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Sorular rasyonel sayılar, küp açılımı, çarpanlara ayırma, köklü sayılar, ondalık sayılar, denklem çözme, mutlak değer, eşitsizlikler, özel üçgenler, fonksiyonlar, teklik-çiftlik kavramları, alim sayılar, hız problemleri, su doldurma-boşaltma problemleri, sayı-yüzde karışımı, yaş problemleri, olasılık, sayı basamakları, sayı tanımlama, sayısal mantık ve geometri konularını kapsamaktadır.","Her soru için detaylı çözüm yöntemleri gösterilmekte ve bazı soruların farklı çözüm yolları da açıklanmaktadır. Video, KPSS, TYT ve AYT sınavlarına hazırlanan öğrenciler için matematik sorularının nasıl çözüleceğini gösteren kapsamlı bir kaynak niteliğindedir."]},"endTime":3875,"title":"2017 KPSS Lisans Matematik Soruları Çözüm Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"KPSS Lisans Matematik Soruları","list":{"type":"unordered","items":["2017 KPSS Lisans matematik soruları çözülecek.","İlk soru rasyonel sayılar konusundan olup, payda eşitleme ve sadeleştirme işlemleriyle 6/5 cevabı bulunuyor."]},"beginTime":14,"endTime":79,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=14&ask_summarization=1"},{"index":1,"title":"Küp Açılımı ve Çarpanlara Ayırma","list":{"type":"unordered","items":["İkinci soru küp açılımı ve çarpanlara ayırma konusundan olup, 20'nin küpü artı 17'nin küpü bölü 20+17-20×17 işleminin sonucu 9 olarak bulunuyor."]},"beginTime":79,"endTime":168,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=79&ask_summarization=1"},{"index":2,"title":"Köklü Sayılar","list":{"type":"unordered","items":["Üçüncü soru köklü sayılar konusundan olup, kök 8 artı kök 8 bölü kök 40 eksi kök 10 çarpı kök 2 bölü kök 5 işleminin sonucu kök 2 olarak bulunuyor."]},"beginTime":168,"endTime":253,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=168&ask_summarization=1"},{"index":3,"title":"Ondalık Sayılar","list":{"type":"unordered","items":["Dördüncü soru ondalık sayılar konusundan olup, 0,40 çarpı 0,60 bölü 1,20'nin karesi eksi 1,80'in karesi işleminin sonucu 0,30 olarak bulunuyor."]},"beginTime":253,"endTime":313,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=253&ask_summarization=1"},{"index":4,"title":"Rakam Problemi","list":{"type":"unordered","items":["Beşinci soru rakam probleminden olup, a, b ve c rakamları için abc+ab=4cb olduğuna göre a+b+c toplamı 10 olarak bulunuyor."]},"beginTime":313,"endTime":413,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=313&ask_summarization=1"},{"index":5,"title":"Üslü Sayılar","list":{"type":"unordered","items":["Altıncı soru üslü sayılar konusundan olup, 5 üzeri 2x eksi 5 üzeri eksi x bölü 5 üzeri x artı 5 üzeri x eşittir eksi 124 çarpı 5 üzeri x olduğuna göre x değeri -3 olarak bulunuyor."]},"beginTime":413,"endTime":537,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=413&ask_summarization=1"},{"index":6,"title":"Çarpanlara Ayırma","list":{"type":"unordered","items":["Yedinci soru çarpanlara ayırma konusundan olup, a kare eşittir 57-8a ve b kare eşittir 57-8b eşitlikleri verildiğinde a çarpı b çarpımı 7 olarak bulunuyor."]},"beginTime":537,"endTime":737,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=537&ask_summarization=1"},{"index":7,"title":"Köklü Sayılar ve Çarpanlara Ayırma","list":{"type":"unordered","items":["Sekizinci soru köklü sayılar ve çarpanlara ayırma konusundan olup, 1 bölü kök x artı y çarpı x y bölü x y eksi y kök x eşittir 1 bölü 2 olduğuna göre x çarpı y çarpımı 4 olarak bulunuyor."]},"beginTime":737,"endTime":814,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=737&ask_summarization=1"},{"index":8,"title":"Mutlak Değer Sorusu","list":{"type":"unordered","items":["x ve y tam sayıları için |x-3| + |y-1| = 1 eşitliği verildiğinde, x×y çarpımının alabileceği en büyük değer soruluyor.","Mutlak değerlerin toplamı sıfırdan küçük olamaz, bu nedenle |x-3| = 0, |y-1| = 1 veya |x-3| = 1, |y-1| = 0 şeklinde iki durum inceleniyor.","x=3, y=1 veya x=4, y=2 değerleri bulunuyor ve x×y çarpımının en büyük değeri 9 olarak hesaplanıyor."]},"beginTime":823,"endTime":953,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=823&ask_summarization=1"},{"index":9,"title":"Eşitsizlik Sorusu","list":{"type":"unordered","items":["a ve b gerçel sayılar için a×b² \u003c a²×b eşitsizlikleri verildiğinde, hangi ifadelerin her zaman doğrudur soruluyor.","a²×b \u003c a²×b eşitsizliğinden a ve b'nin negatif olduğu, b/a \u003c 0 eşitsizliğinden b'nin a'dan küçük olduğu bulunuyor.","a+b \u003c 0 ve a×b \u003c 1 ifadeleri her zaman doğru olmadığı, a×b \u003c 1 için a=-1/3 ve b=-1/2 değerleri verildiğinde 1/6 = 1/3×(-1/2) olduğu gösteriliyor."]},"beginTime":953,"endTime":1114,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=953&ask_summarization=1"},{"index":10,"title":"Özel İşlem Sorusu","list":{"type":"unordered","items":["Sıfırdan farklı gerçel sayılar kümesi üzerinde tanımlı üçgen işlemi için x△y + 2×1/y△x = x/y eşitliği veriliyor.","3△1/4 işleminin sonucu soruluyor ve x=3, y=1/4 değerleri yerine konularak işlem yapılıyor.","İki denklem taraf tarafa toplanarak ve sadeleştirilerek 3△1/4 = 4 sonucu bulunuyor."]},"beginTime":1114,"endTime":1269,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=1114&ask_summarization=1"},{"index":11,"title":"Fonksiyon Sorusu","list":{"type":"unordered","items":["Tam sayılar kümesi üzerinde tanımlı f ve g fonksiyonları için f(x)+g(x)/2 = x²+x-3 ve g(x+1) = g(x)+4 eşitlikleri veriliyor.","g(4) = 10 olduğuna göre f(2) değeri soruluyor ve g(3) = 6 bulunuyor.","x=2 değeri yerine konularak f(2) = 8 sonucu bulunuyor."]},"beginTime":1269,"endTime":1364,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=1269&ask_summarization=1"},{"index":12,"title":"Teklik Çiftlik Sorusu","list":{"type":"unordered","items":["x, y ve z tam sayı olmak üzere 5x - 3y = z ifadesi bir tek sayı olduğunda, x - y'nin tek veya çift olması durumunda z de aynı şekilde tek veya çift olacaktır.","x + y + z tek sayıdır çünkü x - y'nin tek veya çift olması durumunda x + y de aynı şekilde tek veya çift olacaktır.","y çift ise z tektir ifadesi her zaman doğru değildir, bu nedenle doğru cevaplar birinci ve ikinci öncüllerdir."]},"beginTime":1372,"endTime":1495,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=1372&ask_summarization=1"},{"index":13,"title":"Alim Sayılar","list":{"type":"unordered","items":["Alim sayı, kullanılan her rakamın kendi sayı değeri kadar tekrar ettiği sayılardır (örneğin 414144, 312323).","Altı basamaklı alim sayılar: 111111, 222222, 333333, 444444, 555555, 6060'dır.","Tekrarlı permütasyon formülü kullanılarak bu sayıların toplam sayısı 82 olarak hesaplanmıştır."]},"beginTime":1495,"endTime":1690,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=1495&ask_summarization=1"},{"index":14,"title":"Hareket Problemi","list":{"type":"unordered","items":["A ve B araçları birbirine doğru hareket ederek 2 saatte 280 km yol almışlardır.","İki saat sonra A aracı hızını değiştirmeden, B aracı hızını yarıya düşürerek yola devam etmişlerdir.","A aracının yolu boyunca saatteki hızı 40 km'dir."]},"beginTime":1690,"endTime":1878,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=1690&ask_summarization=1"},{"index":15,"title":"Havuz Problemi","list":{"type":"unordered","items":["A deposu 9 saatte tamamen doluyor, B deposu ise 4 saatte tamamen boşalıyor.","İki depodaki su seviyeleri eşitlendikten sonra A deposu 9 saatte tamamen doluyor.","A deposu toplam 15 saatte tamamen dolmuştur."]},"beginTime":1878,"endTime":2084,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=1878&ask_summarization=1"},{"index":16,"title":"Havlu Üretim Problemi","list":{"type":"unordered","items":["Bir fabrikada üretilen havlu sayıları üç gün boyunca incelenmiş, ikinci gün birinci güne göre %50 daha fazla, üçüncü gün ikinci güne göre %50 daha fazla havlu üretilmiş.","İlk iki gün üretilen toplam havlu sayısı üçüncü gün üretilen havlu sayısının iki katı olsaydı toplam 320 havlu daha fazla üretilecekti.","Üç gün boyunca toplam 760 havlu üretilmiştir."]},"beginTime":2094,"endTime":2227,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=2094&ask_summarization=1"},{"index":17,"title":"Yaş Farkı Problemi","list":{"type":"unordered","items":["Emir ile babası arasındaki yaş farkı, Emir'in dedesi ile babası arasındaki yaş farkından bir fazladır.","Emir 20 yaşındayken dedesi 69 yaşında olduğuna göre, Emir'in babası 45 yaşında ve Emir ile babası arasındaki yaş farkı 25'tir."]},"beginTime":2227,"endTime":2318,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=2227&ask_summarization=1"},{"index":18,"title":"Mobilya Mağazası Problemi","list":{"type":"unordered","items":["İki farklı mobilya mağazasından satın alınan ürünleri bir mağaza 8 günde, ikinci mağaza ise 10 günde teslim etmektedir.","Ürünlerin geç teslim edildiği her bir gün için satış fiyatından birinci mağaza %2'sini, ikinci mağaza %5'ini geri demektedir.","Oktay her iki mağazadan aynı gün mobilya satın almış ve aldığı ürünler 11 gün sonra teslim edilmiştir, başlangıçta 9000 TL ödeme yapan Oktay'a ürünler teslim edildikten sonra 500 TL geri ödenmiştir.","Oktay'ın bir mağazadan aldığı ürünün satış fiyatı 50 TL'dir."]},"beginTime":2318,"endTime":2471,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=2318&ask_summarization=1"},{"index":19,"title":"Borç Ödeme Problemi","list":{"type":"unordered","items":["Alper her ay 50 TL ödeyerek arkadaşına olan borcunun tamamını bitirmeyi planlıyor.","İlk beş ay boyunca 40 TL, sonraki ay ise her ay 160 TL ödeyerek borcunun tamamını planladığı sürenin yarısında bitiriyor.","Alper'in arkadaşı olan borcu 1000 TL'dir."]},"beginTime":2471,"endTime":2576,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=2471&ask_summarization=1"},{"index":20,"title":"Sayı Basamakları Problemi","list":{"type":"unordered","items":["Üç basamaklı abc doğal sayısı iki basamaklı bc doğal sayısının 26 katıdır.","Bu koşulu sağlayan en büyük abc doğal sayısının rakamları toplamı 18'dir."]},"beginTime":2576,"endTime":2677,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=2576&ask_summarization=1"},{"index":21,"title":"Olasılık Problemi","list":{"type":"unordered","items":["Aslı hafta içi bir gün ve hafta sonu bir gün olmak üzere haftada iki gün tiyatroya gidiyor.","Aslı'nın herhangi bir haftada Salı ve Pazar günlerinde tiyatroya gitme olasılığı 1/10'dur."]},"beginTime":2677,"endTime":2741,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=2677&ask_summarization=1"},{"index":22,"title":"Sayı Tanımı Problemi","list":{"type":"unordered","items":["Bir doğal sayının en küçük asal çarpanı k ise bu doğal sayıya k sayı denir.","Örneğin 49 yedi'sel bir sayıdır çünkü 49=7² ve en küçük asal çarpanı 7'dir.","300 ise ikisel bir sayıdır çünkü 300=2×4×3×5² ve en küçük asal çarpanı 2'dir."]},"beginTime":2741,"endTime":2781,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=2741&ask_summarization=1"},{"index":23,"title":"Üçsel Sayılar Problemi","list":{"type":"unordered","items":["İki basamaklı en küçük üçsel sayı 15'tir çünkü en küçük asal çarpan 3, ikinci asal çarpan 5'tir.","İki basamaklı en büyük beşsel sayı 95'tir çünkü en büyük asal çarpan 5, ikinci asal çarpan 19'dur.","İki basamaklı en büyük üçsel sayı ile en küçük üçsel sayı ile en büyük beşsel sayının toplamı 110'dur."]},"beginTime":2783,"endTime":2887,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=2783&ask_summarization=1"},{"index":24,"title":"Asal Çarpanlar Problemi","list":{"type":"unordered","items":["210 sayısının asal çarpanları 2, 3, 5 ve 7'dir.","210/n bir üçsel sayı olduğuna göre, n'nin alabileceği tam sayı değerleri 2, 10, 14 ve 70'dir.","n'nin alabileceği tam sayı değerleri toplamı 696'dır."]},"beginTime":2887,"endTime":3076,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=2887&ask_summarization=1"},{"index":25,"title":"Top Çekme Oyunu Problemi","list":{"type":"unordered","items":["Sevim ve Tuğba'nın içinde 20 adet top bulunan bir torbadan top çekerek oynadıkları oyunun kuralları verilmiştir.","Oyun yedinci adım sonunda bittiğine göre, oyuncular toplam 2 kere bir tane top çekmişlerdir.","Oyunun ilk ve son adımında Sevim 6 top çekmiş ve oyun bitmiştir, bu durumda oyun 5 adımda bitmiştir."]},"beginTime":3076,"endTime":3355,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=3076&ask_summarization=1"},{"index":26,"title":"Sayısal Mantık Sorusu","list":{"type":"unordered","items":["Sevim ve Tuğba her adımda eşit sayıda top çekmiş, ancak çektikleri top sayıları birbirinden farklıdır.","Oyun Sevim ile başlayıp Tuğba ile bittiği için adım sayısı çift olmalıdır.","Toplam 20 top var ve bu topların toplamı 4, 7 ve 9 olabilir, ancak 20 birim 4'e bölünür ve toplam adım sayısı 10'dur."]},"beginTime":3357,"endTime":3452,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=3357&ask_summarization=1"},{"index":27,"title":"Eşkenar Üçgen Geometri Sorusu","list":{"type":"unordered","items":["ABC eşkenar üçgeninde CF=8 birim ve DF=x verilmiştir.","Üçgenin kenarları ve açıları kullanılarak DF uzunluğu hesaplanmıştır.","Segor bağıntısı kullanılarak x değeri √21 olarak bulunmuştur."]},"beginTime":3452,"endTime":3571,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=3452&ask_summarization=1"},{"index":28,"title":"Kare ve Üçgen Alan Sorusu","list":{"type":"unordered","items":["ABCD karesinin alanı EFD ikizkenar dik üçgen alanının 16 katıdır.","D noktası EFGH karesinin simetri merkezi olmak zorundadır.","ABCD karesinin alanı EFGH karesinin alanına oranı 16/4=4 olarak hesaplanmıştır."]},"beginTime":3571,"endTime":3678,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=3571&ask_summarization=1"},{"index":29,"title":"Analitik Geometri Sorusu","list":{"type":"unordered","items":["ABC eşkenar üçgeninin AB kenarı x eksenine paraleldir ve A ve B köşeleri sırasıyla D1 ve y=x-4 doğruları üzerindedir.","D1 doğrusu x=8 üzerinde kesişmekte ve B köşesinin apsisi 8'dir.","Eşkenar üçgenin çevresi 16 birim olarak bulunmuştur."]},"beginTime":3678,"endTime":3836,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=3678&ask_summarization=1"},{"index":30,"title":"Video Kapanışı","list":{"type":"unordered","items":["2017 KPSS soruları çözülmüştür.","İzleyicilerden kanala abone olmaları ve sosyal medya adreslerinden takip etmeleri istenmiştir."]},"beginTime":3836,"endTime":3855,"href":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=3836&ask_summarization=1"}],"linkTemplate":"/video/preview/17989910671623261382?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"2017 KPSS Matematik Sorulari VE EN Basit Çözümleri (KPSS 2017 Çıkmış Sorular Ve Çözümleri 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Elbette sınav öncesinde anlatımını yaptığımız tüm kpss konu anlatımları çok önemli fakat 2018 kpss matematik bölümünde olduğu...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1552167/e020ffddac2f4f83520f150dae24ed23/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/-dt2LAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"8","reqid":"1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=videoid:3425108470421906228","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan kapsamlı bir matematik soru çözüm dersidir. Eğitmen, KPSS sınavına hazırlanan öğrenciler için çeşitli matematik sorularını adım adım çözmektedir.","Videoda toplam 30 farklı matematik sorusu çözülmektedir. Sorular rasyonel sayılar, ondalık sayılar, üslü sayılar, köklü sayılar, çarpanlara ayırma, cebirsel ifadeler, mutlak değer, eşitsizlikler, kümeler, bileşke fonksiyonlar, sayı basamakları, modüler aritmetik, olasılık, grafik problemleri, düzenek problemleri, geometri konuları (eşkenar üçgenler, kareler, çember) ve analitik geometri gibi geniş bir yelpazede yer almaktadır.","Her soru için eğitmen detaylı çözüm yöntemleri sunmakta, gerekli matematiksel işlemler ve kuralları açıklamakta ve bazı sorularda alternatif çözüm yolları da göstermektedir. Video, KPSS sınavına hazırlanan veya matematik problemlerinin çözüm tekniklerini öğrenmek isteyen öğrenciler için faydalı bir kaynak niteliğindedir."]},"endTime":3945,"title":"KPSS Matematik Soru Çözüm Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"KPSS Matematik Çıkmış Sorular","list":{"type":"unordered","items":["2018 KPSS matematik çıkmış soruları çözümleniyor.","İlk soru rasyonel sayılarla ilgili olup, işlem paylaşılarak çözülüyor ve cevap 3/5 bulunuyor.","İkinci soru ondalık sayılarla ilgili olup, ondalık işlemlerde zorlananlar rasyonel sayılara çevirerek işlem yapabilir."]},"beginTime":15,"endTime":269,"href":"/video/preview/3425108470421906228?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=15&ask_summarization=1"},{"index":1,"title":"Üslü ve Köklü Sayılar Soruları","list":{"type":"unordered","items":["Üçüncü soru üslü sayılarla ilgili olup, tabanlar aynı ancak üstler farklı olduğunda ortak parantez alınarak çözüm yapılıyor ve cevap 15 bulunuyor.","Dördüncü soru köklü sayılarla ilgili olup, kök içinde dışarı çıkabilen sayılar dışarı çıkarılarak ve payda eşitleme yaparak çözüm yapılıyor.","Beşinci soru çarpanlara ayırma sorusu olup, özdeşlikler yardımıyla çarpanlara ayrılarak ve sadeleştirilerek cevap bulunuyor."]},"beginTime":269,"endTime":527,"href":"/video/preview/3425108470421906228?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=269&ask_summarization=1"},{"index":2,"title":"Sayı Teorisi ve Mutlak Değer Soruları","list":{"type":"unordered","items":["Altıncı soru a ve b pozitif tam sayılar olmak üzere a×b+b ifadesinin tek sayı olması durumunda hangi ifadelerin tek sayı olacağı soruluyor.","Yedinci soru mutlak değer içeren bir eşitlikle ilgili olup, mutlak değerlerin sonucunun daima pozitif olması özelliğinden yararlanılarak çözüm yapılıyor.","Sekizinci soru x ve y sayıları için 1/y \u003c x \u003c 1/x eşitsizliği verilerek hangi ifadelerin her zaman doğru olduğu soruluyor."]},"beginTime":527,"endTime":787,"href":"/video/preview/3425108470421906228?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=527&ask_summarization=1"},{"index":3,"title":"Matematiksel Çözümler","list":{"type":"unordered","items":["Eksi ile eksi çarpımı artı sonucunu verirken, eksi ile eksi toplamı her zaman eksi sonucunu verir.","Eksi bir sayı artı bir sayıdan her zaman küçüktür.","Üçüncü öncülde x çarpı y küçüktür bir sonucu doğru olarak bulunmuştur."]},"beginTime":791,"endTime":882,"href":"/video/preview/3425108470421906228?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=791&ask_summarization=1"},{"index":4,"title":"Kuvvetler Sorusu","list":{"type":"unordered","items":["Dört üzeri iki üzeri x ve iki üzeri x eksi dört üzeri y eşittir altmışdört olduğunda, x çarpı y onbeş olarak hesaplanmıştır.","Dört üzeri y eşittir altmışdört olduğunda, y değeri eksi üç olarak bulunmuştur.","İki üzeri x eşittir otuziki olduğunda, x değeri eksi beş olarak hesaplanmıştır."]},"beginTime":882,"endTime":964,"href":"/video/preview/3425108470421906228?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=882&ask_summarization=1"},{"index":5,"title":"Köklü Sayılar Sorusu","list":{"type":"unordered","items":["Kök içerisinde x iki x sekiz ve kök içerisinde kök içerisinde x yedi iki olduğunda, x değeri sekiz olarak hesaplanmıştır.","Kök x bölü kök iki artı kök sekiz iki kök iki artı kök x bölü otuziki dört kök iki eşittir yedi iki denklemi çözülmüştür.","İçler dışlar çarpımı ve her iki tarafın karesi alınarak x değeri sekiz olarak 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gösterir.","C'den A birleşim B'yi atarak kalan elemanlar bulunmuştur.","Sonuç olarak elma elemanı C kümesinde kalmıştır."]},"beginTime":1212,"endTime":1298,"href":"/video/preview/3425108470421906228?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=1212&ask_summarization=1"},{"index":8,"title":"Fonksiyonlar","list":{"type":"unordered","items":["f(x) = ax + 3 ve g(x) = 3x + 1 fonksiyonları için f bileşke g ve g bileşke f hesaplanmıştır.","f bileşke g = a(3x + 1) + 3 ve g bileşke f = 3(ax + 3) + 1 denklemleri çözülmüştür.","a değeri yedi olarak bulunmuştur."]},"beginTime":1298,"endTime":1394,"href":"/video/preview/3425108470421906228?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=1298&ask_summarization=1"},{"index":9,"title":"Sayı Basamakları","list":{"type":"unordered","items":["Rakamlarından biri beş olan üç basamaklı sayının diğer iki rakamı aynıdır ve yüzler ile birler basamağı yer değiştirdiğinde sayının değeri yüzdoksansekiz azalmaktadır.","Sayı ya 775 ya da 533 şeklinde olabilir ve toplamları binüçyüzsekiz olarak hesaplanmıştır.","775 ve 533 sayıları yer değiştirildiğinde yüzdoksansekiz farkı elde edilmiştir."]},"beginTime":1394,"endTime":1564,"href":"/video/preview/3425108470421906228?parent-reqid=1769623363557134-9992288601664154820-balancer-l7leveler-kubr-yp-sas-113-BAL&text=Violim_Matematica&t=1394&ask_summarization=1"},{"index":10,"title":"Asal Sayılar","list":{"type":"unordered","items":["Rakamları birbirinden farklı birer asal sayı olan üç basamaklı bir doğal sayı üç ile tam bölünebilmektedir.","Asal rakamlar 2, 3, 5 ve 7'dir.","En büyük sayı 753, en küçük sayı 237 olup, aralarındaki fark beşyüzonaltı olarak 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