diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index 4ebe6b3e..b3f623fb 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -316,3 +316,6 @@ 20240203-220459 高二寒假作业1(1-8题) 024418:024422,017769,024423:024424 +20240203-221900 高二寒假作业1(9-16题) +019519,024425:024427,031901,023142,024428:024430,022083 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 64793b55..f2ac1ccb 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -460750,7 +460750,9 @@ "same": [ "018621" ], - "related": [], + "related": [ + "024429" + ], "remark": "", "space": "4em", "unrelated": [] @@ -503146,7 +503148,9 @@ "same": [ "016746" ], - "related": [], + "related": [ + "024429" + ], "remark": "", "space": "4em", "unrelated": [] @@ -503455,7 +503459,9 @@ "edit": [ "20230706\t王伟叶" ], - "same": [], + "same": [ + "024427" + ], "related": [], "remark": "", "space": "", @@ -503477,7 +503483,9 @@ "edit": [ "20230706\t王伟叶" ], - "same": [], + "same": [ + "024428" + ], "related": [], "remark": "", "space": "4em", @@ -564659,7 +564667,9 @@ "20230101\t王伟叶" ], "same": [], - "related": [], + "related": [ + "024427" + ], "remark": "", "space": "", "unrelated": [] @@ -661752,6 +661762,135 @@ "space": "", "unrelated": [] }, + "024425": { + "id": "024425", + "content": "$P$ 是 $\\triangle ABC$ 所在平面外一点, 且 $PA \\perp$ 平面 $ABC$, 则以下结论正确的是\\bracket{20}.\n\\twoch{$\\angle BPC<\\angle BAC$}{$\\angle BPC>\\angle BAC$}{$\\angle BPC=\\angle BAC$}{$\\angle BPC$ 与 $\\angle BAC$ 的大小关系不确定}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240203\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024426": { + "id": "024426", + "content": "相交成 $90^{\\circ}$ 的两条直线和一个平面所成的角分别是 $30^{\\circ}$ 和 $45^{\\circ}$, 且这两条直线在该平面内的射影所成的锐角为 $\\theta$, 则有\\bracket{20}.\n\\fourch{$\\sin \\theta=\\dfrac{\\sqrt{6}}{3}$}{$\\cos \\theta=\\dfrac{\\sqrt{6}}{3}$}{$\\tan \\theta=\\dfrac{\\sqrt{2}}{2}$}{$\\cos \\theta=-\\dfrac{\\sqrt{3}}{3}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240203\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "024427": { + "id": "024427", + "content": "不共面的四个定点到平面 $\\alpha$ 的距离都相等, 这样的平面 $\\alpha$ 共有\\blank{50}个.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240203\t杨懿荔" + ], + "same": [ + "018635" + ], + "related": [ + "020922" + ], + "remark": "", + "space": "", + "unrelated": [] + }, + "024428": { + "id": "024428", + "content": "四面体 $ABCD$ 中, $AC=BD$, $E, F$ 分别为 $AD, BC$ 的中点, 且 $EF=\\dfrac{\\sqrt{2}}{2}AC$, $\\angle BDC=90$, 求证: $BD \\perp$ 平面 $ACD$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240203\t杨懿荔" + ], + "same": [ + "018636" + ], + "related": [], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024429": { + "id": "024429", + "content": "已知正四棱锥 $P-ABCD, M$、$N$ 分别是 $PA$、$BD$ 上的点, 且 $PM: MA=BN: ND$, 求证: 直线 $MN \\parallel $ 平面 $PBC$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (-1,0,1) node [below] {$A$} coordinate (A);\n\\draw (1,0,1) node [below] {$B$} coordinate (B);\n\\draw (1,0,-1) node [right] {$C$} coordinate (C);\n\\draw (-1,0,-1) node [left] {$D$} coordinate (D);\n\\draw (0,2,0) node [above] {$P$} coordinate (P);\n\\filldraw ($(P)!0.4!(A)$) circle (0.03) node [left] {$M$} coordinate (M);\n\\filldraw ($(B)!0.4!(D)$) circle (0.03) node [above] {$N$} coordinate (N);\n\\draw (P)--(A)--(B)--(C)--cycle(B)--(P);\n\\draw [dashed] (P)--(D)--(A)(D)--(C)(D)--(B)(M)--(N);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240203\t杨懿荔" + ], + "same": [], + "related": [ + "018621", + "016746" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, + "024430": { + "id": "024430", + "content": "已知空间一个平面与一个正方体的 12 条棱的所成的角都等于 $\\alpha$, 则 $\\cos \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240203\t杨懿荔" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0