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Eğitmen, tahtada veya whiteboard üzerinde çeşitli matematik sorularını adım adım çözmektedir.","Videoda toplam 30'dan fazla farklı matematik problemi ele alınmaktadır. Problemler işlem önceliği, sayılarla ilgili işlemler, irrasyonel sayılar, asal çarpanlar, ardışık sayılar, faktöriyel, tam kare sayılar, eşitsizlikler, bölme işlemleri ve sayı grupları gibi çeşitli matematik konularını kapsamaktadır. Her problem için eğitmen, çözüm yöntemini detaylı olarak açıklamakta ve doğru cevabı belirtmektedir.","Video, TYT ve AYT sınavlarına hazırlanan öğrenciler için faydalı olabilecek problem çözme stratejilerini içermektedir. Özellikle faktöriyel konusundaki zorlukları gidermek, ardışık sayılarla ilgili problemleri çözmek ve sayıların bölünebilme kurallarını uygulamak isteyen öğrenciler için hazırlanmıştır."]},"endTime":7196,"title":"Matematik Problemleri Çözüm Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Matematik Problemleri Çözümü","list":{"type":"unordered","items":["İlk problemde 6-35÷(-5×-2) işleminin sonucu bulunuyor, önce parantez içindeki çarpma işlemi yapılıyor ((-5×-2)=10), sonra bölme işlemi (35÷7=5) ve son olarak çıkarma işlemi (6-5=1) yapılıyor.","İkinci problemde a+b×c÷d ifadesinde -4, -3, 6 ve 12 sayıları farklı harflere yerleştirilerek hangi sonuçlar elde edilebileceği inceleniyor.","Üçüncü problemde x doğal sayısının rakamları farkının pozitif değeri olarak tanımlanan bir işlem kullanılarak, x'in rakamlarının farkının pozitif değeri 6 olan iki basamaklı sayıların toplamı 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sayılarından 8 ve 4 birbirini böler, bu nedenle 8'i bir yere, 4'ü diğer yere yazmak gerekiyor.","Mavi kutucuğa gelecek sayıların toplamı 11+15=26 olur ve doğru cevap E seçeneğidir."]},"beginTime":561,"endTime":627,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=561&ask_summarization=1"},{"index":4,"title":"Ali, Berk ve Cem Problemi","list":{"type":"unordered","items":["Ali ve Berk'in söylediği sayıların çarpımı, Ali'nin söylediği sayının dört katının 12 fazlasına eşit.","Berk'in söylediği sayı b ise, b=4a+12/a şeklinde ifade edilebilir.","a'nın 12'nin bölenleri olması gerekir ve b'nin 16, 10, 7, 8, 6, 5 değerleri olabilir, bu nedenle 9 olamaz ve doğru cevap C seçeneğidir."]},"beginTime":627,"endTime":793,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=627&ask_summarization=1"},{"index":5,"title":"Kıvanç, Levent ve Mehmet Problemi","list":{"type":"unordered","items":["Kıvanç ve Levent'in yazdığı sayıların çarpımı 30, Kıvanç ve Mehmet'in yazdığı sayıların toplamı 24.","Kıvanç'ın sayısı k olsun, k'nın alabileceği değerler 1, 2, 3 veya 6 olabilir.","Levent'in yazabileceği toplam 8 farklı sayı değeri vardır ve doğru cevap D seçeneğidir."]},"beginTime":793,"endTime":902,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=793&ask_summarization=1"},{"index":6,"title":"Adaletli Sayılar Problemi","list":{"type":"unordered","items":["Tek rakam sayısı çift rakam sayısına eşit olan sayılara adaletli sayı denir.","İki basamaklı adaletli sayılar için birler basamağı 1, 3, 5, 7, 9 olabilir ve onlar basamağı 2, 4, 6, 8 olabilir.","Toplamda 5×9=45 tane adaletli sayı vardır ve doğru cevap C seçeneğidir."]},"beginTime":902,"endTime":1024,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=902&ask_summarization=1"},{"index":7,"title":"Efe, Ela ve Elif Problemi","list":{"type":"unordered","items":["Efe'nin küpünü 5 kez, Ela'nın küpünü 4 kez ve Elif'in küpünü 3 kez havaya atıyorlar.","Efe ve Elif'in küplerinin üst yüzeylerine gelen sayıları çarptıklarında negatif bir sonuç buluyorlar.","Efe'nin küpünün üzerinde negatif sayılar varsa Elif'in küpünün üzerinde pozitif sayılar, Efe'nin küpünün üzerinde pozitif sayılar varsa Elif'in küpünün üzerinde negatif sayılar olur ve doğru cevap B seçeneğidir."]},"beginTime":1024,"endTime":1221,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=1024&ask_summarization=1"},{"index":8,"title":"Reel Sayılarla İlgili Problemler","list":{"type":"unordered","items":["x, y, z reel sayılar olmak üzere x×y², x×z ve x×y×z ifadelerinden iki tanesi negatif, bir tanesi pozitif olduğunda, x pozitif, y pozitif ve z negatif olmalıdır.","a, b, c tam sayılar olmak üzere a+b tek, b+c tek ve b×c tek olduğunda, a çift, b tek ve c tek olmalıdır.","a, b, a×b ve a+b sayılarından üç tanesi tek ve bir tanesi çift olduğunda, a ve b tek sayı olmalıdır."]},"beginTime":1229,"endTime":1471,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=1229&ask_summarization=1"},{"index":9,"title":"Sayı Doğrusu ve Mutlak Değer Problemleri","list":{"type":"unordered","items":["a\u003cc\u003cb olduğunda, b×c negatifse a sayısı b ile c arasında, a+b negatifse a'nın mutlak değeri b'nin mutlak değerinden büyüktür.","Sarı, kırmızı ve mavi kutulara yazılan pozitif tam sayıların çarpımları ve toplamları tek sayı olduğunda, bu sayılardan en az biri çift, geri kalanları tek olmalıdır.","5a+4 çift sayı olduğunda, 5a çift sayıdır ancak a'nın çift olduğu kesin değildir."]},"beginTime":1471,"endTime":1824,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=1471&ask_summarization=1"},{"index":10,"title":"Hava Durumu Problemi","list":{"type":"unordered","items":["Ankara, Bursa ve Erzurum şehirlerinin sıcaklıkları a, b ve e santigrat derece olarak verilmiştir.","Tabloda üç ilin sıcaklıkları santigrat derece cinsinden hangi değere eşit olabileceği sorulmaktadır."]},"beginTime":1824,"endTime":1851,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=1824&ask_summarization=1"},{"index":11,"title":"Matematik Problemleri Çözümü","list":{"type":"unordered","items":["B eksi a kare'den büyükse b pozitif bir sayıdır ve bu durumda hiçbir şıkkı eleyemedik.","B ile e'nin çarpımı eksi a'dan küçük ve a ile e'nin çarpımı negatif olduğundan, biri pozitifken diğeri negatif olmalıdır.","B on büyüktür ve Ankara'nın karesi dört'ün karesi on eksi onaltı'dan büyük olmadığından, cevap D seçeneği olarak bulunmuştur."]},"beginTime":1852,"endTime":1937,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=1852&ask_summarization=1"},{"index":12,"title":"Ardışık Sayılar Problemi","list":{"type":"unordered","items":["Ardışık iki pozitif tam sayının toplamı a, farkının pozitif değeri b'dir ve b'nin bir olması gerekir.","A b eşittir beş olduğundan, a beş gelir ve ardışık iki sayının toplamı beş ise bu sayılardan birisi iki, öteki de üçtür.","Bu sayıların çarpımı iki ile üçün çarpımı olan altıdır ve cevabın A seçeneğinde olduğu belirtilmiştir."]},"beginTime":1937,"endTime":1984,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=1937&ask_summarization=1"},{"index":13,"title":"Üçün Tam Katı Ardışık Sayılar","list":{"type":"unordered","items":["ABC üçün tam katı olan ardışık sayılar ve AB'den BDC'den daha küçüktür.","Üçün tam katı olan ardışık sayılarda aralarında üçer fark olması gerekir.","C sayısı a'dan altı fazla olduğundan, a sayısının yirmidört'e eşit olduğu ve c'nin otuz olduğu bulunmuştur."]},"beginTime":1984,"endTime":2103,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=1984&ask_summarization=1"},{"index":14,"title":"Ardışık Tam Sayıların Toplamı","list":{"type":"unordered","items":["A tane ardışık tam sayının toplamının yirmi olduğu söylenmiş ve a'nın alabileceği en büyük değerin rakamları toplamı sorulmuştur.","Negatif sayıları kullanarak sayı adedini maksimum tutmak için eksi ondokuz artı eksi onsekiz şeklinde başlanmıştır.","Bu şekilde sayı adedinin maksimum değeri kırk olarak bulunmuş ve bunun rakamları toplamı dört olarak hesaplanmıştır."]},"beginTime":2103,"endTime":2182,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=2103&ask_summarization=1"},{"index":15,"title":"İkizkenar Üçgen Problemi","list":{"type":"unordered","items":["İç açılarının ölçüleri derece cinsinden iki'nin tam katı olan ABC ikizkenar üçgeni verilmiştir.","Üçgenin iç açıları toplamı yüzseksen olduğundan, iki k'nın toplamı dört k olduğundan a açısının ölçüsü 180-4k olur.","A açısının alabileceği değerlerin toplamı 4'ten 88'e kadar olan 22 terimin toplamı olarak 1012 olarak bulunmuştur."]},"beginTime":2182,"endTime":2358,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=2182&ask_summarization=1"},{"index":16,"title":"Kutulara Sayı Yazma Problemi","list":{"type":"unordered","items":["Sarı kutunun içine yazılan sayı mavi kutunun içine yazılan sayının iki katı, kırmızı kutunun içine yazılan sayının da üç katıdır.","Sarı kutuların toplamı 18x, mavi kutuların toplamı 9x, kırmızı kutuların toplamı 8x olup bunların toplamı 700'dür.","X değeri 20 olarak bulunmuş ve tüm kutulara mavi renkli kutunun içindeki sayıdan (60) yazmış olsaydı toplam 600 olur."]},"beginTime":2358,"endTime":2474,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=2358&ask_summarization=1"},{"index":17,"title":"Ardışık Çift Sayılar Problemi","list":{"type":"unordered","items":["a, b, c ve d birbirinden farklı rakamlar olmak üzere, a, b ve c, d iki basamaklı ardışık çift sayılardır.","b+c-a+d ifadesinin pozitif değeri sorulduğunda, ardışık çift sayılar için onlar basamağı değiştiği için farklı örnekler denenebilir.","Tüm ihtimallerde b+c-a+d ifadesinin değeri her zaman 9 olarak bulunmuştur."]},"beginTime":2478,"endTime":2598,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=2478&ask_summarization=1"},{"index":18,"title":"Ardışık Sayılar Problemi","list":{"type":"unordered","items":["Ardışık dört doğal sayının toplamı, bu sayıların en büyüğünden sonra gelen üç tek sayının toplamından bir eksiktir.","En küçük sayının alabileceği farklı değerler 14 ve 11 olarak bulunmuştur.","En küçük sayının alabileceği farklı değerlerin toplamı 25'tir."]},"beginTime":2598,"endTime":2772,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=2598&ask_summarization=1"},{"index":19,"title":"Gül Dikme Problemi","list":{"type":"unordered","items":["Belediye bahçe işlerinde görevli iki işçi, üç kırmızı, dört sarı, beş mor ve iki beyaz gülü her seferinde aynı sırayla dikmişlerdir.","Kırmızı ve mor gülleri birinci işçi, sarı ve beyaz gülleri ikinci işçi dikmiştir.","Dikilen toplam gül sayısı 14'ün katından 7 fazla veya 14'ün katı olabilir, 568 sayısı bu formata uymadığından cevaptır."]},"beginTime":2772,"endTime":3009,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=2772&ask_summarization=1"},{"index":20,"title":"Çarpık Asal Toplam Problemi","list":{"type":"unordered","items":["a sayısının bir asal sayı olduğunu belirtmiş ve a³+a²+a toplamının iki asal sayının çarpımı şeklinde yazılıyorsa bu toplama \"çarpık asal toplam\" denir.","14, 39 ve 77 sayıları çarpık asal toplamdır.","77 sayısı 39'dan sonraki ilk çarpık asal toplam olduğu için cevaptır."]},"beginTime":3009,"endTime":3110,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=3009&ask_summarization=1"},{"index":21,"title":"Asal Sayılar Problemi","list":{"type":"unordered","items":["a ve b'nin pozitif tam sayılar olduğu ve 3a+b ile ax+2b'nin aralarında asal olduğu belirtilmiştir.","3a²-5ab-2b²=26 eşitliği verilmiştir.","Sorunun çözümü için bu eşitliğin nasıl halledileceği sorulmuştur."]},"beginTime":3110,"endTime":3137,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=3110&ask_summarization=1"},{"index":22,"title":"Matematik Problemi Çözümü","list":{"type":"unordered","items":["Üç a artı b ile aralarında asal olan a eksi iki b'nin çarpımı 26 olarak hesaplanmıştır.","Üç a artı b = 13 ve a eksi iki b = 2 denklemleri çözülerek a = 4 ve b = 1 bulunmuştur.","a ile b'nin çarpımı 4 olarak hesaplanmıştır."]},"beginTime":3139,"endTime":3274,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=3139&ask_summarization=1"},{"index":23,"title":"Top Asal Sayılar","list":{"type":"unordered","items":["Pozitif bölenlerinin toplamı asal sayı olan doğal sayılara top asal sayı denir.","16 sayısının pozitif bölenlerinin toplamı 31 olduğundan top asal sayıdır.","4, 2 ve 9 sayıları da top asal sayıdır, bu nedenle bir basamaklı iki top asal sayı olduğu iddiası yanlıştır."]},"beginTime":3274,"endTime":3379,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=3274&ask_summarization=1"},{"index":24,"title":"İkinci Matematik Problemi","list":{"type":"unordered","items":["a² - b² = 11 ve c² - d² = 13 denklemleri çözülerek a = 6, b = 5, c = 7 ve d = 6 bulunmuştur.","a = d, b \u003c c ve b + c = 2a ifadeleri doğrudur.","Bu problem için doğru cevap E seçeneğidir."]},"beginTime":3379,"endTime":3487,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=3379&ask_summarization=1"},{"index":25,"title":"Asal Sayıların Katları Problemi","list":{"type":"unordered","items":["Öğretmen tahtaya 1'den 30'a kadar tüm doğal sayıları yazmış ve öğrencilerden asal sayıların tam katı olan sayıları silmesini istemiş.","Çift sayılar, 3'ün, 5'in, 7'nin, 11'in, 13'ün, 17'nin, 19'un, 23'ün ve 29'un katları silinmiş.","Tahtada kalan sayıların toplamı 1 olur."]},"beginTime":3492,"endTime":3577,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=3492&ask_summarization=1"},{"index":26,"title":"Asal Bölenler Problemi","list":{"type":"unordered","items":["12x çarpımının asal bölenlerinin toplamı 12 olduğuna göre, x'in içinde 7 çarpanı vardır.","20x'in pozitif bölenlerinin sayısı 16 olduğuna göre, x'in içinde en az 1 tane 2 çarpanı ve 1 tane 7 çarpanı vardır.","En küçük x sayısı 14'tür."]},"beginTime":3577,"endTime":3716,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=3577&ask_summarization=1"},{"index":27,"title":"Karekök ve Asal Sayı Problemi","list":{"type":"unordered","items":["a, b ve c'nin birer rakam olduğu ve (a+b-c)² ifadesinin değeri asal sayı olduğu verilmiş.","a sayısı asal olmak zorunda ve b-c'nin 1 olması gerekir.","a=3, b=3 ve c=2 seçildiğinde, (a+b-c)²=11 olur."]},"beginTime":3716,"endTime":3866,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=3716&ask_summarization=1"},{"index":28,"title":"Faktöriyel Problemi","list":{"type":"unordered","items":["a! sayısının asal çarpanları sayısı, b! sayısının asal çarpanları sayısından 2 fazladır.","b! = 0, a! = 3! (6) seçildiğinde, 6'nın 2 tane asal çarpanı vardır.","a+b toplamının en az değeri 3+0=3'tür."]},"beginTime":3866,"endTime":3938,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=3866&ask_summarization=1"},{"index":29,"title":"Faktöriyel Eşitsizliği Problemi","list":{"type":"unordered","items":["24/(7-n)! oranı 1'den büyük veya eşit olduğuna göre, 4! ≥ 7-n! olmalıdır.","n sayısı 3 ile 7 kapalı aralığında olmalıdır.","n'nin alabileceği değerlerin toplamı 3+4+5+6+7=25'tir."]},"beginTime":3938,"endTime":4030,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=3938&ask_summarization=1"},{"index":30,"title":"Faktöriyel Problemi","list":{"type":"unordered","items":["7! + 8! ifadesinin k'ya bölünmesi sonucunda tam kare sayı elde edilmesi isteniyor.","7! + 8! ifadesi 7! × 9 şeklinde yazılabilir ve asal çarpanlarına ayrıldığında 2⁴ × 3⁴ × 5¹ × 7¹ şeklinde ifade edilebilir.","k'nın en küçük değeri 35, en büyük değeri ise 35 × 3⁴ × 2² olarak bulunur ve bu değerlerin oranı 324'tür."]},"beginTime":4035,"endTime":4277,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=4035&ask_summarization=1"},{"index":31,"title":"Bayram Harçlığı Problemi","list":{"type":"unordered","items":["Mert, 17 daireye bayramlaşmak için her daireden 16 TL harçlık alıyor ve toplam 16×17 TL harçlık topluyor.","Mert, harçlıklarını 2, 4, 6, 8, 10, 12 şeklinde harcayarak 16 günde bitiriyor.","Mert, günlük ortalama harcama miktarını hesaplamak için yanlış bir yöntem kullanıyor ve bulduğu sonuç doğru sonucun 254/12 katıdır."]},"beginTime":4277,"endTime":4497,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=4277&ask_summarization=1"},{"index":32,"title":"Faktöriyel Sıralama Problemi","list":{"type":"unordered","items":["a, b, c ifadelerinin küçükten büyüğe doğru sıralaması isteniyor.","a = 8! × 7! ve b = 8! × 9 × 6! şeklinde yazılabilir.","Sıralama sonucunda a \u003c b \u003c c olduğu için doğru cevap B seçeneğidir."]},"beginTime":4497,"endTime":4586,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=4497&ask_summarization=1"},{"index":33,"title":"Faktöriyel Denklemi Problemi","list":{"type":"unordered","items":["n-2! + 2 - n! = 1 denklemi çözülüyor.","n-2 ve 2-n faktöriyel ifadeleri sıfırdan büyük veya eşit olduğundan, n-2 ≥ 2 ve 2-n ≥ 0, yani n ≥ 2 ve n ≤ 2 olmalıdır.","n = 2 ve m = 3 olarak bulunur, bu durumda ifadenin değeri 4'tür."]},"beginTime":4586,"endTime":4659,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=4586&ask_summarization=1"},{"index":34,"title":"Faktöriyel Problemi","list":{"type":"unordered","items":["A kümesinde 1'den 10'a kadar olan ardışık sayılar bulunuyor ve bu kümenin elemanlarından dört tanesi seçilerek çarpıldığında 4!, 6! ve 7! sayıları elde edilebilir.","6! sayısı 8×9×10×72 şeklinde yazılabilir, 7! sayısı ise 8×9×10×7×72 şeklinde yazılabilir.","Doğru cevap Edirne seçeneğindeki 1, 2 ve 3'tür."]},"beginTime":4666,"endTime":4749,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=4666&ask_summarization=1"},{"index":35,"title":"Fabrika Paketleme Problemi","list":{"type":"unordered","items":["Bir fabrikadaki makinelerin her biri dakikada 120 paketleme işlemi yapıyor ve aynı anda altı makine günlük 12 saat boyunca ve bir hafta boyunca çalışarak verilen siparişi tamamlayabilmektedir.","Bir makinenin bir haftada yaptığı paketleme sayısı 6×7×12×60×120=10! (on faktöriyel) olarak hesaplanabilir.","Doğru cevap Denizli seçeneğidir."]},"beginTime":4749,"endTime":4852,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=4749&ask_summarization=1"},{"index":36,"title":"Faktöriyel Sayıları Problemi","list":{"type":"unordered","items":["12! sayısının sondan iki basamağının sıfır olduğu bilinmektedir.","2! sayısının içerisinde 9 çarpanı fazlasıyla olduğu için bu sayının 9'un katı olması gerekir ve rakamlar toplamı 9'un katı olmalıdır.","12! sayısının 11'in tam katı olması gerektiği için 11'e bölünme kuralı uygulanarak a+b=4 olarak bulunur."]},"beginTime":4852,"endTime":4998,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=4852&ask_summarization=1"},{"index":37,"title":"Zar Oyunu Problemi","list":{"type":"unordered","items":["Bir çift zarla oyun oynanmakta, her atışta soldaki zarda yazan sayının faktöriyeli alınıp sağdaki zarda yazan sayı ile çarpımı hesaplanmaktadır.","Birinci ve ikinci atışlardan elde edilen sonuçlar toplandığında üçüncü atıştan elde edilen sonuca tam bölünebilmektedir.","Üçüncü atışta zarın üst yüzüne gelen rakamlar arasında 3!×6! olamaz çünkü 5!×4'ü tam bölemez."]},"beginTime":4998,"endTime":5163,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=4998&ask_summarization=1"},{"index":38,"title":"İki Basamaklı Sayı Problemi","list":{"type":"unordered","items":["xy sayısının iki basamaklı olduğu ve rakamları toplamının k+2 katına eşit olduğu belirtilmiştir.","yx sayısının rakamları toplamının k-1 katına eşit olduğu verilmiştir.","x+y çarpı k ifadesinin alabileceği en büyük değer 12 olarak bulunmuştur."]},"beginTime":5166,"endTime":5348,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=5166&ask_summarization=1"},{"index":39,"title":"İki Basamaklı Sayıların Toplamı","list":{"type":"unordered","items":["ab sayısı ile ba sayısının toplamı 11(a+b) ve ab'den ba'yı çıkarmak 9(a-b) olarak ifade edilmiştir.","a+b=3a ve 3b=1 denklemleri çözülerek a=2b ilişkisi bulunmuştur.","a ve b'nin alabileceği değerler 1,2,4,6,8 olup, a×b'nin toplamı 60 olarak hesaplanmıştır."]},"beginTime":5348,"endTime":5467,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=5348&ask_summarization=1"},{"index":40,"title":"Üç Basamaklı Sayı Problemi","list":{"type":"unordered","items":["abc üç basamaklı sayısında a'nın c'nin iki katı ve b'nin c'nin bir eksiği olduğu belirtilmiştir.","c'nin alabileceği değerler 1,2,3,4 olup, b'nin değerleri 0,1,2,3 olarak bulunmuştur.","Yazılabilecek en büyük sayı ile en küçük sayı arasındaki fark 633 olarak hesaplanmıştır."]},"beginTime":5467,"endTime":5528,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=5467&ask_summarization=1"},{"index":41,"title":"Ayna Sayılar","list":{"type":"unordered","items":["En az iki basamaklı tüm rakamları aynı olan doğal sayılara ayna sayı denir.","Rakamlar toplamı yine bir rakam olan ayna sayılar 11, 22, 33, 44, 111, 222, 333, 1111, 2222, 11111, 22222, 111111, 222222, 1111111, 2222222 olarak bulunmuştur.","Toplam 14 tane rakamları toplamı bir rakam olan ayna sayı vardır."]},"beginTime":5528,"endTime":5640,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=5528&ask_summarization=1"},{"index":42,"title":"Rakamları Farklı Sayılar","list":{"type":"unordered","items":["Rakamları farklı iki basamaklı beş tane doğal sayının toplamı 117 olduğuna göre en büyüğü en çok 75 olabilir.","En küçük sayılar 10, 10, 10, 10 seçildiğinde toplam 40 olur ve en büyük sayı 77 olur.","En büyük sayı 77 yerine 75 olmalıdır çünkü 77 rakamları farklıdır."]},"beginTime":5640,"endTime":5722,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=5640&ask_summarization=1"},{"index":43,"title":"İki Basamaklı Sayı Problemi","list":{"type":"unordered","items":["Hatice, iki basamaklı bir ab doğal sayısının sağına bir adet eklediğinde sayının 171 arttığını görmekte.","b'nin 9 olduğu belirlenmiştir.","a'nın soluna bir tane 9 eklendiğinde sayı 900 artar."]},"beginTime":5722,"endTime":5787,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=5722&ask_summarization=1"},{"index":44,"title":"Matematik Problemleri Çözümü","list":{"type":"unordered","items":["Bir matematik problemi çözülürken, d sayısının 3 olduğu, b sayısının 5 olduğu, c sayısının 7 olduğu ve a sayısının 6 olduğu bulunur.","a, b, c, d'nin toplamı 21 olarak hesaplanır ve cevap D seçeneğinde verilmiştir."]},"beginTime":5792,"endTime":5847,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=5792&ask_summarization=1"},{"index":45,"title":"TYT ve AYT Sayıları Problemi","list":{"type":"unordered","items":["TYT ve AYT üç basamaklı doğal sayılar olmak üzere, TYT sayısından AYT sayısını çıkardığımızda A sonucuna ulaşıldığı ve TYT sayısını AYT sayısını eklediğimizde Y sonucuna ulaşıldığı belirtilir.","T'nin 2A'ya eşit olduğu ve T'nin çift sayı olması gerektiği anlaşılır.","T=4, Y=8 ve A=2 olduğunda, A+Y+T toplamı 14 olarak hesaplanır ve cevap D seçeneğinde verilmiştir."]},"beginTime":5847,"endTime":6019,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=5847&ask_summarization=1"},{"index":46,"title":"Düğme Problemi","list":{"type":"unordered","items":["Kırmızı düğmeye basıldığında kutudaki rakam bir artıyor, mavi düğmeye basıldığında bir azalıyor.","A 9'dan küçük ve B 1'den büyük olmak üzere, mavi ve kırmızı düğmelere birer kez basıldığında elde edilen üç basamaklı sayıların toplamı 800A1'e eşit.","B'nin 2 olduğu, A'nın maksimum 8 olduğu ve 2×8=16 olduğu bulunur."]},"beginTime":6019,"endTime":6143,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=6019&ask_summarization=1"},{"index":47,"title":"Ceviz Problemi","list":{"type":"unordered","items":["Mert'in 123, Ali'nin 112 tane cevizi vardır ve cevizlerini her bir grupta eşit sayıda ceviz olacak şekilde ayırdıktan sonra her gün birer grup ceviz yemektedir.","Cevizlerin 11 veya bunun tam bölenleri şeklinde sayıda gruplara ayrılacağı ve her gün her grupta 11 ceviz yedikleri anlaşılır.","Mert ve Ali'nin ilk ve son gün yedikleri ceviz sayısı toplamı 26 olarak hesaplanır ve cevap E seçeneğinde verilmiştir."]},"beginTime":6143,"endTime":6236,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=6143&ask_summarization=1"},{"index":48,"title":"Sayı Problemi","list":{"type":"unordered","items":["AB iki basamaklı ve ABAB dört basamaklı doğal sayılardır.","ABAB'nin üzerine dört tane AB iki basamaklı sayısı eklendiği takdirde AB iki basamaklı sayısına bölünüyor.","Bölme işleminden elde edilen bölüm 105 olarak hesaplanır ve cevap D seçeneğinde verilmiştir."]},"beginTime":6236,"endTime":6294,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=6236&ask_summarization=1"},{"index":49,"title":"Tam Sayı Problemi","list":{"type":"unordered","items":["A ve X birer tam sayı olmak üzere, A sayısı 10-16'ya bölünmüş, bölüm 4X, kalan X2 olarak verilmiştir.","X2'nin 16'dan daha küçük olması gerektiği ve X'in -3 seçilebileceği anlaşılır.","A'nın maksimum değeri 121 olarak hesaplanır ve cevap E seçeneğinde verilmiştir."]},"beginTime":6294,"endTime":6361,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=6294&ask_summarization=1"},{"index":50,"title":"Bölme Problemi","list":{"type":"unordered","items":["Bir A doğal sayısının 9 ile bölümünden kalan 3'tür.","Bu sayıya 4 eklenirse elde edilen sayı 9'da tam bölünür.","Cevap B seçeneğinde verilmiştir."]},"beginTime":6361,"endTime":6424,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=6361&ask_summarization=1"},{"index":51,"title":"Ardışık Üç Çift Doğal Sayının Çarpımı","list":{"type":"unordered","items":["Ardışık üç çift doğal sayının çarpımı 8'in katıdır çünkü (2k)(2k-2)(2k+2) = 8(k²-1)(2k) = 8(k-1)(k)(k+1) şeklinde yazılabilir.","Ardışık üç sayının çarpımı mutlaka 3'ün ve 2'nin katıdır, bu nedenle 16'ya ve 24'e bölünür.","Ardışık üç sayının çarpımı her zaman 18'e bölünmek zorunda değildir, bu nedenle cevap D seçeneğinde verilmiştir."]},"beginTime":6429,"endTime":6591,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=6429&ask_summarization=1"},{"index":52,"title":"Bölme İşleminde Doğru ve Yanlış İfadeler","list":{"type":"unordered","items":["Bölünen ile kalanın farkı, bölenle bölümün çarpımına eşittir (a-k = b×c).","Bölünen sayı, bölüm ile kalanın toplamının bölenle çarpımına eşit olabilir (örneğin 10/5 = 2+0/5).","Bölünen ile bölüm arasındaki fark, bölen ile kalanın toplamından büyüktür ifadesi yanlıştır (örneğin 25/19 = 1+6/19)."]},"beginTime":6591,"endTime":6717,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=6591&ask_summarization=1"},{"index":53,"title":"Üç Basamaklı Sayıların Bölünme Kuralları","list":{"type":"unordered","items":["ABC, BCA, BBA ve CCCB sayıları arasında iki tanesi 4 ile tam bölünüyor, biri 5 ile tam bölünüyor ve hiçbiri 3 ile bölünmüyor.","ABC sayısı 3 ile bölünmediği için rakamlarının toplamı 3'ün katından farklı olmalıdır.","BCA ve CCCB sayıları 4 ile bölünebildiği için son iki hanesi 4'ün katı olmalıdır ve bu sayılar 44, 84 veya 88 olabilir.","Rakamlarının toplamı 3'ün katından farklı olması için B ve C rakamları 4 ve 8 olmalıdır, bu durumda A=5, B=8, C=4 olur ve toplamları 17'dir."]},"beginTime":6717,"endTime":6989,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=6717&ask_summarization=1"},{"index":54,"title":"Dört Basamaklı Sayı Problemi","list":{"type":"unordered","items":["Rakamları birbirinden farklı dört basamaklı bir doğal sayının birler basamağındaki rakam silindiğinde, sayı altı'nın katı oluyor.","Binler basamağındaki rakam silindiğinde, sayı onbeş'in katı oluyor.","Sorunun amacı, dört basamaklı sayının rakamları toplamının en çok kaç olabileceğini bulmaktır."]},"beginTime":6995,"endTime":7036,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=6995&ask_summarization=1"},{"index":55,"title":"Sayıların Özellikleri","list":{"type":"unordered","items":["Onbeş'in katı olan sayıların birler basamağı sıfır veya beş olabilir.","Altı'nın katı olan sayılar çifttir.","Üç'ün katı olan sayıların rakamları toplamı üçün katı olmalıdır."]},"beginTime":7036,"endTime":7069,"href":"/video/preview/15000365387135733887?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=7036&ask_summarization=1"},{"index":56,"title":"Çözüm Süreci","list":{"type":"unordered","items":["Rakamların toplamının en çok olması için birler basamağı beş, binler basamağı sekiz seçilir.","Üç'ün katı olması için diğer basamaklara uygun rakamlar eklenir.","Rakamların 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13 yaşın altındaysa YouTube Kids, üstündeyse normal YouTube kullanılıyor."]},"beginTime":614,"endTime":703,"href":"/video/preview/4225133973687408354?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=614&ask_summarization=1"},{"index":5,"title":"Ayarlar ve Hesap Yönetimi","list":{"type":"unordered","items":["Ayarlar bölümünde ses ve ekran ayarları yapılabiliyor, HCC (HDMI kontrol) özelliği açılarak televizyonunuzda HDMI bölümünden kumandadan kontrol edilebiliyor.","Ekran sesi ayarları yapılabiliyor ve normal telefonda Wi-Fi'ya bağlanma gibi işlem yapılıyor.","Hesap yönetimi bölümünde çocuk hesabı, normal hesabı eklenebiliyor ve ailenizde farklı hesaplar oluşturulup kullanılabiliyor."]},"beginTime":703,"endTime":814,"href":"/video/preview/4225133973687408354?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=703&ask_summarization=1"},{"index":6,"title":"Uygulama Yönetimi ve Bağlantı Özellikleri","list":{"type":"unordered","items":["Kurulan uygulamalar görüntüleniyor ve istenmeyen uygulamalar kaldırılabiliyor.","Uygulama izinleri yönetilebiliyor ve sistem yeniden başlatma gibi seçenekler bulunuyor.","Ekran kapama süresi ayarlanabiliyor ve telefondan yayın yapma özelliği mevcut."]},"beginTime":814,"endTime":881,"href":"/video/preview/4225133973687408354?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=814&ask_summarization=1"},{"index":7,"title":"Bluetooth ve Ekran Yansıtma","list":{"type":"unordered","items":["Bluetooth ile kulaklık gibi aksesuarlar eklenebiliyor ve televizyondaki filmi kulaklıktan dinleyebilirsiniz.","Telefon ekranı televizyona yansıtılabilir, sadece video göndermek için de seçenek bulunuyor.","Android TV'ler akıllı TV'lere göre daha keyifli içerik izleme imkanı sunuyor ve canlı yayınları da izleyebilirsiniz."]},"beginTime":881,"endTime":1060,"href":"/video/preview/4225133973687408354?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=881&ask_summarization=1"}],"linkTemplate":"/video/preview/4225133973687408354?parent-reqid=1769821046352755-15789528366278121976-balancer-l7leveler-kubr-yp-sas-61-BAL&text=Tex4K&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Xiaomi Mi Box S 4K 2. 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Ücretsiz ve ücretli programların özellikleri, fiyat-performans değerlendirmeleri ve kullanım sınırlamaları detaylı olarak anlatılıyor.","Videoda ayrıca ücretsiz olarak kullanılabilecek WiFi 2X ve Video 2X gibi GitHub üzerinden indirilebilen programlar da tanıtılıyor. Topaz'ın bulut tabanlı olmayan, ömür boyu kullanılabilen ve detaylı kalite iyileştirmesi yapan bir program olduğu, ancak ücretsiz versiyonların beş dakikalık video sınırı olduğu belirtiliyor."]},"endTime":778,"title":"Düşük Kaliteli Videoları 4K Kalitesine Yükseltme Rehberi","beginTime":0}],"fullResult":[{"index":0,"title":"Video Kalitesini Yükseltme Amacı","list":{"type":"unordered","items":["Bu derste düşük kaliteyle çekilmiş videoların 4K kalitesine nasıl yükseltilmesi öğretiliyor.","Eski videoları daha kaliteli hale getirmek veya Full HD (1080p) çekilmiş videoları YouTube'a 4K olarak yüklemek için yapay zeka destekli programlar kullanılacak.","Aynı video farklı programlarda 4K kalitesine yükseltilecek ve kıyaslama yapılacak, böylece programların artıları ve eksileri 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