2)² olarak bulunur.","K noktasından geçen teğet doğrusunun eğimi, f'(k) = -7/(k-2)² olarak hesaplanır.","Eğim formülü (y₂-y₁)/(x₂-x₁) kullanılarak k = -12 bulunur ve f(-12) = 1/2 olarak hesaplanır."]},"beginTime":2853,"endTime":3068,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=2853&ask_summarization=1"},{"index":22,"title":"Dijital Yayın Platformu Problemi","list":{"type":"unordered","items":["Bir dijital yayın platformu en fazla 3000 müşteriye hizmet vermektedir ve aylık ücreti 200 lira olarak belirlediğinde bu sayıya ulaşabilmektedir.","Aylık internet ücreti her 8 liralık artış sonrasında müşteri sayısı 40 azalma göstermektedir.","Toplam gelirin maksimum olması için aylık üyelik ücreti 200 liralık bir artış yapmalıdır."]},"beginTime":3068,"endTime":3235,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=3068&ask_summarization=1"},{"index":23,"title":"Polinom Fonksiyonunun Türevi ve Parabol Denklemi","list":{"type":"unordered","items":["Üçüncü dereceden bir polinom fonksiyonunun türevi alındığında parabol fonksiyonuna dönüşür.","Parabol fonksiyonunun denklemi f(x) = a(x-r)² + k şeklinde yazılır ve tepe noktası (r,k) olarak belirlenir.","Verilen parabol fonksiyonunun türevi f'(x) = -x² + 6x - 8 olarak bulunur."]},"beginTime":3237,"endTime":3343,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=3237&ask_summarization=1"},{"index":24,"title":"Fonksiyonun İntegrali ve Sabit Sayısının Bulunması","list":{"type":"unordered","items":["Türev fonksiyonunun integrali alınarak f(x) = -x³/3 + 3x² - 8x + c olarak bulunur.","h(x) = 3f(x) + 1 şeklinde tanımlanan fonksiyonun denklemi h(x) = -x³ + 9x² - 24x + 3c + 1 olarak hesaplanır.","h(2) = 3 ve h(3) = 18 değerleri kullanılarak sabit sayı c = 8 bulunur ve h(0) = 25 olarak hesaplanır."]},"beginTime":3343,"endTime":3517,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=3343&ask_summarization=1"},{"index":25,"title":"İntegral Sorusu ve Değişken Değiştirme","list":{"type":"unordered","items":["-1 ile 3 arası f(x) + g(x) fonksiyonunun integrali 12 olarak verilmiştir.","Değişken değiştirme yöntemiyle 2 - u = x dönüşümü yapılarak integral sınırları -1 ile 3'ten -3 ile 3'e değiştirilir.","İntegral değeri içindeki değişkenden bağımsız olduğundan, integral -1 ile 3 arası f(x) + g(x) dx = 12 olarak yazılır."]},"beginTime":3517,"endTime":3652,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=3517&ask_summarization=1"},{"index":26,"title":"İntegralin Hesaplanması","list":{"type":"unordered","items":["İntegral değerleri taraf tarafa toplanarak -1 ile 3 arası f(x) = 8 ve -1 ile 3 arası g(x) = 4 bulunur.","İntegral -1 ile 1 arası 2x + 1 dx ve -1 ile 1 arası 2x + 2 g(x)² dx şeklinde ayrılır.","Değişken değiştirme yöntemiyle 2x + 1 = u ve x² + 2x = t dönüşümleri yapılarak integral 0,5 u du + 0,5 t dt = 0,5(8 - 4) = 0,5 = 0,5 olarak hesaplanır."]},"beginTime":3652,"endTime":3811,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=3652&ask_summarization=1"},{"index":27,"title":"İntegral Problemi Çözümü","list":{"type":"unordered","items":["İkinci fonksiyonun denklemi f(x) = a(x+3)(x-4) şeklinde kurulmuş ve a katsayısı -1 olarak bulunmuştur.","Fonksiyonun denklemi -x² + x + 12 olarak düzenlenmiş ve kesişim noktası (-6, 0,5) olarak hesaplanmıştır.","Boyalı bölgenin alanı için integral hesaplaması yapılmış ve sonuç 256/3 olarak bulunmuştur."]},"beginTime":3814,"endTime":4110,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=3814&ask_summarization=1"},{"index":28,"title":"Fonksiyon Alanları Problemi","list":{"type":"unordered","items":["Fonksiyonun grafiğinin x ekseninde kalan bölgenin alanı 5'e ayrılmış, kırmızı bölgenin alanı 4, mavi bölgenin alanı 2, mor bölgenin alanı 3 ve yeşil bölgenin alanı 5 olarak verilmiştir.","İntegral hesaplamalarında değişken değiştirme yöntemi kullanılmış ve fonksiyonun değeri 8 olarak bulunmuştur.","İntegral ve türev konuları tamamlanmış, trigonometri konusuna geçilmiş."]},"beginTime":4110,"endTime":4307,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=4110&ask_summarization=1"},{"index":29,"title":"Trigonometri Problemi Çözümü","list":{"type":"unordered","items":["Soruda 90-180 derece arasında bir açı değeri için tanx değeri bulunması isteniyor.","Trigonometrik ifadeler düzenlenerek sinx ve cosx değerleri kullanılarak tanx = -3/5 olarak bulunuyor."]},"beginTime":4309,"endTime":4450,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=4309&ask_summarization=1"},{"index":30,"title":"Trigonometrik Değerlerin Karşılaştırılması","list":{"type":"unordered","items":["Soruda sinüs, kotanjant ve sekant değerleri verilmiş ve en büyük açı bulunması isteniyor.","Açılar 30°, 120° ve 240° olarak belirleniyor ve kotanjant değerleri karşılaştırılıyor.","En büyük açı 240° olarak bulunuyor."]},"beginTime":4450,"endTime":4614,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=4450&ask_summarization=1"},{"index":31,"title":"İkizkenar Üçgen ve Dikdörtgen Problemi","list":{"type":"unordered","items":["ABC ikizkenar üçgen ve ABCD dikdörtgen verilmiş, A ile EB kenarları birbirine eşit.","E noktasından çizilen dik doğru hem kenarortay hem açıortaydır.","Üçgenin alanı 2tx olarak bulunuyor."]},"beginTime":4614,"endTime":4694,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=4614&ask_summarization=1"},{"index":32,"title":"Kosinüs Teoremi Uygulaması","list":{"type":"unordered","items":["ABC üçgeninde x, y ve z kenarları verilmiş ve kosinüs teoremi kullanılarak çözüm yapılıyor.","Kosinüs teoremi uygulanarak cosz = -2/3 bulunuyor.","Üçgen çizilerek sinα = √5/3 olarak hesaplanıyor."]},"beginTime":4694,"endTime":4813,"href":"/video/preview/14185011889160335760?parent-reqid=1776519954305541-15407720861108277777-balancer-l7leveler-kubr-yp-vla-206-BAL&text=MIRAY&t=4694&ask_summarization=1"},{"index":33,"title":"Trigonometrik Denklem Çözümü","list":{"type":"unordered","items":["Soruda x değerinin 0, 450 derece arasındaki bütün kökleri bulunması isteniyor.","sinx = cos60° denklemi iki şekilde çözülebilir: sinx = cos60° ve sinx = 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