217 lines
36 KiB
SQL
217 lines
36 KiB
SQL
-- 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：2026-09-18T14:58:35
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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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DELETE FROM question_knowledge;
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DELETE FROM questions;
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DELETE FROM knowledge_resources;
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DELETE FROM knowledge_relations;
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DELETE FROM courses;
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DELETE FROM chapter_knowledge;
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DELETE FROM knowledge;
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DELETE FROM chapters;
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DELETE FROM textbooks;
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-- textbooks: 7 行
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INSERT INTO textbooks (id, name, author, publisher, isbn, edition, grade, link, description, position, ebook_file, ebook_name, ebook_format, ebook_size, ebook_pages, ebook_uploaded_at) VALUES (1, '函数和图像（盖尔范德中学生数学思维丛书）', 'I. M. Gelfand, E. G. Glagoleva, E. E. Shnol 著；麻希南、胡长青 译', '中国科学技术大学出版社', '9787312050053', '2020年12月第1版', '初中至高中低年级', '', '本系统的主教材。以大量真实图像（地震图、心电图等）引入函数，强调“画图就是看见公式”，系统训练函数概念、图像与性质直觉；英译本 Functions and Graphs 由 Dover 出版。现有函数与对称性题库以本书为依据。', 0, 'da4d4ff2d0b0448fac3719cb7d536d5b.pdf', '函数和图像（盖尔范德中学生数学思维丛书）.pdf', 'pdf', 2352775, 108, '2026-09-18 05:52:20.133460');
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INSERT INTO textbooks (id, name, author, publisher, isbn, edition, grade, link, description, position, ebook_file, ebook_name, ebook_format, ebook_size, ebook_pages, ebook_uploaded_at) VALUES (2, '代数（盖尔范德中学生数学思维丛书）', 'I. M. Gelfand, A. Shen 著；胡长青、麻希南 译', '中国科学技术大学出版社', '9787312048937', '2020年第1版', '初中至高中低年级', '', '用问题驱动的叙述串联自然数、负数、代数式与方程，重视“为什么可以这样变形”的代数思维，适合作为代数学基础。', 1, '', '', '', 0, 0, NULL);
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INSERT INTO textbooks (id, name, author, publisher, isbn, edition, grade, link, description, position, ebook_file, ebook_name, ebook_format, ebook_size, ebook_pages, ebook_uploaded_at) VALUES (3, '几何（盖尔范德中学生数学思维丛书）', 'I. M. Gelfand 等 著', '中国科学技术大学出版社', '9787312057793', '2023年第1版', '初中至高中低年级', '', '以直观可视的方式从图形构造逐步建立几何，突出“先看见、再证明”的思维路线。', 2, '', '', '', 0, 0, NULL);
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INSERT INTO textbooks (id, name, author, publisher, isbn, edition, grade, link, description, position, ebook_file, ebook_name, ebook_format, ebook_size, ebook_pages, ebook_uploaded_at) VALUES (4, '三角函数（盖尔范德中学生数学思维丛书）', 'I. M. Gelfand, M. Saul 著；王作勤 译', '中国科学技术大学出版社', '9787312046957', '2020年第1版', '初中至高中低年级', '', '从初等几何直觉进入正弦、余弦与正切，解释周期与波动现象的数学本质。', 3, 'c1945315d608455eb429eacc3378d7d5.pdf', '三角函数（盖尔范德中学生数学思维丛书）.pdf', 'pdf', 4804517, 228, '2026-09-18 05:52:20.155476');
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INSERT INTO textbooks (id, name, author, publisher, isbn, edition, grade, link, description, position, ebook_file, ebook_name, ebook_format, ebook_size, ebook_pages, ebook_uploaded_at) VALUES (5, '坐标方法（盖尔范德中学生数学思维丛书）', 'I. M. Gelfand, E. G. Glagoleva, A. A. Kirillov 著；王作勤 译', '中国科学技术大学出版社', '9787312050060', '2020年12月第1版', '初中至高中低年级', '', '讲解如何用坐标把几何问题转化为代数问题，是解析几何与函数图像方法的基础。', 4, '', '', '', 0, 0, NULL);
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INSERT INTO textbooks (id, name, author, publisher, isbn, edition, grade, link, description, position, ebook_file, ebook_name, ebook_format, ebook_size, ebook_pages, ebook_uploaded_at) VALUES (6, '普林斯顿微积分读本(修订版)', '阿德里安·班纳 (Adrian Banner)', '人民邮电出版社', '', '', '高中至大学先修', '', '面向微积分入门的系统辅导书，覆盖极限、导数、积分与级数，按考点组织，适合自学与考前查漏补缺。', 5, '4559e9e2fa084fb7a8e8a06aea5196bc.epub', '普林斯顿微积分读本(修订版).epub', 'epub', 9842024, 190, '2026-09-18 05:52:20.122225');
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INSERT INTO textbooks (id, name, author, publisher, isbn, edition, grade, link, description, position, ebook_file, ebook_name, ebook_format, ebook_size, ebook_pages, ebook_uploaded_at) VALUES (7, '柯西-施瓦茨大师课：不等式的艺术', 'J. Michael Steele 著；欧阳顺湘 译', '高等教育出版社 · 世界数学精品译丛 7', '9787040278678', '', '高中至大学', '', 'Cambridge 出版的不等式专题大师课：以 Cauchy-Schwarz 不等式为主线，串起凸性、排序、切比雪夫、Young、Hölder、Minkowski 等常用不等式，每章配大量例题与习题，适合竞赛与数学分析进阶训练。', 6, '8dc7e48036ac4db8abf0020334b47b07.pdf', '柯西-施瓦茨大师课：不等式的艺术.pdf', 'pdf', 44110741, 268, '2026-09-18 06:44:14.147181');
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-- chapters: 29 行
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (1, 1, '引言', 0, '函数、自变量、定义域与函数值：从真实图像理解函数。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (2, 1, '第1章 例子', 1, '不同函数图像的直观例子与作图方法。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (3, 1, '第2章 线性函数', 2, '一次函数的图像、斜率与直线。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (4, 1, '第3章 函数 y=|x|', 3, '绝对值函数的图像与性质，关于 y 轴对称的典型例子。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (5, 1, '第4章 二次三项式', 4, '二次函数图像、配方、判别式与零点。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (6, 1, '第5章 分式线性函数', 5, 'y=1/x 类函数图像与渐近行为。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (7, 1, '第6章 幂函数', 6, 'y=x、y=x²、y=x³ 等幂函数的奇偶性与对称性。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (8, 1, '第7章 有理函数', 7, '更一般的有理函数图像与性质综合。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (9, 3, '点与直线：走进射影几何', 0, '从点与直线的位置关系出发理解射影几何的基本思想。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (10, 3, '平行线：走进仿射几何', 1, '以平行关系为线索建立仿射几何的直观框架。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (11, 3, '面积：走进辛几何', 2, '通过面积概念与保持面积变换认识辛几何。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (12, 3, '圆：走进欧氏几何', 3, '以圆为核心回到经典欧氏几何的结构与性质。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (13, 4, '第1章 三角函数', 0, '从角与旋转进入三角函数，建立正弦、余弦、正切的基本概念。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (14, 4, '第2章 三角形中的三角比', 1, '在直角三角形中定义正弦、余弦与正切，理解锐角三角比。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (15, 4, '第3章 三角比之间的关系', 2, '同角三角比的关系、互余关系与基本恒等式推导。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (16, 4, '第4章 三角形内的关系', 3, '正弦定理、余弦定理以及三角形中边角关系的应用。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (17, 4, '第5章 角与旋转', 4, '把角推广到任意旋转角，定义任意角的三角函数。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (18, 4, '第6章 弧度法', 5, '引入弧度制，理解弧长、扇形与角度制换算。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (19, 4, '第7章 加法公式', 6, '两角和与差的三角函数公式及其几何与代数证明。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (20, 4, '第8章 三角恒等式', 7, '倍角、半角与和差化积等常用三角恒等式。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (21, 4, '第9章 三角函数的图形', 8, '正弦、余弦、正切函数的图像、周期与变换。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (22, 4, '第10章 反函数与三角方程', 9, '反三角函数的基本概念与三角方程的求解方法。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (23, 5, '绪论', 0, '用坐标把几何问题转化为代数问题的方法引言。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (24, 5, '第1章 直线上点的坐标', 1, '数轴、数的绝对值与两点之间的距离。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (25, 5, '第2章 平面里点的坐标', 2, '坐标平面、坐标间关系、距离公式、确定平面图形与其他坐标系。', 0);
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INSERT INTO chapters (id, textbook_id, name, position, summary, ebook_page) VALUES (26, 5, '第3章 三维空间里点的坐标', 3, '空间坐标轴与坐标平面，确定空间中的图形。', 0);
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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: 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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INSERT INTO knowledge (id, name, domain, category, description) VALUES (4, '图像对称性', '初等', '函数与图像', '函数图像的轴对称与中心对称性质，与奇偶性、平移伸缩等变换密切相关。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (5, '初等数学', '初等', '总纲', '中学与竞赛基础的数学知识总图');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (6, '数与式', '初等', '数与式', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (7, '方程与不等式', '初等', '方程与不等式', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (8, '函数与图像', '初等', '函数与图像', '以图像直观呈现自变量与函数值对应关系的分支：先“看见”图像，再回到公式与性质。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (9, '三角函数', '初等', '三角函数', '以角为自变量、以三角比为函数值的函数，包括正弦、余弦、正切等，具有周期性与有界性。');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (10, '平面几何', '初等', '平面几何', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (11, '坐标与解析几何', '初等', '坐标与解析几何', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (12, '数列与证明', '初等', '数列与证明', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (13, '概率统计', '初等', '概率统计', '');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (14, '高等数学', '高等', '总纲', '大学基础数学知识总图');
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INSERT INTO knowledge (id, name, domain, category, description) VALUES (15, '分析与微积分', '高等', '分析与微积分', '');
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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', '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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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (4, 1, 21);
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INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (5, 5, 22);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (6, 7, 1);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (7, 7, 2);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (8, 7, 4);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (9, 9, 23);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (10, 9, 24);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (11, 10, 25);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (12, 11, 26);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (13, 12, 27);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (14, 13, 9);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (15, 14, 28);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (17, 15, 30);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (19, 16, 32);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (20, 16, 33);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (21, 17, 34);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (22, 17, 35);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (23, 18, 35);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (27, 20, 39);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (28, 20, 30);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (29, 21, 40);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (31, 22, 42);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (32, 22, 43);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (33, 23, 44);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (34, 23, 45);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (35, 24, 44);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (36, 24, 46);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (37, 24, 47);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (38, 25, 45);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (39, 25, 47);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (40, 25, 48);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (41, 26, 45);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (42, 26, 23);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (43, 27, 45);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (44, 27, 48);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (45, 28, 45);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (46, 28, 48);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (47, 29, 45);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (48, 29, 48);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (49, 15, 49);
|
||
INSERT INTO chapter_knowledge (id, chapter_id, knowledge_id) VALUES (50, 19, 50);
|
||
-- courses: 3 行
|
||
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);
|
||
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);
|
||
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);
|
||
-- knowledge_relations: 12 行
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (1, 1, 2, '前置');
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (2, 8, 9, '前置');
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (3, 19, 3, '前置');
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (4, 19, 20, '前置');
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (5, 19, 1, '前置');
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (6, 19, 2, '前置');
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (7, 3, 22, '前置');
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (8, 28, 34, '前置');
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (9, 34, 35, '前置');
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (10, 35, 40, '前置');
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (11, 50, 39, '前置');
|
||
INSERT INTO knowledge_relations (id, source_id, target_id, relation_type) VALUES (12, 39, 30, '前置');
|
||
-- knowledge_resources: 16 行
|
||
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);
|
||
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);
|
||
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);
|
||
INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (4, 4, 'video', 'Khan Academy · Algebra 1: Functions', 'https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions', NULL, 1, 0);
|
||
INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (5, 8, 'video', 'Khan Academy · Algebra 1: Functions', 'https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions', NULL, 1, 0);
|
||
INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (6, 9, '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);
|
||
INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (7, 19, 'video', 'Khan Academy · Algebra 1: Functions', 'https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions', NULL, 1, 0);
|
||
INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (8, 20, 'video', 'Khan Academy · Algebra 1: Functions', 'https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions', NULL, 1, 0);
|
||
INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (9, 22, 'video', 'Khan Academy · Algebra 1: Functions', 'https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions', NULL, 1, 0);
|
||
INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (10, 34, '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);
|
||
INSERT INTO knowledge_resources (id, knowledge_id, kind, title, url, textbook_id, course_id, position) VALUES (11, 35, '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);
|
||
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);
|
||
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);
|
||
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);
|
||
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);
|
||
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);
|
||
-- questions: 18 行
|
||
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);
|
||
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);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (3, 'bank', '下列函数的图像关于 $y$ 轴对称的是？', '["A. $y=x+1$", "B. $y=x^3$", "C. $y=x^2+2$", "D. $y=x^2+x$"]', 2, '偶函数', '$y=x^2+2$ 满足 $f(-x)=f(x)$，因此图像关于 $y$ 轴对称，属于偶函数。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (4, 'bank', '函数 y=1/(x²-9) 的图像不可能经过哪个点？', '["A. (0,-1/9)", "B. (4,1/7)", "C. (-4,1/7)", "D. (3,1)"]', 3, '定义域', '分母 x²-9 不能为 0，x=±3 不在定义域内，所以图像不可能经过 (3,1)。', 1, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (5, 'bank', '若函数图像关于原点对称，则下列关系一定成立的是？', '["A. f(-x)=f(x)", "B. f(-x)=-f(x)", "C. f(x)=0", "D. f(x)>0"]', 1, '奇函数', '图像关于原点对称对应奇函数，即对任意定义域内的 x 有 f(-x)=-f(x)。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (6, 'bank', '已知 $f(-x)=f(x)$，则函数图像的几何性质是？', '["A. 关于 x 轴对称", "B. 关于 y 轴对称", "C. 关于原点对称", "D. 无法判断"]', 1, '偶函数', 'f(-x)=f(x) 是偶函数的定义式，几何上等价于图像关于 y 轴对称。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (7, 'bank', '函数 y=2/(x²-1) 的图像不可能经过哪个点？', '["A. (0,-2)", "B. (2,2/3)", "C. (-2,2/3)", "D. (1,2)"]', 3, '定义域', '分母 x²-1 不能为 0，x=±1 不在定义域内，所以图像不可能经过 (1,2)。', 1, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (8, 'bank', '若 f(-x)=-f(x)，且图像经过 (5,-2)，则一定经过？', '["A. (-5,-2)", "B. (-5,2)", "C. (5,2)", "D. (2,5)"]', 1, '奇函数', '奇函数图像关于原点对称，(5,-2) 关于原点的对称点是 (-5,2)。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (9, 'bank', '若 f(-x)=f(x)，且图像经过 (4,7)，则下列点一定在图像上的是？', '["(-4,7)", "(-4,-7)", "(4,-7)", "(7,4)"]', 0, '偶函数', '由偶函数定义得到关于 y 轴的镜像点。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (10, 'bank', '若 f(-x)=-f(x)，且图像经过 (3,5)，则下列点一定在图像上的是？', '["(-3,5)", "(-3,-5)", "(3,-5)", "(5,3)"]', 1, '奇函数', '由奇函数定义得到关于原点的对称点。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (11, 'bank', '下列函数中属于偶函数的是？', '["$y=x^3$", "$y=x^2+1$", "$y=x+1$", "$y=x^3+x$"]', 1, '偶函数', '代入 $-x$ 检验 $f(-x)=f(x)$。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (12, 'bank', '下列函数中属于奇函数的是？', '["y=x²", "y=x^3", "y=x²+1", "y=x^3+1"]', 1, '奇函数', '代入 -x 检验 f(-x)=-f(x)。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (13, 'bank', '函数 y=1/(x-2) 的图像不可能经过哪个点？', '["(0,-1/2)", "(3,1)", "(2,0)", "(4,1/2)"]', 2, '定义域', '分母不能为 0，因此 x=2 不属于定义域。', 1, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (14, 'bank', '若一个函数图像关于 y 轴对称，则该函数通常满足？', '["f(-x)=f(x)", "f(-x)=-f(x)", "f(x)=0", "f(x)>0"]', 0, '图像对称性', '关于 y 轴对称对应偶函数。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (15, 'bank', '若一个函数图像关于原点对称，则该函数通常满足？', '["f(-x)=f(x)", "f(-x)=-f(x)", "f(x)=1", "f(x)>0"]', 1, '图像对称性', '关于原点对称对应奇函数。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (16, 'bank', '若 f(x) 是偶函数，且 f(-5)=9，则 f(5)=？', '["-9", "0", "9", "无法确定"]', 2, '偶函数', '偶函数的两个对称自变量对应相同函数值。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (17, 'bank', '若 f(x) 是奇函数，且 f(-6)=4，则 f(6)=？', '["4", "-4", "0", "无法确定"]', 1, '奇函数', '奇函数的两个相反自变量对应相反函数值。', 7, 1, 0, 1);
|
||
INSERT INTO questions (id, source, stem, options, correct_index, knowledge_name, explanation, chapter_id, difficulty, is_generated, used_count) VALUES (18, 'bank', '判断函数 y=x⁴-x² 的奇偶性。', '["偶函数", "奇函数", "既奇又偶", "非奇非偶"]', 0, '偶函数', '偶次幂组成，代入 -x 后表达式不变。', 7, 1, 0, 1);
|
||
-- question_knowledge: 18 行
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (1, 1, 1);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (2, 2, 2);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (3, 3, 1);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (4, 4, 3);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (5, 5, 2);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (6, 6, 1);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (7, 7, 3);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (8, 8, 2);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (9, 9, 1);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (10, 10, 2);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (11, 11, 1);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (12, 12, 2);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (13, 13, 3);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (14, 14, 4);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (15, 15, 4);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (16, 16, 1);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (17, 17, 2);
|
||
INSERT INTO question_knowledge (id, question_id, knowledge_id) VALUES (18, 18, 1);
|
||
COMMIT;
|
||
VACUUM;
|