内容快照对齐重启后的规范状态：知识点按规范名合并（48→44），题目与章节归章不变
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-- nex_math 内容快照（教材 / 章节 / 知识点 / 课程 / 题库）
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-- 生成时间：2026-09-18T14:52:08
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-- 生成时间：2026-09-18T14:58:35
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-- 恢复：./scripts/db.sh load data/dump/catalog.sql
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PRAGMA foreign_keys=OFF;
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BEGIN TRANSACTION;
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@ -50,7 +50,7 @@ INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALU
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (27, 5, '第4章 引言', 4, '从三维推广到四维空间的动机：几何、计算与物理。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (28, 5, '第5章 四维空间', 5, '四维空间中的坐标轴、坐标平面与距离问题。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (29, 5, '第6章 四维方体', 6, '球与方体的定义、四维方体的结构与相关问题。', 0);
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-- knowledge: 48 行
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-- knowledge: 44 行
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (1, '偶函数', '初等', '函数与图像', '满足 f(-x)=f(x) 的函数，其图像关于 y 轴对称。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (2, '奇函数', '初等', '函数与图像', '满足 f(-x)=-f(x) 的函数，其图像关于原点中心对称；若 0 在定义域内，则 f(0)=0。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (3, '定义域', '初等', '函数与图像', '使函数表达式有意义的所有自变量取值组成的集合，常见限制有分母不为零、偶次根号下非负、对数的真数为正等。');
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@ -69,37 +69,33 @@ INSERT INTO knowledge (id, name, domain, category, description) VALUES (15, '分
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (16, '线性代数', '高等', '线性代数', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (17, '概率论与数理统计', '高等', '概率论与数理统计', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (18, '离散与优化', '高等', '离散与优化', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (19, '函数概念', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (20, '函数值', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (21, '正负性', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (22, '零点', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (23, '点线面的基本关系', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (24, '几何变换', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (25, '平行与垂直', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (26, '面积与周长', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (27, '圆', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (28, '三角比', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (29, '直角三角形', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (30, '三角恒等式', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (31, '同角关系', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (32, '正弦定理', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (33, '余弦定理', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (34, '任意角', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (35, '弧度制', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (36, '弧长与扇形', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (37, '和角公式', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (38, '差角公式', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (39, '倍角公式', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (40, '三角函数图像', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (41, '周期函数', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (42, '反三角函数', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (43, '三角方程', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (44, '数轴', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (45, '平面直角坐标系', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (46, '实数', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (47, '两点间距离', '初等', '', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (48, '曲线与方程', '初等', '', '');
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-- chapter_knowledge: 48 行
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (19, '函数概念', '初等', '函数与图像', '设 x 取数集 D 中的值，若按确定的对应法则，每个 x 都有唯一确定的 y 与之对应，则称 y 是 x 的函数，记作 y=f(x)，x∈D。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (20, '函数值', '初等', '函数与图像', '当自变量取定 x=a 时，按对应法则算出的 f(a) 就是函数在 a 处的函数值，它是图像上点 (a, f(a)) 的纵坐标。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (21, '正负性', '初等', '函数与图像', '函数在区间上取正值或负值的性质，由 f(x)>0 与 f(x)<0 的解集刻画，对应图像位于 x 轴上方或下方。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (22, '零点', '初等', '函数与图像', '使 f(x)=0 的自变量 x 的值，几何上对应函数图像与 x 轴交点的横坐标。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (23, '点线面的基本关系', '初等', '平面几何', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (24, '几何变换', '初等', '平面几何', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (25, '平行与垂直', '初等', '平面几何', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (26, '面积与周长', '初等', '平面几何', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (27, '圆', '初等', '平面几何', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (28, '三角比', '初等', '三角函数', '直角三角形中边与边的比值（正弦、余弦、正切），并可借助单位圆推广到任意角。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (30, '三角恒等式', '初等', '三角函数', '对定义域内任意角都成立的三角关系式，包括平方关系、和差角、倍角与半角公式等。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (32, '正弦定理', '初等', '三角函数', '在 △ABC 中 a/sinA = b/sinB = c/sinC = 2R（R 为外接圆半径），用于已知边角组合解三角形。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (33, '余弦定理', '初等', '三角函数', '在 △ABC 中 a²=b²+c²-2bc·cosA，用于已知两边及夹角或三边求解三角形。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (34, '任意角', '初等', '三角函数', '由射线绕顶点旋转生成的角，按旋转方向分为正角、负角与零角，并用终边位置统一刻画。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (35, '弧度制', '初等', '三角函数', '用弧长与半径之比度量角的大小，π 弧度 = 180°，使弧长与扇形面积公式的形式更简洁。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (39, '倍角公式', '初等', '三角函数', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (40, '三角函数图像', '初等', '三角函数', '正弦、余弦、正切函数的图像及其周期、振幅、相位与图像变换规律。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (42, '反三角函数', '初等', '三角函数', '三角函数在限定单调区间上的反函数，如反正弦 arcsin、反余弦 arccos、反正切 arctan。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (43, '三角方程', '初等', '三角函数', '含有未知角的三角函数的方程，通常先化为基本三角方程，再结合周期性写出通解。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (44, '数轴', '初等', '坐标与解析几何', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (45, '平面直角坐标系', '初等', '坐标与解析几何', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (46, '实数', '初等', '数与式', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (47, '两点间距离', '初等', '坐标与解析几何', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (48, '曲线与方程', '初等', '坐标与解析几何', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (49, '同角三角函数关系', '初等', '三角函数', '同一个角的正弦、余弦、正切之间的基本关系，如 sin²α+cos²α=1、tanα=sinα/cosα。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (50, '和角与差角公式', '初等', '三角函数', '描述两角和或差的三角函数公式，如 sin(α±β)=sinαcosβ±cosαsinβ，是推导倍角公式的基础。');
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-- chapter_knowledge: 44 行
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (1, 1, 19);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (2, 1, 20);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (3, 1, 3);
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@ -115,21 +111,15 @@ INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (12, 11, 26)
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (13, 12, 27);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (14, 13, 9);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (15, 14, 28);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (16, 14, 29);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (17, 15, 30);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (18, 15, 31);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (19, 16, 32);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (20, 16, 33);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (21, 17, 34);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (22, 17, 35);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (23, 18, 35);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (24, 18, 36);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (25, 19, 37);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (26, 19, 38);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (27, 20, 39);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (28, 20, 30);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (29, 21, 40);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (30, 21, 41);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (31, 22, 42);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (32, 22, 43);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (33, 23, 44);
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@ -148,14 +138,26 @@ INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (45, 28, 45)
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (46, 28, 48);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (47, 29, 45);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (48, 29, 48);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (49, 15, 49);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (50, 19, 50);
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-- courses: 3 行
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INSERT INTO courses (id, name, provider, url, grade, description, position) VALUES (1, 'Khan Academy · Algebra 1: Functions', 'Khan Academy', 'https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions', '初中衔接 / 高中', '函数单元含函数求值、定义域值域、函数图像与性质等大量免费练习，英文界面，适合配合盖尔范德丛书做自动化巩固。', 0);
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INSERT INTO courses (id, name, provider, url, grade, description, position) VALUES (2, '3Blue1Brown · Essence of Calculus', '3Blue1Brown', 'https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr', '高中高年级 / 大学先修', '微积分本质系列：从几何直觉理解导数与积分，适合函数图像直觉建立后进入微积分阶段使用。', 1);
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INSERT INTO courses (id, name, provider, url, grade, description, position) VALUES (3, '国家中小学智慧教育平台 · 高中数学（人教A版）', '教育部教育技术与资源发展中心', 'https://basic.smartedu.cn/syncClassroom', '高中全学段', '官方免费同步课程与配套课件，可按教材版本与册次点播，适合做课内进度对照。', 2);
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-- knowledge_relations: 2 行
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-- knowledge_relations: 12 行
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (1, 1, 2, '前置');
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (2, 8, 9, '前置');
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-- knowledge_resources: 14 行
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (3, 19, 3, '前置');
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (4, 19, 20, '前置');
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (5, 19, 1, '前置');
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (6, 19, 2, '前置');
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (7, 3, 22, '前置');
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (8, 28, 34, '前置');
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (9, 34, 35, '前置');
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (10, 35, 40, '前置');
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (11, 50, 39, '前置');
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INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (12, 39, 30, '前置');
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-- knowledge_resources: 16 行
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INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (1, 3, 'video', 'Khan Academy · Algebra 1: Functions', 'https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions', NULL, 1, 0);
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INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (2, 1, 'video', 'Khan Academy · Algebra 1: Functions', 'https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions', NULL, 1, 0);
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INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (3, 2, 'video', 'Khan Academy · Algebra 1: Functions', 'https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions', NULL, 1, 0);
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@ -170,6 +172,8 @@ INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id
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INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (12, 28, 'video', '国家中小学智慧教育平台 · 高中数学（人教A版）', 'https://basic.smartedu.cn/syncClassroom', NULL, 3, 0);
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INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (13, 30, 'video', '国家中小学智慧教育平台 · 高中数学（人教A版）', 'https://basic.smartedu.cn/syncClassroom', NULL, 3, 0);
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INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (14, 40, 'video', '国家中小学智慧教育平台 · 高中数学（人教A版）', 'https://basic.smartedu.cn/syncClassroom', NULL, 3, 0);
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INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (15, 49, 'video', '国家中小学智慧教育平台 · 高中数学（人教A版）', 'https://basic.smartedu.cn/syncClassroom', NULL, 3, 0);
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INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (16, 50, 'video', '国家中小学智慧教育平台 · 高中数学（人教A版）', 'https://basic.smartedu.cn/syncClassroom', NULL, 3, 0);
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-- questions: 18 行
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INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (1, 'bank', '已知函数 f(x) 满足 f(-x)=f(x)，且 f(3)=5。下列哪个点一定在图像上？', '["A. (-3,5)", "B. (-3,-5)", "C. (3,-5)", "D. (5,-3)"]', 0, '偶函数', '由偶函数定义 f(-x)=f(x) 可知，点 (3,5) 关于 y 轴的镜像点 (-3,5) 一定在图像上。', 7, 1, 0, 1);
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INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (2, 'bank', '已知函数 f(x) 满足 f(-x)=-f(x)，且 f(2)=4。下列哪个点一定在图像上？', '["A. (-2,4)", "B. (-2,-4)", "C. (2,-4)", "D. (4,-2)"]', 1, '奇函数', '由奇函数定义 f(-x)=-f(x) 可知，(2,4) 关于原点的对称点 (-2,-4) 一定在图像上。', 7, 1, 0, 1);
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