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Öğretmen, öğrencilere hitap ederek konuları adım adım anlatmaktadır.","Videoda öncelikle toplama ve çarpma yoluyla sayma kavramları tanımlanmakta, ardından şehirler arası yol problemleri ve olasılık problemleri ele alınmaktadır. Öğretmen, giyim kombinasyonları, sınıf başkanı seçimi, lokanta menüsü, mektup ve posta kutusu problemi gibi çeşitli örnekler üzerinden konuları pekiştirmektedir.","Öğretmen, bir sonraki derste yol problemleri ve küme problemleri gibi diğer soru tiplerini ele alacağını belirtmektedir. Ayrıca, 11 ile çarpma işleminin kısa bir yöntemi de gösterilmektedir."]},"endTime":1150,"title":"10. Sınıf Matematik: Sayma, Yol ve Olasılık Problemleri","beginTime":0}],"fullResult":[{"index":0,"title":"Giriş ve Kaynaklar","list":{"type":"unordered","items":["Mehmet hocanın 10. sınıf matematik dersinde sayma konusunu ele alacağı bir derstir.","Öğrenciler WW.öğrenci burada.com adresi üzerinden ücretsiz PDF'leri indirebilir ve çıktılarını alabilir."]},"beginTime":0,"endTime":38,"href":"/video/preview/10107220366220648468?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=0&ask_summarization=1"},{"index":1,"title":"Toplama Yoluyla Sayma","list":{"type":"unordered","items":["Toplama yoluyla sayma, ayrık iki veya daha fazla kümenin elemanları sayısının toplama işlemi yapılarak bulunması işlemidir.","Toplama yoluyla saymada verilen kümenin elemanları A+B şeklinde toplanır.","Toplama yoluyla sayma sorularında genellikle \"veya\" bağlacı kullanılır."]},"beginTime":38,"endTime":57,"href":"/video/preview/10107220366220648468?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=38&ask_summarization=1"},{"index":2,"title":"Çarpma Yoluyla Sayma","list":{"type":"unordered","items":["Çarpma yoluyla sayma, birbirinden bağımsız sırayla yapılan işlemlerin sonucunun bulunması işlemidir.","Çarpma yoluyla saymada elemanların her biri tek tek birbiriyle çarpılır ve işlemin sonucu bulunur.","Çarpma yoluyla sayma sorularında genellikle \"ve\" bağlacı kullanılır."]},"beginTime":57,"endTime":110,"href":"/video/preview/10107220366220648468?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=57&ask_summarization=1"},{"index":3,"title":"Örnekler","list":{"type":"unordered","items":["Cenk'in 4 farklı şort ve 5 farklı tişörtü var, bunları toplama yoluyla sayma ile 4+5=9 farklı şekilde giyebilir.","Caner'in 3 farklı pantolon ve 4 farklı gömleği var, bunları çarpma yoluyla sayma ile 3×4=12 farklı şekilde giyebilir.","Bir sınıfta 17 kız ve 12 erkek öğrenci var, sınıf başkanı seçimi toplama yoluyla sayma ile 17+12=29 farklı şekilde yapılabilir.","Bir sınıfta 11 kız ve 9 erkek öğrenci var, bir kız ve bir erkek seçimi çarpma yoluyla sayma ile 11×9=99 farklı şekilde yapılabilir.","Altı kişilik bir gruptan başkan, başkan yardımcısı ve sekreter seçimi çarpma yoluyla sayma ile 6×5×4=120 farklı şekilde yapılabilir.","Lokantaya giden bir kişi 2 çorba, 4 yemek ve 3 tatlı çeşidinden birer tane seçerek 2×4×3=24 farklı şekilde öğle yemeği yiyebilir.","Hamdi 3 pantolon, 4 gömlek, 3 ayakkabı ve 2 botu var, evden çıkarken 3×4×(3+2)=60 farklı şekilde giyinebilir çünkü ayakkabı ve bot arasında seçim yapması gerekir."]},"beginTime":110,"endTime":503,"href":"/video/preview/10107220366220648468?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=110&ask_summarization=1"},{"index":4,"title":"Yol Problemleri","list":{"type":"unordered","items":["Toplama ve çarpma yoluyla saymada yol problemleri de bulunmaktadır.","Bir sonraki videoda bu konuların devamı ve daha fazla örnek sunulacaktır."]},"beginTime":503,"endTime":532,"href":"/video/preview/10107220366220648468?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=503&ask_summarization=1"},{"index":5,"title":"Yol Problemleri Çözümü","list":{"type":"unordered","items":["A şehriyle C şehri arasında gidilirken B şehrine uğramak gerekiyor, A'dan B'ye 4 farklı yol, B'den C'ye 3 farklı yol olduğu için toplam 12 farklı yol bulunuyor.","A'dan C'ye gidip dönmek için, gidişte 12 farklı yol, dönüşte de 12 farklı yol olduğu için toplam 144 farklı yol bulunuyor.","Gidişte kullanılan yolları dönüşte kullanmamak şartıyla gidip dönmek için, gidişte 12 farklı yol varken dönüşte 11 farklı yol kullanılabildiği için toplam 132 farklı yol bulunuyor."]},"beginTime":533,"endTime":775,"href":"/video/preview/10107220366220648468?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=533&ask_summarization=1"},{"index":6,"title":"Yol Problemlerinin Çözüm Yöntemi","list":{"type":"unordered","items":["A, B, C, D kentleri arasındaki yolları gösteren bir şemada, A'dan C'ye gidilmesi için farklı yollar hesaplanıyor.","A'dan B'ye 3 farklı yol, B'den C'ye 2 farklı yol olduğu için A'dan C'ye 6 farklı yol bulunuyor.","A'dan C'ye doğrudan 2 farklı otoban yolu olduğu için, toplam 8 farklı yol bulunuyor ve C'den A'ya 3 farklı yol olduğu için toplam 24 farklı yol hesaplanıyor."]},"beginTime":775,"endTime":873,"href":"/video/preview/10107220366220648468?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=775&ask_summarization=1"},{"index":7,"title":"Mektup Sorusu Çözümü","list":{"type":"unordered","items":["Mektup sorusu, oyuncak sorularıyla aynı mantıkla çözülür ve tahayyül etmek gerekiyor.","Dört farklı mektup ve altı farklı posta kutusu olduğunda, her mektup için altı farklı ihtimal olduğu için toplam 6 üzeri 4 ihtimal vardır.","Aynı kutuya birden çok mektup atılmaması şartı ile, ilk mektup için 6, ikinci için 5, üçüncü için 4, dördüncü için 3 ihtimal olduğu için toplam 360 farklı şekilde mektuplar atılabilir."]},"beginTime":876,"endTime":1049,"href":"/video/preview/10107220366220648468?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=876&ask_summarization=1"},{"index":8,"title":"Sınav Başarısı 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Öğretmen, yeni Maarif modeline uygun şekilde trigonometri konusunu anlatmaktadır.","Video, dik üçgende trigonometrik oranlar (sinüs, kosinüs, tanjant, kotanjant) konusunu kapsamlı şekilde ele almaktadır. İlk olarak temel trigonometrik oranlar tanımlanmakta, ardından özel dik üçgenler (3-4-5, 7-24-25, 8-15-17) kullanılarak örnekler çözülmektedir. Daha sonra benzer üçgenlerde trigonometrik oranların eşitliği ve sin²α + cos²α = 1, tanα × cotα = 1 gibi trigonometrik özdeşlikler ispatlanmaktadır.","Videoda ayrıca not alma teknikleri, soru avcısı bölümü ve pratik problemler çözülmektedir. Öğretmen, trigonometrik değerlerin ezberlenmeden mantığının öğrenilmesi gerektiğini vurgulamakta ve Pisagor bağıntısı kullanarak ispatlar yapmaktadır. Video, 10 sorudan oluşan bir dersin son bölümünü oluşturmaktadır."]},"endTime":3407,"title":"10. Sınıf Matematik: Dik Üçgende Trigonometrik Oranlar ve Özdeşlikler","beginTime":0}],"fullResult":[{"index":0,"title":"10. Sınıf Matematik Derslerine Giriş","list":{"type":"unordered","items":["Mehmet hocanın Rehber Matematik kanalında 10. sınıf yeni Maarif modele uygun matematik dersleri başlıyor.","Tüm PDF'ler ve soru avcıları ücretsiz olarak Instagram hesabından paylaşılacak.","10. sınıf matematik müfredatı tanımıyla, kavramıyla ve ispatıyla birlikte bitirilecek."]},"beginTime":0,"endTime":98,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=0&ask_summarization=1"},{"index":1,"title":"Yeni Maarif Modeli ve Sınav Sistemi","list":{"type":"unordered","items":["Derslerin tek amacı okul notları değil, yeni Maarif model ve sınav sistemine hazırlıklı olmak.","12. sınıfa geldiğinde sınav sistemi değişeceği için bu konuları canavar gibi öğrenmek gerekiyor.","Bu seneki 10. sınıf matbu kitabı yetiştirilemedi, önümüzdeki sene 11. sınıf matbook'u PDF'lerle değil kitaplarla 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denir."]},"beginTime":133,"endTime":253,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=133&ask_summarization=1"},{"index":3,"title":"Trigonometrik Oranların Tanımları","list":{"type":"unordered","items":["Sinüs, karşı dik kenar uzunluğunun hipotenüs uzunluğuna oranıdır ve sin alfa olarak gösterilir.","Kosinüs, komşu dik kenar uzunluğunun hipotenüs uzunluğuna oranıdır ve cos alfa olarak gösterilir.","Tanjant, karşı dik kenarın uzunluğunun komşu dik kenar uzunluğuna oranıdır ve tan alfa ile gösterilir.","Kotanjant, komşu dik kenarın uzunluğunun karşı dik kenar uzunluğuna oranıdır ve cot alfa ile gösterilir."]},"beginTime":253,"endTime":391,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=253&ask_summarization=1"},{"index":4,"title":"Trigonometrik Oranlar ve Özel Dik Üçgenler","list":{"type":"unordered","items":["Dik üçgenlerde trigonometrik oranlar (sinüs, kosinüs, tanjant, kotanjant) hesaplanırken karşı dik kenar, komşu dik kenar ve hipotenüs kullanılır.","Özel dik üçgenler (3-4-5, 7-24-25, 8-15-17) kenar oranları ile ilgili işlemler yapılabilir ve Pisagor bağıntısına girmeden doğrudan hesaplanabilir.","Sinüs alfa = karşı dik kenar / hipotenüs, kosinüs alfa = komşu dik kenar / hipotenüs, tanjant alfa = karşı dik kenar / komşu dik kenar, kotanjant alfa = komşu dik kenar / karşı dik kenar formülleri kullanılır."]},"beginTime":395,"endTime":704,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=395&ask_summarization=1"},{"index":5,"title":"Trigonometrik Özdeşlikler","list":{"type":"unordered","items":["Alfa ile beta açılarının toplamı 90 derece ise, sinüs alfa = kosinüs beta olur.","Tanjant alfa ile kotanjant beta değerleri birbirine eşittir.","Sinüs alfa² + kosinüs alfa² = 1 özdeşliği vardır."]},"beginTime":704,"endTime":896,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=704&ask_summarization=1"},{"index":6,"title":"Trigonometrik Değerler ve Dik Üçgenler","list":{"type":"unordered","items":["Trigonometrik değerler (tanjant, kotanjant, kosinüs, sinüs) dik üçgenlerde hesaplanır.","Tanjant, karşı dik kenar bölü komşu dik kenardır; kotanjant ise komşu dik kenar bölü karşı dik kenardır.","Trigonometrik değerleri hesaplamak için dik üçgen çizmek gerekir ve açıların ölçüsü 90 derece olmalıdır."]},"beginTime":901,"endTime":1106,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=901&ask_summarization=1"},{"index":7,"title":"Trigonometrik Değerlerin Hesaplanması","list":{"type":"unordered","items":["39 birim uzunluğundaki çubuğun duvara uzaklığı 15 birimdir ve zemine değdiği nokta sabit kalacak biçimde duvara doğru devrildiğinde zeminle alfa derecelik bir dar açı oluşturur.","Sinüs alfa, kosinüs alfa ve kotanjant alfa değerleri hesaplanırken, kenar uzunlukları Pisagor teoremi veya özel dik üçgenler kullanılarak bulunur.","Benzer üçgenlerde eşit açıların karşısındaki kenarların oranları birbirine eşittir."]},"beginTime":1106,"endTime":1412,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=1106&ask_summarization=1"},{"index":8,"title":"Benzer Üçgenlerde Trigonometrik Değerler","list":{"type":"unordered","items":["İki benzer dik üçgende, birbirini 90 dereceye tamamlayan açıların trigonometrik değerleri (sinüs-kosinüs, tanjant-kotanjant) birbirine eşittir.","Benzer üçgenlerde kenar uzunlukları orantılıdır ve bu oran trigonometrik değerleri hesaplamada kullanılır.","Kenar-açı-kenar benzerliği veya kenar-kenar-kenar bağıntısı kullanılarak benzer üçgenler belirlenebilir."]},"beginTime":1412,"endTime":1586,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=1412&ask_summarization=1"},{"index":9,"title":"Benzer Üçgenlerde Trigonometrik Değerler","list":{"type":"unordered","items":["Benzer üçgenlerde eşit açıların trigonometrik değerleri birbirine eşittir.","Benzer üçgenlerin eşit açılarına ait trigonometrik oranlar eşittir.","Bir üçgende sinüs A açısı ile başka bir üçgende sinüs B açısı eşitse, bu açılar birbirine eşittir."]},"beginTime":1590,"endTime":1724,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=1590&ask_summarization=1"},{"index":10,"title":"Trigonometrik Oranların Özellikleri","list":{"type":"unordered","items":["Dar açının trigonometrik oranları verilirse, diğer trigonometrik oranlara ulaşmak için dik üçgen çizilir.","Bir açının trigonometrik oranı biliniyorsa, kenar uzunlukları aynı olmak zorunda değildir, katları olabilir.","Benzer üçgenlerde aynı açıların trigonometrik değerleri eşittir, ancak kenar uzunlukları farklı olabilir."]},"beginTime":1724,"endTime":1840,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=1724&ask_summarization=1"},{"index":11,"title":"Özel Üçgenler ve Trigonometrik Değerler","list":{"type":"unordered","items":["5-12-13 üçgeninde sinüs alfa değeri 12/13, kosinüs alfa değeri 5/13, tanjant alfa değeri 12/5 ve kotanjant alfa değeri 5/12'dir.","8-15-17 özel üçgeninde sinüs beta değeri 8/17, kosinüs beta değeri 15/17, tanjant beta değeri 8/15'tir.","Trigonometrik oranlar hesaplanırken karşı kenar bölü komşu kenar veya komşu kenar bölü karşı kenar formülü kullanılır."]},"beginTime":1840,"endTime":2041,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=1840&ask_summarization=1"},{"index":12,"title":"Trigonometrik Değerler ve Dik Üçgenler","list":{"type":"unordered","items":["Trigonometrik değerler hesaplamak için dik üçgen çizmek gerekir.","Sinüs alfa, karşı kenar bölü hipotenüs; kosinüs alfa, komşu kenar bölü hipotenüs; tanjant alfa, karşı kenar bölü komşu kenar; kotanjant alfa, komşu kenar bölü karşı kenar formülleri kullanılır.","Paydada köklü ifade kalırsa, genişletme işlemi yaparak köklü ifadeyi paydan kaldırabiliriz."]},"beginTime":2044,"endTime":2175,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=2044&ask_summarization=1"},{"index":13,"title":"Gölge Problemi","list":{"type":"unordered","items":["Bir parkta 9 metre yüksekliğinde yere dik duran direğin gölgesi hesaplanırken dik üçgen oluşturulur.","Gölge boyu hesaplanırken tanjant 30 derece veya kotanjant 30 derece formülleri kullanılabilir.","Kotanjant 30 derece değeri kök 3'tür ve bu değer kullanılarak gölge boyu hesaplanabilir."]},"beginTime":2175,"endTime":2342,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=2175&ask_summarization=1"},{"index":14,"title":"İki Dar Açı Problemi","list":{"type":"unordered","items":["İki dar açı (alfa ve beta) için kosinüs alfa 3/5 ve sinüs beta 4/√17 verildiğinde, tanjant alfa çarpı kotanjant beta çarpımı hesaplanır.","Sinüs beta değeri için Pisagor bağıntısı kullanılarak dik kenar bulunur.","Tanjant alfa 4/3, kotanjant beta 1/4 olarak hesaplanır ve çarpımı 1/3 olarak bulunur."]},"beginTime":2342,"endTime":2439,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=2342&ask_summarization=1"},{"index":15,"title":"Trigonometrik Özdeşlikler","list":{"type":"unordered","items":["Ders, sorular üzerinden trigonometrik teknik bilgileri öğrenmeye başlıyor.","Dik üçgende sinüs, kosinüs, tanjant ve kotanjant değerleri hesaplanıyor.","Aynı açılara ait sin²α + cos²α toplamının her zaman 1'e eşit olduğu gösteriliyor."]},"beginTime":2441,"endTime":2642,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=2441&ask_summarization=1"},{"index":16,"title":"Tanjant ve Kotanjant Özdeşliği","list":{"type":"unordered","items":["Tanjant ve kotanjant değerleri arasında tanα × cotα = 1 özdeşliği bulunuyor.","Bu özdeşlik, trigonometrik fonksiyonların değerlerini hesaplamada kullanılıyor.","Trigonometrik özdeşlikler, dik üçgende Pisagor bağıntısı ve trigonometrik fonksiyonların tanımlarından türetiliyor."]},"beginTime":2642,"endTime":2829,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=2642&ask_summarization=1"},{"index":17,"title":"Sin²α ve Cos²α Özdeşlikleri","list":{"type":"unordered","items":["Sin²α = 1 - cos²α özdeşliği bulunuyor.","Bu özdeşlik, iki kare farkı formülüne dayanarak (1 - cos²α) = (1 - cosα)(1 + cosα) şeklinde yazılabilir.","Benzer şekilde cos²α = 1 - sin²α özdeşliği de bulunuyor."]},"beginTime":2829,"endTime":2978,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=2829&ask_summarization=1"},{"index":18,"title":"Trigonometrik Özdeşlikler","list":{"type":"unordered","items":["Tanjant alfa (tan α) b/a, kotanjant alfa (cot α) a/b olarak tanımlanır.","Tanjant alfa çarpı kotanjant alfa her zaman 1'e eşittir.","Tanjant alfa = 1/cotanjant alfa ve kotanjant alfa = 1/tanjant alfa şeklinde de yazılabilir."]},"beginTime":2981,"endTime":3070,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=2981&ask_summarization=1"},{"index":19,"title":"Trigonometrik Özdeşlik Sorusu","list":{"type":"unordered","items":["Sin α + cos α = 5/4 olduğuna göre sin α × cos α çarpımı sorulmaktadır.","(x + y)² = x² + 2xy + y² özdeşliği kullanılarak sin² α + 2sin α cos α + cos² α = 25/16 ifadesi elde edilir.","sin² α + cos² α = 1 özdeşliği kullanılarak 2sin α cos α = 9/16 bulunur ve sonucun 32 olduğu hesaplanır."]},"beginTime":3070,"endTime":3327,"href":"/video/preview/13163913345582469369?parent-reqid=1769550598188211-15906437684618015444-balancer-l7leveler-kubr-yp-vla-101-BAL&text=skymatt10&t=3070&ask_summarization=1"},{"index":20,"title":"Dersin 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