[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"public-settings":3,"content:materi:rumus-peluang":11,"public-catalog":196},{"features.tutoring.enabled":4,"sections.subjects.enabled":5,"sections.pricing.enabled":5,"sections.teachers.enabled":5,"sections.testimonials.enabled":4,"sections.faqs.enabled":5,"bankSoal.enabled":5,"site.maintenance":4,"whatsapp.number":6,"brand.name":7,"brand.tagline":8,"contact.email":9,"contact.address":10},false,true,"6285156084435","MyFismat","Platform belajar Matematika, Fisika, dan Pemrograman untuk SD, SMP, SMA, dan Kuliah","support@myfismat.com","Indonesia",{"id":12,"type":13,"slug":14,"title":15,"excerpt":16,"coverUrl":17,"status":18,"publishedAt":19,"featured":4,"subjectId":20,"blocks":21,"seoTitle":17,"seoDescription":17,"readingMinutes":94,"order":95,"createdAt":96,"updatedAt":96,"subject":97,"levels":102,"topics":107,"tags":111,"author":17,"resolved":112,"related":122},"demo-v2-m-matematika-sma-3","MATERIAL","rumus-peluang","Rumus Peluang Kejadian Matematika dan Contoh Soal","Rumus peluang P(A) = n(A)\u002Fn(S), ruang sampel, peluang komplemen, frekuensi harapan, kejadian saling lepas dan saling bebas, plus contoh soal dadu dan koin.",null,"PUBLISHED","2026-10-08T23:58:22.961Z","cmuzbyhdg000471r9l54yc9ia",[22,27,34,38,42,46,50,54,58,62,66,72,76,80,84,88],{"id":23,"data":24,"type":26},"s1-1",{"markdown":25},"**Rumus peluang** suatu kejadian adalah $P(A)=\\frac{n(A)}{n(S)}$, yaitu banyak hasil yang diinginkan dibagi banyak semua hasil yang mungkin, asalkan setiap hasil sama mungkin terjadi. Nilai peluang selalu di antara 0 dan 1. Contohnya, peluang muncul angka genap pada satu dadu adalah $\\frac36=\\frac12$.","text",{"id":28,"data":29,"type":33},"s1-2",{"title":30,"variant":31,"markdown":32},"Rumus peluang","info","$$P(A)=\\frac{n(A)}{n(S)},\\qquad 0\\le P(A)\\le1$$\nKomplemen: $P(A^c)=1-P(A)$\n\nFrekuensi harapan: $F_h=P(A)\\times n$, dengan $n$ banyak percobaan.","callout",{"id":35,"data":36,"type":26},"s2-1",{"markdown":37},"## Apa Itu Peluang?\n\n**Peluang** mengukur seberapa mungkin suatu kejadian terjadi. Untuk menghitungnya, kita perlu dua istilah:\n\n- **Ruang sampel** $S$: himpunan semua hasil yang mungkin. Satu dadu: $S=\\{1,2,3,4,5,6\\}$, jadi $n(S)=6$.\n- **Kejadian** $A$: bagian dari ruang sampel yang memenuhi syarat. Angka prima: $A=\\{2,3,5\\}$, jadi $n(A)=3$.\n\nPeluang 0 berarti mustahil (misalnya angka 7 pada dadu), dan peluang 1 berarti pasti terjadi.",{"id":39,"data":40,"type":26},"s3-1",{"markdown":41},"## Ruang Sampel Dua Koin dan Dua Dadu\n\nGunakan urutan agar tidak ada hasil yang terlewat. Dua koin (G = gambar, A = angka) mempunyai 4 hasil: GG, GA, AG, AA. GA dan AG berbeda, karena koin pertama dan kedua bisa dibedakan.\n\nDua dadu mempunyai $6\\times6=36$ hasil. Tabel berikut membantu menghitung jumlah mata dadu:\n\n| Jumlah mata | Pasangan | Banyak |\n|---|---|---|\n| 7 | (1,6) (2,5) (3,4) (4,3) (5,2) (6,1) | 6 |\n| 8 | (2,6) (3,5) (4,4) (5,3) (6,2) | 5 |\n| 10 | (4,6) (5,5) (6,4) | 3 |",{"id":43,"data":44,"type":26},"s4-1",{"markdown":45},"## Peluang Komplemen dan Frekuensi Harapan\n\n**Komplemen** $A^c$ berarti \"A tidak terjadi\". Karena keduanya mengisi seluruh ruang sampel, $P(A^c)=1-P(A)$. Cara ini sangat berguna untuk soal \"**paling sedikit satu**\".\n\n**Frekuensi harapan** adalah perkiraan berapa kali kejadian muncul dalam $n$ percobaan: $F_h=P(A)\\times n$. Jika dadu dilempar 120 kali, angka prima diharapkan muncul sekitar $\\frac12\\times120=60$ kali. Hasil nyata bisa sedikit berbeda; frekuensi harapan adalah perkiraan, bukan jaminan.",{"id":47,"data":48,"type":26},"s5-1",{"markdown":49},"## Peluang Kejadian Majemuk: Saling Lepas dan Saling Bebas\n\nUntuk dua kejadian $A$ dan $B$:\n\n$$P(A\\cup B)=P(A)+P(B)-P(A\\cap B)$$\n\n- **Saling lepas**: $A$ dan $B$ tidak bisa terjadi bersamaan, jadi $P(A\\cap B)=0$ dan $P(A\\cup B)=P(A)+P(B)$.\n- **Saling bebas**: terjadinya $A$ tidak memengaruhi $B$, jadi $P(A\\cap B)=P(A)\\times P(B)$.",{"id":51,"data":52,"type":26},"s6-1",{"markdown":53},"## Pengambilan dengan dan tanpa Pengembalian\n\nJika benda diambil **tanpa pengembalian**, isi kantong berubah sehingga peluang tahap kedua ikut berubah. Peluang ini disebut **peluang bersyarat**:\n\n$$P(A\\text{ lalu }B)=P(A)\\times P(B\\mid A)$$\n\nJika benda **dikembalikan**, isi kantong kembali seperti semula dan kedua pengambilan saling bebas.",{"id":55,"data":56,"type":26},"s7-1",{"markdown":57},"## Kombinasi untuk Menghitung Ruang Sampel yang Besar\n\nJika hasilnya terlalu banyak untuk didaftar, gunakan **kombinasi**. Banyak cara memilih $r$ benda dari $n$ benda tanpa memperhatikan urutan adalah\n\n$$C(n,r)=\\frac{n!}{r!\\,(n-r)!}.$$\n\nContoh: dari 5 bola (3 merah, 2 biru) diambil 2 sekaligus. Semua kemungkinan $C(5,2)=10$, dan kemungkinan keduanya merah $C(3,2)=3$. Peluangnya $\\frac3{10}$, sama dengan hasil cara bertahap pada Contoh 4 di bawah. Jika urutan diperhatikan, misalnya memilih ketua dan wakil, gunakan **permutasi** $P(n,r)=\\frac{n!}{(n-r)!}$.",{"id":59,"data":60,"type":26},"s8-1",{"markdown":61},"## Contoh Soal Peluang dan Pembahasan\n\n### Contoh 1: Jumlah dua dadu\n\nDua dadu dilempar. Peluang jumlah mata 7 adalah $\\frac6{36}=\\frac16$, karena ada 6 pasangan dari tabel di atas.\n\n### Contoh 2: Paling sedikit satu gambar\n\nDua koin dilempar. Komplemen dari \"paling sedikit satu gambar\" adalah AA, dengan peluang $\\frac14$. Jadi peluangnya $1-\\frac14=\\frac34$.\n\n### Contoh 3: Kartu as atau hati\n\nDari 52 kartu remi, ambil satu. $P(\\text{as})=\\frac4{52}$, $P(\\text{hati})=\\frac{13}{52}$, dan as hati dihitung dua kali, $\\frac1{52}$. Maka $P=\\frac{4+13-1}{52}=\\frac{16}{52}=\\frac4{13}$.\n\n### Contoh 4: Bola tanpa pengembalian\n\nKantong berisi 3 bola merah dan 2 biru. Dua bola diambil satu per satu tanpa pengembalian. Peluang keduanya merah $=\\frac35\\times\\frac24=\\frac6{20}=\\frac3{10}$. Jika bola pertama dikembalikan, peluangnya menjadi $\\frac35\\times\\frac35=\\frac9{25}$.\n\n### Contoh 5: Frekuensi harapan\n\nSebuah dadu dilempar 120 kali. Peluang muncul angka prima (2, 3, atau 5) adalah $\\frac36=\\frac12$, sehingga frekuensi harapannya $\\frac12\\times120=60$ kali. Jika hasil nyata 57 atau 63 kali, itu wajar karena percobaan acak selalu sedikit bervariasi.",{"id":63,"data":64,"type":26},"s9-1",{"markdown":65},"## Kesalahan yang Sering Terjadi",{"id":67,"data":68,"type":33},"s9-2",{"title":69,"variant":70,"markdown":71},"Perhatikan kata \"tepat\" dan \"paling sedikit\"","warning","Pada dua koin, \"tepat satu gambar\" = GA, AG (peluang $\\frac12$), sedangkan \"paling sedikit satu gambar\" = GG, GA, AG (peluang $\\frac34$).",{"id":73,"data":74,"type":26},"s9-3",{"markdown":75},"- Menggabungkan GA dan AG menjadi satu hasil.\n- Tetap memakai penyebut awal setelah benda diambil tanpa pengembalian.\n- Menghitung irisan dua kali pada kejadian yang tidak saling lepas.",{"id":77,"data":78,"type":26},"s10-1",{"markdown":79},"## Ringkasan\n\n- $P(A)=\\frac{n(A)}{n(S)}$ untuk hasil yang sama mungkin; $0\\le P(A)\\le1$.\n- $P(A^c)=1-P(A)$; frekuensi harapan $F_h=P(A)\\times n$.\n- Gabungan: $P(A\\cup B)=P(A)+P(B)-P(A\\cap B)$.\n- Tanpa pengembalian: kalikan peluang tiap tahap dengan isi kantong yang sudah berubah.",{"id":81,"data":82,"type":26},"s11-1",{"markdown":83},"## Materi Terkait\n\nPeluang selalu berbentuk pecahan, jadi pastikan lancar [penjumlahan pecahan](\u002Fmateri\u002Fpenjumlahan-pecahan). Peluang percobaan berulang, misalnya tiga kali berturut-turut muncul gambar, yaitu $\\left(\\frac12\\right)^3=\\frac18$, memakai perpangkatan dari [eksponen dan logaritma](\u002Fmateri\u002Feksponen-dan-logaritma). Di kuliah, peluang variabel kontinu dihitung dengan [integral tentu](\u002Fmateri\u002Fintegral-tentu).",{"id":85,"data":86,"type":26},"sources",{"markdown":87},"## Sumber belajar\n\n- [OpenStax Introductory Statistics 2e — Terminology](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Fintroductory-statistics-2e\u002Fpages\u002F3-1-terminology)\n- [OpenStax Introductory Statistics 2e — Independent and Mutually Exclusive Events](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Fintroductory-statistics-2e\u002Fpages\u002F3-2-independent-and-mutually-exclusive-events)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.",{"id":89,"data":90,"type":93},"practice",{"title":91,"questionSetId":92},"Latihan soal Peluang Kejadian","demo-v2-p-matematika-sma-3","quiz",4,2,"2026-10-08T23:58:22.963Z",{"id":20,"slug":98,"name":99,"color":100,"icon":101},"matematika","Matematika","#8B5CF6","sigma",[103],{"id":104,"slug":105,"name":106},"cmuzbyhdb000271r9up0bfli4","sma","SMA",[108],{"id":109,"slug":14,"name":110,"subjectId":20},"demo-v2-topic-matematika-sma-3","Peluang Kejadian",[],{"assets":113,"videos":114,"questionSets":115},{},{},{"demo-v2-p-matematika-sma-3":116},{"id":92,"slug":117,"title":118,"mode":119,"description":120,"questionCount":121,"durationMinutes":17},"latihan-soal-rumus-peluang","Latihan Soal Peluang Kejadian","PRACTICE","5 soal Peluang Kejadian (Matematika SMA) lengkap dengan pembahasan langkah demi langkah dan alasan pilihan yang keliru.",5,[123,150,165,181],{"id":124,"type":125,"slug":126,"title":127,"excerpt":128,"coverUrl":17,"status":18,"publishedAt":129,"featured":5,"readingMinutes":130,"order":131,"updatedAt":132,"subject":133,"levels":134,"topics":148,"tags":149,"author":17},"demo-v2-a-matematika","ARTICLE","cara-belajar-matematika-dari-nol","Cara Belajar Matematika dari Nol: Urutan Materi SD–Kuliah","Cara belajar matematika dari nol: urutan materi dari pecahan, bangun ruang, aljabar, hingga kalkulus, kebiasaan belajar efektif, dan rencana 4 minggu.","2026-10-08T23:58:23.084Z",7,0,"2026-10-08T23:58:23.086Z",{"id":20,"slug":98,"name":99,"color":100,"icon":101},[135,139,143,144],{"id":136,"slug":137,"name":138},"cmv0762210004113f6m6v04vs","sd","SD",{"id":140,"slug":141,"name":142},"cmuzbyhdb000171r9dcbyf0qg","smp","SMP",{"id":104,"slug":105,"name":106},{"id":145,"slug":146,"name":147},"cmuzbyhdb000371r9qk125qjd","kuliah","Kuliah",[],[],{"id":151,"type":13,"slug":152,"title":153,"excerpt":154,"coverUrl":17,"status":18,"publishedAt":155,"featured":4,"readingMinutes":121,"order":95,"updatedAt":156,"subject":157,"levels":158,"topics":160,"tags":164,"author":17},"demo-v2-m-matematika-kuliah-3","vektor-3-dimensi-dot-product","Vektor 3 Dimensi dan Dot Product (Perkalian Titik)","Vektor 3 dimensi: komponen, panjang vektor, vektor satuan, dot product atau perkalian titik, sudut antara dua vektor, proyeksi, dan contoh soal.","2026-10-08T23:58:23.070Z","2026-10-08T23:58:23.072Z",{"id":20,"slug":98,"name":99,"color":100,"icon":101},[159],{"id":145,"slug":146,"name":147},[161],{"id":162,"slug":152,"name":163,"subjectId":20},"demo-v2-topic-matematika-kuliah-3","Vektor 3D dan Dot Product",[],{"id":166,"type":13,"slug":167,"title":168,"excerpt":169,"coverUrl":17,"status":18,"publishedAt":170,"featured":4,"readingMinutes":94,"order":171,"updatedAt":172,"subject":173,"levels":174,"topics":176,"tags":180,"author":17},"demo-v2-m-matematika-kuliah-2","integral-tentu","Integral Tentu: Rumus, Luas, dan Volume Benda Putar","Integral tentu dan teorema dasar kalkulus, sifat-sifatnya, luas daerah antara kurva, volume benda putar metode cakram dan kulit tabung, plus contoh soal.","2026-10-08T23:58:23.034Z",1,"2026-10-08T23:58:23.037Z",{"id":20,"slug":98,"name":99,"color":100,"icon":101},[175],{"id":145,"slug":146,"name":147},[177],{"id":178,"slug":167,"name":179,"subjectId":20},"cmuzbyhvn00gc71r9tl4peyfx","Integral Tentu",[],{"id":182,"type":13,"slug":183,"title":184,"excerpt":185,"coverUrl":17,"status":18,"publishedAt":186,"featured":5,"readingMinutes":94,"order":131,"updatedAt":187,"subject":188,"levels":189,"topics":191,"tags":195,"author":17},"demo-v2-m-matematika-kuliah-1","definisi-turunan-limit","Definisi Turunan dengan Limit dan Garis Singgung","Definisi turunan dengan limit f′(x) = lim [f(x+h) − f(x)]\u002Fh, langkah menghitungnya, gradien garis singgung, syarat diferensiabel, dan contoh soal.","2026-10-08T23:58:23.002Z","2026-10-08T23:58:23.004Z",{"id":20,"slug":98,"name":99,"color":100,"icon":101},[190],{"id":145,"slug":146,"name":147},[192],{"id":193,"slug":183,"name":194,"subjectId":20},"demo-v2-topic-matematika-kuliah-1","Definisi Turunan",[],{"subjects":197,"levels":217,"topics":229,"tags":2016},[198,201,209],{"id":20,"slug":98,"name":99,"description":199,"icon":101,"color":100,"order":131,"published":5,"createdAt":200,"updatedAt":200},"Aljabar, geometri, kalkulus, statistika, dan cara berpikir matematis.","2026-10-08T09:24:40.948Z",{"id":202,"slug":203,"name":204,"description":205,"icon":206,"color":207,"order":171,"published":5,"createdAt":208,"updatedAt":208},"cmuzbyhdq000571r9nsdk6scx","fisika","Fisika","Gerak, gaya, energi, listrik, gelombang, hingga fisika modern.","atom","#0EA5E9","2026-10-08T09:24:40.958Z",{"id":210,"slug":211,"name":212,"description":213,"icon":214,"color":215,"order":95,"published":5,"createdAt":216,"updatedAt":216},"cmuzbyhdt000671r91cdnnt22","pemrograman","Pemrograman","Logika, algoritma, dan coding dari dasar sampai proyek nyata.","code","#3B82F6","2026-10-08T09:24:40.962Z",[218,221,224,226],{"id":136,"slug":137,"name":138,"description":219,"order":131,"createdAt":220,"updatedAt":220},"Jenjang SD","2026-10-08T23:58:22.441Z",{"id":140,"slug":141,"name":142,"description":222,"order":171,"createdAt":223,"updatedAt":223},"Sekolah Menengah Pertama","2026-10-08T09:24:40.943Z",{"id":104,"slug":105,"name":106,"description":225,"order":95,"createdAt":223,"updatedAt":223},"Sekolah Menengah Atas",{"id":145,"slug":146,"name":147,"description":227,"order":228,"createdAt":223,"updatedAt":223},"Perguruan tinggi \u002F universitas",3,[230,237,243,249,255,261,266,272,278,284,289,295,301,307,313,319,325,331,337,343,349,355,361,367,373,379,385,391,397,403,409,415,421,427,433,439,445,451,457,463,468,474,480,486,492,498,504,510,516,522,528,534,540,546,552,558,564,570,575,580,585,590,595,600,605,610,615,620,626,631,636,641,646,651,656,661,666,671,676,681,686,691,693,698,703,708,713,718,723,728,733,738,743,748,753,758,763,768,774,779,784,789,794,799,804,809,814,819,824,829,834,839,844,849,854,859,864,869,874,879,884,889,895,900,905,910,915,920,925,930,935,940,945,950,955,960,965,970,975,980,985,991,996,1001,1006,1011,1016,1021,1026,1031,1036,1041,1046,1051,1056,1061,1066,1071,1076,1081,1086,1091,1096,1101,1107,1112,1117,1122,1127,1132,1137,1142,1147,1152,1157,1162,1167,1172,1177,1182,1187,1192,1197,1202,1207,1212,1217,1222,1227,1232,1235,1241,1246,1251,1256,1261,1266,1271,1276,1281,1285,1290,1295,1300,1305,1310,1315,1320,1325,1330,1335,1340,1345,1350,1355,1360,1365,1370,1375,1380,1385,1390,1395,1400,1405,1410,1415,1420,1425,1430,1435,1440,1445,1450,1454,1459,1464,1469,1474,1479,1484,1490,1495,1500,1505,1510,1515,1520,1525,1530,1535,1540,1545,1550,1555,1561,1566,1572,1577,1583,1588,1594,1599,1605,1610,1616,1622,1628,1633,1639,1644,1650,1653,1659,1664,1670,1675,1680,1685,1691,1696,1702,1707,1713,1718,1724,1728,1734,1739,1745,1750,1756,1761,1767,1772,1778,1783,1789,1794,1800,1805,1812,1819,1826,1829,1835,1841,1847,1853,1859,1865,1871,1877,1883,1889,1895,1902,1908,1914,1920,1926,1932,1938,1944,1950,1956,1959,1965,1971,1977,1983,1989,1991,1997,2004,2010],{"id":231,"subjectId":202,"levelId":104,"parentId":232,"slug":233,"name":234,"description":235,"order":131,"createdAt":236,"updatedAt":236},"cmuzbyhm9007o71r91e76ir5n","cmuzbyhm6007m71r9multkwzz","arus-dan-tegangan-listrik-bolak-balik","Arus dan Tegangan Listrik Bolak Balik","","2026-10-08T09:24:41.265Z",{"id":238,"subjectId":20,"levelId":104,"parentId":239,"slug":240,"name":241,"description":235,"order":131,"createdAt":242,"updatedAt":242},"cmuzbyht500e271r9p86b0fxe","cmuzbyht300e071r93gyvjn0r","barisan","Barisan","2026-10-08T09:24:41.514Z",{"id":244,"subjectId":20,"levelId":104,"parentId":245,"slug":246,"name":247,"description":235,"order":131,"createdAt":248,"updatedAt":248},"cmuzbyhok009w71r9688mekrn","cmuzbyhoi009u71r9i6j09wcn","barisan-dan-deret-barisan-dan-deret-kelas-10","Barisan dan Deret","2026-10-08T09:24:41.348Z",{"id":250,"subjectId":20,"levelId":104,"parentId":251,"slug":252,"name":253,"description":235,"order":131,"createdAt":254,"updatedAt":254},"cmuzbyhpm00aw71r94xosa04y","cmuzbyhpk00au71r9d9ugx39r","bentuk-umum-dan-akar-persamaan-kuadrat","Bentuk Umum dan Akar Persamaan Kuadrat","2026-10-08T09:24:41.386Z",{"id":256,"subjectId":202,"levelId":104,"parentId":257,"slug":258,"name":259,"description":235,"order":131,"createdAt":260,"updatedAt":260},"cmuzbyhea000a71r9vz07bjjd","cmuzbyhe6000871r9fojy2euz","besaran-pokok","Besaran Pokok","2026-10-08T09:24:40.978Z",{"id":257,"subjectId":202,"levelId":104,"parentId":17,"slug":262,"name":263,"description":264,"order":131,"createdAt":265,"updatedAt":265},"besaran-dan-pengukuran","Besaran dan Pengukuran","Besaran dan Pengukuran — Kelas 10.","2026-10-08T09:24:40.973Z",{"id":267,"subjectId":20,"levelId":104,"parentId":268,"slug":269,"name":270,"description":235,"order":131,"createdAt":271,"updatedAt":271},"cmuzbyhtc00e871r96y3gdtr5","cmuzbyhta00e671r9rt9do1nw","bunga-tunggal","Bunga 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Wajib.","2026-10-08T09:24:41.547Z",{"id":411,"subjectId":20,"levelId":104,"parentId":17,"slug":1729,"name":1730,"description":1731,"order":1732,"createdAt":1733,"updatedAt":1733},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":405,"subjectId":202,"levelId":104,"parentId":17,"slug":1735,"name":1736,"description":1737,"order":1732,"createdAt":1738,"updatedAt":1738},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":280,"subjectId":20,"levelId":104,"parentId":17,"slug":1740,"name":1741,"description":1742,"order":1743,"createdAt":1744,"updatedAt":1744},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":232,"subjectId":202,"levelId":104,"parentId":17,"slug":1746,"name":1747,"description":1748,"order":1743,"createdAt":1749,"updatedAt":1749},"listrik-ac-arus-bolak-balik","Listrik AC \u002F Arus Bolak Balik","Listrik AC \u002F Arus Bolak Balik — Kelas 12.","2026-10-08T09:24:41.263Z",{"id":470,"subjectId":202,"levelId":104,"parentId":17,"slug":1751,"name":1752,"description":1753,"order":1754,"createdAt":1755,"updatedAt":1755},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":286,"subjectId":20,"levelId":104,"parentId":17,"slug":1757,"name":1758,"description":1759,"order":1754,"createdAt":1760,"updatedAt":1760},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":494,"subjectId":20,"levelId":104,"parentId":17,"slug":1762,"name":1763,"description":1764,"order":1765,"createdAt":1766,"updatedAt":1766},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":524,"subjectId":202,"levelId":104,"parentId":17,"slug":1768,"name":1769,"description":1770,"order":1765,"createdAt":1771,"updatedAt":1771},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":369,"subjectId":20,"levelId":104,"parentId":17,"slug":1773,"name":1774,"description":1775,"order":1776,"createdAt":1777,"updatedAt":1777},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":512,"subjectId":202,"levelId":104,"parentId":17,"slug":1779,"name":1780,"description":1781,"order":1776,"createdAt":1782,"updatedAt":1782},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":518,"subjectId":202,"levelId":104,"parentId":17,"slug":1784,"name":1785,"description":1786,"order":1787,"createdAt":1788,"updatedAt":1788},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":417,"subjectId":20,"levelId":104,"parentId":17,"slug":1790,"name":1791,"description":1792,"order":1787,"createdAt":1793,"updatedAt":1793},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":309,"subjectId":20,"levelId":104,"parentId":17,"slug":1795,"name":1796,"description":1797,"order":1798,"createdAt":1799,"updatedAt":1799},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":453,"subjectId":202,"levelId":104,"parentId":17,"slug":1801,"name":1802,"description":1803,"order":1798,"createdAt":1804,"updatedAt":1804},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1806,"subjectId":20,"levelId":104,"parentId":17,"slug":1807,"name":1808,"description":1809,"order":1810,"createdAt":1811,"updatedAt":1811},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1813,"subjectId":20,"levelId":104,"parentId":17,"slug":1814,"name":1815,"description":1816,"order":1817,"createdAt":1818,"updatedAt":1818},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1820,"subjectId":20,"levelId":104,"parentId":17,"slug":1821,"name":1822,"description":1823,"order":1824,"createdAt":1825,"updatedAt":1825},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":193,"subjectId":20,"levelId":145,"parentId":17,"slug":183,"name":194,"description":185,"order":1827,"createdAt":1828,"updatedAt":1828},100,"2026-10-08T23:58:22.977Z",{"id":1830,"subjectId":20,"levelId":104,"parentId":17,"slug":1831,"name":1832,"description":1833,"order":1827,"createdAt":1834,"updatedAt":1834},"demo-v2-topic-matematika-sma-1","fungsi-kuadrat","Fungsi Kuadrat","Fungsi kuadrat f(x) = ax² + bx + c: pengaruh a, b, c pada grafik, rumus titik puncak, sumbu simetri, diskriminan, dan contoh soal nilai maksimum.","2026-10-08T23:58:22.868Z",{"id":1836,"subjectId":210,"levelId":104,"parentId":17,"slug":1837,"name":1838,"description":1839,"order":1827,"createdAt":1840,"updatedAt":1840},"demo-v2-topic-pemrograman-sma-1","fungsi-python-def-return","Fungsi Python","Pelajari cara membuat fungsi Python dengan def, parameter, nilai default, dan return, plus perbedaan return dan print lewat contoh program yang jelas.","2026-10-08T23:58:23.661Z",{"id":1842,"subjectId":202,"levelId":140,"parentId":17,"slug":1843,"name":1844,"description":1845,"order":1827,"createdAt":1846,"updatedAt":1846},"demo-v2-topic-fisika-smp-1","glb-dan-glbb","GLB dan GLBB","Rumus GLB dan GLBB lengkap: jarak, kecepatan, percepatan, grafik posisi–waktu, perbedaan GLB dan GLBB, plus contoh soal gerak lurus dan pembahasannya.","2026-10-08T23:58:23.189Z",{"id":1848,"subjectId":202,"levelId":145,"parentId":17,"slug":1849,"name":1850,"description":1851,"order":1827,"createdAt":1852,"updatedAt":1852},"demo-v2-topic-fisika-kuliah-1","gerak-harmonik-sederhana","Gerak Harmonik Sederhana","Gerak harmonik sederhana untuk fisika dasar: persamaan x = A cos(ωt + φ), kecepatan, percepatan, periode pegas dan bandul, energi, serta contoh soal.","2026-10-08T23:58:23.364Z",{"id":1854,"subjectId":202,"levelId":104,"parentId":17,"slug":1855,"name":1856,"description":1857,"order":1827,"createdAt":1858,"updatedAt":1858},"demo-v2-topic-fisika-sma-1","hukum-newton-2","Hukum Newton 2","Hukum Newton 2: bunyi, rumus ΣF = m·a, diagram gaya, gaya gesek statis dan kinetis, serta contoh soal mencari percepatan dan massa beserta pembahasan.","2026-10-08T23:58:23.280Z",{"id":1860,"subjectId":210,"levelId":145,"parentId":17,"slug":1861,"name":1862,"description":1863,"order":1827,"createdAt":1864,"updatedAt":1864},"demo-v2-topic-pemrograman-kuliah-1","notasi-big-o-kompleksitas-waktu","Notasi Big O","Pahami notasi Big O dan kompleksitas waktu algoritma: O(1), O(log n), O(n), O(n²), cara menghitungnya dari kode Python, dan contoh soalnya.","2026-10-08T23:58:23.797Z",{"id":1866,"subjectId":210,"levelId":136,"parentId":17,"slug":1867,"name":1868,"description":1869,"order":1827,"createdAt":1870,"updatedAt":1870},"demo-v2-topic-pemrograman-sd-1","pengertian-algoritma","Pengertian Algoritma","Algoritma adalah langkah-langkah urut untuk menyelesaikan masalah. Pelajari pengertian, ciri, dan contoh algoritma sehari-hari untuk siswa SD.","2026-10-08T23:58:23.477Z",{"id":1872,"subjectId":202,"levelId":136,"parentId":17,"slug":1873,"name":1874,"description":1875,"order":1827,"createdAt":1876,"updatedAt":1876},"demo-v2-topic-fisika-sd-1","pengukuran-panjang","Pengukuran Panjang","Belajar pengukuran panjang untuk SD: satuan baku, alat ukur panjang, cara memakai penggaris, dan tangga satuan panjang km sampai mm + contoh soal.","2026-10-08T23:58:23.095Z",{"id":1878,"subjectId":20,"levelId":136,"parentId":17,"slug":1879,"name":1880,"description":1881,"order":1827,"createdAt":1882,"updatedAt":1882},"demo-v2-topic-matematika-sd-1","penjumlahan-pecahan","Penjumlahan Pecahan","Cara penjumlahan pecahan berpenyebut sama dan beda penyebut memakai KPK, pecahan senilai, dan pecahan campuran, lengkap dengan contoh soal SD.","2026-10-08T23:58:22.508Z",{"id":1884,"subjectId":20,"levelId":140,"parentId":17,"slug":1885,"name":1886,"description":1887,"order":1827,"createdAt":1888,"updatedAt":1888},"demo-v2-topic-matematika-smp-1","teorema-pythagoras","Teorema Pythagoras","Teorema Pythagoras a² + b² = c² untuk mencari sisi miring dan sisi siku-siku, tripel Pythagoras, diagonal ruang balok, dan contoh soal kelas 8.","2026-10-08T23:58:22.690Z",{"id":1890,"subjectId":210,"levelId":140,"parentId":17,"slug":1891,"name":1892,"description":1893,"order":1827,"createdAt":1894,"updatedAt":1894},"demo-v2-topic-pemrograman-smp-1","variabel-dan-tipe-data-python","Variabel dan Tipe Data Python","Belajar variabel dan tipe data Python dari nol: int, float, string, boolean, operator, print, dan input, lengkap dengan contoh program dan latihan.","2026-10-08T23:58:23.562Z",{"id":1896,"subjectId":210,"levelId":145,"parentId":17,"slug":1897,"name":1898,"description":1899,"order":1900,"createdAt":1901,"updatedAt":1901},"demo-v2-topic-pemrograman-kuliah-2","class-dan-object-python","Class dan Object Python","Pelajari class dan object Python untuk OOP: __init__, self, atribut, method, inheritance, dan invarian objek lewat contoh program dompet digital.",101,"2026-10-08T23:58:23.830Z",{"id":1903,"subjectId":20,"levelId":104,"parentId":17,"slug":1904,"name":1905,"description":1906,"order":1900,"createdAt":1907,"updatedAt":1907},"demo-v2-topic-matematika-sma-2","eksponen-dan-logaritma","Eksponen dan Logaritma","Materi eksponen dan logaritma kelas 10: sifat-sifat eksponen, definisi dan sifat logaritma, persamaan eksponen dan logaritma, serta contoh soal.","2026-10-08T23:58:22.902Z",{"id":1909,"subjectId":202,"levelId":136,"parentId":17,"slug":1910,"name":1911,"description":1912,"order":1900,"createdAt":1913,"updatedAt":1913},"demo-v2-topic-fisika-sd-2","macam-macam-gaya","Gaya dan Macam-Macamnya","Gaya adalah tarikan atau dorongan. Pelajari macam-macam gaya (otot, gravitasi, magnet, gesek, pegas), pengaruhnya pada benda, dan contoh soalnya.","2026-10-08T23:58:23.126Z",{"id":1915,"subjectId":20,"levelId":136,"parentId":17,"slug":1916,"name":1917,"description":1918,"order":1900,"createdAt":1919,"updatedAt":1919},"demo-v2-topic-matematika-sd-2","rumus-keliling-dan-luas-bangun-datar","Keliling dan Luas Bangun Datar","Rumus keliling dan luas bangun datar: persegi, persegi panjang, segitiga, jajargenjang, trapesium, dan lingkaran, dengan cara mudah dan contoh soal.","2026-10-08T23:58:22.588Z",{"id":1921,"subjectId":210,"levelId":104,"parentId":17,"slug":1922,"name":1923,"description":1924,"order":1900,"createdAt":1925,"updatedAt":1925},"demo-v2-topic-pemrograman-sma-2","list-dan-dictionary-python","List dan Dictionary Python","Pahami list dan dictionary Python: indeks, append, key-value, get, dan perulangan, plus perbedaan keduanya lewat contoh pengolahan data nilai siswa.","2026-10-08T23:58:23.694Z",{"id":1927,"subjectId":202,"levelId":140,"parentId":17,"slug":1928,"name":1929,"description":1930,"order":1900,"createdAt":1931,"updatedAt":1931},"demo-v2-topic-fisika-smp-2","rumus-massa-jenis","Massa Jenis","Rumus massa jenis ρ = m\u002FV lengkap dengan satuan kg\u002Fm³ dan g\u002Fcm³, tabel massa jenis air, besi, dan minyak, cara menghitung, serta contoh soal pembahasan.","2026-10-08T23:58:23.217Z",{"id":1933,"subjectId":210,"levelId":140,"parentId":17,"slug":1934,"name":1935,"description":1936,"order":1900,"createdAt":1937,"updatedAt":1937},"demo-v2-topic-pemrograman-smp-2","percabangan-python-if-else","Percabangan Python","Pelajari percabangan Python dengan if, elif, dan else: operator perbandingan, operator logika, dan contoh program nilai rapor lengkap dengan outputnya.","2026-10-08T23:58:23.592Z",{"id":1939,"subjectId":210,"levelId":136,"parentId":17,"slug":1940,"name":1941,"description":1942,"order":1900,"createdAt":1943,"updatedAt":1943},"demo-v2-topic-pemrograman-sd-2","percabangan-dalam-algoritma","Percabangan dalam Algoritma","Percabangan dalam algoritma memilih tindakan berdasarkan syarat jika-maka. Pelajari pengertian, contoh sehari-hari, dan simbol flowchart-nya.","2026-10-08T23:58:23.503Z",{"id":1945,"subjectId":20,"levelId":140,"parentId":17,"slug":1946,"name":1947,"description":1948,"order":1900,"createdAt":1949,"updatedAt":1949},"demo-v2-topic-matematika-smp-2","persamaan-garis-lurus","Persamaan Garis Lurus","Persamaan garis lurus y = mx + c, rumus gradien dari dua titik, garis sejajar dan tegak lurus, cara menggambar grafik, serta contoh soal kelas 8.","2026-10-08T23:58:22.730Z",{"id":1951,"subjectId":202,"levelId":145,"parentId":17,"slug":1952,"name":1953,"description":1954,"order":1900,"createdAt":1955,"updatedAt":1955},"demo-v2-topic-fisika-kuliah-2","usaha-oleh-gaya-berubah","Usaha Gaya Berubah","Usaha oleh gaya berubah dengan integral W = ∫F dx, rumus usaha W = F·s sebagai dot product, usaha pegas, dan teorema usaha–energi, plus contoh soal.","2026-10-08T23:58:23.394Z",{"id":109,"subjectId":20,"levelId":104,"parentId":17,"slug":14,"name":110,"description":16,"order":1957,"createdAt":1958,"updatedAt":1958},102,"2026-10-08T23:58:22.934Z",{"id":1960,"subjectId":210,"levelId":104,"parentId":17,"slug":1961,"name":1962,"description":1963,"order":1957,"createdAt":1964,"updatedAt":1964},"demo-v2-topic-pemrograman-sma-3","pencarian-linear-dan-biner","Pencarian Linear dan Biner","Pelajari pencarian linear dan pencarian biner (binary search): cara kerja, syarat data terurut, kode Python, dan perbandingan jumlah langkahnya.","2026-10-08T23:58:23.724Z",{"id":1966,"subjectId":210,"levelId":140,"parentId":17,"slug":1967,"name":1968,"description":1969,"order":1957,"createdAt":1970,"updatedAt":1970},"demo-v2-topic-pemrograman-smp-3","perulangan-python-for-while","Perulangan Python","Pelajari perulangan Python dengan for, range(), dan while, lengkap dengan contoh program menghitung total, break, continue, dan latihan soal.","2026-10-08T23:58:23.624Z",{"id":1972,"subjectId":210,"levelId":136,"parentId":17,"slug":1973,"name":1974,"description":1975,"order":1957,"createdAt":1976,"updatedAt":1976},"demo-v2-topic-pemrograman-sd-3","perulangan-dalam-algoritma","Perulangan dalam Algoritma","Perulangan dalam algoritma mengulang langkah yang sama beberapa kali. Pelajari pengertian, contoh perulangan sehari-hari, dan cara menghitung hasilnya.","2026-10-08T23:58:23.529Z",{"id":1978,"subjectId":20,"levelId":140,"parentId":17,"slug":1979,"name":1980,"description":1981,"order":1957,"createdAt":1982,"updatedAt":1982},"demo-v2-topic-matematika-smp-3","rumus-prisma-dan-limas","Prisma dan Limas","Rumus volume prisma dan limas, luas permukaan, sifat sisi-rusuk-titik sudut, jaring-jaring, limas 3D interaktif, dan contoh soal bangun ruang sisi datar.","2026-10-08T23:58:22.780Z",{"id":1984,"subjectId":210,"levelId":145,"parentId":17,"slug":1985,"name":1986,"description":1987,"order":1957,"createdAt":1988,"updatedAt":1988},"demo-v2-topic-pemrograman-kuliah-3","unit-test-python","Unit Test Python","Pelajari unit test Python dengan modul unittest: assertEqual, assertRaises, nilai batas, dan cara menjalankan tes, lengkap dengan contoh dan versi pytest.","2026-10-08T23:58:23.864Z",{"id":162,"subjectId":20,"levelId":145,"parentId":17,"slug":152,"name":163,"description":154,"order":1957,"createdAt":1990,"updatedAt":1990},"2026-10-08T23:58:23.045Z",{"id":1992,"subjectId":20,"levelId":136,"parentId":17,"slug":1993,"name":1994,"description":1995,"order":1957,"createdAt":1996,"updatedAt":1996},"demo-v2-topic-matematika-sd-3","rumus-volume-kubus","Volume dan Luas Permukaan Kubus","Rumus volume kubus V = s³ dan luas permukaan kubus L = 6s², sifat kubus, jaring-jaring, kubus 3D interaktif, dan contoh soal bertingkat.","2026-10-08T23:58:22.619Z",{"id":1998,"subjectId":20,"levelId":140,"parentId":17,"slug":1999,"name":2000,"description":2001,"order":2002,"createdAt":2003,"updatedAt":2003},"demo-v2-topic-matematika-smp-4","rumus-tabung-dan-kerucut","Tabung dan Kerucut","Rumus volume tabung dan kerucut, luas permukaan, garis pelukis, jaring-jaring berupa persegi panjang dan juring, kerucut 3D interaktif, dan contoh soal.",103,"2026-10-08T23:58:22.828Z",{"id":2005,"subjectId":210,"levelId":104,"parentId":17,"slug":2006,"name":2007,"description":2008,"order":2002,"createdAt":2009,"updatedAt":2009},"demo-v2-topic-pemrograman-sma-4","try-except-python","Try Except dan Membaca File","Pelajari try except Python untuk menangani error seperti ValueError dan FileNotFoundError, serta cara membaca dan menulis file txt dengan with open.","2026-10-08T23:58:23.755Z",{"id":2011,"subjectId":20,"levelId":136,"parentId":17,"slug":2012,"name":2013,"description":2014,"order":2002,"createdAt":2015,"updatedAt":2015},"demo-v2-topic-matematika-sd-4","rumus-volume-balok","Volume dan Luas Permukaan Balok","Rumus volume balok V = p × l × t dan luas permukaan balok L = 2(pl + pt + lt), sifat balok, jaring-jaring, balok 3D interaktif, dan contoh soal.","2026-10-08T23:58:22.651Z",[]]