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İlk beş soru karmaşık sayılar, gerçel sayılar, EBOB-EKOK, asal sayılar ve ikinci dereceden eşitsizlikler konularını içermektedir. Daha sonra eşitsizlikler, polinomlar, fonksiyonlar, paraboller, aritmetik diziler, kombinatoryal problemler, küme teorisi, logaritma, limit, sürekli fonksiyonlar, türevler, integral, trigonometri ve geometri konularındaki problemler çözülmektedir.","Her soru için eğitmen, çözüm yöntemlerini detaylı şekilde açıklamakta, gerekli formülleri göstermekte ve grafikler üzerinden anlatımlar yapmaktadır. Video, matematik sınavlarına hazırlanan öğrenciler için faydalı olabilecek kapsamlı bir problem çözüm dersidir."]},"endTime":5808,"title":"Barış Yayınları 8. 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soruluyor.","a=3b ve b=4 olduğu bulunuyor.","EKOK(2^a, 2^b) = 2^12 olarak hesaplanıyor."]},"beginTime":255,"endTime":450,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=255&ask_summarization=1"},{"index":4,"title":"Dördüncü Soru Çözümü","list":{"type":"unordered","items":["n pozitif bir tam sayı olmak üzere, [n] sembolü n sayısının pozitif tam sayı bölenlerinin toplamı olarak tanımlanıyor.","m>5 bir asal sayı olmak üzere, 25m sayısının pozitif tam sayı bölenlerinin toplamı 2^5 × m eşitliğini sağlayan m değeri soruluyor.","25m sayısının bölenleri toplandığında 32m elde ediliyor ve m=31 olarak bulunuyor."]},"beginTime":450,"endTime":532,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=450&ask_summarization=1"},{"index":5,"title":"Eşitsizlik Çözümü ve Köklerin 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arasında \"P ise Q veya R\" önermesi yanlış olduğu bilinmektedir.","Butonlara basılan kişilerin doğru sıralaması incelenerek çözüme ulaşılır."]},"beginTime":1204,"endTime":1324,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=1204&ask_summarization=1"},{"index":11,"title":"Denklem ve Kökler","list":{"type":"unordered","items":["Verilen denklemin diskriminantı (delta) hesaplanarak 8 olarak bulunur.","Kökler çarpımı 14, kökler toplamı 8 ve kökler farkının mutlak değeri 2√2 olarak hesaplanır.","İstenen ifadenin değeri 224√2 olarak bulunur."]},"beginTime":1324,"endTime":1447,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=1324&ask_summarization=1"},{"index":12,"title":"Parabol Problemi","list":{"type":"unordered","items":["Kökleri -1 ve 6 olan bir parabolün denklemi bulunur.","X ekseni üzerinde bulunan yamuğun alanı hesaplanır ve a'nın 24 katı olarak bulunur."]},"beginTime":1447,"endTime":1551,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=1447&ask_summarization=1"},{"index":13,"title":"Aritmetik Dizi Problemi","list":{"type":"unordered","items":["R asal sayı olmak üzere bir a_n aritmetik dizisi için b_n=r^(a_n) şeklinde tanımlanmıştır.","b_7/b_5 oranı 16 olarak hesaplanarak r=2 bulunur.","Aritmetik dizinin ortak farkının 4 olduğu ve a_8-a_5'in 6 olduğu sonucuna ulaşılır."]},"beginTime":1551,"endTime":1626,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=1551&ask_summarization=1"},{"index":14,"title":"Turnuva Problemi","list":{"type":"unordered","items":["Altı kişi arasında oynanan turnuvada aynı iki kişi arasında en fazla bir oyun oynanabilmektedir.","Turnuvaya katılan altı kişinin oynadığı oyun sayıları 1, 2, 4 ve 5 elemanlarından oluşmaktadır."]},"beginTime":1626,"endTime":1672,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=1626&ask_summarization=1"},{"index":15,"title":"Oyun Oynama Problemi","list":{"type":"unordered","items":["Bir grup kişi farklı sayıda oyun oynamış ve bu durum grafiksel olarak gösterilmektedir.","Grafikte bir kişi oyun oynamış, iki kişi iki oyun oynamış, bir kişi beş oyun oynamış ve bir kişi dört oyun oynamıştır.","Toplam oynanan oyun sayısı sekiz olduğundan, sorunun doğru cevabı B şıkkıdır."]},"beginTime":1675,"endTime":1769,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=1675&ask_summarization=1"},{"index":16,"title":"Polinom Problemi","list":{"type":"unordered","items":["Verilen ifade (x³y - 2xy²)⁵ kuvvetinin açılımında y⁸'e tam bölünebilen terim bulunmak istenmektedir.","x³y'nin karesi, -2'nin üçüncü kuvveti ve xy²'nin üçüncü kuvveti çarpılarak -80x⁹y⁸ terimi elde edilir.","P(x) polinomunda x=2 yerine konulduğunda, ilk terimin katsayısı -6! (faktöriyel) olarak hesaplanmıştır."]},"beginTime":1769,"endTime":1975,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=1769&ask_summarization=1"},{"index":17,"title":"Sözlü Sınav Problemi","list":{"type":"unordered","items":["Merve öğretmen 10 kişilik bir öğrenci grubuna mola vermeden 5 dakikalık sözlü sınav yapmaktadır.","Fulya 10:15'te sözlü sınavına başlamış ve ondan önceki kişilerin sayısı, ondan sonraki kişilerin sayısının iki katıdır.","Sözlü sınavına ilk katılan kişi 9:45'te başlamıştır."]},"beginTime":1975,"endTime":2075,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=1975&ask_summarization=1"},{"index":18,"title":"Kavşak Problemi","list":{"type":"unordered","items":["Bir kavşakta belirli bir noktada yerleştirilmiş tabelada adları yazan köyler gösterilmektedir.","Necmi, Ali ve Veli aynı anda kavşağa geldiğinde rastgele seçtikleri farklı köylere gideceklerdir.","Üç kişiden sadece ikisinin aynı yöne gitme olasılığı 45/56 olarak hesaplanmıştır."]},"beginTime":2075,"endTime":2188,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=2075&ask_summarization=1"},{"index":19,"title":"Logaritma Problemi","list":{"type":"unordered","items":["f(x) fonksiyonunun grafiği üzerinde apsisleri log₃105, log₅105 ve log₇105 olan noktaların ordinat değerleri toplanmaktadır.","Logaritma ifadeleri ters çevrilerek log₁₀₅₃, log₁₀₅₅ ve log₁₀₅₇ olarak yazılır.","Bu logaritma ifadelerinin toplamı log₁₀₅₁₀₅'e eşittir ve bu da 1'e eşittir."]},"beginTime":2188,"endTime":2234,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=2188&ask_summarization=1"},{"index":20,"title":"Robotun Matematiksel İşlemlerde Hatası","list":{"type":"unordered","items":["Bir teknoloji firması ürettiği robota matematiksel işlemler yaptırdığında, robotun bulduğu sonuç gerçek sonuçtan logaritma x kadar eksik çıkıyor.","x² işlemi yapıldığında logaritma x kadar eksik sonuç bulunurken, x/10 işlemi yapıldığında logaritma x/10 kadar eksik sonuç bulunuyor.","Toplam eksik sonuç logaritma x³ olup, 2 ile 3 aralığındaki bir sayı olduğundan, x değeri 10 ile 100 arasındadır."]},"beginTime":2237,"endTime":2359,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=2237&ask_summarization=1"},{"index":21,"title":"Fonksiyonların Limitleri","list":{"type":"unordered","items":["f, g ve h fonksiyonlarının grafikleri verilmiş olup, x=3'e soldan yaklaşırken h(x) en büyük değer alıyor.","f(x) sinüs fonksiyonu olduğu için maksimum değeri 1, h(x) ise 2 değerine yaklaşırken, bu nedenle h(x) fonksiyonudur.","x=1'e yaklaşırken f(x), g(x) ve h(x) limitleri hesaplanarak, h(x) limiti -14/3 olarak bulunuyor."]},"beginTime":2359,"endTime":2484,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=2359&ask_summarization=1"},{"index":22,"title":"Parçalı Tanımlı Fonksiyonların Sürekliliği","list":{"type":"unordered","items":["f ve g fonksiyonları parçalı tanımlı olup, h(x)=f(x)-g(x) fonksiyonu gerçek sayılar kümesi üzerinde sürekli.","f fonksiyonunun parçalama noktası a=1 olmalıdır ki, h(x) sürekli olsun.","a=1 ve b değerleri hesaplanarak, a×b=5 olarak bulunuyor."]},"beginTime":2484,"endTime":2594,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=2484&ask_summarization=1"},{"index":23,"title":"İkinci Dereceden Fonksiyonların Türevleri","list":{"type":"unordered","items":["f ve g ikinci dereceden fonksiyonlarının birinci türevlerine ait grafiklerinin bir kısmı çizilmiş ve tepe noktaları aynı apsisli.","f'(x)=2x+a ve g'(x)=-2x+b şeklinde ifade edilebilir.","g(1)-f(2) hesaplanarak, cevabın -3 olduğu bulunuyor."]},"beginTime":2594,"endTime":2842,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=2594&ask_summarization=1"},{"index":24,"title":"Fonksiyonların Türevi ve Teğet Denklemleri","list":{"type":"unordered","items":["f(x) = a/x + a fonksiyonunun grafiğindeki (a,a) noktasına çizilen teğetin denklemi y = -x/8 + c olarak verilmiş ve a×c çarpımı soruluyor.","f(x) fonksiyonunun türevi f'(x) = -2ax/(x²+a²) olarak bulunmuş ve f'(a) = -1/8 eşitliği kullanılarak a = 3 değeri hesaplanmış.","a = 3 değeri kullanılarak c = -5 bulunmuş ve a×c çarpımı -15 olarak hesaplanmış."]},"beginTime":2846,"endTime":3053,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=2846&ask_summarization=1"},{"index":25,"title":"Parabol ve Döndürme","list":{"type":"unordered","items":["f(x) = ax² parabolü orijinden 45 derece döndürüldüğünde, B noktası y ekseninde, A noktası ise x ekseninde yer alıyor.","B noktasından çizilen teğetin eğimi f'(b) = 2ab olarak hesaplanmış ve 45 derece açıdan a = 1 bulunmuş.","Teğetin eğimi 2×1×b = 2 olarak hesaplanmış."]},"beginTime":3053,"endTime":3155,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=3053&ask_summarization=1"},{"index":26,"title":"Fonksiyonların Türevleri ve İntegral","list":{"type":"unordered","items":["f(x) = ax²+bx+c fonksiyonunun grafiği, birinci ve ikinci türevlerinin grafikleri verilmiş.","f(x) = ax²-2a olarak bulunmuş ve parabolün simetri ekseninin x = r olduğu belirlenmiş.","Mavi doğru uzunluğu 4 birim olarak hesaplanmış."]},"beginTime":3155,"endTime":3318,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=3155&ask_summarization=1"},{"index":27,"title":"Fonksiyon Ailesi ve İntegral","list":{"type":"unordered","items":["fₙ(x) = n/x+n fonksiyon ailesi ve ∫[1,4] (f₂(x)-f₁(x)+f₄(x)-f₃(x)+...+fₐ(x)-fₐ₋₁(x)) dx = 240 integrali verilmiş.","İntegraldeki ifade (x+1) olarak sadeleşmiş ve a çift olduğu belirlenmiş.","a = 40 olarak bulunmuş."]},"beginTime":3318,"endTime":3449,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=3318&ask_summarization=1"},{"index":28,"title":"İntegral Hesaplama","list":{"type":"unordered","items":["∫[4,10] dx/(x-1) = a ve ∫[4,10] dx/(x²-1) = b olarak verilmiş.","∫[4,10] x/(x+1) dx integrali hesaplanırken, x/(x+1) = 1 - 1/(x+1) şeklinde yazılabilmiş.","İntegral sonucu 6 - ∫[4,10] 1/(x+1) dx olarak bulunmuş."]},"beginTime":3449,"endTime":3501,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=3449&ask_summarization=1"},{"index":29,"title":"İntegral Hesaplama","list":{"type":"unordered","items":["Bir bölü x eksi bir ve bir bölü x kare eksi bir arasındaki ilişki kurulabilir.","Bir bölü x artı bir ile bir bölü x eksi bir'in farkı alınarak eksi iki bölü x kare eksi bir elde edilir.","İntegral hesaplaması yapılarak C değeri 6+2B-A olarak bulunur."]},"beginTime":3503,"endTime":3601,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=3503&ask_summarization=1"},{"index":30,"title":"Fonksiyon Simetri Sorusu","list":{"type":"unordered","items":["E eğrisinin x eksenine göre simetri alındıktan sonra g doğrusuna y ekseni boyunca simetri ve genişleme işlemleri yapılmıştır.","G fonksiyonu iki ile çarpılmış ve x eksenine göre simetri alınmıştır.","Mavi boyalı bölgenin alanı, sarı boyalı bölgenin alanından 6 birim kare fazladır."]},"beginTime":3601,"endTime":3503,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=3601&ask_summarization=1"},{"index":31,"title":"Trigonometri Sorusu","list":{"type":"unordered","items":["0\u003cx\u003cπ/2 aralığında 3(1+sinx/cosx)=4cosx denklemi çözülür.","Denklem düzenlenerek 4sin²x+3sinx-1=0 denklemi elde edilir.","Sinüs x değeri 1/4 olarak bulunur, çünkü 0\u003cx\u003cπ/2 aralığında sinüs değeri pozitiftir."]},"beginTime":3925,"endTime":4035,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=3925&ask_summarization=1"},{"index":32,"title":"Trigonometri Sorusu","list":{"type":"unordered","items":["90\u003cx\u003c180 aralığında a=(1+sin²x)(1+sin⁴x)(1+sin⁸x) verilmiştir.","Kosinüs fonksiyonunda yanında bir olan ifade 2cos²x-1 olarak yazılır.","Verilen ifade ile a çarpılıp sin²16x eklenerek sonucun 2 olduğu bulunur."]},"beginTime":4035,"endTime":4135,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=4035&ask_summarization=1"},{"index":33,"title":"Geometri Sorusu","list":{"type":"unordered","items":["Birim kare biçimindeki cisim çembersel bir cisme değdiği noktada teğettir.","Çembersel cismin merkezi O olup tanjant β ile tanjant α'nın çarpımı 1'dir.","Çemberde yarıçap çizer ve teğet noktasına dik indirilir."]},"beginTime":4135,"endTime":4187,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=4135&ask_summarization=1"},{"index":34,"title":"Trigonometrik Hesaplamalar","list":{"type":"unordered","items":["Tanjant 2alfa hesaplaması için tanjant alfa değeri kullanılarak 2r/(1-r) formülü elde edilir.","İçler dışlar çarpımı yapılarak r değeri 1/3 olarak bulunur.","Çembersel cismin yarıçapı r isteniyordu ve cevap 1/3 olarak C şıkkında verilmiştir."]},"beginTime":4188,"endTime":4275,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=4188&ask_summarization=1"},{"index":35,"title":"Dik Koordinat Düzleminde Açı Hesaplaması","list":{"type":"unordered","items":["X ekseni üzerindeki kırmızı doğru 110 derece, mavi doğru 45 derece döndürülmüştür.","Turuncu doğrunun kırmızı doğruya göre simetri açısı 115 derece olarak hesaplanmıştır.","Eğim açısı sorulduğu için doğru cevap C şıkkında verilmiştir."]},"beginTime":4275,"endTime":4351,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=4275&ask_summarization=1"},{"index":36,"title":"Üçgen ve Düzgün Altıgen Problemi","list":{"type":"unordered","items":["Üçgen biçimindeki kartonda içine çizilen düzgün dokuzgenin üç kenarı üçgenin kenarlarıyla çakışmıştır.","Çevre uzunluğu 1 birim olan düzgün altıgenin bir kenarı 1/6 birimdir.","Sarı renkle belirtilen üçgenin çevresi 1,5 birim olarak hesaplanmıştır ve cevap A şıkkında verilmiştir."]},"beginTime":4351,"endTime":4529,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=4351&ask_summarization=1"},{"index":37,"title":"Dik Koordinat Düzleminde Dönme Problemi","list":{"type":"unordered","items":["Dik koordinat düzleminin ikinci bölgesine yerleştirilen ABC üçgeni saat yönünde döndürülmüştür.","A noktasının ordinatı 1/4, B noktasının apsisi -3/4 olarak hesaplanmıştır.","Doğru cevap C şıkkında verilmiştir."]},"beginTime":4529,"endTime":4618,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=4529&ask_summarization=1"},{"index":38,"title":"Parfüm Şişesi Problemi","list":{"type":"unordered","items":["Yarım daire biçiminde kapağı ve dikdörtgen biçiminde gövdesi olan parfüm şişesinin görünümü verilmiştir.","Kapağın çapı 10 birim olarak hesaplanmıştır.","A ve A' noktaları arasındaki uzaklık 8√5 birim olarak bulunmuştur ve cevap D şıkkında verilmiştir."]},"beginTime":4618,"endTime":4714,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=4618&ask_summarization=1"},{"index":39,"title":"Matematik Problemlerinin Çözümü","list":{"type":"unordered","items":["34. soruda, sapın uzantısının merkezinden geçen daire biçimli bir tava ve sapın ucu zeminden 20 birim yükseklikte olduğu bir problem çözülüyor.","Çözümde yarıçap (r) ve sapın uzunluğu (k) kullanılarak, r=10 ve k=16 olarak bulunuyor, sapın uzunluğu 16 birim olarak hesaplanıyor.","35. soruda, Rafet Bey'in cep telefonundan görüntülü konuşma yaparken ekranın kenarlarına teğet olan dairelerin yarıçapları arasındaki fark hesaplanıyor.","Dairelerin yarıçapları arasındaki fark 1 birim olarak bulunuyor.","36. soruda, dik koordinat düzleminde bir karenin köşelerinin koordinatları ve orijine olan uzaklıkları kullanılarak a×b×c değeri hesaplanıyor.","Karedeki köşelerin y eksenine olan uzaklıkları 3, 7 ve 10 birim olarak bulunuyor, a×b×c=210 olarak hesaplanıyor."]},"beginTime":4720,"endTime":5244,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=4720&ask_summarization=1"},{"index":40,"title":"Dik Üçgen Problemi","list":{"type":"unordered","items":["Dik koordinat düzleminde köşeleri eksenler üzerinde bulunan ABC dik üçgenin AC kenarı sola, AB kenarı sağa kaydırılıyor.","Kaydırma sonrası kesişim noktası (12,5) ve (44,5) olarak belirleniyor.","A noktasının ordinatı sorulduğunda, iç içe geçtikten sonra oluşan dik üçgenin yüksekliği hesaplanarak 2 birim bulunuyor."]},"beginTime":5248,"endTime":5453,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=5248&ask_summarization=1"},{"index":41,"title":"Çember Problemi","list":{"type":"unordered","items":["İlk koordinat düzleminde çapı x ekseni üzerinde ve y ekseni orijin teğet olan çember, AB doğrusu tarafından kesiliyor.","Çemberin denklemi için çap uzunluğu hesaplanıyor ve 26 birim bulunuyor.","Merkezi (13,0) noktasında ve yarıçapı 13 birim olan çemberin denklemi (x-13)² + y² = 169 olarak belirleniyor."]},"beginTime":5453,"endTime":5671,"href":"/video/preview/14252312901396120462?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=5453&ask_summarization=1"},{"index":42,"title":"Küp Problemi","list":{"type":"unordered","items":["Uzunluğu x cm olan küp biçimindeki karton kutunun kapakları kesildiğinde oluşan mavi bölge, A, B, C, D dikdörtgeni ile benzerlik gösteriyor.","Dikdörtgenin kısa kenarı uzun kenarına oranı 3/2 olarak belirleniyor.","Küpün yüzey alanı 6 × 81 = 486 cm² olarak 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koyuyorlar.","Kartonu hızlıca çektiklerinde metal paranın kartonla beraber gelmediğini ve bardağın içine düştüğünü gözlemliyorlar.","Duran madeni paraların altındaki kağıt aniden çekildiğinde paraya yeterince itme kuvveti uygulanmadığından para bardağın içine düşmüştür."]},"beginTime":258,"endTime":328,"href":"/video/preview/4965155463330117375?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=258&ask_summarization=1"},{"index":5,"title":"Elektrostatik Sorusu","list":{"type":"unordered","items":["Eşit boyda yalıtkan iplerle birbirine değecek şekilde asılmış olan eşit kütleli iletken kürelerine yüklü iletken bir cisim dokundurulup çekiliyor.","Dokunma ile elektriklenme de yüklü cisimler sonuç olarak aynı işaretli yüklenir.","Birbirlerine uyguladığı elektriksel kuvvet ise yüklerinin büyüklükleriyle doğru orantılı, aralarındaki kareyle ters 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gösterilen potasyum değil, fosfordur.","A şıkkında N elementin adının azot olduğunu söylemiş ki bu da doğrudur.","E ile gösterilen demirdir ve Au ile gösterilen altını sembolüdür."]},"beginTime":475,"endTime":518,"href":"/video/preview/4965155463330117375?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=475&ask_summarization=1"},{"index":8,"title":"Bor Atom Modeli Sorusu","list":{"type":"unordered","items":["Bor atom modelinde elektronlar çekirdek etrafında yörüngelerde bulunur.","Yörüngelerin enerjisi çekirdekten uzaklaştıkça artar, azalır dediği için yanlıştır.","Negatif yükler pozitiflerin içerisinde homojen olarak dağılmıştır, bu da bor atom modeline göre yanlıştır."]},"beginTime":518,"endTime":586,"href":"/video/preview/4965155463330117375?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=518&ask_summarization=1"},{"index":9,"title":"Bağlar ve Enerji","list":{"type":"unordered","items":["X ile gösterilen bağ hidrojen bağıdır ve Y ile gösterilen bağ polar kovalent bağdır.","Polar kovalent bağ farklı atomlar arasında oluştuğu için hidrojen bağıdan daha güçlüdür.","Hidrojen bağı kırmak için gereken enerji, polar kovalent bağı kırmak için gereken enerjiden daha azdır."]},"beginTime":590,"endTime":699,"href":"/video/preview/4965155463330117375?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=590&ask_summarization=1"},{"index":10,"title":"Kimyasal Hesaplama","list":{"type":"unordered","items":["Kalsiyum oksit ve karbondioksit tepkimesinden kalsiyum karbonat oluşur ve 1 mol karbondioksit harcandığında 1 mol kalsiyum karbonat oluşur.","100 gram kalsiyum karbonat oluştuğunda 1 mol karbondioksit harcanır ve normal koşullarda 22,4 litre karbondioksit harcanır.","25 gram kalsiyum karbonat oluşması için 5,6 litre karbondioksit gazının harcanması gerekir."]},"beginTime":699,"endTime":799,"href":"/video/preview/4965155463330117375?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=699&ask_summarization=1"},{"index":11,"title":"Viskozite","list":{"type":"unordered","items":["Viskozite, maddelerin akmaya karşı gösterdiği dirençtir ve bal en yüksek viskoziteye sahiptir.","Akıcılık en yüksek olan sıvı asetondur çünkü viskozitesi en küçüktür.","Sıcaklık arttıkça viskozite azalır ve akışkanlık artar."]},"beginTime":799,"endTime":885,"href":"/video/preview/4965155463330117375?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=799&ask_summarization=1"},{"index":12,"title":"Çözünürlük","list":{"type":"unordered","items":["20°C'de 100 gram suda 140 gram potasyum iyodu çözünür.","400 gram suya 600 gram potasyum iyodu eklenildiğinde, 560 gram potasyum iyodu çözünür ve 40 gram çözülmeden 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özelliği değildir."]},"beginTime":1002,"endTime":1105,"href":"/video/preview/4965155463330117375?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=1002&ask_summarization=1"},{"index":15,"title":"Beslenme Tipleri","list":{"type":"unordered","items":["Karbon kaynağı karbondioksit olan canlılar fotosentez veya kemosentez yapan canlılardır.","Fotoototrop ve kemoototrof canlılar karbondioksit ve suyu birleşerek besin elde ederler.","Dörtlüler dışarıdan beslenme ile besin alırlar."]},"beginTime":1105,"endTime":1160,"href":"/video/preview/4965155463330117375?parent-reqid=1765326350957252-5790129665560400415-balancer-l7leveler-kubr-yp-klg-105-BAL&text=BRANS_+00&t=1105&ask_summarization=1"},{"index":16,"title":"Kan Grubu Genetik Sorusu","list":{"type":"unordered","items":["Bir ailedeki bireylerin kan grupları ile ilgili fenotipleri incelenerek, hangi bireyin genotipinin doğru verildiği belirleniyor.","A ve B kan grubu bireylerinin 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