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Wajib.","2026-10-08T09:24:41.433Z",{"id":290,"subjectId":14,"levelId":48,"parentId":91,"slug":1448,"name":1449,"description":1450,"order":1451,"createdAt":1452,"updatedAt":1452},"matriks","Matriks","Matriks — Kelas 11 Lanjut.",13,"2026-10-08T09:24:41.441Z",{"id":1454,"subjectId":23,"levelId":48,"parentId":91,"slug":1455,"name":1456,"description":1457,"order":1451,"createdAt":1458,"updatedAt":1458},"cmuzbyhhz003k71r9s7s8evk1","rangkaian-pegas","Rangkaian Pegas","Rangkaian Pegas — Kelas 11.","2026-10-08T09:24:41.111Z",{"id":152,"subjectId":23,"levelId":48,"parentId":91,"slug":1460,"name":1461,"description":1462,"order":1463,"createdAt":1464,"updatedAt":1464},"fluida","Fluida","Fluida — Kelas 11.",14,"2026-10-08T09:24:41.113Z",{"id":266,"subjectId":14,"levelId":48,"parentId":91,"slug":1466,"name":1467,"description":1468,"order":1463,"createdAt":1469,"updatedAt":1469},"polinomial","Polinomial","Polinomial — Kelas 11 Lanjut.","2026-10-08T09:24:41.454Z",{"id":182,"subjectId":14,"levelId":48,"parentId":91,"slug":1471,"name":1472,"description":1473,"order":1474,"createdAt":1475,"updatedAt":1475},"fungsi-trigonometri","Fungsi Trigonometri","Fungsi Trigonometri — Kelas 11 Lanjut.",15,"2026-10-08T09:24:41.469Z",{"id":176,"subjectId":23,"levelId":48,"parentId":91,"slug":1477,"name":1478,"description":1479,"order":1474,"createdAt":1480,"updatedAt":1480},"gerak-harmonik-sederhana-ghs","Gerak Harmonik Sederhana (GHS)","Gerak Harmonik Sederhana (GHS) — Kelas 11.","2026-10-08T09:24:41.119Z",{"id":206,"subjectId":23,"levelId":48,"parentId":91,"slug":1482,"name":1483,"description":1484,"order":1485,"createdAt":1486,"updatedAt":1486},"gelombang-mekanik","Gelombang Mekanik","Gelombang Mekanik — Kelas 11.",16,"2026-10-08T09:24:41.132Z",{"id":272,"subjectId":14,"levelId":48,"parentId":91,"slug":1241,"name":1242,"description":1488,"order":1485,"createdAt":1489,"updatedAt":1489},"Vektor — Kelas 11 Lanjut.","2026-10-08T09:24:41.485Z",{"id":128,"subjectId":23,"levelId":48,"parentId":91,"slug":1491,"name":1492,"description":1493,"order":1494,"createdAt":1495,"updatedAt":1495},"gelombang-cahaya","Gelombang Cahaya","Gelombang Cahaya — Kelas 11.",17,"2026-10-08T09:24:41.150Z",{"id":212,"subjectId":14,"levelId":48,"parentId":91,"slug":1497,"name":1498,"description":1499,"order":1494,"createdAt":1500,"updatedAt":1500},"transformasi-geometri","Transformasi Geometri","Transformasi Geometri — Kelas 11 Lanjut.","2026-10-08T09:24:41.498Z",{"id":158,"subjectId":14,"levelId":48,"parentId":91,"slug":1502,"name":1503,"description":1504,"order":1505,"createdAt":1506,"updatedAt":1506},"fungsi-dan-pemodelannya","Fungsi dan Pemodelannya","Fungsi dan Pemodelannya — Kelas 11 Lanjut.",18,"2026-10-08T09:24:41.504Z",{"id":194,"subjectId":23,"levelId":48,"parentId":91,"slug":1508,"name":1509,"description":1510,"order":1505,"createdAt":1511,"updatedAt":1511},"optik","Optik","Optik — Kelas 11.","2026-10-08T09:24:41.161Z",{"id":68,"subjectId":14,"levelId":48,"parentId":91,"slug":1513,"name":76,"description":1514,"order":1515,"createdAt":1516,"updatedAt":1516},"barisan-dan-deret-kelas-12-wajib","Barisan dan Deret — Kelas 12 Wajib.",19,"2026-10-08T09:24:41.512Z",{"id":367,"subjectId":23,"levelId":48,"parentId":91,"slug":1518,"name":1519,"description":1520,"order":1515,"createdAt":1521,"updatedAt":1521},"suhu-dan-kalor","Suhu dan Kalor","Suhu dan Kalor — Kelas 11.","2026-10-08T09:24:41.169Z",{"id":98,"subjectId":14,"levelId":48,"parentId":91,"slug":1523,"name":1524,"description":1525,"order":1526,"createdAt":1527,"updatedAt":1527},"bunga","Bunga","Bunga — Kelas 12 Wajib.",20,"2026-10-08T09:24:41.518Z",{"id":164,"subjectId":23,"levelId":48,"parentId":91,"slug":1529,"name":1530,"description":1531,"order":1526,"createdAt":1532,"updatedAt":1532},"teori-kinetik-gas","Teori Kinetik Gas","Teori Kinetik Gas — Kelas 11.","2026-10-08T09:24:41.188Z",{"id":373,"subjectId":14,"levelId":48,"parentId":91,"slug":1534,"name":1535,"description":1536,"order":1537,"createdAt":1538,"updatedAt":1538},"investasi-dan-pinjaman","Investasi dan Pinjaman","Investasi dan Pinjaman — Kelas 12 Wajib.",21,"2026-10-08T09:24:41.525Z",{"id":391,"subjectId":23,"levelId":48,"parentId":91,"slug":1540,"name":1541,"description":1542,"order":1537,"createdAt":1543,"updatedAt":1543},"termodinamika","Termodinamika","Termodinamika — Kelas 11.","2026-10-08T09:24:41.202Z",{"id":319,"subjectId":14,"levelId":48,"parentId":91,"slug":1545,"name":1546,"description":1547,"order":1548,"createdAt":1549,"updatedAt":1549},"kaidah-pencacahan","Kaidah Pencacahan","Kaidah Pencacahan — Kelas 12 Wajib.",22,"2026-10-08T09:24:41.540Z",{"id":260,"subjectId":23,"levelId":48,"parentId":91,"slug":1551,"name":1552,"description":1553,"order":1548,"createdAt":1554,"updatedAt":1554},"listrik-statis","Listrik Statis","Listrik Statis — Kelas 12.","2026-10-08T09:24:41.215Z",{"id":230,"subjectId":23,"levelId":48,"parentId":91,"slug":1556,"name":1557,"description":1558,"order":1559,"createdAt":1560,"updatedAt":1560},"listrik-arus-searah","Listrik Arus Searah","Listrik Arus Searah — Kelas 12.",23,"2026-10-08T09:24:41.227Z",{"id":278,"subjectId":14,"levelId":48,"parentId":91,"slug":1562,"name":1411,"description":1563,"order":1559,"createdAt":1564,"updatedAt":1564},"peluang-kelas-12-wajib","Peluang — Kelas 12 Wajib.","2026-10-08T09:24:41.547Z",{"id":242,"subjectId":14,"levelId":48,"parentId":91,"slug":1566,"name":1567,"description":1568,"order":1569,"createdAt":1570,"updatedAt":1570},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":236,"subjectId":23,"levelId":48,"parentId":91,"slug":1572,"name":1573,"description":1574,"order":1569,"createdAt":1575,"updatedAt":1575},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":110,"subjectId":14,"levelId":48,"parentId":91,"slug":1577,"name":1578,"description":1579,"order":1580,"createdAt":1581,"updatedAt":1581},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":61,"subjectId":23,"levelId":48,"parentId":91,"slug":1583,"name":1584,"description":1585,"order":1580,"createdAt":1586,"updatedAt":1586},"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":301,"subjectId":23,"levelId":48,"parentId":91,"slug":1588,"name":1589,"description":1590,"order":1591,"createdAt":1592,"updatedAt":1592},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":116,"subjectId":14,"levelId":48,"parentId":91,"slug":1594,"name":1595,"description":1596,"order":1591,"createdAt":1597,"updatedAt":1597},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":325,"subjectId":14,"levelId":48,"parentId":91,"slug":1599,"name":1600,"description":1601,"order":1602,"createdAt":1603,"updatedAt":1603},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":355,"subjectId":23,"levelId":48,"parentId":91,"slug":1605,"name":1606,"description":1607,"order":1602,"createdAt":1608,"updatedAt":1608},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":200,"subjectId":14,"levelId":48,"parentId":91,"slug":1610,"name":1611,"description":1612,"order":1613,"createdAt":1614,"updatedAt":1614},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":343,"subjectId":23,"levelId":48,"parentId":91,"slug":1616,"name":1617,"description":1618,"order":1613,"createdAt":1619,"updatedAt":1619},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":349,"subjectId":23,"levelId":48,"parentId":91,"slug":1621,"name":1622,"description":1623,"order":1624,"createdAt":1625,"updatedAt":1625},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":248,"subjectId":14,"levelId":48,"parentId":91,"slug":1627,"name":1628,"description":1629,"order":1624,"createdAt":1630,"updatedAt":1630},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":140,"subjectId":14,"levelId":48,"parentId":91,"slug":1632,"name":1633,"description":1634,"order":1635,"createdAt":1636,"updatedAt":1636},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":284,"subjectId":23,"levelId":48,"parentId":91,"slug":1638,"name":1639,"description":1640,"order":1635,"createdAt":1641,"updatedAt":1641},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1643,"subjectId":14,"levelId":48,"parentId":91,"slug":1644,"name":1645,"description":1646,"order":1647,"createdAt":1648,"updatedAt":1648},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1650,"subjectId":14,"levelId":48,"parentId":91,"slug":1651,"name":1652,"description":1653,"order":1654,"createdAt":1655,"updatedAt":1655},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1657,"subjectId":14,"levelId":48,"parentId":91,"slug":1658,"name":1659,"description":1660,"order":1661,"createdAt":1662,"updatedAt":1662},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":1664,"subjectId":32,"levelId":91,"parentId":91,"slug":1665,"name":1666,"description":1667,"order":1668,"createdAt":1669,"updatedAt":1669},"demo-v2-topic-pemrograman-sd-1","demo-v2-sd-1","Algoritma: Urutan Perintah yang Jelas","Susun instruksi sederhana, lalu telusuri hasilnya selangkah demi selangkah.",100,"2026-10-08T10:03:56.954Z",{"id":1671,"subjectId":14,"levelId":48,"parentId":91,"slug":1672,"name":1673,"description":1674,"order":1668,"createdAt":1675,"updatedAt":1675},"demo-v2-topic-matematika-sma-1","demo-v2-sma-1","Fungsi kuadrat: akar, puncak, dan bentuk grafik","Menghubungkan bentuk umum, faktor, dan kuadrat sempurna untuk memahami parabola dan nilai optimum.","2026-10-08T10:03:56.485Z",{"id":1677,"subjectId":32,"levelId":48,"parentId":91,"slug":1672,"name":1678,"description":1679,"order":1668,"createdAt":1680,"updatedAt":1680},"demo-v2-topic-pemrograman-sma-1","Fungsi: Memisahkan Masukan, Proses, dan Hasil","Buat fungsi Python yang bisa dipakai ulang dan bedakan return dari print.","2026-10-08T10:03:57.108Z",{"id":1682,"subjectId":23,"levelId":42,"parentId":91,"slug":1683,"name":1684,"description":1685,"order":1668,"createdAt":1686,"updatedAt":1686},"demo-v2-topic-fisika-smp-1","demo-v2-smp-1","Gerak Lurus: Jarak, Perpindahan, dan Grafik Posisi","Membedakan kelajuan dan kecepatan rata-rata serta membaca arti kemiringan grafik posisi terhadap waktu.","2026-10-08T10:03:56.729Z",{"id":1688,"subjectId":23,"levelId":48,"parentId":91,"slug":1672,"name":1689,"description":1690,"order":1668,"createdAt":1691,"updatedAt":1691},"demo-v2-topic-fisika-sma-1","Hukum II Newton dan Gesekan pada Bidang Datar","Membuat diagram gaya, menentukan resultan, dan membedakan gesekan statis dari gesekan kinetik.","2026-10-08T10:03:56.801Z",{"id":1693,"subjectId":23,"levelId":91,"parentId":91,"slug":1665,"name":1694,"description":1695,"order":1668,"createdAt":1696,"updatedAt":1696},"demo-v2-topic-fisika-sd-1","Mengukur Panjang dan Volume Benda","Membaca penggaris, memakai satuan baku, dan menghitung isi kubus melalui susunan kubus kecil.","2026-10-08T10:03:56.657Z",{"id":1698,"subjectId":32,"levelId":53,"parentId":91,"slug":1699,"name":1700,"description":1701,"order":1668,"createdAt":1702,"updatedAt":1702},"demo-v2-topic-pemrograman-kuliah-1","demo-v2-kuliah-1","Pencarian Linear, Set, dan Biaya Operasi","Bandingkan cara mencari anggota data melalui langkah yang benar-benar dikerjakan.","2026-10-08T10:03:57.182Z",{"id":1704,"subjectId":14,"levelId":42,"parentId":91,"slug":1683,"name":1705,"description":1706,"order":1668,"createdAt":1707,"updatedAt":1707},"demo-v2-topic-matematika-smp-1","Perbandingan senilai dan berbalik nilai","Memilih model dari besaran yang tetap: rasio tetap untuk senilai dan hasil kali tetap untuk berbalik nilai.","2026-10-08T10:03:56.412Z",{"id":1709,"subjectId":14,"levelId":53,"parentId":91,"slug":1699,"name":1710,"description":1711,"order":1668,"createdAt":1712,"updatedAt":1712},"demo-v2-topic-matematika-kuliah-1","Turunan sebagai laju sesaat dan pendekatan lokal","Menurunkan fungsi dari limit hasil bagi selisih serta menghubungkan kemiringan, kecepatan, dan garis singgung.","2026-10-08T10:03:56.556Z",{"id":1714,"subjectId":32,"levelId":42,"parentId":91,"slug":1683,"name":1715,"description":1716,"order":1668,"createdAt":1717,"updatedAt":1717},"demo-v2-topic-pemrograman-smp-1","Variabel, Tipe Data, dan Keluaran Python","Simpan nilai dengan nama yang jelas dan bedakan angka dari teks.","2026-10-08T10:03:57.035Z",{"id":1719,"subjectId":23,"levelId":53,"parentId":91,"slug":1699,"name":1720,"description":1721,"order":1668,"createdAt":1722,"updatedAt":1722},"demo-v2-topic-fisika-kuliah-1","Vektor Tiga Dimensi dan Usaha sebagai Hasil Kali Titik","Menghubungkan komponen, panjang vektor, vektor satuan, proyeksi, dan makna fisik hasil kali titik.","2026-10-08T10:03:56.874Z",{"id":1724,"subjectId":14,"levelId":48,"parentId":91,"slug":1725,"name":1726,"description":1727,"order":1728,"createdAt":1729,"updatedAt":1729},"demo-v2-topic-matematika-sma-2","demo-v2-sma-2","Eksponen dan logaritma: mencari pangkat yang belum diketahui","Membedakan kenaikan tetap dan faktor tetap, lalu membaca logaritma sebagai operasi balik eksponen.",101,"2026-10-08T10:03:56.507Z",{"id":1731,"subjectId":14,"levelId":42,"parentId":91,"slug":1732,"name":1733,"description":1734,"order":1728,"createdAt":1735,"updatedAt":1735},"demo-v2-topic-matematika-smp-2","demo-v2-smp-2","Fungsi linear: gradien dan titik potong","Membaca y = mx + b sebagai perubahan tetap, menghitung gradien dari dua titik, dan memeriksa grafik.","2026-10-08T10:03:56.434Z",{"id":1737,"subjectId":23,"levelId":91,"parentId":91,"slug":1738,"name":1739,"description":1740,"order":1728,"createdAt":1741,"updatedAt":1741},"demo-v2-topic-fisika-sd-2","demo-v2-sd-2","Gaya: Dorongan, Tarikan, dan Perubahan Gerak","Mengenali siapa yang memberikan gaya, arah gaya, dan perubahan gerak atau bentuk yang dapat diamati.","2026-10-08T10:03:56.679Z",{"id":1743,"subjectId":23,"levelId":48,"parentId":91,"slug":1725,"name":1744,"description":1745,"order":1728,"createdAt":1746,"updatedAt":1746},"demo-v2-topic-fisika-sma-2","Gerak Peluru: Dua Arah dengan Satu Waktu","Menguraikan kecepatan awal, menghitung waktu terbang, tinggi maksimum, dan jangkauan untuk model ideal.","2026-10-08T10:03:56.824Z",{"id":1748,"subjectId":14,"levelId":53,"parentId":91,"slug":1749,"name":1750,"description":1751,"order":1728,"createdAt":1752,"updatedAt":1752},"demo-v2-topic-matematika-kuliah-2","demo-v2-kuliah-2","Integral tentu: akumulasi dan luas bertanda","Menghubungkan jumlah Riemann, antiturunan, dan teorema dasar kalkulus tanpa menyamakan perpindahan dengan jarak.","2026-10-08T10:03:56.578Z",{"id":1754,"subjectId":32,"levelId":53,"parentId":91,"slug":1749,"name":1755,"description":1756,"order":1728,"createdAt":1757,"updatedAt":1757},"demo-v2-topic-pemrograman-kuliah-2","Kelas dan Invarian pada Objek","Kelola keadaan dan perilaku bersama, lalu jaga agar objek selalu valid.","2026-10-08T10:03:57.206Z",{"id":1759,"subjectId":32,"levelId":48,"parentId":91,"slug":1725,"name":1760,"description":1761,"order":1728,"createdAt":1762,"updatedAt":1762},"demo-v2-topic-pemrograman-sma-2","List dan Dictionary untuk Mengolah Data","Pilih struktur data sesuai cara mengaksesnya dan hitung ringkasan data.","2026-10-08T10:03:57.131Z",{"id":1764,"subjectId":23,"levelId":42,"parentId":91,"slug":1732,"name":1765,"description":1766,"order":1728,"createdAt":1767,"updatedAt":1767},"demo-v2-topic-fisika-smp-2","Massa Jenis: Menghubungkan Massa dan Volume","Menghitung massa jenis, mengukur volume dengan perpindahan air, dan menjaga konsistensi satuan.","2026-10-08T10:03:56.750Z",{"id":1769,"subjectId":23,"levelId":53,"parentId":91,"slug":1749,"name":1770,"description":1771,"order":1728,"createdAt":1772,"updatedAt":1772},"demo-v2-topic-fisika-kuliah-2","Osilasi Harmonik Sederhana: Fase, Turunan, dan Energi","Menganalisis model x = A cos(ωt), menurunkan kecepatan dan percepatan, serta memeriksa kekekalan energi.","2026-10-08T10:03:56.896Z",{"id":1774,"subjectId":32,"levelId":91,"parentId":91,"slug":1738,"name":1775,"description":1776,"order":1728,"createdAt":1777,"updatedAt":1777},"demo-v2-topic-pemrograman-sd-2","Pengulangan: Langkah yang Dikerjakan Berkali-kali","Kenali pola berulang dan hitung hasil tiap putaran tanpa kehilangan jejak.","2026-10-08T10:03:56.978Z",{"id":1779,"subjectId":32,"levelId":42,"parentId":91,"slug":1732,"name":1780,"description":1781,"order":1728,"createdAt":1782,"updatedAt":1782},"demo-v2-topic-pemrograman-smp-2","Percabangan Python dan Batas Keputusan","Tulis if, elif, dan else serta uji nilai di sekitar batas.","2026-10-08T10:03:57.057Z",{"id":1784,"subjectId":23,"levelId":48,"parentId":91,"slug":1785,"name":1786,"description":1787,"order":1788,"createdAt":1789,"updatedAt":1789},"demo-v2-topic-fisika-sma-3","demo-v2-sma-3","Hukum Ohm, Daya, dan Energi pada Resistor","Menghubungkan tegangan, arus, hambatan, dan energi listrik tanpa mencampurkan satuan volt, ampere, watt, dan joule.",102,"2026-10-08T10:03:56.846Z",{"id":1791,"subjectId":32,"levelId":48,"parentId":91,"slug":1785,"name":1792,"description":1793,"order":1788,"createdAt":1794,"updatedAt":1794},"demo-v2-topic-pemrograman-sma-3","Membaca Berkas dan Menangani Masukan Salah","Ubah baris teks menjadi angka dan tangani kesalahan yang bisa diperkirakan.","2026-10-08T10:03:57.153Z",{"id":1796,"subjectId":14,"levelId":48,"parentId":91,"slug":1785,"name":1797,"description":1798,"order":1788,"createdAt":1799,"updatedAt":1799},"demo-v2-topic-matematika-sma-3","Peluang: ruang sampel, kejadian, dan pengambilan bertahap","Menghitung peluang melalui hasil yang sama mungkin dan memahami pengaruh pengembalian pada pengambilan kedua.","2026-10-08T10:03:56.528Z",{"id":1801,"subjectId":32,"levelId":53,"parentId":91,"slug":1802,"name":1803,"description":1804,"order":1788,"createdAt":1805,"updatedAt":1805},"demo-v2-topic-pemrograman-kuliah-3","demo-v2-kuliah-3","Pengujian Otomatis dan Kasus Batas","Uji kontrak fungsi dengan contoh biasa, batas, dan masukan tidak sah.","2026-10-08T10:03:57.229Z",{"id":1807,"subjectId":32,"levelId":91,"parentId":91,"slug":1808,"name":1809,"description":1810,"order":1788,"createdAt":1811,"updatedAt":1811},"demo-v2-topic-pemrograman-sd-3","demo-v2-sd-3","Percabangan: Memilih Tindakan dengan Syarat","Gunakan pertanyaan ya atau tidak untuk menentukan tindakan yang tepat.","2026-10-08T10:03:57.006Z",{"id":1813,"subjectId":32,"levelId":42,"parentId":91,"slug":1814,"name":1815,"description":1816,"order":1788,"createdAt":1817,"updatedAt":1817},"demo-v2-topic-pemrograman-smp-3","demo-v2-smp-3","Perulangan for dan Akumulator","Hitung total data dengan jejak putaran yang dapat diperiksa.","2026-10-08T10:03:57.079Z",{"id":1819,"subjectId":23,"levelId":91,"parentId":91,"slug":1808,"name":1820,"description":1821,"order":1788,"createdAt":1822,"updatedAt":1822},"demo-v2-topic-fisika-sd-3","Suhu dan Perpindahan Kalor di Sekitar Kita","Membaca perubahan suhu dan membedakan konduksi, konveksi, serta radiasi melalui kejadian sehari-hari.","2026-10-08T10:03:56.700Z",{"id":1824,"subjectId":14,"levelId":42,"parentId":91,"slug":1814,"name":1825,"description":1826,"order":1788,"createdAt":1827,"updatedAt":1827},"demo-v2-topic-matematika-smp-3","Teorema Pythagoras dan jarak diagonal","Menentukan sisi segitiga siku-siku dengan kuadrat panjang, lalu memeriksa hasil melalui geometri dan satuan.","2026-10-08T10:03:56.456Z",{"id":1829,"subjectId":23,"levelId":53,"parentId":91,"slug":1802,"name":1830,"description":1831,"order":1788,"createdAt":1832,"updatedAt":1832},"demo-v2-topic-fisika-kuliah-3","Usaha Gaya Berubah: Integral dan Teorema Energi Kinetik","Menghitung luas bertanda di bawah grafik gaya, menghubungkannya dengan integral, dan menentukan kelajuan akhir.","2026-10-08T10:03:56.918Z",{"id":1834,"subjectId":23,"levelId":42,"parentId":91,"slug":1814,"name":1835,"description":1836,"order":1788,"createdAt":1837,"updatedAt":1837},"demo-v2-topic-fisika-smp-3","Usaha dan Energi: Memeriksa Perubahan dengan Joule","Menghitung usaha gaya searah atau berlawanan, energi gerak, dan perubahan energi ketika benda diangkat.","2026-10-08T10:03:56.772Z",{"id":1839,"subjectId":14,"levelId":53,"parentId":91,"slug":1802,"name":1840,"description":1841,"order":1788,"createdAt":1842,"updatedAt":1842},"demo-v2-topic-matematika-kuliah-3","Vektor tiga dimensi dan hasil kali titik","Membaca komponen, menghitung panjang dan sudut, serta menafsirkan hasil kali titik sebagai keselarasan arah.","2026-10-08T10:03:56.615Z",[],{"id":1845,"type":1846,"slug":1847,"title":1848,"excerpt":1849,"coverUrl":91,"status":1850,"publishedAt":1851,"featured":5,"subjectId":14,"blocks":1852,"seoTitle":91,"seoDescription":91,"readingMinutes":57,"order":20,"createdAt":1882,"updatedAt":1882,"subject":1883,"levels":1884,"topics":1888,"tags":1889,"author":91,"resolved":1890,"related":1894},"demo-v2-a-matematika","ARTICLE","demo-artikel-matematika","Memilih model matematika dari cerita sehari-hari","Cara mengubah cerita menjadi variabel, memeriksa asumsi, dan menilai apakah hasil hitungan masuk akal.","PUBLISHED","2026-10-08T10:03:56.648Z",[1853,1858,1862,1866,1870,1874,1878],{"id":1854,"data":1855,"type":1857},"section-1",{"markdown":1856},"## Cerita menjadi hitungan ketika besaran jelas\n\nMatematika membantu mengambil keputusan ketika cerita sehari-hari dapat diterjemahkan menjadi hubungan antarbesaran. Namun, rumus baru berguna setelah kita tahu apa yang dihitung. Saat membandingkan paket belajar, misalnya, harga yang lebih rendah pada iklan belum tentu berarti biaya total lebih rendah untuk kebutuhan kita. Ada biaya pendaftaran, biaya per pertemuan, batas pemakaian, dan satuan waktu yang perlu diperiksa.\n\nMulailah dengan pertanyaan yang dapat dijawab. “Paket mana yang terbaik?” masih terlalu luas karena terbaik dapat berarti murah, jadwal cocok, atau pendampingan lebih banyak. Pertanyaan “Paket mana yang mempunyai biaya lebih rendah untuk delapan pertemuan?” mempunyai keluaran jelas: biaya total. Kualitas layanan tetap dapat dipertimbangkan terpisah dengan informasi yang sesuai.\n","text",{"id":1859,"data":1860,"type":1857},"section-2",{"markdown":1861},"## Menamai variabel dan menulis satuan\n\nMisalkan paket A mengenakan biaya awal Rp40.000 dan Rp15.000 per pertemuan. Paket B tanpa biaya awal, dengan Rp20.000 per pertemuan. Ini contoh rekaan untuk berlatih, bukan daftar harga suatu lembaga. Definisikan $n$ sebagai jumlah pertemuan dan $C$ sebagai biaya dalam ribuan rupiah. Maka $C_A(n)=40+15n$ dan $C_B(n)=20n$.\n\nMenulis satuan menghindari kesalahan sepuluh atau seribu kali lipat. Angka 40 pada rumus berarti Rp40.000 karena biaya diukur dalam ribuan. Variabel n adalah bilangan bulat tidak negatif; 2,5 pertemuan tidak termasuk pilihan jika setiap pertemuan dibeli utuh. Domain ini menjadi bagian model, sama pentingnya dengan persamaan.\n\nKonstanta 40 menyatakan pembayaran sekali di awal, sedangkan 15 menyatakan tambahan biaya untuk setiap pertemuan. Memahami peran angka membantu mendeteksi rumus salah seperti $55n$, yang mengenakan biaya awal berulang pada semua pertemuan.\n",{"id":1863,"data":1864,"type":1857},"section-3",{"markdown":1865},"## Menentukan batas keputusan\n\nUntuk mencari kapan kedua biaya sama, selesaikan $40+15n=20n$. Kurangi $15n$ dari kedua ruas sehingga $40=5n$, lalu bagi lima: $n=8$. Pada delapan pertemuan, keduanya Rp160.000. Untuk lebih dari delapan, paket A lebih murah pada asumsi yang digunakan. Untuk kurang dari delapan, paket B lebih murah.\n\nPeriksa beberapa nilai agar persamaan mempunyai makna. Empat pertemuan pada A berbiaya Rp100.000, sedangkan B Rp80.000. Dua belas pertemuan pada A Rp220.000, sedangkan B Rp240.000. Selisihnya $C_A-C_B=40-5n$: setiap tambahan pertemuan mengurangi selisih biaya sebesar Rp5.000. Tabel atau grafik dua garis akan memperlihatkan perpotongan pada keputusan delapan pertemuan yang sama.\n",{"id":1867,"data":1868,"type":1857},"section-4",{"markdown":1869},"## Asumsi menentukan kapan rumus berlaku\n\nModel tadi menganggap tarif tetap, semua pertemuan dibayar, dan tidak ada pajak atau potongan tambahan. Jika paket B memberi diskon setelah pertemuan kesepuluh, persamaan $20n$ tidak lagi cocok untuk seluruh domain. Jika biaya awal pada A berlaku setiap bulan, kita perlu menambahkan variabel atau mempersempit perbandingan menjadi satu bulan. Rumus yang benar untuk satu kondisi dapat memberi kesimpulan salah ketika kondisi berubah.\n\nPemeriksaan ini dapat dilakukan sebelum menghitung jauh. Bacalah keterangan tarif dan tulis setiap aturan sebagai kalimat: pembayaran sekali, biaya per unit, minimum pembelian, serta masa berlaku. Tanyakan juga apakah jumlah pertemuan yang direncanakan pasti. Membeli paket yang murah per pertemuan tetapi menyisakan banyak pertemuan tidak terpakai dapat menaikkan biaya efektif per pertemuan yang benar-benar dihadiri.\n",{"id":1871,"data":1872,"type":1857},"section-5",{"markdown":1873},"## Menguji hasil dengan tiga cara\n\nPertama, substitusikan hasil ke cerita awal. Pada batas delapan pertemuan, biaya A dan B harus sama; jika tidak, ada salah aljabar atau salah menulis model. Kedua, periksa satuan. Biaya per pertemuan dikalikan jumlah pertemuan harus menghasilkan biaya, bukan waktu atau luas. Ketiga, periksa arah perubahan. Dengan tarif positif, total biaya seharusnya bertambah ketika jumlah pertemuan bertambah.\n\nGunakan pula nilai sederhana seperti nol atau satu. Pada nol pertemuan, model A masih mengenakan biaya awal 40 ribu jika pendaftaran sudah dilakukan. Jika aturan sebenarnya hanya mengenakan biaya ketika pertemuan pertama dimulai, domain atau aturan pada nol perlu dijelaskan. Uji kecil semacam ini sering menemukan asumsi tersembunyi lebih cepat daripada perhitungan panjang.\n",{"id":1875,"data":1876,"type":1857},"section-6",{"markdown":1877},"## Membawa hasil kembali ke keputusan\n\nSimpan rumus bersama catatan asumsi, kemudian ubah masukan jika rencana berubah. Untuk enam pertemuan, pilih berdasarkan biaya enam pertemuan; untuk sepuluh, hitung sepuluh. Jika jumlahnya belum pasti, bandingkan beberapa kemungkinan yang realistis. Hasil matematika memberi hubungan yang dapat diperiksa, sementara keputusan akhir menggabungkannya dengan jadwal, kebutuhan, dan kualitas layanan.\n\nKebiasaan yang dapat dipakai pada banyak masalah adalah menetapkan pertanyaan, menamai besaran, menulis satuan, menyusun hubungan, memeriksa kondisi, dan menguji hasil. Dengan langkah tersebut, angka menjadi alasan keputusan yang bisa kamu jelaskan kembali kepada orang lain.",{"id":1879,"data":1880,"type":1857},"sources",{"markdown":1881},"## Sumber belajar\n\n- [OpenStax Algebra and Trigonometry 2e — Linear Functions](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Falgebra-and-trigonometry-2e\u002Fpages\u002F4-1-linear-functions)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.","2026-10-08T10:03:56.650Z",{"id":14,"slug":15,"name":16,"color":19,"icon":18},[1885,1886,1887],{"id":42,"slug":43,"name":44},{"id":48,"slug":49,"name":50},{"id":53,"slug":54,"name":55},[],[],{"assets":1891,"videos":1892,"questionSets":1893},{},{},{},[1895,1907,1918,1929],{"id":1896,"type":1897,"slug":1898,"title":1840,"excerpt":1841,"coverUrl":91,"status":1850,"publishedAt":1899,"featured":4,"readingMinutes":57,"order":38,"updatedAt":1900,"subject":1901,"levels":1902,"topics":1904,"tags":1906},"demo-v2-m-matematika-kuliah-3","MATERIAL","demo-materi-matematika-kuliah-3","2026-10-08T10:03:56.635Z","2026-10-08T10:03:56.637Z",{"id":14,"slug":15,"name":16,"color":19,"icon":18},[1903],{"id":53,"slug":54,"name":55},[1905],{"id":1839,"slug":1802,"name":1840,"subjectId":14},[],{"id":1908,"type":1897,"slug":1909,"title":1750,"excerpt":1751,"coverUrl":91,"status":1850,"publishedAt":1910,"featured":4,"readingMinutes":57,"order":29,"updatedAt":1911,"subject":1912,"levels":1913,"topics":1915,"tags":1917},"demo-v2-m-matematika-kuliah-2","demo-materi-matematika-kuliah-2","2026-10-08T10:03:56.600Z","2026-10-08T10:03:56.602Z",{"id":14,"slug":15,"name":16,"color":19,"icon":18},[1914],{"id":53,"slug":54,"name":55},[1916],{"id":1748,"slug":1749,"name":1750,"subjectId":14},[],{"id":1919,"type":1897,"slug":1920,"title":1710,"excerpt":1711,"coverUrl":91,"status":1850,"publishedAt":1921,"featured":5,"readingMinutes":57,"order":20,"updatedAt":1922,"subject":1923,"levels":1924,"topics":1926,"tags":1928},"demo-v2-m-matematika-kuliah-1","demo-materi-matematika-kuliah-1","2026-10-08T10:03:56.572Z","2026-10-08T10:03:56.573Z",{"id":14,"slug":15,"name":16,"color":19,"icon":18},[1925],{"id":53,"slug":54,"name":55},[1927],{"id":1709,"slug":1699,"name":1710,"subjectId":14},[],{"id":1930,"type":1897,"slug":1931,"title":1797,"excerpt":1798,"coverUrl":91,"status":1850,"publishedAt":1932,"featured":4,"readingMinutes":57,"order":38,"updatedAt":1933,"subject":1934,"levels":1935,"topics":1937,"tags":1939},"demo-v2-m-matematika-sma-3","demo-materi-matematika-sma-3","2026-10-08T10:03:56.543Z","2026-10-08T10:03:56.545Z",{"id":14,"slug":15,"name":16,"color":19,"icon":18},[1936],{"id":48,"slug":49,"name":50},[1938],{"id":1796,"slug":1785,"name":1797,"subjectId":14},[]]