添加部分2025届校本改编的题目
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@ -516517,6 +516517,111 @@
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"space": "4em",
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"019870": {
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"id": "019870",
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"content": "$\\triangle ABC$ 所在平面 $\\alpha$ 外一点 $D$, $AB=BC=AC=BD=CD=1$, 设 $AD=x$, 当 $\\triangle BCD$ 绕 $BC$ 边旋转时, 求 $x$ 的取值范围.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,1) node [below] {$B$} coordinate (B);\n\\draw (0,0,-1) node [right] {$C$} coordinate (C);\n\\draw ({-sqrt(3)},0,0) node [left] {$A$} coordinate (A);\n\\draw (-0.5,{sqrt(3-0.25)},0) node [above] {$D$} coordinate (D);\n\\draw (A)--(B)--(C)--(D)--cycle (B)--(D);\n\\draw [dashed] (A)--(C);\n\\end{tikzpicture}\n\\end{center}",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231014\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"019871": {
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"id": "019871",
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"content": "如图, 在四棱锥 $P-ABCD$ 中, 底面 $ABCD$ 是 $\\angle DAB=60$ 且边长为 $a$ 的菱形, 侧面 $PAD$ 是等边三角形, 且平面 $PAD$ 垂直于底面 $ABCD$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [below] {$A$} coordinate (A);\n\\draw (2,0,0) node [below] {$B$} coordinate (B);\n\\draw (1,0,{-sqrt(3)}) node [above] {$D$} coordinate (D);\n\\draw (D) ++ (2,0,0) node [right] {$C$} coordinate (C);\n\\draw ($(A)!0.5!(D)$) ++ (0,{sqrt(3)},0) node [above] {$P$} coordinate (P);\n\\draw (P)--(A)--(B)--(C)--cycle (P)--(B);\n\\draw [dashed] (A)--(D)--(C)(D)--(P);\n\\end{tikzpicture}\n\\end{center}\n(1) 若 $G$ 为 $AD$ 的中点, 求证: $BG \\perp$ 平面 $PAD$;\\\\\n(2) 求证: $AD \\perp PB$;\\\\\n(3) 求二面角 $A-BC-P$ 的大小.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231014\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"019872": {
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"id": "019872",
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"content": "已知正方体 $ABCD-A_1B_1C_1D_1$ 的棱长为 $1$ , 则异面直线 $A_1B_1$ 与 $BC_1$ 的距离为\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231014\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"019873": {
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"id": "019873",
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"content": "已知正方体 $ABCD-A_1B_1C_1D_1$ 的棱长为 $a$,\\\\\n(1) 若 $BD_1=2 \\sqrt{3}$, 求异面直线 $BD_1$ 与 $AC$ 之间的距离;\\\\\n(2) 若 $a=1$, 求异面直线 $A_1D$ 与 $AC$ 之间的距离.",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20231014\t王伟叶"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"019874": {
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"id": "019874",
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"content": "在空间四边形$ABCD$中, $AB=DC=4$, $BC=AD=3$, $AD \\perp BC$, $AB \\perp BC$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.7]\n\\draw (0,0,0) node [left] {$A$} coordinate (A);\n\\draw (5,0,0) node [right] {$C$} coordinate (C);\n\\draw ({16/5},0,{12/5}) node [below] {$B$} coordinate (B);\n\\draw ({9/5},{3*sqrt(7)/4},{27/20}) node [above] {$D$} coordinate (D);\n\\draw (A) -- (B) -- (C) -- (D) -- cycle;\n\\draw (B) -- (D);\n\\draw [dashed] (A) -- (C);\n\\end{tikzpicture}\n\\end{center}\n(1) 求$BD$的长;\\\\\n(2) 求证:$BD$是$AD$、$BC$的公垂线.",
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"objs": [],
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"tags": [
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"第六单元"
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],
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"genre": "4em",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "2024届高二校本作业必修第十章-20231014修改",
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"edit": [
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"20230101\t王伟叶",
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"20231014\t王伟叶"
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],
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"same": [],
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"related": [
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"020969"
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"remark": "",
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"space": "4em",
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"020001": {
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"020001": {
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"id": "020001",
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"id": "020001",
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"content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",
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"content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",
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@ -542864,7 +542969,9 @@
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"20230101\t王伟叶"
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"20230101\t王伟叶"
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],
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],
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"same": [],
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"same": [],
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"related": [],
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"related": [
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"019874"
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],
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"remark": "",
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"remark": "",
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"space": "4em",
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"space": "4em",
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"unrelated": []
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"unrelated": []
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