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İçerik, asal sayılar, temel kavramlar, mutlak değer, bölünebilme kuralları, olasılık, kombinasyon, polinomlar, fonksiyonlar, logaritma, dizi, trigonometri ve geometri gibi çeşitli matematik konularını kapsamaktadır. Her soru için detaylı çözüm adımları gösterilmekte ve eğitmen hatalarını da itiraf etmektedir.","Video, sınav hazırlığı yapan öğrenciler için faydalı olabilecek bir kaynak niteliğindedir. Özellikle olasılık, kombinasyon ve polinom sorularının kaliteli ve seçici olduğu vurgulanmakta ve trigonometrik alan hesaplamaları, sinüs teoremi gibi konular detaylı olarak anlatılmaktadır. Video, TYT geometrisi sorularının çözüleceği bilgisiyle sonlanmaktadır."]},"endTime":4136,"title":"2023 AYT Matematik Sınavı Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"2023 AYT Sınavı Değerlendirmesi","list":{"type":"unordered","items":["2023 AYT sınavının çözümleri yapılacak.","İtibar, TYT ve AYT sınavları tamamlandı, bu süreç deprem ve seçim gibi zorluklarla geçildi.","Konuşmacı geçen sene girdiği sınavı 35-40 dakikada bitirdiğine karşılık, 2023 sınavı daha zordu ve 55 dakika sürdü."]},"beginTime":1,"endTime":52,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1&ask_summarization=1"},{"index":1,"title":"Sınavın Zorluk Düzeyi","list":{"type":"unordered","items":["Sınavda seçici ve kaliteli sorular vardı, özellikle olasılık, kombinasyon ve polinom soruları beğenildi.","Geçen seneye göre matematik soruları daha zor geldi.","Temel kavramlar kısmında deneme yanılma ve uğraştırıcı sorular vardı."]},"beginTime":52,"endTime":92,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=52&ask_summarization=1"},{"index":2,"title":"Çözüm Yöntemi","list":{"type":"unordered","items":["Konuşmacı sınavda çözdüğü tarzda çözümleri aktaracağını belirtiyor.","İzleyicilerden kısayolları paylaşmalarını ve tartışmalarını bekliyor."]},"beginTime":92,"endTime":119,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=92&ask_summarization=1"},{"index":3,"title":"Birinci Soru Çözümü","list":{"type":"unordered","items":["Birinci soru bir işlem sorusu olup, çokgen sembolünün değeri belirtiliyor.","Dışındaki sayılar toplanıp, kenar sayısı ile çarpılıp, içindeki sayı ekleniyor.","Denklem çözülerek x değeri 14 olarak bulunuyor."]},"beginTime":119,"endTime":188,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=119&ask_summarization=1"},{"index":4,"title":"İkinci Soru Çözümü","list":{"type":"unordered","items":["İkinci soru bir deneme olma sorusu olup, abc birbirinden farklı rakamlar olmak üzere a×b\u003c8 ve a×c>10 koşulları var.","a=3, b=2 ve c=6 değerleri verilerek soru çözülüyor.","a+b+c toplamı 11 olarak bulunuyor."]},"beginTime":188,"endTime":259,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=188&ask_summarization=1"},{"index":5,"title":"Üçüncü Soru Çözümü","list":{"type":"unordered","items":["Üçüncü soru üst sıralarda bir işlem sorusu olup, 2 ve 3'ün kuvvetleri kullanılarak çözülüyor.","Denklemler eşitlenerek x=5 ve y=-2 olarak bulunuyor.","x×y çarpımı -10 olarak hesaplanıyor."]},"beginTime":259,"endTime":370,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=259&ask_summarization=1"},{"index":6,"title":"Asal Sayılarla İşlem","list":{"type":"unordered","items":["p, q ve r asal sayılar olmak üzere p+q+r toplamı beşin katı olduğundan, p'nin 5 olması gerekir.","Verilen denklemde p=5 yazıldığında, 5q-10r=280 denklemi elde edilir ve sadeleştirildiğinde 5q-2r=56 bulunur.","Bu denklemi sağlayan asal sayılar p=5, q=2 ve r=7'dir ve toplamları 14'tür."]},"beginTime":374,"endTime":474,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=374&ask_summarization=1"},{"index":7,"title":"Sayı Karşılaştırması","list":{"type":"unordered","items":["x²y² \u003c xy² \u003c x²y eşitsizliklerinden x ve y'nin pozitif sayılar olduğu anlaşılır.","xy² \u003c x²y eşitsizliğinden y \u003c y² çıkarılıp, 0 \u003c y \u003c 1 olduğu belirlenir.","x²y \u003c xy² eşitsizliğinden x² \u003c x çıkarılıp, x > 1 olduğu belirlenir.","xy ifadesi 0 ile 1 arasında bir sayıdır, bu nedenle \"xy \u003c 1\" yorumu doğrudur."]},"beginTime":474,"endTime":588,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=474&ask_summarization=1"},{"index":8,"title":"Mutlak Değer Sorusu","list":{"type":"unordered","items":["|a+b+c| = |a+b| eşitliğinden c = -2(a+b) bulunur.","|a+b|² = 8 denkleminden a+b = 2 veya a+b = -2 çıkar, ancak mutlak değer olduğu için sadece a+b = 2 olabilir.","a-b = 8 denklemiyle birlikte çözüldüğünde a = 5, b = -3 ve c = -4 bulunur, bu sayıların çarpımı 60'tır."]},"beginTime":588,"endTime":729,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=588&ask_summarization=1"},{"index":9,"title":"Sayı Özellikleri","list":{"type":"unordered","items":["4 basamaklı abcd sayısı 20'ye tam bölünebiliyorsa, d = 0 veya 5 olmalı, ancak 20'ye bölünebilmek için çift sayı olması gerekir, bu nedenle d = 0'dır.","abcd sayısı 18'in katı olduğundan 2 ve 9'a bölünebilir, abc sayısı 15'in katı olduğundan 3 ve 5'e bölünebilir.","a = 5, b = 4 ve c = 4 olarak bulunur, toplamları 13'tür."]},"beginTime":729,"endTime":839,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=729&ask_summarization=1"},{"index":10,"title":"Asal Sayılarla İlgili Problemler","list":{"type":"unordered","items":["a, b iki, ab, bc iki basamaklı sayılar ve rakamları farklı, her iki asal sayı ve üç basamaklı abc sayısı asal sayıdır.","En büyük asal sayı 97 ve 73 ile 973 sayısı oluşturulurken, en küçük asal sayı 13 ve 37 ile 137 sayısı oluşturulur.","En küçük ve en büyük asal sayıların toplamı 1110'dur."]},"beginTime":848,"endTime":945,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=848&ask_summarization=1"},{"index":11,"title":"Kümeler Problemi","list":{"type":"unordered","items":["A ve C kümelerinin birleşimi 5, A çarpı B birleşimi 30, B çarpı A birleşimi 16 olarak verilmiştir.","Kümelerin eleman sayıları hesaplanarak A kümesinin 5, B kümesinin 2 elemanlı olduğu bulunmuştur.","A kesişim C kümesinin eleman sayısı 1 olarak hesaplanmıştır."]},"beginTime":945,"endTime":1049,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=945&ask_summarization=1"},{"index":12,"title":"Mantık Problemi","list":{"type":"unordered","items":["İki basamaklı ve doğal sayı için a+b=5 ve a×b=6 önermeleri verilmiştir.","Bu önermenin yanlış olması durumunda, a+b=5 ve a×b≠6 veya a+b≠5 ve a×b=6 olmalıdır.","a=5, b=0 ve a=1, b=6 değerleri bulunarak toplamları 182 olarak hesaplanmıştır."]},"beginTime":1049,"endTime":1177,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1049&ask_summarization=1"},{"index":13,"title":"Fonksiyon Problemi","list":{"type":"unordered","items":["Gerçek sayılar kümesinde tanımlı f ve g fonksiyonları için f(3)+g(3)=4 ve f(5)-g(5)=6 işlemleri tanımlanmıştır.","a ve b değerleri hesaplanarak a=5/3 ve b=-17 bulunmuştur.","a-b farkı 56/3 olarak hesaplanmıştır."]},"beginTime":1177,"endTime":1294,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1177&ask_summarization=1"},{"index":14,"title":"Kombinasyon Problemi","list":{"type":"unordered","items":["(x+7/x)^13 açılımında x^11'li terimin katsayısı 234 olarak verilmiştir.","Kombinasyon formülü kullanılarak 13C1×7^1=234 denklemi çözülmüştür.","a değeri 9 olarak bulunmuştur."]},"beginTime":1294,"endTime":1408,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1294&ask_summarization=1"},{"index":15,"title":"Permütasyon Problemi","list":{"type":"unordered","items":["Bir manav 6 meyveden oluşan tezgahında muzları belirli bir bölmede yerleştirmiştir.","Kalan 5 meyvenin her biri farklı bir bölmede yerleştirilmeli ve önde olan her meyvenin arkasındaki meyvesinin fiyatı daha ucuz olmalıdır.","Çırak meyvelerin kaç farklı şekilde yerleştirilebileceği sorulmaktadır."]},"beginTime":1408,"endTime":1450,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1408&ask_summarization=1"},{"index":16,"title":"Meyve Sıralama Problemi","list":{"type":"unordered","items":["En pahalı ürün (çilek) kesinlikle arka kısımda kalacak çünkü önde olursa ondan daha pahalı bir meyve olmadığı için yer değiştirilemez.","Çileğin altına dört meyveden biri yerleştirilebilir, muzun altına ise üç meyveden biri yerleştirilebilir.","Toplam 24 (2 x 4 x 3) farklı seçenek bulunuyor ve bu da B seçeneğini getiriyor."]},"beginTime":1453,"endTime":1545,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1453&ask_summarization=1"},{"index":17,"title":"Hediye Çeki Problemi","list":{"type":"unordered","items":["Veysel Bey, iki kızına (Yasemin ve Zehra) 200, 400, 600 ve 800 TL değerindeki dört hediye çeki arasından birer tanesini veriyor.","Yasemin 300 TL, Zehra ise 500 TL değerinde bir elbise beğeniyor ve her iki kızın da sadece babalarından aldıkları hediye çekleriyle elbiselerini alabilme olasılığı soruluyor.","Sorunun iki farklı çözüm yöntemiyle çözülmesi sonucunda 3/4 olasılık değeri bulunuyor ve B seçeneği olarak belirleniyor."]},"beginTime":1545,"endTime":1788,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1545&ask_summarization=1"},{"index":18,"title":"Matematik Denklem Problemi","list":{"type":"unordered","items":["x gerçek sayı olmak üzere x² + 8xy = 60 denklemi verilmiş ve x×y değeri soruluyor.","Denklem 4 ile çarpılıp düzenlendiğinde (x+2y)² = 0 ifadesi elde ediliyor ve x = 2y olarak bulunuyor.","x = 2y değeri denklemde yerine konularak y² = 3 bulunuyor, yani y = ±√3 ve x = ±2√3 oluyor, bu da x×y = ±6 sonucunu veriyor."]},"beginTime":1788,"endTime":1882,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1788&ask_summarization=1"},{"index":19,"title":"Eşitsizlik Sorusu Çözümü","list":{"type":"unordered","items":["Eşitsizlik sorusunda x=a ve x=-2a denkleminin kökleri bulunuyor.","Denklemlerin çözüm kümesi belirlenirken, a\u003cb kabul edilerek köklerin sıralaması yapılır.","Çözüm kümesindeki değerler kullanılarak a=7 ve b=-4 bulunur, a×b çarpımı 16 olarak hesaplanır."]},"beginTime":1891,"endTime":2205,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1891&ask_summarization=1"},{"index":20,"title":"Fonksiyon Sorusu","list":{"type":"unordered","items":["Gerçek sayılar kümesi üzerinde f∘g fonksiyonu verilmiş ve a×b değeri sorulmuş.","f∘g=f(x) olduğundan g(x)=2x-4/3 olarak bulunur ve a=-4 olarak hesaplanır.","f(-4)=b olduğundan b=-4 olarak bulunur ve a×b=16 olarak sonucu E seçeneği verir."]},"beginTime":2205,"endTime":2280,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2205&ask_summarization=1"},{"index":21,"title":"Polinom Sorusu","list":{"type":"unordered","items":["Derecesi üç olan gerçek katsayılı P(x) polinomunun sadece iki farklı gerçek kökü olduğu biliniyor.","P(1)=0 ve P(2)=0 olduğuna göre P(3) değerinin alabileceği değerler incelenir.","P(3) değeri 6 veya 12 olabilir, bu değerler E seçeneği olarak verilir."]},"beginTime":2280,"endTime":2360,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2280&ask_summarization=1"},{"index":22,"title":"Sınavın En Zor Sorusu","list":{"type":"unordered","items":["Sınavın en zor sorusu, a ve b gerçek tam sayılar olmak üzere, bir polinomun sadece bir tane gerçek kökü olduğundan bahsediyor.","Polinomun birinci türevinin delta değeri sıfırdan küçük olması gerektiği, böylece sadece bir gerçek kök olabileceği açıklanıyor.","Polinomun katsayıları arasındaki ilişkiler kullanılarak, a'nın en küçük değeri -3 olarak bulunuyor."]},"beginTime":2362,"endTime":2651,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2362&ask_summarization=1"},{"index":23,"title":"Tarla Alanı Problemi","list":{"type":"unordered","items":["Dayız Ahmet amcanın kare biçimli tarlasında, x metre kenar uzunluğunda bir kısma ayçiçek yetiştirildiği ve geriye kalan alanın 1400 metrekare olduğu belirtiliyor.","Tüm alandan bahçenin alanı çıkarılarak, x'in değeri 10 olarak bulunuyor.","Tarlanın çevresi 160 olarak hesaplanıyor."]},"beginTime":2651,"endTime":2752,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2651&ask_summarization=1"},{"index":24,"title":"Parabol Sorusu","list":{"type":"unordered","items":["Üç farklı parabol grafiği verilmiş ve a×b×c>0 koşulunu sağlayan hangi grafiklerin doğru olduğu soruluyor.","Parabollerin kökleri ve yönleri incelenerek, a, b ve c değerlerinin işaretleri belirleniyor.","Birinci ve üçüncü grafiklerin doğru olduğu, diğerlerinin yanlış olduğu sonucuna varılıyor."]},"beginTime":2752,"endTime":2967,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2752&ask_summarization=1"},{"index":25,"title":"Logaritma Sorusu","list":{"type":"unordered","items":["Bir logaritma sorusunda, tanım kümesinin bulunması için gerekli koşullar inceleniyor.","x²+14x-24>0 eşitsizliği ve x≠6 koşuluyla tanım kümesi belirleniyor.","Koordinat düzlemindeki ifadelerin neyi nereye yazıldığını bilmek tüm matematik konularında önemli olduğu vurgulanıyor."]},"beginTime":2967,"endTime":2995,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2967&ask_summarization=1"},{"index":26,"title":"Üçgen Alan Hesaplama","list":{"type":"unordered","items":["ABC üçgeninin alanı 6 verilmiş ve soruda sarı üçgenin alanı isteniyor.","Üçgenin alanı için taban ve yükseklik bilgileri bulunmalı, taban 4 birim, yükseklik ise logaritma hesaplamalarıyla 3 birim olarak hesaplanıyor.","Üçgenin alanı 3×4/2=6 olarak bulunuyor."]},"beginTime":2999,"endTime":3117,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2999&ask_summarization=1"},{"index":27,"title":"Logaritma Sorusu","list":{"type":"unordered","items":["x pozitif gerçek sayı olmak üzere logaritma eşitliği verilmiş ve x'in değeri soruluyor.","Logaritma ifadeleri eşitlenerek x²+9x+20=9x+27 denklemi elde ediliyor.","Denklemin çözümü x=√7 olarak bulunuyor."]},"beginTime":3117,"endTime":3214,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=3117&ask_summarization=1"},{"index":28,"title":"Fonksiyon Değerleri","list":{"type":"unordered","items":["a(n) fonksiyonu için n yerine 1, 2, 3, 4, 5 değerleri verilerek a(3), a(4), a(5) değerleri hesaplanıyor.","a(3)=3, a(4)=-2, a(5)=18, a(6)=-14 olarak bulunuyor.","a(3) ile a(6) arasındaki değerlerin toplamı 8 olarak hesaplanıyor."]},"beginTime":3214,"endTime":3413,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=3214&ask_summarization=1"},{"index":29,"title":"Geometrik Dizi Sorusu","list":{"type":"unordered","items":["İlk iki terimi b₁ ve b₂ olan geometrik dizinin ortak çarpanı 3/2 olarak bulunuyor.","b₇=a₁+10 eşitliği kullanılarak a₁ değeri hesaplanıyor.","a₁=3/16 olarak bulunuyor."]},"beginTime":3413,"endTime":3534,"href":"/video/preview/6788562601587801717?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=3413&ask_summarization=1"},{"index":30,"title":"Trigonometri Sorusu","list":{"type":"unordered","items":["135°\u003ca\u003c140° aralığında sin3a×cos3a+2cos3a×tan3a+sin3a×cot3a ifadesinin işaretleri inceleniyor.","Sin3a×cos3a ifadesi pozitif, 2cos3a×tan3a ifadesi 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İçerik, sayı basamakları, denklem, faktöriyel, asal sayılar, eşitsizlik, fonksiyon grafikleri, kümeler, mantık, ikinci dereceden denklemler, aritmetik diziler, logaritma, sayma, koşullu olasılık, binom, limit, parabol, türev, integral ve alan hesaplama gibi konuları kapsamaktadır. Video, matematik sınavlarına hazırlanan öğrenciler için kapsamlı bir problem çözüm seti sunmaktadır.","Eğitmen, her soru için çözüm yöntemlerini detaylı olarak anlatmakta, gerekli formülleri kullanmakta ve görselleştirme teknikleri ile konuları daha anlaşılır hale getirmektedir. Video, matematik kısmının sonunda geometri konusunun ayrı bir videoda ele alınacağı bilgisiyle sonlanmaktadır."]},"endTime":4553,"title":"2024 AYT Matematik Sınavı Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"2024 AYT Matematik Sınavı Değerlendirmesi","list":{"type":"unordered","items":["2024 AYT matematik sınavı 10 üzerinden 8'lik, zor ve ayırt ediciliği yüksek bir sınav olarak değerlendiriliyor.","Sınav işlem ağırlıklı ve mantık odaklı değil, bu nedenle 30 net yapanların düştüğü, full yapanların 5-6 yanlış yaptığı bir sınav olarak değerlendirilebilir.","Sınav 2021'in bir tık üstü olarak değerlendirilebilir ve kendi puanlarınızı bu şekilde değerlendirmeniz daha sağlıklı olacaktır."]},"beginTime":0,"endTime":57,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=0&ask_summarization=1"},{"index":1,"title":"İlk Soru - Sayı 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bulunuyor."]},"beginTime":166,"endTime":226,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=166&ask_summarization=1"},{"index":3,"title":"Üçüncü Soru - Faktöriyel","list":{"type":"unordered","items":["Üçüncü soru herkesin zorlandığı ve tartışılan bir soru olup, 25! sayısının 23!a'ya bölünmesi ve kalanın 60² olduğu bilgisi verilmiş.","Bölme algoritması kullanılarak 25! = 23!a + 600² ilişkisi elde ediliyor.","a=6 olarak bulunuyor ve sonuç e seçeneği olarak belirleniyor."]},"beginTime":226,"endTime":337,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=226&ask_summarization=1"},{"index":4,"title":"Dördüncü Soru - Asal Sayılar","list":{"type":"unordered","items":["Dördüncü soru asal sayılar konusundan olup, x+y×z=1 ve x, y, z'nin farklı asal sayılar olduğu bilgisi verilmiş.","x, y ve z'nin biri tek, biri çift olması gerektiği belirleniyor.","x=2, y=5, z=11 değerleri bulunuyor ve toplamları 18 olarak hesaplanıyor."]},"beginTime":337,"endTime":430,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=337&ask_summarization=1"},{"index":5,"title":"Beşinci Soru - Eşitsizlik","list":{"type":"unordered","items":["Beşinci soru eşitsizlik konusundan olup, a bir tam sayı olmak üzere x²-(2x+2) mutlak değerden çıkarılması gerektiği belirtiliyor.","Delta hesaplanarak x²-2x+2 ifadesinin her zaman pozitif olduğu bulunuyor.","Eşitsizlik çözülerek a'nın alabileceği değerlerin toplamı 39 olarak hesaplanıyor."]},"beginTime":430,"endTime":642,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=430&ask_summarization=1"},{"index":6,"title":"Fonksiyonların Karşılaştırılması","list":{"type":"unordered","items":["Bir açık aralığında abc gerçek sayılar olmak üzere, f(a) \u003c g(a) olduğunda, f ve g fonksiyonlarının hangi bölgede en küçük olduğu incelenir.","Grafik dört bölgeye ayrılarak incelenir ve f > b > g olduğunda, b değeri ortada, f fonksiyonu üstteki, g fonksiyonu alttaki olarak belirlenir.","a değeri g(a) dan daha büyük olduğunda, c değeri en küçük olduğunda, abc'nin sıralaması b > c > a olarak bulunur."]},"beginTime":651,"endTime":814,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=651&ask_summarization=1"},{"index":7,"title":"Doğrusal Fonksiyonların Grafikleri","list":{"type":"unordered","items":["Dik koordinat düzleminde f, g ve h doğrusal fonksiyonların grafikleri verilmiş ve f(x-5) = g(x) olduğu belirtilmiştir.","h(x) = f(-x) olduğundan, h fonksiyonu f fonksiyonunun x eksenine göre simetriği olarak belirlenir.","Grafiklerde f en üstte, h ikinci sırada, g en altta olduğu için f > h > g sıralaması yapılır."]},"beginTime":814,"endTime":902,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=814&ask_summarization=1"},{"index":8,"title":"Kümeler ve Kartezyen Çarpım","list":{"type":"unordered","items":["A ve B kümeleri için A×B ile B×A'nın ortak elemanları 209 ise, birleşim formülü kullanılarak hesaplamalar yapılır.","A×B ve B×A'nın eleman sayıları birbirine eşit olduğundan, her birinin eleman sayısı 117 olarak bulunur.","A×B'nin eleman sayısı 117 olduğundan, A ve B kümelerinin eleman sayıları 9 ve 13 olarak belirlenir ve A∪B'nin eleman sayısı 17 olarak hesaplanır."]},"beginTime":902,"endTime":1064,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=902&ask_summarization=1"},{"index":9,"title":"Kümelerle Mantık Sorusu","list":{"type":"unordered","items":["Soruda \"veya\" bağlacında sıfıra sıfır gelmesi gerektiği belirtiliyor.","P ise R'nin değili veya Q ve P ifadeleri doğru olarak değerlendiriliyor.","A ve B kümelerinin birleşimi 8 eleman içerirken, kesişimleri boş küme olduğu için A kesişim B 7 eleman olarak bulunuyor."]},"beginTime":1066,"endTime":1191,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1066&ask_summarization=1"},{"index":10,"title":"İkinci Dereceden Denklem Sorusu","list":{"type":"unordered","items":["Her bir köklerinin toplamı köklerinin çarpımından bir fazla olan ikinci dereceden denklem soruluyor.","Kökler toplamı ve çarpımı formülleri kullanılarak a=4/3 ve b=2 değerleri bulunuyor.","Kökleri 2 ve 8 olan denklem 9x²-18x+8=0 olarak yazılıyor."]},"beginTime":1191,"endTime":1338,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1191&ask_summarization=1"},{"index":11,"title":"Grafik Yorumlama Sorusu","list":{"type":"unordered","items":["Gerçek sayılar kümesi üzerinde tanımlanan f(x) fonksiyonu pozitif gerçek sayılarda pozitif, negatiflerde negatif değer alıyor.","Fonksiyonun bir kökü sıfırdan geçtiği ve diğer kökünün olmadığı belirtiliyor.","a'nın en küçük tam sayı değeri 21 olarak bulunuyor."]},"beginTime":1338,"endTime":1463,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1338&ask_summarization=1"},{"index":12,"title":"Aritmetik Dizi Sorusu","list":{"type":"unordered","items":["a ortak fark aritmetik dizi olmak üzere, a₃₀ ve a₈ terimleri için eşitsizlikler kuruluyor.","r'nin alabileceği tam sayı değerleri 4, 5, 6, 7, 8, 9 ve 10 olarak bulunuyor.","r'nin alabileceği tam sayı değerlerinin toplamı 49 olarak hesaplanıyor."]},"beginTime":1463,"endTime":1570,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1463&ask_summarization=1"},{"index":13,"title":"Logaritma Sorusu Çözümü","list":{"type":"unordered","items":["Soruda a, x, y pozitif gerçek sayılar küçükten büyüğe doğru sıralanmış ve ardışık tam sayılar olarak verilmiştir.","Logaritma a tabanında x+1 = logaritma a tabanında y ve logaritma a tabanında x+2 = logaritma a tabanında x+y ilişkileri kullanılarak a² = 1+a denklemi elde edilmiştir.","Logaritma a tabanında a² + a ifadesi hesaplanarak cevap 3 olarak bulunmuştur."]},"beginTime":1580,"endTime":1777,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1580&ask_summarization=1"},{"index":14,"title":"Sayma Sorusu Çözümü","list":{"type":"unordered","items":["Melisa, yarıçapları farklı doğal sayı olan 1'den 10'a kadar 10 karton çember kartonu merkeze çakışacak şekilde üst üste dizecektir.","Üstteki dairelerin yalnızca bir hiç görünmeyecek şekilde sıralama yapılabilir.","Her bir dairenin görünmemesi için 9 farklı seçenek olduğu için toplam 45 farklı sıralama yapılabilir."]},"beginTime":1777,"endTime":1871,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1777&ask_summarization=1"},{"index":15,"title":"Koşullu Olasılık Sorusu Çözümü","list":{"type":"unordered","items":["Duru'nun evinin yakınında bulunan otobüs durağına belli bir yolda 7/10 olasılıkla tam saat 9:12'de, 3/10 olasılıkla 9:03'te gelmektedir.","Duru saat 9'da evden çıkıp durağa varması 1/2 olasılıkla 100 saniye, 3 olasılıkla 150 saniye, 1/5 olasılıkla 250 saniye sürmektedir.","Duru'nun durakta bulunma ihtimali 900/100+150/100=900/150=5/9 olarak hesaplanmıştır."]},"beginTime":1871,"endTime":2053,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1871&ask_summarization=1"},{"index":16,"title":"Binom Sorusu Çözümü","list":{"type":"unordered","items":["(2x+5/2)ⁿ ifadesinde sabit terim 60 olduğuna göre n+m değeri sorulmaktadır.","Sabit terim bulmak için x ve y'nin kuvvetlerinin sıfır olması gerekir, bu nedenle m+1=n denklemi elde edilmiştir.","Binom formülü kullanılarak n=12 ve m=11 bulunmuş, toplamları 23 olarak hesaplanmıştır."]},"beginTime":2053,"endTime":2154,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2053&ask_summarization=1"},{"index":17,"title":"Limit Sorusu Çözümü","list":{"type":"unordered","items":["Soruda limit ifadesi verilmiş ve iki farklı yöntemle çözülebileceği belirtilmiştir.","İlk yöntemde değişken değiştirme kavramı kullanılarak x⁶=a dönüşümü yapılmıştır.","İkinci yöntemde ifade çarpanlarına ayrılarak sadeleştirme yapılmıştır."]},"beginTime":2154,"endTime":2255,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2154&ask_summarization=1"},{"index":18,"title":"Limit Probleminin Çözümü","list":{"type":"unordered","items":["Limit a bir'e giderken, üst taraf a'nın karesi eksi iki, alt taraf a'nın dördüncü kuvveti olarak hesaplanıyor.","Küp açılımı kullanılarak a'nın küpü eksi b'nin küpü eşittir a b çarpı a'nın karesi artı ab artı b'nin karesi formülü uygulanıyor.","Çarpanlara ayırma yöntemiyle limit değeri 1/14 olarak bulunuyor."]},"beginTime":2258,"endTime":2362,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2258&ask_summarization=1"},{"index":19,"title":"Leos Kuralı ile Çözüm","list":{"type":"unordered","items":["Leos kuralı, üstün türevi bölü altın türevidir.","Üst ve alt ifadelerin türevleri alınarak limit değeri hesaplanıyor.","Türevler yerine yazılıp hesaplandığında da limit değeri 1/14 olarak bulunuyor."]},"beginTime":2362,"endTime":2454,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2362&ask_summarization=1"},{"index":20,"title":"Fonksiyonların Sürekliliği","list":{"type":"unordered","items":["f(x) fonksiyonunun grafiği ve g(x) fonksiyonunun limit değeri verilmiş.","f(x) çarpı g(x) fonksiyonunun sürekli olduğu bilgisi kullanılarak limit değerleri hesaplanıyor.","g(3) değeri 8 olarak bulunuyor."]},"beginTime":2454,"endTime":2555,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2454&ask_summarization=1"},{"index":21,"title":"Parabol Sorusu Çözümü","list":{"type":"unordered","items":["Parabol x eksenine ve y=x doğrusuna teğet olduğunda, delta'nın sıfır olması gerekir.","Denklem x²+ax+b=x şeklinde yazıldığında, x'i diğer tarafa göndererek x²+a-1x+b=0 şeklinde düzenlenir.","Delta'nın sıfır olması için a²-4b=0 ve (a-1)²-4b=0 denklemleri çözülür, sonuç olarak a=1/2 ve b=1/16 bulunur, a×b=2 olarak hesaplanır."]},"beginTime":2557,"endTime":2684,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2557&ask_summarization=1"},{"index":22,"title":"Fonksiyon Sorusu Çözümü","list":{"type":"unordered","items":["Daima artan bir fonksiyonun türevi, artan ifadelerde ikinci derece denklem gelirse delta'nın sıfırdan küçük eşit olması gerekir.","f(x)=ax²+bx+1 fonksiyonunun türevi f'(x)=3ax²+2bx+1 olarak bulunur ve delta\u003c0 koşulu uygulanır.","f(-1)=0 koşulu kullanılarak a=-b+6 bulunur ve b'nin alabileceği tam sayı değerleri (-3, -2, -1, 0, 1, 2, 3, 4, 5, 6) toplamı 15 olarak hesaplanır."]},"beginTime":2684,"endTime":2859,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2684&ask_summarization=1"},{"index":23,"title":"Türev ve Ekstremum Sorusu","list":{"type":"unordered","items":["f(x)=6x²-18x+m ve g(x)=3x²f(x)+2g(x) fonksiyonları için x=-1 noktasında yerel ekstremum olması için f'(-1)=g'(-1) olmalıdır.","f'(x)=6x²-18x+m türevinden f'(-1)=0 denklemi çözülür ve m=24 bulunur.","g'(x) türevinden g'(-1)=0 denklemi çözülür ve k=13 bulunur, m+k=37 olarak hesaplanır."]},"beginTime":2859,"endTime":2983,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2859&ask_summarization=1"},{"index":24,"title":"Dikdörtgen Alanı Problemi","list":{"type":"unordered","items":["İki x artı üç ve oniki x doğruları pozitif x ve y eksenleri arasında kalan bölgede, bir kenarı x ekseni üzerinde, diğer köşeleri bu doğrular üzerinde olan en büyük dikdörtgenin x ekseni üzerindeki kenarın uzunluğu soruluyor.","Üçgenin içine çizilen en büyük dörtgenin alanı, üçgenin alanının yarısıdır ve bu durumda dörtgenin yüksekliği 19/3 birim olarak bulunuyor.","Dikdörtgenin x ekseni üzerindeki kenarı, üçgenin tabanının yarısı olan 19/3 birimdir."]},"beginTime":2987,"endTime":3196,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=2987&ask_summarization=1"},{"index":25,"title":"İntegral Sorusu","list":{"type":"unordered","items":["İntegral sorusunda değişken değiştirme yöntemi kullanılarak x²+4x-4=u dönüşümü yapılıyor ve dx=2du ilişkisi bulunuyor.","İntegral sınırları x=1 için u=1 ve x=2 için u=8 olarak belirleniyor.","İntegral hesaplanarak sonucu 45/8 olarak buluyoruz."]},"beginTime":3196,"endTime":3343,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=3196&ask_summarization=1"},{"index":26,"title":"Grafik Problemi","list":{"type":"unordered","items":["Dik koordinat düzleminde verilen grafikte, A-B arasındaki alan A, B-C arasındaki alan B olarak adlandırılıyor ve mutlak değer aldığı için A+B=20 olarak belirleniyor.","A-C arasındaki alan B-A=8 olarak hesaplanıyor ve B'nin değeri 14 olarak bulunuyor.","İntegral hesaplaması yapılarak sonucun -3 olduğu bulunuyor."]},"beginTime":3343,"endTime":3465,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=3343&ask_summarization=1"},{"index":27,"title":"Alan Hesaplama Problemi","list":{"type":"unordered","items":["Mavi boyalı bölgenin alanı A₁, sarı boyalı bölgenin alanı A₂ ise A₁×A₂=96 olarak veriliyor.","A₂'nin alanı hesaplanarak 8/3 olarak bulunuyor ve A₁×8/3=96 denkleminden A₁=36 olarak hesaplanıyor.","İntegral hesaplaması yapılarak A'nın değeri 3 olarak bulunuyor."]},"beginTime":3465,"endTime":3687,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=3465&ask_summarization=1"},{"index":28,"title":"Değişken Değiştirme ve İntegral Sorusu","list":{"type":"unordered","items":["Değişken değiştirme konusu iyi oturmazsa, integral sorularında hata yapma oranı artar.","İntegral sorusunda değişken değiştirme yaparak f'(x) yerine u alarak integral çözülür.","İntegral sonucunda f(6) = 17 bulunur ve g'(3) = 17 olarak hesaplanır."]},"beginTime":3691,"endTime":3810,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=3691&ask_summarization=1"},{"index":29,"title":"Trigonometrik Sıralama Sorusu","list":{"type":"unordered","items":["Sin alfa ve tan alfa arasında seçim yaparken, tan alfa alfa'dan daha büyüktür.","Secant ve cosecant ifadeleri kesinlikle 1'den büyük veya -1'den küçük değerler alır.","Sıralama sorusunda b > c > a olarak işaretlenir ve cevap B seçeneğidir."]},"beginTime":3810,"endTime":3882,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=3810&ask_summarization=1"},{"index":30,"title":"Trigonometrik Toplam Fark Sorusu","list":{"type":"unordered","items":["Trigonometrik toplam fark formülü kullanılarak cos(2x+y) ve sin(2x+y) ifadeleri açılır.","Ortak çarpan parantezine alınarak sadeleştirme yapılır.","Sonuç olarak cosx.siny bulunur ve cevap A seçeneğinde mevcuttur."]},"beginTime":3882,"endTime":4004,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=3882&ask_summarization=1"},{"index":31,"title":"Trigonometrik Denklem Sorusu","list":{"type":"unordered","items":["cos²a - sin²a = 2sina.cosa denklemi açılarak sina = 2cosa bulunur.","sina/cosa = 2 olarak hesaplanır ve üçgen çizilerek tan a = 2, cos a = 1/√5 bulunur.","cosec a = 1/sin a = √5/2 olarak hesaplanır ve cevap C seçeneğidir."]},"beginTime":4004,"endTime":4122,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=4004&ask_summarization=1"},{"index":32,"title":"Zor Trigonometrik Denklem Sorusu","list":{"type":"unordered","items":["cos8x ifadesi cos²4x - sin²4x şeklinde yazılır ve denklem düzenlenir.","Denklem çarpanlarına ayrılır ve sin4x = -2/3 veya sin4x = 1/2 kökleri bulunur.","x değerleri hesaplanarak toplamı 3π/2 olarak bulunur ve cevap D seçeneğidir."]},"beginTime":4122,"endTime":4406,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=4122&ask_summarization=1"},{"index":33,"title":"Geometri Sorusu Çözümü","list":{"type":"unordered","items":["Eğitmen, geometri konusunu ayrı bir videoda çözeceğini ve TYT sınavında ilerleyen zamanda bu konuyu da çözeceğini belirtiyor.","Soruda ABCD dörtgeninin bir köşegeninin uzunluğunun x türünden hangi ifadeye eşit olduğu soruluyor.","AE uzunluğu 1/2 olarak verilmiş ve köşegen uzunluğu bulunması isteniyor."]},"beginTime":4410,"endTime":4443,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=4410&ask_summarization=1"},{"index":34,"title":"Trigonometrik Çözüm","list":{"type":"unordered","items":["AO uzunluğu kotanjant x cinsinden bulunarak 2AO = kotanjant x denklemi elde ediliyor.","AO uzunluğu cotanjant x/2 olarak hesaplanıyor.","Dörtgenin köşegen uzunluğu için a² = 1 + cot²x denklemi kuruluyor."]},"beginTime":4443,"endTime":4504,"href":"/video/preview/13446622350859574680?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=4443&ask_summarization=1"},{"index":35,"title":"Sonuç ve Kapanış","list":{"type":"unordered","items":["Denklem düzenlenerek a = 1/√(sin²x + cos²x) = 1/sin2x olarak bulunuyor.","Matematik kısmında 31 soru çözüldüğü belirtiliyor.","İzleyicilerden yorumlarını, net sayılarını 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Kitabı beraber takip etmeye ne dersin ? düşüncelerini mutlaka yorum kısmına istiyorum iyi çalışmalar :) SORU - Görüş VE Öneri...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2129470/85c2eaa1455356c6fe1d3dc3aa0912ec/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/boNLQgIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"16","reqid":"1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=videoid:8857430685569662221","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin 345 Yayınları AYT soru bankasının logaritma konusunun altıncı testini çözdüğü eğitim içeriğidir. Öğretmen, ÖSYM'den önceki en zor test olduğunu belirterek öğrencilere sabır dilemektedir.","Videoda 13 sorunun adım adım çözümü gösterilmektedir. Sorular arasında logaritma tabanlarının değiştirilmesi, logaritma ifadelerinin sadeleştirilmesi, logaritma denklemlerinin çözümü, fonksiyonların tersi, bileşke fonksiyonlar ve logaritma ekleme gibi konular yer almaktadır. Öğretmen her soru için farklı çözüm yöntemlerini göstermekte ve öğrencilerin sık yaptığı hataları vurgulamaktadır.","Video, 2022 sınavından çıkmış bir logaritma sorusunu da içermekte ve altı testin sonunda ÖSYM sorularının çözüleceği belirtilmektedir. Matematik sınavlarına hazırlanan öğrenciler için fonksiyon ve logaritma konularında pratik çözümler sunmaktadır."]},"endTime":1847,"title":"AYT Logaritma Konusu Test Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Logaritma Konusunun Altıncı Testi","list":{"type":"unordered","items":["Üçyüzkırkbeş yayınları AYT soru bankasının logaritma konusunun altıncı testi çözülecek.","Bu test, ÖSYM den önceki en zor test olup, sorular kaliteli ve zorlayıcıdır.","İlk soru 2022'den çıkmış olup, logaritma beş tabanında a ifadesinin logaritma tabanında a kapalı alanda bulunan tam sayılarla aynı olduğu belirtilmiştir."]},"beginTime":0,"endTime":47,"href":"/video/preview/8857430685569662221?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=0&ask_summarization=1"},{"index":1,"title":"İlk Sorunun Çözümü","list":{"type":"unordered","items":["Soruda a bir tam sayı olmak üzere logaritma beş tabanında a logaritma tabanında a kapalı alanda bulunan tam sayılar dört ve beş kapalılar alanındaki tam sayılarla aynıdır.","a değerlerinin toplamı 456 ise, a'nın alabileceği değerler toplamı sorulmaktadır.","Çözüm için logaritma beş tabanında a > 3 ve logaritma iki tabanında a \u003c 7 aralıkları belirlenir, bu aralıkta a = 126 ve a = 127 değerleri bulunur ve toplamları 253'tür."]},"beginTime":47,"endTime":183,"href":"/video/preview/8857430685569662221?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=47&ask_summarization=1"},{"index":2,"title":"İkinci Sorunun Çözümü","list":{"type":"unordered","items":["İkinci soruda karışık bir ifade verilmiş ve düzeltilmesi gerekmektedir.","İşlem sonucunda 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a = 300a × 2^a ="]},"beginTime":183,"endTime":436,"href":"/video/preview/8857430685569662221?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=183&ask_summarization=1"},{"index":3,"title":"Fonksiyon Uygulaması Soruları","list":{"type":"unordered","items":["Dördüncü soruda f(x) fonksiyonu verilmiş ve x'in f(x) türünden değeri isteniyor.","Fonksiyonun özellikleri ve logaritma kuralları kullanılarak f(x) = -f(x+1) sonucuna ulaşılmış ve cevap C seçeneği olarak belirlenmiş.","Beşinci soruda fonksiyon uygulaması sorusu çözülmüş, f(ln4x) = ln4y eşitliği kullanılarak x'in y türünden değeri x = 2y olarak bulunmuş ve cevap E seçeneği olarak belirlenmiş."]},"beginTime":442,"endTime":622,"href":"/video/preview/8857430685569662221?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=442&ask_summarization=1"},{"index":4,"title":"Zor Fonksiyon Sorusu","list":{"type":"unordered","items":["Altıncı soru testin en zor sorusu olarak tanımlanmış ve uzun bir çözüm gerektirmiş.","Logaritma ifadeleri düzenlenerek beta1 ve beta2 fonksiyonları tanımlanmış ve f(8) değeri hesaplanmış.","Hesaplamalar sonucunda f(8) = 3(beta1+1) olarak bulunmuş ve cevap E seçeneği olarak belirlenmiş."]},"beginTime":622,"endTime":880,"href":"/video/preview/8857430685569662221?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=622&ask_summarization=1"},{"index":5,"title":"Fonksiyonun Tersi ve Y Eksenini Kesme","list":{"type":"unordered","items":["Yedinci soruda fonksiyonun tersini bulmak için x=y doğrusuna göre simetri kuralı kullanılmış.","f, g ve h fonksiyonlarının tersleri çizilmiş ve y eksenini kesme durumları incelenmiş.","f'in tersi ve h'in tersi y eksenini keserken, g'nin tersi y eksenini kesmediği için cevap C seçeneği olarak belirlenmiş."]},"beginTime":880,"endTime":1042,"href":"/video/preview/8857430685569662221?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=880&ask_summarization=1"},{"index":6,"title":"Logaritma Problemi Çözümü","list":{"type":"unordered","items":["Logaritma probleminde m = 2³ = 8 olarak hesaplanır.","Logaritma ifadeleri düzenlenerek m² + n² = 100 bulunur ve bu ifade log₁₀² = 2 olarak ifade edilir.","Sonuç olarak log₁₀ = 2 olarak bulunur ve cevap C seçeneğidir."]},"beginTime":1045,"endTime":1196,"href":"/video/preview/8857430685569662221?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1045&ask_summarization=1"},{"index":7,"title":"Çarpanlara Ayırma Problemi","list":{"type":"unordered","items":["2^(a-b) × (a+b) = x şeklinde verilen ifadede, a+b = logₐₓ olarak bulunur.","a+b ifadesi logₐₓ olarak ifade edilir ve cevap A seçeneğidir."]},"beginTime":1196,"endTime":1244,"href":"/video/preview/8857430685569662221?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1196&ask_summarization=1"},{"index":8,"title":"Logaritma İşaretleri ve Koşulları","list":{"type":"unordered","items":["Logaritma ifadesinin alt tabanı b sıfırdan küçükse, b \u003c 1 ve a \u003c 1 olmalıdır.","Logaritma ifadesinin alt tabanı b sıfırdan büyükse, a > 1 ve b > 1 olmalıdır.","Verilen koşullara göre a+b > 1 ve b-a > 0, ancak a×b > 1 olmayabilir."]},"beginTime":1244,"endTime":1368,"href":"/video/preview/8857430685569662221?parent-reqid=1765304988816244-14098137667830775886-balancer-l7leveler-kubr-yp-vla-238-BAL&text=Matematik+Avc%C4%B1s%C4%B1&t=1244&ask_summarization=1"},{"index":9,"title":"Logaritma Özellikleri ve Çözüm Yöntemleri","list":{"type":"unordered","items":["a üzeri logₓₐ = b üzeri logₓₐ şeklinde yer değiştirme yapılabilir.","Logaritma ifadelerinde kısır 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